What's wrong with loop quantum gravity [Archive]

Lubos Motl

Sep19-04, 10:38 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nDear Ladies and Gentlemen,\nI want to check whether everyone agrees with the text below. Thanks, Lubos\n\n--------\nIn theoretical physics, loop gravity is one speculative approach to\nquantum gravity, sometimes cited as a competitor theory to string theory.\nThe loop quantum gravity page summarises the theory as it appears to those\nworking in the field.\n\nAs a physical theory, loop gravity has been subject to some heavy\ncriticisms. Some objections to the ideas of loop quantum gravity are given\nhere.\n\nContents\n\n1 Too many assumptions\n2 Commentary from the renormalization group aspect\n3 As a predictive theory\n4 Self-consistency\n5 Gap to high-energy physics\n6 Smooth space as limiting case\n7 Clash with special relativity\n8 Global justification of variables\n9 Testability of the discrete area spectrum\n10 The S-matrix\n11 Ultraviolet divergences\n12 Black hole entropy\n13 Foundational lacks\n14 Prejudices claimed\n15 Background independence\n16 Claims on non-principled approach\n\nToo many assumptions\n\nLoop quantum gravity makes too many assumptions about the behavior of\ngeometry at very short distances. It assumes that the metric tensor is a\ngood variable at all distance scales, and it is the only relevant\nvariable. It even assumes that Einstein\'s equations are more or less exact\nin the Planckian regime.\n\nThe spacetime dimensionality (four) is another assumption that cannot be\nquestioned, much like the field content. Each of these assumptions is\nchallenged in a general enough theory of quantum gravity, for example all\nthe models that emerge from string theory. These assumptions have neither\ntheoretical nor experimental justification. Examples will be listed in a\nseparate entry.\n\nCommentary from the renormalization group aspect\n\nAccording to the logic of the renormalization group, the Einstein-Hilbert\naction is just an effective description at long distances and it is\nguaranteed that it receives corrections at shorter distances. String\ntheory even allows us to calculate these corrections in many cases. There\ncan be additional spatial dimensions; they have emerged in string theory\nand they are also naturally used in many other modern models of particle\nphysics such as the Randall-Sundrum models. An infinite amount of new\nfields and variables associated with various objects (strings and branes)\ncan appear, and indeed does appear according to string theory. Geometry\nunderlying physics may become noncommutative, fuzzy, non-local, and so on.\nLoop quantum gravity ignores all these 20th and 21st century\npossibilities, and it insists on a 19th century image of the world which\nhas become naive after the 20th century breakthroughs.\n\nAs a predictive theory\n\nLoop quantum gravity is not a predictive theory. It does not offer any\npossibility to predict new particles, forces and phenomena at shorter\ndistances: all these objects must be added to the theory by hand. Loop\nquantum gravity therefore also makes it impossible to explain any\nrelations between the known physical objects and laws.\n\nLoop quantum gravity is not a unifying theory. This is not just an\naesthetic imperfection: it is impossible to find a regime in real physics\nof this Universe in which non-gravitational forces can be completely\nneglected, except for classical physics of neutral stars and galaxies that\nalso ignores quantum mechanics. For example, the electromagnetic and\nstrong force are rather strong even at the Planck scale, and the character\nof the black hole evaporation would change dramatically had the Nature\nomitted the other forces and particles. Also, the loop quantum gravity\nadvocates often claim that the framework of loop quantum gravity\nregularizes all possible UV divergences of gravity as well as other fields\ncoupled to it. That would be a real catastrophy because any quantum field\ntheory - including all non-renormalizable theories with any fields and any\ninteractions - could be coupled to loop quantum gravity and the results of\nthe calculations could be equal to anything in the world. The predictive\npower would be exactly equal to zero, much like in the case of a generic\nnon-renormalizable theory. There is absolutely no uniqueness found in the\nrealistic models based on loop quantum gravity. The only universal\npredictions - such as the Lorentz symmetry breaking discussed below - seem\nto be more or less ruled out on experimental grounds.\n\nSelf-consistency\n\nUnlike string theory, loop quantum gravity has not offered any non-trivial\nself-consistency checks of its statements and it has had no impact on the\nworld of mathematics. While string theory smells by God, loop quantum\ngravity smells by Man. It seems that the people are constructing it,\ninstead of discovering it. There are no nice surprises in loop quantum\ngravity - the amount of consistency in the results never exceeds the\namount of assumptions and input. For example, no answer has ever been\ncalculated in two different ways so that the results would match. Whenever\na really interesting question is asked - even if it is apparently a\nuniversal question, for example: "Can topology of space change?" - one can\npropose two versions of loop quantum gravity which lead to different\nanswers.\n\nThere are many reasons to think that loop quantum gravity is internally\ninconsistent, or at least that it is inconsistent with the desired\nlong-distance limit (which should be smooth space). Too many physical\nwisdoms seem to be violated. Unfortunately the loop quantum gravity\nadvocates usually choose to ignore the problems. For example, the spin\nfoam (path-integral) version of loop quantum gravity is believed to break\nunitarity. The usual reaction of the loop quantum gravity practitioners is\nthe statement that unitarity follows from time-translation symmetry, and\nbecause this symmetry is broken (by a generic background) in GR, we do not\nhave to require unitarity anymore. But this is a serious misunderstanding\nof the meaning and origin of unitarity. Unitarity is the requirement that\nthe total probability of all alternatives (the squared length of a vector\nin the Hilbert space) must be conserved (well, it must always be 100%),\nand this requirement - or an equally strong generalization of it - must\nhold under any circumstances, in any physically meaningful theory,\nincluding the case of the curved, time-dependent spacetime. Incidentally,\nthe time-translation symmetry is related, via Noether\'s theorem, to a\ntime-independent, conserved Hamiltonian, which is a completely different\nthing than unitarity.\n\nA similar type of "anything goes" approach seems to be applied to other\nno-go theorems in physics.\n\nGap to high-energy physics\n\nLoop quantum gravity is isolated from particle physics. While extra fields\nmust be added by hand, even this ad hoc procedure seems to be impossible\nin some cases. Scalar fields can\'t really work well within loop quantum\ngravity, and therefore this theory potentially contradicts the observed\nelectroweak symmetry breaking; the violation of the CP symmetry, and other\nwell-known and tested properties of particle physics.\n\nLoop quantum gravity also may deny the importance of many methods and\ntools of particle physics - e.g. the perturbative techniques; the\nS-matrix, and so on. Loop quantum gravity therefore potentially disagrees\nwith 99% of physics as we know it. Unfortunately, the isolation from\nparticle physics follows from the basic opinions of loop quantum gravity\npractitioners and it seems very hard to imagine that a deeper theory can\nbe created if the successful older theories, insights, and methods (and\nexciting newer ones) in the same or closely related fields are ignored.\n\nSmooth space as limiting case\n\nLoop quantum gravity does not guarantee that smooth space as we know it\nwill emerge as the correct approximation of the theory at long distances;\nthere are in fact many reasons to be almost certain that the smooth space\ncannot emerge, and these problems of loop quantum gravity are analogous to\nother attempts to discretize gravity (e.g. putting gravity on lattice).\n\nWhile string theory confirms general relativity or its extensions at long\ndistances - where GR is tested - and modifies it at the shorter ones, loop\nquantum gravity does just the opposite. It claims that GR is formally\nexact at the Planck scale, but implies nothing about the correct behavior\nat long distances. It is reasonable to assume that the usual ultraviolet\nproblems in quantum gravity are simply transmuted into infrared problems,\nexcept that the UV problems seem to be present in loop quantum gravity,\ntoo.\n\nClash with special relativity\n\nLoop quantum gravity violates the rules of special relativity that must be\nvalid for all local physical observations. Spin networks represent a new\nreincarnation of the 19th century idea of the luminiferous aether -\nenvironment whose entropy density is probably Planckian and that picks a\npriviliged reference frame. In other words, the very concept of a minimal\ndistance (or area) is not compatible with the Lorentz contractions. The\nLorentz invariance was the only real reason why Einstein had to find a new\ntheory of gravity - Newton\'s gravitational laws were not compatible with\nhis special relativity.\n\nDespite claims about the background independence, loop quantum gravity\ndoes not respect even the special 1905 rules of Einstein; it is a\nnon-relativistic theory. It conceptually belongs to the pre-1905 era and\neven if we imagine that loop quantum gravity has a realistic long-distance\nlimit, loop quantum gravity has even less symmetries and nice properties\nthan Newton\'s gravitational laws (which have an extra Galilean symmetry,\nand can also be written in a "background independent" way - and moreover,\nthey allow us to calculate most of the observed gravitational effects\nwell, unlike loop quantum gravity). It is a well-known fact that general\nrelativity is called "general" because it has the same form for all\nobservers including those undergoing a general accelerated motion - it is\nsymmetric under all coordinate transformations - while "special"\nrelativity is only symmetric under a subset of special (Lorentz and\nPoincare) transformations that interchange inertial observers. The\nsymmetry under any coordinate transformation is only broken spontaneously\nin general relativity, by the vacuum expectation value of the metric\ntensor, not explicitly (by the physical laws), and the local physics of\nall backgrounds is invariant under the Lorentz transformations.\n\nLoop quantum gravity proponents often and explicitly state that they think\nthat general relativity does not have to respect the Lorentz symmetry in\nany way - which displays a misunderstanding of the symmetry structure of\nspecial and general relativity (the symmetries in general relativity\nextend those in special relativity), as well as of the overwhelming\nexperimental support for the postulates of special relativity. Loop\nquantum gravity also depends on the background in a lot of other ways -\nfor example, the Hamiltonian version of loop quantum gravity requires us\nto choose a pre-determined spacetime topology which cannot change.\n\nOne can imagine that the Lorentz invariance is restored by fine-tuning of\nan infinite number of parameters, but nothing is known about the question\nwhether it is possible, how such a fine-tuning should be done, and what it\nwould mean. Also, it has been speculated that special relativity in loop\nquantum gravity may be superseded by the so-called doubly special\nrelativity, but doubly special relativity is even more problematic than\nloop quantum gravity itself. For example, its new Lorentz transformations\nare non-local (two observers will not agree whether the lion is caught\ninside the cage) and their action on an object depends on whether the\nobject is described as elementary or composite.\n\nGlobal justification of variables\n\nThe discrete area spectrum is not a consequence, but a questionable\nassumption of loop quantum gravity. The redefinition of the variables -\nthe formulae to express the metric in terms of the Ashtekar variables (a\ngauge field) - is legitimate locally on the configuration space, but it is\nnot justified globally because it imposes new periodicities and\nquantization laws that do not follow from the metric itself. The area\nquantization does not represent physics of quantum gravity but rather\nspecific properties of this not-quite-legitimate field redefinition. One\ncan construct infinitely many similar field redefinitions (sibblings of\nloop quantum gravity) that would lead to other quantization rules for\nother quantities. It is probably not consistent to require any of these\nnew quantization rules - for instance, one can see that these choices\ninevitably break the Lorentz invariance which is clearly a bad thing.\n\nTestability of the discrete area spectrum\n\nThe discrete area spectrum is not testable, not even in principle. Loop\nquantum gravity does not provide us with any "sticks" that could measure\ndistances and areas with a sub-Planckian precision, and therefore a\nprediction about the exact sub-Planckian pattern of the spectrum is not\nverifiable. One would have to convert this spectrum into a statement about\nthe scattering amplitudes.\n\nThe S-matrix\n\nLoop quantum gravity provides us with no tools to calculate the S-matrix,\nscattering cross sections, or any other truly physical observable. It is\nnot surprising; if loop quantum gravity cannot predict the existence of\nspace itself, it is even more difficult to decide whether it predicts the\nexistence of gravitons and their interactions. The S-matrix is believed to\nbe essentially the only gauge-invariant observable in quantum gravity, and\nany meaningful theory of quantum gravity should allow us to calculate it,\nat least in principle.\n\nUltraviolet divergences\n\nLoop quantum gravity does not really solve any UV problems. Quantized\neigenvalues of geometry are not enough, and one can see UV singular and\nambiguous terms in the volume operators and most other operators,\nespecially the Hamiltonian constraint. Because the Hamiltonian defines all\nof dynamics, which contains most of the information about a physical\ntheory, it is a serious object. The whole dynamics of loop quantum gravity\nis therefore at least as singular as it is in the usual perturbative\ntreatment based on semiclassical physics.\n\nWe simply do have enough evidence that a pure theory of gravity, without\nany new degrees of freedom or new physics at the Planck scale, cannot be\nconsistent at the quantum level, and loop quantum gravity advocates need\nto believe that the mathematical calculations leading to the infinite and\ninconsistent results (for example, the two-loop non-renormalizable terms\nin the effective action) must be incorrect, but they cannot say what is\ntechnically incorrect about them and how exactly is loop quantum gravity\nsupposed to fix them. Moreover, the loop quantum gravity proponents seem\nto believe that the naive notion of "atoms of space" is the only way to\nfix the UV problems. String theory, which allows us to make real\nquantitative computations, proves that it is not the case and there are\nmore natural ways to "smear out" the UV problems. In fact, a legitimate\nviewpoint implies that the discrete, sharp character of the metric tensor\nand other fields at very short distances makes the UV behavior worse, not\nbetter.\n\nMoreover, as explained above, the "universal solution of the UV problems\nby discreteness of space" implies at least as serious loss of predictive\npower as in a generic non-renormalizable theory. Even if loop quantum\ngravity solved all the UV problems, it would mean that infinitely many\ncoupling constants are undetermined - a situation analogous to a\nnon-renormalizable theory.\n\nBlack hole entropy\n\nDespite various claims, loop quantum gravity is not able to calculate the\nblack hole entropy, unlike string theory. The fact that the entropy is\nproportional to the area does not follow from loop quantum gravity. It is\nrather an assumption of the calculation. The calculation assumes that the\nblack hole interior can be neglected and the entropy comes from a new kind\nof dynamics attached to the surface area - there is no justification of\nthis assumption. Not surprisingly, one is led to an area/entropy\nproportionality law. The only non-trivial check could be the coefficient,\nbut it comes out incorrectly (see the Immirzi discrepancy).\n\nThe Immirzi discrepancy was believed to be proportional to the logarithm\nof two or three, and a speculative explanation in terms of quasinormal\nmodes was proposed. However it only worked for one type of the black hole\n- a clear example of a numerical coincidence - and moreover it was\nrealized in July 2004 that the original calculation of the Immirzi\nparameter was incorrect, and the correct value (described by Meissner) is\nnot proportional to the logarithm of an integer. The value of the Immirzi\nparameter - even according to the optimists - remains unexplained. Another\ndescription of the situation goes as follows: Because the Immirzi\nparameter represents the renormalization of Newton\'s constant and there is\nno renormalization in a finite theory - and loop quantum gravity claims to\nbe one - the Immirzi parameter should be equal to one which leads to a\nwrong value of the black hole entropy.\n\nFoundational lacks\n\nLoop quantum gravity has no tools and no solid foundations to answer other\nimportant questions of quantum gravity - the details of Hawking radiation;\nthe information loss paradox; the existence of naked singularities in the\nfull theory; the origin of holography and the AdS/CFT correspondence;\nmechanisms of appearance and disappearance of spacetime dimensions; the\ntopology changing transitions (which are most likely forbidden in loop\nquantum gravity); the behavior of scattering at the Planck energy; physics\nof spacetime singularities; quantum corrections to geometry and Einstein\'s\nequations; the effect of the fluctuating metric tensor on locality,\ncausality, CPT-symmetry, and the arrow of time; interpretation of quantum\nmechanics in non-geometric contexts including questions from quantum\ncosmology; the replacement for the S-matrix in de Sitter space and other\ncausally subtle backgrounds; the interplay of gravity and other forces;\nthe issues about T-duality and mirror symmetry.\n\nLoop quantum gravity is criticised as a philosophical framework that wants\nus to believe that these questions should not be asked. As if general\nrelativity is virtually a complete theory of everything (even though it\napparently can\'t be) and all ideas in physics after 1915 can be ignored.\n\nPrejudices claimed\n\nThe criticisms of loop quantum gravity regarding other fields of physics\nare misguided. They often dislike perturbative expansions. While it is a\ngreat advantage to look for a framework that allows us to calculate more\nthan the perturbative expansions, it should never be less powerful. In\nother words, any meaningful theory should be able to allow us to perform\n(at least) approximative, perturbative calculations (e.g. around a\nwell-defined classical solution, such as flat space). Loop quantum gravity\ncannot do this, definitely a huge disadvantage, not an advantage as some\nhave claimed. A good quantum theory of gravity should also allow us to\ncalculate the S-matrix.\n\nBackground independence\n\nLoop quantum gravity\'s calls for "background independence" are misled. A\nfirst constraint for a correct physical theory is that it allows the\n(nearly) smooth space(time) - or the background - which we know to be\nnecessary for all known physical phenomena in this Universe. If a theory\ndoes not admit such a smooth space, it can be called "background\nindependent" or "background free", but it may be a useless theory and a\nphysically incorrect theory.\n\nIt is a very different question whether a theory treats all possible\nshapes of spacetime on completely equal footing or whether all these\nsolutions follow from a more fundamental starting point. However, it is\nnot a priori clear on physical grounds whether it must be so (it can be\njust an aesthetic feature of a particular formulation of a theory, not the\ntheory itself), and moreover, for a theory that does not predict many\nwell-behaved backgrounds the question is meaningless altogether. Physics\nof string theory certainly does respect the basic rules of general\nrelativity exactly - general covariance is seen as the decoupling of\nunphysical (pure gauge) modes of the graviton. This exact decoupling can\nbe proved in string theory quite easily. It can also be seen in\nperturbative string theory that a condensation of gravitons is equivalent\nto a change of the background; therefore physics is independent of the\nbackground we start with, even if it is hard to see for the loop quantum\ngravity advocates.\n\nClaims on non-principled approach\n\nLoop quantum gravity is not science because every time a new calculation\nshows that some quantitative conjectures were incorrect, the loop quantum\ngravity advocates invent a non-quantitative, ad hoc explanation why it\ndoes not matter. Some borrow concepts from unrelated and fields, including\nnoiseless information theory and philosophy, and some explanations why\nprevious incorrect results should be kept are not easily credible.\n_______________________________________ _______________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Dear Ladies and Gentlemen,
I want to check whether everyone agrees with the text below. Thanks, Lubos

--------
In theoretical physics, loop gravity is one speculative approach to
quantum gravity, sometimes cited as a competitor theory to string theory.
The loop quantum gravity page summarises the theory as it appears to those
working in the field.

As a physical theory, loop gravity has been subject to some heavy
criticisms. Some objections to the ideas of loop quantum gravity are given
here.

Contents

1 Too many assumptions
2 Commentary from the renormalization group aspect
3 As a predictive theory
4 Self-consistency
5 Gap to high-energy physics
6 Smooth space as limiting case
7 Clash with special relativity
8 Global justification of variables
9 Testability of the discrete area spectrum
10 The S-matrix
11 Ultraviolet divergences
12 Black hole entropy
13 Foundational lacks
14 Prejudices claimed
15 Background independence
16 Claims on non-principled approach

Too many assumptions

Loop quantum gravity makes too many assumptions about the behavior of
geometry at very short distances. It assumes that the metric tensor is a
good variable at all distance scales, and it is the only relevant
variable. It even assumes that Einstein's equations are more or less exact
in the Planckian regime.

The spacetime dimensionality (four) is another assumption that cannot be
questioned, much like the field content. Each of these assumptions is
challenged in a general enough theory of quantum gravity, for example all
the models that emerge from string theory. These assumptions have neither
theoretical nor experimental justification. Examples will be listed in a
separate entry.

Commentary from the renormalization group aspect

According to the logic of the renormalization group, the Einstein-Hilbert
action is just an effective description at long distances and it is
guaranteed that it receives corrections at shorter distances. String
theory even allows us to calculate these corrections in many cases. There
can be additional spatial dimensions; they have emerged in string theory
and they are also naturally used in many other modern models of particle
physics such as the Randall-Sundrum models. An infinite amount of new
fields and variables associated with various objects (strings and branes)
can appear, and indeed does appear according to string theory. Geometry
underlying physics may become noncommutative, fuzzy, non-local, and so on.
Loop quantum gravity ignores all these 20th and 21st century
possibilities, and it insists on a 19th century image of the world which
has become naive after the 20th century breakthroughs.

As a predictive theory

Loop quantum gravity is not a predictive theory. It does not offer any
possibility to predict new particles, forces and phenomena at shorter
distances: all these objects must be added to the theory by hand. Loop
quantum gravity therefore also makes it impossible to explain any
relations between the known physical objects and laws.

Loop quantum gravity is not a unifying theory. This is not just an
aesthetic imperfection: it is impossible to find a regime in real physics
of this Universe in which non-gravitational forces can be completely
neglected, except for classical physics of neutral stars and galaxies that
also ignores quantum mechanics. For example, the electromagnetic and
strong force are rather strong even at the Planck scale, and the character
of the black hole evaporation would change dramatically had the Nature
omitted the other forces and particles. Also, the loop quantum gravity
advocates often claim that the framework of loop quantum gravity
regularizes all possible UV divergences of gravity as well as other fields
coupled to it. That would be a real catastrophy because any quantum field
theory - including all non-renormalizable theories with any fields and any
interactions - could be coupled to loop quantum gravity and the results of
the calculations could be equal to anything in the world. The predictive
power would be exactly equal to zero, much like in the case of a generic
non-renormalizable theory. There is absolutely no uniqueness found in the
realistic models based on loop quantum gravity. The only universal
predictions - such as the Lorentz symmetry breaking discussed below - seem
to be more or less ruled out on experimental grounds.

Self-consistency

Unlike string theory, loop quantum gravity has not offered any non-trivial
self-consistency checks of its statements and it has had no impact on the
world of mathematics. While string theory smells by God, loop quantum
gravity smells by Man. It seems that the people are constructing it,
instead of discovering it. There are no nice surprises in loop quantum
gravity - the amount of consistency in the results never exceeds the
amount of assumptions and input. For example, no answer has ever been
calculated in two different ways so that the results would match. Whenever
a really interesting question is asked - even if it is apparently a
universal question, for example: "Can topology of space change?" - one can
propose two versions of loop quantum gravity which lead to different
answers.

There are many reasons to think that loop quantum gravity is internally
inconsistent, or at least that it is inconsistent with the desired
long-distance limit (which should be smooth space). Too many physical
wisdoms seem to be violated. Unfortunately the loop quantum gravity
advocates usually choose to ignore the problems. For example, the spin
foam (path-integral) version of loop quantum gravity is believed to break
unitarity. The usual reaction of the loop quantum gravity practitioners is
the statement that unitarity follows from time-translation symmetry, and
because this symmetry is broken (by a generic background) in GR, we do not
have to require unitarity anymore. But this is a serious misunderstanding
of the meaning and origin of unitarity. Unitarity is the requirement that
the total probability of all alternatives (the squared length of a vector
in the Hilbert space) must be conserved (well, it must always be 100%),
and this requirement - or an equally strong generalization of it - must
hold under any circumstances, in any physically meaningful theory,
including the case of the curved, time-dependent spacetime. Incidentally,
the time-translation symmetry is related, via Noether's theorem, to a
time-independent, conserved Hamiltonian, which is a completely different
thing than unitarity.

A similar type of "anything goes" approach seems to be applied to other
no-go theorems in physics.

Gap to high-energy physics

Loop quantum gravity is isolated from particle physics. While extra fields
must be added by hand, even this ad hoc procedure seems to be impossible
in some cases. Scalar fields can't really work well within loop quantum
gravity, and therefore this theory potentially contradicts the observed
electroweak symmetry breaking; the violation of the CP symmetry, and other
well-known and tested properties of particle physics.

Loop quantum gravity also may deny the importance of many methods and
tools of particle physics - e.g. the perturbative techniques; the
S-matrix, and so on. Loop quantum gravity therefore potentially disagrees
with 99% of physics as we know it. Unfortunately, the isolation from
particle physics follows from the basic opinions of loop quantum gravity
practitioners and it seems very hard to imagine that a deeper theory can
be created if the successful older theories, insights, and methods (and
exciting newer ones) in the same or closely related fields are ignored.

Smooth space as limiting case

Loop quantum gravity does not guarantee that smooth space as we know it
will emerge as the correct approximation of the theory at long distances;
there are in fact many reasons to be almost certain that the smooth space
cannot emerge, and these problems of loop quantum gravity are analogous to
other attempts to discretize gravity (e.g. putting gravity on lattice).

While string theory confirms general relativity or its extensions at long
distances - where GR is tested - and modifies it at the shorter ones, loop
quantum gravity does just the opposite. It claims that GR is formally
exact at the Planck scale, but implies nothing about the correct behavior
at long distances. It is reasonable to assume that the usual ultraviolet
problems in quantum gravity are simply transmuted into infrared problems,
except that the UV problems seem to be present in loop quantum gravity,
too.

Clash with special relativity

Loop quantum gravity violates the rules of special relativity that must be
valid for all local physical observations. Spin networks represent a new
reincarnation of the 19th century idea of the luminiferous aether -
environment whose entropy density is probably Planckian and that picks a
priviliged reference frame. In other words, the very concept of a minimal
distance (or area) is not compatible with the Lorentz contractions. The
Lorentz invariance was the only real reason why Einstein had to find a new
theory of gravity - Newton's gravitational laws were not compatible with
his special relativity.

Despite claims about the background independence, loop quantum gravity
does not respect even the special 1905 rules of Einstein; it is a
non-relativistic theory. It conceptually belongs to the pre-1905 era and
even if we imagine that loop quantum gravity has a realistic long-distance
limit, loop quantum gravity has even less symmetries and nice properties
than Newton's gravitational laws (which have an extra Galilean symmetry,
and can also be written in a "background independent" way - and moreover,
they allow us to calculate most of the observed gravitational effects
well, unlike loop quantum gravity). It is a well-known fact that general
relativity is called "general" because it has the same form for all
observers including those undergoing a general accelerated motion - it is
symmetric under all coordinate transformations - while "special"
relativity is only symmetric under a subset of special (Lorentz and
Poincare) transformations that interchange inertial observers. The
symmetry under any coordinate transformation is only broken spontaneously
in general relativity, by the vacuum expectation value of the metric
tensor, not explicitly (by the physical laws), and the local physics of
all backgrounds is invariant under the Lorentz transformations.

Loop quantum gravity proponents often and explicitly state that they think
that general relativity does not have to respect the Lorentz symmetry in
any way - which displays a misunderstanding of the symmetry structure of
special and general relativity (the symmetries in general relativity
extend those in special relativity), as well as of the overwhelming
experimental support for the postulates of special relativity. Loop
quantum gravity also depends on the background in a lot of other ways -
for example, the Hamiltonian version of loop quantum gravity requires us
to choose a pre-determined spacetime topology which cannot change.

One can imagine that the Lorentz invariance is restored by fine-tuning of
an infinite number of parameters, but nothing is known about the question
whether it is possible, how such a fine-tuning should be done, and what it
would mean. Also, it has been speculated that special relativity in loop
quantum gravity may be superseded by the so-called doubly special
relativity, but doubly special relativity is even more problematic than
loop quantum gravity itself. For example, its new Lorentz transformations
are non-local (two observers will not agree whether the lion is caught
inside the cage) and their action on an object depends on whether the
object is described as elementary or composite.

Global justification of variables

The discrete area spectrum is not a consequence, but a questionable
assumption of loop quantum gravity. The redefinition of the variables -
the formulae to express the metric in terms of the Ashtekar variables (a
gauge field) - is legitimate locally on the configuration space, but it is
not justified globally because it imposes new periodicities and
quantization laws that do not follow from the metric itself. The area
quantization does not represent physics of quantum gravity but rather
specific properties of this not-quite-legitimate field redefinition. One
can construct infinitely many similar field redefinitions (sibblings of
loop quantum gravity) that would lead to other quantization rules for
other quantities. It is probably not consistent to require any of these
new quantization rules - for instance, one can see that these choices
inevitably break the Lorentz invariance which is clearly a bad thing.

Testability of the discrete area spectrum

The discrete area spectrum is not testable, not even in principle. Loop
quantum gravity does not provide us with any "sticks" that could measure
distances and areas with a sub-Planckian precision, and therefore a
prediction about the exact sub-Planckian pattern of the spectrum is not
verifiable. One would have to convert this spectrum into a statement about
the scattering amplitudes.

The S-matrix

Loop quantum gravity provides us with no tools to calculate the S-matrix,
scattering cross sections, or any other truly physical observable. It is
not surprising; if loop quantum gravity cannot predict the existence of
space itself, it is even more difficult to decide whether it predicts the
existence of gravitons and their interactions. The S-matrix is believed to
be essentially the only gauge-invariant observable in quantum gravity, and
any meaningful theory of quantum gravity should allow us to calculate it,
at least in principle.

Ultraviolet divergences

Loop quantum gravity does not really solve any UV problems. Quantized
eigenvalues of geometry are not enough, and one can see UV singular and
ambiguous terms in the volume operators and most other operators,
especially the Hamiltonian constraint. Because the Hamiltonian defines all
of dynamics, which contains most of the information about a physical
theory, it is a serious object. The whole dynamics of loop quantum gravity
is therefore at least as singular as it is in the usual perturbative
treatment based on semiclassical physics.

We simply do have enough evidence that a pure theory of gravity, without
any new degrees of freedom or new physics at the Planck scale, cannot be
consistent at the quantum level, and loop quantum gravity advocates need
to believe that the mathematical calculations leading to the infinite and
inconsistent results (for example, the two-loop non-renormalizable terms
in the effective action) must be incorrect, but they cannot say what is
technically incorrect about them and how exactly is loop quantum gravity
supposed to fix them. Moreover, the loop quantum gravity proponents seem
to believe that the naive notion of "atoms of space" is the only way to
fix the UV problems. String theory, which allows us to make real
quantitative computations, proves that it is not the case and there are
more natural ways to "smear out" the UV problems. In fact, a legitimate
viewpoint implies that the discrete, sharp character of the metric tensor
and other fields at very short distances makes the UV behavior worse, not
better.

Moreover, as explained above, the "universal solution of the UV problems
by discreteness of space" implies at least as serious loss of predictive
power as in a generic non-renormalizable theory. Even if loop quantum
gravity solved all the UV problems, it would mean that infinitely many
coupling constants are undetermined - a situation analogous to a
non-renormalizable theory.

Black hole entropy

Despite various claims, loop quantum gravity is not able to calculate the
black hole entropy, unlike string theory. The fact that the entropy is
proportional to the area does not follow from loop quantum gravity. It is
rather an assumption of the calculation. The calculation assumes that the
black hole interior can be neglected and the entropy comes from a new kind
of dynamics attached to the surface area - there is no justification of
this assumption. Not surprisingly, one is led to an area/entropy
proportionality law. The only non-trivial check could be the coefficient,
but it comes out incorrectly (see the Immirzi discrepancy).

The Immirzi discrepancy was believed to be proportional to the logarithm
of two or three, and a speculative explanation in terms of quasinormal
modes was proposed. However it only worked for one type of the black hole
- a clear example of a numerical coincidence - and moreover it was
realized in July 2004 that the original calculation of the Immirzi
parameter was incorrect, and the correct value (described by Meissner) is
not proportional to the logarithm of an integer. The value of the Immirzi
parameter - even according to the optimists - remains unexplained. Another
description of the situation goes as follows: Because the Immirzi
parameter represents the renormalization of Newton's constant and there is
no renormalization in a finite theory - and loop quantum gravity claims to
be one - the Immirzi parameter should be equal to one which leads to a
wrong value of the black hole entropy.

Foundational lacks

Loop quantum gravity has no tools and no solid foundations to answer other
important questions of quantum gravity - the details of Hawking radiation;
the information loss paradox; the existence of naked singularities in the
full theory; the origin of holography and the AdS/CFT correspondence;
mechanisms of appearance and disappearance of spacetime dimensions; the
topology changing transitions (which are most likely forbidden in loop
quantum gravity); the behavior of scattering at the Planck energy; physics
of spacetime singularities; quantum corrections to geometry and Einstein's
equations; the effect of the fluctuating metric tensor on locality,
causality, CPT-symmetry, and the arrow of time; interpretation of quantum
mechanics in non-geometric contexts including questions from quantum
cosmology; the replacement for the S-matrix in de Sitter space and other
causally subtle backgrounds; the interplay of gravity and other forces;
the issues about T-duality and mirror symmetry.

Loop quantum gravity is criticised as a philosophical framework that wants
us to believe that these questions should not be asked. As if general
relativity is virtually a complete theory of everything (even though it
apparently can't be) and all ideas in physics after 1915 can be ignored.

Prejudices claimed

The criticisms of loop quantum gravity regarding other fields of physics
are misguided. They often dislike perturbative expansions. While it is a
great advantage to look for a framework that allows us to calculate more
than the perturbative expansions, it should never be less powerful. In
other words, any meaningful theory should be able to allow us to perform
(at least) approximative, perturbative calculations (e.g. around a
well-defined classical solution, such as flat space). Loop quantum gravity
cannot do this, definitely a huge disadvantage, not an advantage as some
have claimed. A good quantum theory of gravity should also allow us to
calculate the S-matrix.

Background independence

Loop quantum gravity's calls for "background independence" are misled. A
first constraint for a correct physical theory is that it allows the
(nearly) smooth space(time) - or the background - which we know to be
necessary for all known physical phenomena in this Universe. If a theory
does not admit such a smooth space, it can be called "background
independent" or "background free", but it may be a useless theory and a
physically incorrect theory.

It is a very different question whether a theory treats all possible
shapes of spacetime on completely equal footing or whether all these
solutions follow from a more fundamental starting point. However, it is
not a priori clear on physical grounds whether it must be so (it can be
just an aesthetic feature of a particular formulation of a theory, not the
theory itself), and moreover, for a theory that does not predict many
well-behaved backgrounds the question is meaningless altogether. Physics
of string theory certainly does respect the basic rules of general
relativity exactly - general covariance is seen as the decoupling of
unphysical (pure gauge) modes of the graviton. This exact decoupling can
be proved in string theory quite easily. It can also be seen in
perturbative string theory that a condensation of gravitons is equivalent
to a change of the background; therefore physics is independent of the
background we start with, even if it is hard to see for the loop quantum
gravity advocates.

Claims on non-principled approach

Loop quantum gravity is not science because every time a new calculation
shows that some quantitative conjectures were incorrect, the loop quantum
gravity advocates invent a non-quantitative, ad hoc explanation why it
does not matter. Some borrow concepts from unrelated and fields, including
noiseless information theory and philosophy, and some explanations why
previous incorrect results should be kept are not easily credible.
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^

mathman

Sep20-04, 03:38 AM

I am not qualified to comment on the particulars you described, but I just have one general comment about LQG and String theory.

A. They are compatible, therefore both are valid or neither.

B. They are not compatible, therefore one is valid or neither.

At the moment I don't think anyone can say more until there is some experimental work on validity or theoretical work on compatibility.

Marty Tysanner

Sep20-04, 04:57 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nWhat are you trying to do, start a brawl on s.p.r.? :)\n\nAnyway, I may be representative of one kind of person you want to\nreach with this piece (I have just entered UC Santa Cruz in the\ndoctoral program, and am interested in learning high energy theory\nas well as gravitation). Since I am not knowledgeable about either\nstring theory or loop gravity at this point, I will restrict my\ncomments to the presentation itself -- in particular what seems\nquestionable and what might make it more convincing to someone like me.\n\nLubos Motl wrote:\n\n> In theoretical physics, loop gravity is one speculative approach to\n> quantum gravity, sometimes cited as a competitor theory to string theory.\n> The loop quantum gravity page summarises the theory as it appears to those\n> working in the field.\n\nObvious informational question: what is the URL of this page?\n\n> As a physical theory, loop gravity has been subject to some heavy\n> criticisms. Some objections to the ideas of loop quantum gravity are given\n> here.\n\nGeneral comment: you say you are summarizing objections to LQG, but\nin reading further you often contrast LQG and ST. You might frame\nthe discussion as a compare/contrast piece rather than a summary of\nobjections.\n\n>\n> Contents\n>\n> 1 Too many assumptions\n> 2 Commentary from the renormalization group aspect\n> 3 As a predictive theory\n> 4 Self-consistency\n> 5 Gap to high-energy physics\n> 6 Smooth space as limiting case\n> 7 Clash with special relativity\n> 8 Global justification of variables\n> 9 Testability of the discrete area spectrum\n> 10 The S-matrix\n> 11 Ultraviolet divergences\n> 12 Black hole entropy\n> 13 Foundational lacks\n> 14 Prejudices claimed\n> 15 Background independence\n> 16 Claims on non-principled approach\n>\n> Too many assumptions\n>\n> Loop quantum gravity makes too many assumptions about the behavior of\n> geometry at very short distances. It assumes that the metric tensor is a\n> good variable at all distance scales, and it is the only relevant\n> variable. It even assumes that Einstein\'s equations are more or less exact\n> in the Planckian regime.\n\nThis may be true, but by what standard are you determining what is\n"too many?" This seems like a very subjective comment and might\nimmediately set some people to questioning your basic premise. You\nprobably want to be forceful, which is good in a persuasive essay,\nbut unsupported "blanket" statements are both unnecessary and a clue\nto questionable logic.\n\n> The spacetime dimensionality (four) is another assumption that cannot be\n> questioned, much like the field content. Each of these assumptions is\n> challenged in a general enough theory of quantum gravity, for example all\n> the models that emerge from string theory. These assumptions have neither\n> theoretical nor experimental justification. Examples will be listed in a\n> separate entry.\n\nThe implication here seems to be that the models that emerge from\nstring theory don\'t agree with some LQG assumptions, so therefore\nthe LQG assumptions are questionable. Is this convincing to someone\nwho doesn\'t know whether ST is correct either? My understanding is\nthat ST is much more deeply developed and attempts to answer more\nquestions than LQG, but I doubt that anyone would argue that this\nlogically implies that ST is correct. Bringing up "experimental\njustification" seems to open a can of worms, since ST seems to have\nits own problems in connecting with experiment.\n\n> Commentary from the renormalization group aspect\n>\n> According to the logic of the renormalization group, the Einstein-Hilbert\n> action is just an effective description at long distances and it is\n> guaranteed that it receives corrections at shorter distances. String\n> theory even allows us to calculate these corrections in many cases. There\n> can be additional spatial dimensions; they have emerged in string theory\n> and they are also naturally used in many other modern models of particle\n> physics such as the Randall-Sundrum models.\n\nMuch of what precedes this is general and nontechnical, definitely\nnot aimed at the string theorist. Bringing up specific models\nwithout informally defining them is a jarring change of tone.\n\n> An infinite amount of new\n> fields and variables associated with various objects (strings and branes)\n> can appear, and indeed does appear according to string theory. Geometry\n> underlying physics may become noncommutative, fuzzy, non-local, and so on.\n> Loop quantum gravity ignores all these 20th and 21st century\n> possibilities, and it insists on a 19th century image of the world which\n> has become naive after the 20th century breakthroughs.\n\nI have seen you cite periods of time elsewhere, with comments like,\n"That may have been interesting 100 years ago, but we are now in the\n21st century," or "That may have been a valid criticism in 1995, but\na lot has happened in the last 10 years." It may just be me, but I\nfind this rhetorical technique annoying. Its purpose seems to be to\nargue against an idea based on its age, as though new means better.\nBut this is logically falacious, so the argument based on age is\nonly effective with those who don\'t read or think carefully. All\nideas both good and bad are "new" when they are first proposed; some\n"bad" ideas have consumed a lot of energy at various times in the\npast, and by some very smart people too. Once everything is\nunderstood then it is obvious what is "good" and what is "bad," but\nI imagine the general consensus in the physics community is that\nwe haven\'t achieved that level of understanding yet.\n\nIn short: framing LQG as embracing the 19th century and not waking\nup to 20th and 21st century ideas strikes me as a largely\ncontent-free rhetorical technique to denigrate LQG by association\nwith the past. Knowing this, a reader would be justified in\nquestioning the solidity of your reasoning.\n\n> As a predictive theory\n\n[...]\n\n> Loop quantum gravity is not a unifying theory. This is not just an\n> aesthetic imperfection: it is impossible to find a regime in real physics\n> of this Universe in which non-gravitational forces can be completely\n> neglected, except for classical physics of neutral stars and galaxies that\n> also ignores quantum mechanics. For example, the electromagnetic and\n> strong force are rather strong even at the Planck scale, and the character\n> of the black hole evaporation would change dramatically had the Nature\n> omitted the other forces and particles.\n\nYou might want to say "we believe" in citing the above. As far as I\nknow, nobody has actually measured Planck scale phenomena or black\nhole evaporation. :)\n\n>\n> Self-consistency\n>\n> Unlike string theory, loop quantum gravity has not offered any non-trivial\n> self-consistency checks of its statements and it has had no impact on the\n> world of mathematics. While string theory smells by God, loop quantum\n> gravity smells by Man.\n\nI have to admit, I still smile when I see you write "smells of God"\nand "smells of Man." Even though it is kind of meaningless because\nit is so subjective, it is funny rhetoric.\n\n> It seems that the people are constructing it,\n> instead of discovering it. There are no nice surprises in loop quantum\n> gravity - the amount of consistency in the results never exceeds the\n> amount of assumptions and input. For example, no answer has ever been\n> calculated in two different ways so that the results would match. Whenever\n> a really interesting question is asked - even if it is apparently a\n> universal question, for example: "Can topology of space change?" - one can\n> propose two versions of loop quantum gravity which lead to different\n> answers.\n\nIs this criticism completely fair? I was under the impression that\nLQG theorists were primarily using LQG as a tool to investigate some\nideas, starting from the GR end of things rather the QFT and see\nwhere it goes. If it is an exploration of ideas, then it seems like\nit should be held to a different standard than if it were being\ndeveloped as a general theory.\n\n>\n> There are many reasons to think that loop quantum gravity is internally\n> inconsistent, or at least that it is inconsistent with the desired\n> long-distance limit (which should be smooth space). Too many physical\n> wisdoms seem to be violated. Unfortunately the loop quantum gravity\n> advocates usually choose to ignore the problems. For example, the spin\n> foam (path-integral) version of loop quantum gravity is believed to break\n> unitarity.\n\nI think you are arguing from authority here, so who are the\nauthorities? By whom is it believed -- by you or by general\nconsensus of everyone except LQG theorists?\n\n[...]\n\n>\n> Gap to high-energy physics\n>\n> Loop quantum gravity is isolated from particle physics. While extra fields\n> must be added by hand, even this ad hoc procedure seems to be impossible\n> in some cases. Scalar fields can\'t really work well within loop quantum\n> gravity, and therefore this theory potentially contradicts the observed\n> electroweak symmetry breaking; the violation of the CP symmetry, and other\n> well-known and tested properties of particle physics.\n>\n\nYour presentation style here seems reasonable, although I am not\nqualified to assess its validity. But do LQG proponents claim to\nexplain particle physics, i.e., are you criticizing them for not\nhaving what they don\'t claim to have?\n\n> Loop quantum gravity also may deny the importance of many methods and\n> tools of particle physics - e.g. the perturbative techniques; the\n> S-matrix, and so on. Loop quantum gravity therefore potentially disagrees\n> with 99% of physics as we know it.\n\nReally, 99%? Not 98% or even 97%? Sorry, but this seems like\nunsupported rhetoric that is unnecessary to your argument.\n\n[...]\n\n>\n> Clash with special relativity\n>\n> Loop quantum gravity violates the rules of special relativity that must be\n> valid for all local physical observations. Spin networks represent a new\n> reincarnation of the 19th century idea of the luminiferous aether -\n> environment whose entropy density is probably Planckian and that picks a\n> priviliged reference frame.\n\nAgain, you are resorting to date-based rhetoric. I already object\nto that technique, so the main question at this point is: Why are\nyou using that technique? If you are trying to convince a lay\naudience then that may be effective (but get rid of talk about the\nrenormalization group if that is who you are trying to reach! :) ).\nBut people who are more involved in physics have better b.s.\ndetectors and comparing the work of some bright people today with\nold ideas of an aether only undermines the credibility of your argument.\n\n>\n> Despite claims about the background independence, loop quantum gravity\n> does not respect even the special 1905 rules of Einstein; it is a\n> non-relativistic theory. It conceptually belongs to the pre-1905 era ...\n\nMore insinuation based on a date... Arghh!\n\nRelated to special relativity, I think I remember you saying at one\ntime that you could prove that part of LQG was wrong, that edges\ncould be boosted to arbitrary length which is nonphysical, or\nsomething like that. I don\'t remember the discussion very well, so\nI have probably munged up the description. Do you still believe you\ncan somewhat rigorously prove part of LQG wrong? If so, that would\nmake a pretty strong argument that belongs in your essay.\n\n[...]\n\n> Testability of the discrete area spectrum\n>\n> The discrete area spectrum is not testable, not even in principle. Loop\n> quantum gravity does not provide us with any "sticks" that could measure\n> distances and areas with a sub-Planckian precision, and therefore a\n> prediction about the exact sub-Planckian pattern of the spectrum is not\n> verifiable. One would have to convert this spectrum into a statement about\n> the scattering amplitudes.\n\nHere we\'re opening up the experimental can of worms again. I\nthought ST had its own problems with testability...\n\n>\n> The S-matrix\n>\n> Loop quantum gravity provides us with no tools to calculate the S-matrix,\n> scattering cross sections, or any other truly physical observable. It is\n> not surprising; if loop quantum gravity cannot predict the existence of\n> space itself, it is even more difficult to decide whether it predicts the\n> existence of gravitons and their interactions. The S-matrix is believed to\n> be essentially the only gauge-invariant observable in quantum gravity, and\n> any meaningful theory of quantum gravity should allow us to calculate it,\n> at least in principle.\n\nWho are the authorities to whom you implicity refer? Are you\nclaiming the S-matrix is really the only observable in principle, or\njust the only one that seems tractable to calculate at this point?\nMy own hope is that there are more observables than just the\nS-matrix in a complete theory, but only time and a lot more work can\ntell.\n\n[...]\n\n>\n> Black hole entropy\n>\n> Despite various claims, loop quantum gravity is not able to calculate the\n> black hole entropy, unlike string theory. The fact that the entropy is\n> proportional to the area does not follow from loop quantum gravity. It is\n> rather an assumption of the calculation. The calculation assumes that the\n> black hole interior can be neglected and the entropy comes from a new kind\n> of dynamics attached to the surface area - there is no justification of\n> this assumption. Not surprisingly, one is led to an area/entropy\n> proportionality law. The only non-trivial check could be the coefficient,\n> but it comes out incorrectly (see the Immirzi discrepancy).\n\nWhile I can\'t assess your argument, I haven\'t heard of any\nexperimental work for verifying the "real" black hole entropy. To\nbe fair, you should mention that the black hole entropy is an\nexperimentally untested theoretical prediction, but that ST gets it\nright while LQG appears to fudge things.\n\n[...]\n\n> Foundational lacks\n>\n> Loop quantum gravity has no tools and no solid foundations to answer other\n> important questions of quantum gravity - [...]\n\nDoes LQG make claims to have the answers here?\n\n> ... and all ideas in physics after 1915 can be ignored.\n\nArghh!\n\n[...]\n\n> Background independence\n>\n> Loop quantum gravity\'s calls for "background independence" are misled. A\n> first constraint for a correct physical theory is that it allows the\n> (nearly) smooth space(time) - or the background - which we know to be\n> necessary for all known physical phenomena in this Universe. If a theory\n> does not admit such a smooth space, it can be called "background\n> independent" or "background free", but it may be a useless theory and a\n> physically incorrect theory.\n\nThe fact that there is a controversy among reasonable and bright\npeople about this subject leads me to believe that the issue is not\nas clear as you imply. Maybe different people start with different\nassumptions or have different requirements in a theory? I don\'t\nknow, but it seems like a clearly correct argument along the lines\nabove would be convincing to smart people if were true, and it would\nalso save them from a lot of wasted effort. Maybe a well-reasoned\npeer-reviewed paper on the subject would be useful?\n\n[...]\n\n>\n> Claims on non-principled approach\n>\n> Loop quantum gravity is not science because every time a new calculation\n> shows that some quantitative conjectures were incorrect, the loop quantum\n> gravity advocates invent a non-quantitative, ad hoc explanation why it\n> does not matter. Some borrow concepts from unrelated and fields, including\n> noiseless information theory and philosophy, and some explanations why\n> previous incorrect results should be kept are not easily credible.\n\nThis conclusion makes some strong claims that are bound to stir up\nemotions. If your goal is to convince someone who has the least bit\nof sympathy for LQG, you will probably lose them with this\nparagraph. In terms of effectiveness, it also seems like a weak\nconclusion. If you are aiming at someone like me, you should give\nit a more well-reasoned flavor. You make some unsupported blanket\nstatements that should have been developed more in the main body of\nthe essay if they were really important, not just a couple of\nsentences here. Instead of summarizing your position you present an\nemotional appeal: "This isn\'t science, it\'s just a big kludge mixed\nin with philosophy!" It seems like you could do better than that.\n\nHope these comments help.\n\nRegards,\nMarty\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>What are you trying to do, start a brawl on s.p.r.? :)

Anyway, I may be representative of one kind of person you want to
reach with this piece (I have just entered UC Santa Cruz in the
doctoral program, and am interested in learning high energy theory
as well as gravitation). Since I am not knowledgeable about either
string theory or loop gravity at this point, I will restrict my
comments to the presentation itself -- in particular what seems
questionable and what might make it more convincing to someone like me.

Lubos Motl wrote:

> In theoretical physics, loop gravity is one speculative approach to
> quantum gravity, sometimes cited as a competitor theory to string theory.
> The loop quantum gravity page summarises the theory as it appears to those
> working in the field.

Obvious informational question: what is the URL of this page?

> As a physical theory, loop gravity has been subject to some heavy
> criticisms. Some objections to the ideas of loop quantum gravity are given
> here.

General comment: you say you are summarizing objections to LQG, but
in reading further you often contrast LQG and ST. You might frame
the discussion as a compare/contrast piece rather than a summary of
objections.

>
> Contents
>
> 1 Too many assumptions
> 2 Commentary from the renormalization group aspect
> 3 As a predictive theory
> 4 Self-consistency
> 5 Gap to high-energy physics
> 6 Smooth space as limiting case
> 7 Clash with special relativity
> 8 Global justification of variables
> 9 Testability of the discrete area spectrum
> 10 The S-matrix
> 11 Ultraviolet divergences
> 12 Black hole entropy
> 13 Foundational lacks
> 14 Prejudices claimed
> 15 Background independence
> 16 Claims on non-principled approach
>
> Too many assumptions
>
> Loop quantum gravity makes too many assumptions about the behavior of
> geometry at very short distances. It assumes that the metric tensor is a
> good variable at all distance scales, and it is the only relevant
> variable. It even assumes that Einstein's equations are more or less exact
> in the Planckian regime.

This may be true, but by what standard are you determining what is
"too many?" This seems like a very subjective comment and might
immediately set some people to questioning your basic premise. You
probably want to be forceful, which is good in a persuasive essay,
but unsupported "blanket" statements are both unnecessary and a clue
to questionable logic.

> The spacetime dimensionality (four) is another assumption that cannot be
> questioned, much like the field content. Each of these assumptions is
> challenged in a general enough theory of quantum gravity, for example all
> the models that emerge from string theory. These assumptions have neither
> theoretical nor experimental justification. Examples will be listed in a
> separate entry.

The implication here seems to be that the models that emerge from
string theory don't agree with some LQG assumptions, so therefore
the LQG assumptions are questionable. Is this convincing to someone
who doesn't know whether ST is correct either? My understanding is
that ST is much more deeply developed and attempts to answer more
questions than LQG, but I doubt that anyone would argue that this
logically implies that ST is correct. Bringing up "experimental
justification" seems to open a can of worms, since ST seems to have
its own problems in connecting with experiment.

> Commentary from the renormalization group aspect
>
> According to the logic of the renormalization group, the Einstein-Hilbert
> action is just an effective description at long distances and it is
> guaranteed that it receives corrections at shorter distances. String
> theory even allows us to calculate these corrections in many cases. There
> can be additional spatial dimensions; they have emerged in string theory
> and they are also naturally used in many other modern models of particle
> physics such as the Randall-Sundrum models.

Much of what precedes this is general and nontechnical, definitely
not aimed at the string theorist. Bringing up specific models
without informally defining them is a jarring change of tone.

> An infinite amount of new
> fields and variables associated with various objects (strings and branes)
> can appear, and indeed does appear according to string theory. Geometry
> underlying physics may become noncommutative, fuzzy, non-local, and so on.
> Loop quantum gravity ignores all these 20th and 21st century
> possibilities, and it insists on a 19th century image of the world which
> has become naive after the 20th century breakthroughs.

I have seen you cite periods of time elsewhere, with comments like,
"That may have been interesting 100 years ago, but we are now in the
21st century," or "That may have been a valid criticism in 1995, but
a lot has happened in the last 10 years." It may just be me, but I
find this rhetorical technique annoying. Its purpose seems to be to
argue against an idea based on its age, as though new means better.
But this is logically falacious, so the argument based on age is
only effective with those who don't read or think carefully. All
ideas both good and bad are "new" when they are first proposed; some
"bad" ideas have consumed a lot of energy at various times in the
past, and by some very smart people too. Once everything is
understood then it is obvious what is "good" and what is "bad," but
I imagine the general consensus in the physics community is that
we haven't achieved that level of understanding yet.

In short: framing LQG as embracing the 19th century and not waking
up to 20th and 21st century ideas strikes me as a largely
content-free rhetorical technique to denigrate LQG by association
with the past. Knowing this, a reader would be justified in
questioning the solidity of your reasoning.

> As a predictive theory

[...]

> Loop quantum gravity is not a unifying theory. This is not just an
> aesthetic imperfection: it is impossible to find a regime in real physics
> of this Universe in which non-gravitational forces can be completely
> neglected, except for classical physics of neutral stars and galaxies that
> also ignores quantum mechanics. For example, the electromagnetic and
> strong force are rather strong even at the Planck scale, and the character
> of the black hole evaporation would change dramatically had the Nature
> omitted the other forces and particles.

You might want to say "we believe" in citing the above. As far as I
know, nobody has actually measured Planck scale phenomena or black
hole evaporation. :)

>
> Self-consistency
>
> Unlike string theory, loop quantum gravity has not offered any non-trivial
> self-consistency checks of its statements and it has had no impact on the
> world of mathematics. While string theory smells by God, loop quantum
> gravity smells by Man.

I have to admit, I still smile when I see you write "smells of God"
and "smells of Man." Even though it is kind of meaningless because
it is so subjective, it is funny rhetoric.

> It seems that the people are constructing it,
> instead of discovering it. There are no nice surprises in loop quantum
> gravity - the amount of consistency in the results never exceeds the
> amount of assumptions and input. For example, no answer has ever been
> calculated in two different ways so that the results would match. Whenever
> a really interesting question is asked - even if it is apparently a
> universal question, for example: "Can topology of space change?" - one can
> propose two versions of loop quantum gravity which lead to different
> answers.

Is this criticism completely fair? I was under the impression that
LQG theorists were primarily using LQG as a tool to investigate some
ideas, starting from the GR end of things rather the QFT and see
where it goes. If it is an exploration of ideas, then it seems like
it should be held to a different standard than if it were being
developed as a general theory.

>
> There are many reasons to think that loop quantum gravity is internally
> inconsistent, or at least that it is inconsistent with the desired
> long-distance limit (which should be smooth space). Too many physical
> wisdoms seem to be violated. Unfortunately the loop quantum gravity
> advocates usually choose to ignore the problems. For example, the spin
> foam (path-integral) version of loop quantum gravity is believed to break
> unitarity.

I think you are arguing from authority here, so who are the
authorities? By whom is it believed -- by you or by general
consensus of everyone except LQG theorists?

[...]

>
> Gap to high-energy physics
>
> Loop quantum gravity is isolated from particle physics. While extra fields
> must be added by hand, even this ad hoc procedure seems to be impossible
> in some cases. Scalar fields can't really work well within loop quantum
> gravity, and therefore this theory potentially contradicts the observed
> electroweak symmetry breaking; the violation of the CP symmetry, and other
> well-known and tested properties of particle physics.
>

Your presentation style here seems reasonable, although I am not
qualified to assess its validity. But do LQG proponents claim to
explain particle physics, i.e., are you criticizing them for not
having what they don't claim to have?

> Loop quantum gravity also may deny the importance of many methods and
> tools of particle physics - e.g. the perturbative techniques; the
> S-matrix, and so on. Loop quantum gravity therefore potentially disagrees
> with 99% of physics as we know it.

Really, 99%? Not 98% or even 97%? Sorry, but this seems like
unsupported rhetoric that is unnecessary to your argument.

[...]

>
> Clash with special relativity
>
> Loop quantum gravity violates the rules of special relativity that must be
> valid for all local physical observations. Spin networks represent a new
> reincarnation of the 19th century idea of the luminiferous aether -
> environment whose entropy density is probably Planckian and that picks a
> priviliged reference frame.

Again, you are resorting to date-based rhetoric. I already object
to that technique, so the main question at this point is: Why are
you using that technique? If you are trying to convince a lay
audience then that may be effective (but get rid of talk about the
renormalization group if that is who you are trying to reach! :) ).
But people who are more involved in physics have better b.s.
detectors and comparing the work of some bright people today with
old ideas of an aether only undermines the credibility of your argument.

>
> Despite claims about the background independence, loop quantum gravity
> does not respect even the special 1905 rules of Einstein; it is a
> non-relativistic theory. It conceptually belongs to the pre-1905 era ...

More insinuation based on a date... Arghh!

Related to special relativity, I think I remember you saying at one
time that you could prove that part of LQG was wrong, that edges
could be boosted to arbitrary length which is nonphysical, or
something like that. I don't remember the discussion very well, so
I have probably munged up the description. Do you still believe you
can somewhat rigorously prove part of LQG wrong? If so, that would
make a pretty strong argument that belongs in your essay.

[...]

> Testability of the discrete area spectrum
>
> The discrete area spectrum is not testable, not even in principle. Loop
> quantum gravity does not provide us with any "sticks" that could measure
> distances and areas with a sub-Planckian precision, and therefore a
> prediction about the exact sub-Planckian pattern of the spectrum is not
> verifiable. One would have to convert this spectrum into a statement about
> the scattering amplitudes.

Here we're opening up the experimental can of worms again. I
thought ST had its own problems with testability...

>
> The S-matrix
>
> Loop quantum gravity provides us with no tools to calculate the S-matrix,
> scattering cross sections, or any other truly physical observable. It is
> not surprising; if loop quantum gravity cannot predict the existence of
> space itself, it is even more difficult to decide whether it predicts the
> existence of gravitons and their interactions. The S-matrix is believed to
> be essentially the only gauge-invariant observable in quantum gravity, and
> any meaningful theory of quantum gravity should allow us to calculate it,
> at least in principle.

Who are the authorities to whom you implicity refer? Are you
claiming the S-matrix is really the only observable in principle, or
just the only one that seems tractable to calculate at this point?
My own hope is that there are more observables than just the
S-matrix in a complete theory, but only time and a lot more work can
tell.

[...]

>
> Black hole entropy
>
> Despite various claims, loop quantum gravity is not able to calculate the
> black hole entropy, unlike string theory. The fact that the entropy is
> proportional to the area does not follow from loop quantum gravity. It is
> rather an assumption of the calculation. The calculation assumes that the
> black hole interior can be neglected and the entropy comes from a new kind
> of dynamics attached to the surface area - there is no justification of
> this assumption. Not surprisingly, one is led to an area/entropy
> proportionality law. The only non-trivial check could be the coefficient,
> but it comes out incorrectly (see the Immirzi discrepancy).

While I can't assess your argument, I haven't heard of any
experimental work for verifying the "real" black hole entropy. To
be fair, you should mention that the black hole entropy is an
experimentally untested theoretical prediction, but that ST gets it
right while LQG appears to fudge things.

[...]

> Foundational lacks
>
> Loop quantum gravity has no tools and no solid foundations to answer other
> important questions of quantum gravity - [...]

Does LQG make claims to have the answers here?

> ... and all ideas in physics after 1915 can be ignored.

Arghh!

[...]

> Background independence
>
> Loop quantum gravity's calls for "background independence" are misled. A
> first constraint for a correct physical theory is that it allows the
> (nearly) smooth space(time) - or the background - which we know to be
> necessary for all known physical phenomena in this Universe. If a theory
> does not admit such a smooth space, it can be called "background
> independent" or "background free", but it may be a useless theory and a
> physically incorrect theory.

The fact that there is a controversy among reasonable and bright
people about this subject leads me to believe that the issue is not
as clear as you imply. Maybe different people start with different
assumptions or have different requirements in a theory? I don't
know, but it seems like a clearly correct argument along the lines
above would be convincing to smart people if were true, and it would
also save them from a lot of wasted effort. Maybe a well-reasoned
peer-reviewed paper on the subject would be useful?

[...]

>
> Claims on non-principled approach
>
> Loop quantum gravity is not science because every time a new calculation
> shows that some quantitative conjectures were incorrect, the loop quantum
> gravity advocates invent a non-quantitative, ad hoc explanation why it
> does not matter. Some borrow concepts from unrelated and fields, including
> noiseless information theory and philosophy, and some explanations why
> previous incorrect results should be kept are not easily credible.

This conclusion makes some strong claims that are bound to stir up
emotions. If your goal is to convince someone who has the least bit
of sympathy for LQG, you will probably lose them with this
paragraph. In terms of effectiveness, it also seems like a weak
conclusion. If you are aiming at someone like me, you should give
it a more well-reasoned flavor. You make some unsupported blanket
statements that should have been developed more in the main body of
the essay if they were really important, not just a couple of
sentences here. Instead of summarizing your position you present an
emotional appeal: "This isn't science, it's just a big kludge mixed
in with philosophy!" It seems like you could do better than that.

Hope these comments help.

Regards,
Marty

Frank Hellmann

Sep21-04, 03:31 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\nLubos Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0409191107160.12769-100000@feynman.harvard.edu>...\n> Dear Ladies and Gentlemen,\n> I want to check whether everyone agrees with the text below. Thanks, Lubos\n>\n\nJust to point towards one person who disagrees (and addresses some of\nthe critizism specifically):\n\nhttp://arxiv.org/abs/hep-th/0310077\n\nOh and considering the problems String theory has with reproducing\nexisting verified physics and with being a predictive theory these\nkind of attacks seem kind of pointless. Everybody seems to be in the\nsame boat at the moment.\n\n---\nfrank.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Lubos Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0409191107160.12769-100000@feynman.harvard.edu>...
> Dear Ladies and Gentlemen,
> I want to check whether everyone agrees with the text below. Thanks, Lubos
>

Just to point towards one person who disagrees (and addresses some of
the critizism specifically):

http://arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0310077

Oh and considering the problems String theory has with reproducing
existing verified physics and with being a predictive theory these
kind of attacks seem kind of pointless. Everybody seems to be in the
same boat at the moment.

---
frank.

Lubos Motl

Sep22-04, 03:45 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\nOn Tue, 21 Sep 2004, Frank Hellmann wrote:\n\n> Oh and considering the problems String theory has with reproducing\n> existing verified physics and with being a predictive theory these\n> kind of attacks seem kind of pointless. Everybody seems to be in the\n> same boat at the moment.\n\nThe only problem is that I am not sure which boat you are talking about.\nString theory is a maximally predictive theory we ever had. It has no\nadjustable dimensionless constants, although it predicts - at least\nqualitatively - all observed features of the Universe around us. And if\nit, at the end, unluckily happens to predict a large number of possible\nclassical backgrounds or "Universes", I am sorry, but you, me, as well as\neveryone else will have to accept the existence of these Universes.\n\nIt would be a sad outcome, but if we happen to see that a point in the\n"landscape" is the only way how to describe the real world without jumping\nto theories with infinitely many arbitrary parameters, we will have to\ntake this possibility seriously.\n\nWell, I am not sure whether the article you referred to is too serious. An\nindication that it is not too serious can be obtained if you click on\n"cited by" and you see that it has 0 citations. Well, it\'s because it\ncontains an equal mixture of well-known ideas and well-known\nmisconceptions, but no new correct ideas.\n__________________________________________ ____________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Tue, 21 Sep 2004, Frank Hellmann wrote:

> Oh and considering the problems String theory has with reproducing
> existing verified physics and with being a predictive theory these
> kind of attacks seem kind of pointless. Everybody seems to be in the
> same boat at the moment.

The only problem is that I am not sure which boat you are talking about.
String theory is a maximally predictive theory we ever had. It has no
adjustable dimensionless constants, although it predicts - at least
qualitatively - all observed features of the Universe around us. And if
it, at the end, unluckily happens to predict a large number of possible
classical backgrounds or "Universes", I am sorry, but you, me, as well as
everyone else will have to accept the existence of these Universes.

It would be a sad outcome, but if we happen to see that a point in the
"landscape" is the only way how to describe the real world without jumping
to theories with infinitely many arbitrary parameters, we will have to
take this possibility seriously.

Well, I am not sure whether the article you referred to is too serious. An
indication that it is not too serious can be obtained if you click on
"cited by" and you see that it has citations. Well, it's because it
contains an equal mixture of well-known ideas and well-known
misconceptions, but no new correct ideas.
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Daniel Elander

Sep22-04, 03:45 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n> The spacetime dimensionality (four) is another assumption that cannot be\n> questioned, much like the field content. Each of these assumptions is\n> challenged in a general enough theory of quantum gravity, for example all\n> the models that emerge from string theory. These assumptions have neither\n> theoretical nor experimental justification.\n\nWhile it would indeed be very interesting for a theory to, in\nprinciple, allow the number of dimensions to vary and have 4 come out\nas a prediction, I think it is pretty unreasonable to claim that if\nthe number of dimensions is instead fixed to 4, this is an assumption\nwith *no experimental justification*!\n\nDaniel\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>The spacetime dimensionality (four) is another assumption that cannot be
> questioned, much like the field content. Each of these assumptions is
> challenged in a general enough theory of quantum gravity, for example all
> the models that emerge from string theory. These assumptions have neither
> theoretical nor experimental justification.

While it would indeed be very interesting for a theory to, in
principle, allow the number of dimensions to vary and have 4 come out
as a prediction, I think it is pretty unreasonable to claim that if
the number of dimensions is instead fixed to 4, this is an assumption
with *no experimental justification*!

Daniel

Lubos Motl

Sep22-04, 07:23 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Wed, 22 Sep 2004, Daniel Elander wrote:\n\n> While it would indeed be very interesting for a theory to, in\n> principle, allow the number of dimensions to vary and have 4 come out\n> as a prediction, I think it is pretty unreasonable to claim that if\n> the number of dimensions is instead fixed to 4, this is an assumption\n> with *no experimental justification*!\n\nDear Daniel, I understand where you\'re coming from. ;-) Nevertheless if we\ntalk about the Planckian physics - and loop quantum gravity tries to - I\nthink that you are not right. Theories with extra dimensions *can* agree\nwith all observed phenomena much like the 4D theories - in fact they agree\nbetter than the simple 4-dimensional GR; the latter cannot be quantized.\n\nThe only reason that can lead someone to say that she prefers 4 dimensions\nis a notion of "simplicity". While simplicity is good, it is not really\nthe exact key idea that can be applied in physics. At the end, Nature does\nnot care how much paper you need to understand a physical system. In\nphysics, we have something similar to simplicity, but not quite the same\nthing: it is symmetry.\n\nIn fact, I think that Gell-Mann is the discoverer of what is called the\n"totalitarian" (or alternatively, "anarchic") principle that states that\neverything that is not forbidden can happen, which also means that we must\nalways think about the most general (equally consistent) theory that is\ncompatible with the same symmetries. Compactified higher-dimensional\ntheories can respect all the known symmetries of the simple 4D theories.\n\nTherefore we must include them as possibilities (otherwise we are using\nsome sort of random selection process) together with purely 4D theories\n(well there are no pure 4D quantum theories of gravity, but let me not\nrepeat this point too many times).\n\nFrom this perspective, and I think that it is the most rational\napplication of the principles we learned from Renormalization Group and\nelsewhere, having exactly four dimensions at the Planck scale is a form of\nfine-tuning that does not have much justification. Of course, I don\'t have\nany unique algorithm to calculate "how much" fine-tuning it is; very\nsmall, Planckian dimensions do not really "exist" (or their existence is\nnot sharp), and large hidden dimensions require a kind of fine-tuning\nthemselves.\n\nIn the words of Kaluza-Klein decomposition, requiring 4 dimensions at very\nhigh energies is a constraint about which fields cannot occur.\n\nHowever what we do have are consistent theories with extra hidden\ndimensions that not only can agree with the predictions of the older 4D\ntheories, but the lead to much more meaningful quantum results. If one\nconstruct something equally functioning but having 4 dimensions only, that\nwill be interesting. However, at the present, the ensemble of quantum\ntheories with gravity which only has 4 dimensions contains 0\nrepresentatives, so of course my measure is dominated by theories with\nextra dimensions that are more or less hidden.\n_________________________________________ _____________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Wed, 22 Sep 2004, Daniel Elander wrote:

> While it would indeed be very interesting for a theory to, in
> principle, allow the number of dimensions to vary and have 4 come out
> as a prediction, I think it is pretty unreasonable to claim that if
> the number of dimensions is instead fixed to 4, this is an assumption
> with *no experimental justification*!

Dear Daniel, I understand where you're coming from. ;-) Nevertheless if we
talk about the Planckian physics - and loop quantum gravity tries to - I
think that you are not right. Theories with extra dimensions *can* agree
with all observed phenomena much like the 4D theories - in fact they agree
better than the simple 4-dimensional GR; the latter cannot be quantized.

The only reason that can lead someone to say that she prefers 4 dimensions
is a notion of "simplicity". While simplicity is good, it is not really
the exact key idea that can be applied in physics. At the end, Nature does
not care how much paper you need to understand a physical system. In
physics, we have something similar to simplicity, but not quite the same
thing: it is symmetry.

In fact, I think that Gell-Mann is the discoverer of what is called the
"totalitarian" (or alternatively, "anarchic") principle that states that
everything that is not forbidden can happen, which also means that we must
always think about the most general (equally consistent) theory that is
compatible with the same symmetries. Compactified higher-dimensional
theories can respect all the known symmetries of the simple 4D theories.

Therefore we must include them as possibilities (otherwise we are using
some sort of random selection process) together with purely 4D theories
(well there are no pure 4D quantum theories of gravity, but let me not
repeat this point too many times).

From this perspective, and I think that it is the most rational
application of the principles we learned from Renormalization Group and
elsewhere, having exactly four dimensions at the Planck scale is a form of
fine-tuning that does not have much justification. Of course, I don't have
any unique algorithm to calculate "how much" fine-tuning it is; very
small, Planckian dimensions do not really "exist" (or their existence is
not sharp), and large hidden dimensions require a kind of fine-tuning
themselves.

In the words of Kaluza-Klein decomposition, requiring 4 dimensions at very
high energies is a constraint about which fields cannot occur.

However what we do have are consistent theories with extra hidden
dimensions that not only can agree with the predictions of the older 4D
theories, but the lead to much more meaningful quantum results. If one
construct something equally functioning but having 4 dimensions only, that
will be interesting. However, at the present, the ensemble of quantum
theories with gravity which only has 4 dimensions contains
representatives, so of course my measure is dominated by theories with
extra dimensions that are more or less hidden.
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Aaron Denney

Sep23-04, 04:46 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nOn 2004-09-22, Lubos Motl <motl@feynman.harvard.edu> wrote:\n> It would be a sad outcome, but if we happen to see that a point in the\n> "landscape" is the only way how to describe the real world without jumping\n> to theories with infinitely many arbitrary parameters, we will have to\n> take this possibility seriously.\n\nA point in an high-dimensional "landscape" sounds like just another way\nof describing a theory with many arbitrary parameters to me.\n\n--\nAaron Denney\n-><-\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On 2004-09-22, Lubos Motl <motl@feynman.harvard.edu> wrote:
> It would be a sad outcome, but if we happen to see that a point in the
> "landscape" is the only way how to describe the real world without jumping
> to theories with infinitely many arbitrary parameters, we will have to
> take this possibility seriously.

A point in an high-dimensional "landscape" sounds like just another way
of describing a theory with many arbitrary parameters to me.

--
Aaron Denney
-><-

John Gonsowski

Sep24-04, 08:09 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>mathman <mathnucl@optonline.net> wrote in message news:<mathman.1cumyl@physicsforums.com>...\n> I am not qualified to comment on the particulars you described, but I\n> just have one general comment about LQG and String theory.\n>\n> A. They are compatible, therefore both are valid or neither.\n>\n> B. They are not compatible, therefore one is valid or neither.\n>\n> At the moment I don\'t think anyone can say more until there is some\n> experimental work on validity or theoretical work on compatibility.\n>\n> ------------------------------------------------------------------------\n> This post submitted through the LaTeX-enabled physicsforums.com\n> To view this post with LaTeX images:\n> http://www.physicsforums.com/showthread.php?t=43682#post317808\n\nYes Lee Smolin in particular works on both and will use whatever works\nfor whatever model. He would like to get down to one model eventually.\nI personally like Tony Smith\'s string theory which would mean LQG has\nan opportunity to help string theory in general forget about\nsupersymmetry and include discrete Planck scale lattices.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>mathman <mathnucl@optonline.net> wrote in message news:<mathman.1cumyl@physicsforums.com>...
> I am not qualified to comment on the particulars you described, but I
> just have one general comment about LQG and String theory.
>
> A. They are compatible, therefore both are valid or neither.
>
> B. They are not compatible, therefore one is valid or neither.
>
> At the moment I don't think anyone can say more until there is some
> experimental work on validity or theoretical work on compatibility.
>
> ------------------------------------------------------------------------
> This post submitted through the LaTeX-enabled physicsforums.com
> To view this post with LaTeX images:
> http://www.physicsforums.com/showthread.php?t=43682#post317808

Yes Lee Smolin in particular works on both and will use whatever works
for whatever model. He would like to get down to one model eventually.
I personally like Tony Smith's string theory which would mean LQG has
an opportunity to help string theory in general forget about
supersymmetry and include discrete Planck scale lattices.

alistair

Sep24-04, 08:11 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Lubos Motl said in message:\n\n>Dear Daniel, I understand where you\'re coming from. ;-) Nevertheless\nif we\n>talk about the Planckian physics - and loop quantum gravity tries to\n- I\n>think that you are not right. Theories with extra dimensions *can*\nagree\n>with all observed phenomena much like the 4D theories - in fact they\nagree\n>better than the simple 4-dimensional GR; the latter cannot be\nquantized.\n\nThe validity of QFT which has been tested to 12 decimal places (and is\nprobably the most accurate theory known to science)is often called\ninto question whereas the validity of 4D SR is not.If there is\nsomething wrong with SR (the error would have to show up beyond 12\ndecimal places) then there would be something wrong with GR and that\ncould explain why\ngravity cannot be quantized.As for string theory itself, I would much\nrather believe in the existence of strings than point particles - as\nfar as I am concerned a mathematical point does not ,by\ndefinition,exist!\nPaul Dirac believed that the force of gravity was stronger in the\npast.\nThis can only be true if the electric force was stronger too (or else\nthe Sun would be much less luminous nowadays).String theory allows\nforces to change strength over time,so I\'m sure Dirac would have been\nat least a partial fan of\nit.But he did not believe that any theory that involved\nrenormalisation could be correct.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Lubos Motl said in message:

>Dear Daniel, I understand where you're coming from. ;-) Nevertheless
if we
>talk about the Planckian physics - and loop quantum gravity tries to
- I
>think that you are not right. Theories with extra dimensions *can*
agree
>with all observed phenomena much like the 4D theories - in fact they
agree
>better than the simple 4-dimensional GR; the latter cannot be
quantized.

The validity of QFT which has been tested to 12 decimal places (and is
probably the most accurate theory known to science)is often called
into question whereas the validity of 4D SR is not.If there is
something wrong with SR (the error would have to show up beyond 12
decimal places) then there would be something wrong with GR and that
could explain why
gravity cannot be quantized.As for string theory itself, I would much
rather believe in the existence of strings than point particles - as
far as I am concerned a mathematical point does not ,by
definition,exist!
Paul Dirac believed that the force of gravity was stronger in the
past.
This can only be true if the electric force was stronger too (or else
the Sun would be much less luminous nowadays).String theory allows
forces to change strength over time,so I'm sure Dirac would have been
at least a partial fan of
it.But he did not believe that any theory that involved
renormalisation could be correct.

jbg

Sep24-04, 08:12 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Lubos Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0409212112400.4640-100000@feynman.harvard.edu>...\n> On Tue, 21 Sep 2004, Frank Hellmann wrote:\n>\n> > Oh and considering the problems String theory has with reproducing\n> > existing verified physics and with being a predictive theory these\n> > kind of attacks seem kind of pointless. Everybody seems to be in the\n> > same boat at the moment.\n>\n> The only problem is that I am not sure which boat you are talking about.\n> String theory is a maximally predictive theory we ever had. It has no\n> adjustable dimensionless constants, although it predicts - at least\n> qualitatively - all observed features of the Universe around us. And if\n> it, at the end, unluckily happens to predict a large number of possible\n> classical backgrounds or "Universes", I am sorry, but you, me, as well as\n> everyone else will have to accept the existence of these Universes.\n\nwhy? are you saying that a (mathematical) model of reality is reality?\n\nwhen can we be sure something exists? when our formal representations\nof reality predict the feature or when our technology experimentally\nmeasures the feature?\n\nof course it is very tempting to believe that the (300 year) success\nof coding reality into mathematical concepts, "computing" information\nwithin this framework and deducing predictions from it, which turn out\nto be actual features of reality, is not going to end any time soon.\nbut then we don\'t know this for sure. we don\'t even know why the\nworkings of reality can, in the first place, be described by\nmathematical models and rules.\n\nwithout getting lost in philosophical musings ("do we discover or\ninvent mathematics?", "is mathematics the blueprint of reality?", "why\ncan we devise formal systems in our thinking?") I find the question\nnot to be:\n\nWhat\'s wrong with loop quantum gravity?\n\nbut more to the point:\n\nWhat\'s wrong with our fundamental description of reality?\n\nyou seem to give the impression that string/m-theory has solved all\n(major) puzzles. that it\'s futile to spend any time on any other\ntheory. without wanting to be judgmental or insulting (really:-), i\njust wonder how much your "lobbying" gives justice to the (long) list\nof unsolved problems, the current unsatisfactory state of fundamental\nphysics and the possibility for new and orthogonal ideas...\n\nregards,\n\nj\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Lubos Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0409212112400.4640-100000@feynman.harvard.edu>...
> On Tue, 21 Sep 2004, Frank Hellmann wrote:
>
> > Oh and considering the problems String theory has with reproducing
> > existing verified physics and with being a predictive theory these
> > kind of attacks seem kind of pointless. Everybody seems to be in the
> > same boat at the moment.
>
> The only problem is that I am not sure which boat you are talking about.
> String theory is a maximally predictive theory we ever had. It has no
> adjustable dimensionless constants, although it predicts - at least
> qualitatively - all observed features of the Universe around us. And if
> it, at the end, unluckily happens to predict a large number of possible
> classical backgrounds or "Universes", I am sorry, but you, me, as well as
> everyone else will have to accept the existence of these Universes.

why? are you saying that a (mathematical) model of reality is reality?

when can we be sure something exists? when our formal representations
of reality predict the feature or when our technology experimentally
measures the feature?

of course it is very tempting to believe that the (300 year) success
of coding reality into mathematical concepts, "computing" information
within this framework and deducing predictions from it, which turn out
to be actual features of reality, is not going to end any time soon.
but then we don't know this for sure. we don't even know why the
workings of reality can, in the first place, be described by
mathematical models and rules.

without getting lost in philosophical musings ("do we discover or
invent mathematics?", "is mathematics the blueprint of reality?", "why
can we devise formal systems in our thinking?") I find the question
not to be:

What's wrong with loop quantum gravity?

but more to the point:

What's wrong with our fundamental description of reality?

you seem to give the impression that string/m-theory has solved all
(major) puzzles. that it's futile to spend any time on any other
theory. without wanting to be judgmental or insulting (really:-), i
just wonder how much your "lobbying" gives justice to the (long) list
of unsolved problems, the current unsatisfactory state of fundamental
physics and the possibility for new and orthogonal ideas...

regards,

j

rof@maths.tcd.ie

Sep24-04, 08:13 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Denney <wnoise@ofb.net> writes:\n\n>On 2004-09-22, Lubos Motl <motl@feynman.harvard.edu> wrote:\n>> It would be a sad outcome, but if we happen to see that a point in the\n>> "landscape" is the only way how to describe the real world without jumping\n>> to theories with infinitely many arbitrary parameters, we will have to\n>> take this possibility seriously.\n\n>A point in an high-dimensional "landscape" sounds like just another way\n>of describing a theory with many arbitrary parameters to me.\n\nQuite right. In fact, there\'s a quantitative way to see how good a theory\nis. Take the amount of information (measured in bits, or digits if you\nprefer) required to specify the theory (and any auxiliary parameters,\nfor example, a point in the landscape) and compare this to the\namount of information correctly predicted by the theory. If the\nformer is not smaller than the latter, then the theory has failed\nto compress the observed data, and should be discarded.\n\nFor example, if somebody starts using string theory to predict the numerical\nvalues of the fundamental constants, but needs to first specify a point\non the landscape, then the amount of information needed to specify\nthe point (in digits) had better not exceed the total number of digits\nsuccessfully "explained". Given that the known fundamental constants\ngive us less than 100 digits of information altogether, even complete\ncertainty that an explanation lies somewhere in a discretuum of\n10^100 possible choices shouldn\'t convince us of anything. Of\ncourse, digits in fundamental constants aren\'t everything - you\nneed a few more bits to specify which gauge groups describe the\nobserved fields, dimensionality of observed space and so forth, but\nmost of the information is in the constants (log log n digits for\nthe order of magnitude and one digit for each known digit).\n\nA vacuum selection principle is needed, and anthropic arguments\nwill never be predictive, since they basically tell us that\nthe universe must be as it is, so go looking (among the 10^100\npossibilities) for something which looks like our universe. If\nthere are 70 digits to be explained, then we\'ll find an explanation\n(by chance) once for every 10^70 options we examine, leaving\nus with 10^30 different universes to choose from; take any\ntwo of these selected universes - the chance that they will\nagree on the next digit of alpha will be one in ten. That is,\nthere\'ll be no predictive power.\n\nR.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Denney <wnoise@ofb.net> writes:

>On 2004-09-22, Lubos Motl <motl@feynman.harvard.edu> wrote:
>> It would be a sad outcome, but if we happen to see that a point in the
>> "landscape" is the only way how to describe the real world without jumping
>> to theories with infinitely many arbitrary parameters, we will have to
>> take this possibility seriously.

>A point in an high-dimensional "landscape" sounds like just another way
>of describing a theory with many arbitrary parameters to me.

Quite right. In fact, there's a quantitative way to see how good a theory
is. Take the amount of information (measured in bits, or digits if you
prefer) required to specify the theory (and any auxiliary parameters,
for example, a point in the landscape) and compare this to the
amount of information correctly predicted by the theory. If the
former is not smaller than the latter, then the theory has failed
to compress the observed data, and should be discarded.

For example, if somebody starts using string theory to predict the numerical
values of the fundamental constants, but needs to first specify a point
on the landscape, then the amount of information needed to specify
the point (in digits) had better not exceed the total number of digits
successfully "explained". Given that the known fundamental constants
give us less than 100 digits of information altogether, even complete
certainty that an explanation lies somewhere in a discretuum of
10^100 possible choices shouldn't convince us of anything. Of
course, digits in fundamental constants aren't everything - you
need a few more bits to specify which gauge groups describe the
observed fields, dimensionality of observed space and so forth, but
most of the information is in the constants (log log n digits for
the order of magnitude and one digit for each known digit).

A vacuum selection principle is needed, and anthropic arguments
will never be predictive, since they basically tell us that
the universe must be as it is, so go looking (among the 10^100
possibilities) for something which looks like our universe. If
there are 70 digits to be explained, then we'll find an explanation
(by chance) once for every 10^70 options we examine, leaving
us with 10^30 different universes to choose from; take any
two of these selected universes - the chance that they will
agree on the next digit of \alpha will be one in ten. That is,
there'll be no predictive power.

R.

Boris Borcic

Sep27-04, 01:57 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Aaron Denney wrote:\n> On 2004-09-22, Lubos Motl <motl@feynman.harvard.edu> wrote:\n>\n>>It would be a sad outcome, but if we happen to see that a point in the\n>>"landscape" is the only way how to describe the real world without jumping\n>>to theories with infinitely many arbitrary parameters, we will have to\n>>take this possibility seriously.\n>\n>\n> A point in an high-dimensional "landscape" sounds like just another way\n> of describing a theory with many arbitrary parameters to me.\n>\n\nIndeed Lubos you sound here rather like how the Church would sound, if it\nclaimed that time did not prove Giordano Bruno right, since Bruno (in 1600)\nmultiplied the equation stars="distant solar systems" by an *infinite*\nquantity of stars in the Universe, while our current beliefs admit "only" a\n*finite* number of them.\n\nCheers, Boris Borcic\n--\n666?? -- 666 ~ .666 ~ 2/3 ~ 1 - 1/3 ~ tertium non datur ~ the excluded middle\n~ "either you are with us, or you are against us" !!\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Aaron Denney wrote:
> On 2004-09-22, Lubos Motl <motl@feynman.harvard.edu> wrote:
>
>>It would be a sad outcome, but if we happen to see that a point in the
>>"landscape" is the only way how to describe the real world without jumping
>>to theories with infinitely many arbitrary parameters, we will have to
>>take this possibility seriously.
>
>
> A point in an high-dimensional "landscape" sounds like just another way
> of describing a theory with many arbitrary parameters to me.
>

Indeed Lubos you sound here rather like how the Church would sound, if it
claimed that time did not prove Giordano Bruno right, since Bruno (in 1600)
multiplied the equation stars="distant solar systems" by an *infinite*
quantity of stars in the Universe, while our current beliefs admit "only" a
*finite* number of them.

Cheers, Boris Borcic
--
666?? -- 666 ~ .666 ~ 2/3 ~ 1 - 1/3 ~ tertium non datur ~ the excluded middle
~ "either you are with us, or you are against us" !!

Lubos Motl

Sep27-04, 03:32 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>NNTP-Posting-Host: lfa222122.richmond.edu\nX-Trace: rumor.richmond.edu 1096274503 19904 141.166.222.122 (27 Sep 2004 08:41:43 GMT)\nX-Complaints-To: usenet@rumor.richmond.edu\nNNTP-Posting-Date: Mon, 27 Sep 2004 08:41:43 +0000 (UTC)\nXref: core-easynews sci.physics.research:59567\n\n\n\n\nOn Fri, 24 Sep 2004 rof@maths.tcd.ie wrote:\n\n> Quite right. In fact, there\'s a quantitative way to see how good a theory\n> is. Take the amount of information (measured in bits, or digits if you\n> prefer) required to specify the theory (and any auxiliary parameters,\n> for example, a point in the landscape) and compare this to the\n> amount of information correctly predicted by the theory. If the\n> former is not smaller than the latter, then the theory has failed\n> to compress the observed data, and should be discarded.\n\nIncidentally, I agree that this counting or a very related one - including\nthe bits, to make it quantitative - is a good criterion to judge the\npredictive success of a theory! Of course, a good theory predicts\neverything in the Standard Model, which are terabytes of information\n(results) recorded not only at Tevatron. ;-) We must refine your criterion\nin such a way that we are not multiply-counting the same or very related\nsuccessful predictions, which is of course subtle. This decision requires\nus to know which experiments are just minor copies of some previous\nexperiments, and which ones have the potential to give completely new\ndata. We need to be smart in order to make such decisions, and these\ndecisions will still depend on our models.\n\nIf we really exclude all theories that have no chance to describe these\nterabytes - for example loop quantum gravity - then I agree with your\ncounting, assuming that an appropriate compression of the information is\nmade.\n\nIf something reproduces the Standard Model, it only has 19 parameters\n(plus 10 for neutrino masses), and we only want to count the information\nabout these parameters as the "output" of your theory. Incidentally, if\nyou measure the 29 parameters of the nu-Standard Model with precision of\n11 digits per each parameter, then you get over 300 decimal digits of\ninformation from the experiment - which means that even among 10^{300} of\ndiscrete vacua, it is unlikely that one of the will work exactly, and if\nit would, it would be a highly impressive, unlikely prediction. (And I\nhave not included the extra bits that describe the "discrete" properties\nof the Standard Model, like the number of generations and the gauge\ngroups and representations.)\n\nWhat I want to emphasize is that in theories with potentially infinite\naccuracy, a discrete choice of the vacua - even if it is one vacuum from a\nfamily of 10^{320} sibblings - is still much much smaller fine-tuning than\nthe fine-tuning of new continuous parameters, especially if the number of\nsuch continuous parameters is infinite (like in nonrenormalizable\ntheories or loop quantum gravity coupled to general matter). When the\ntheory of everything is found, time will be playing for us - the\nquantitative predictive power will increase as the accuracy of the\nexperiments gets better.\n\nOn the other hand, I agree that this is not a dogma - that discrete\nchoices are always more acceptable - and the border that decides whether\ndiscrete or continuous parameters are more acceptable in a predictive\ntheory is determined by the accuracy of the predictions that a given\ntheory can offer. If the accuracy is rough and bad, there is not much\ndifference between continuous parameters and discrete choices from a large\nensemble. As the accuracy increases, the new continuous parameters become\nmuch worse for predictivity.\n\nI am still nearly sure that in this counting, string theory is the most\npredictive theory of fundamental physics we have.\n___________________________________________ ___________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>NNTP-Posting-Host: lfa222122.richmond.edu
X-Trace: rumor.richmond.edu 1096274503 19904 141.166.222.122 (27 Sep 2004 08:41:43 GMT)
X-Complaints-To: usenet@rumor.richmond.edu
NNTP-Posting-Date: Mon, 27 Sep 2004 08:41:43 +0000 (UTC)
Xref: core-easynews sci.physics.research:59567

On Fri, 24 Sep 2004 rof@maths.tcd.ie wrote:

> Quite right. In fact, there's a quantitative way to see how good a theory
> is. Take the amount of information (measured in bits, or digits if you
> prefer) required to specify the theory (and any auxiliary parameters,
> for example, a point in the landscape) and compare this to the
> amount of information correctly predicted by the theory. If the
> former is not smaller than the latter, then the theory has failed
> to compress the observed data, and should be discarded.

Incidentally, I agree that this counting or a very related one - including
the bits, to make it quantitative - is a good criterion to judge the
predictive success of a theory! Of course, a good theory predicts
everything in the Standard Model, which are terabytes of information
(results) recorded not only at Tevatron. ;-) We must refine your criterion
in such a way that we are not multiply-counting the same or very related
successful predictions, which is of course subtle. This decision requires
us to know which experiments are just minor copies of some previous
experiments, and which ones have the potential to give completely new
data. We need to be smart in order to make such decisions, and these
decisions will still depend on our models.

If we really exclude all theories that have no chance to describe these
terabytes - for example loop quantum gravity - then I agree with your
counting, assuming that an appropriate compression of the information is
made.

If something reproduces the Standard Model, it only has 19 parameters
(plus 10 for neutrino masses), and we only want to count the information
about these parameters as the "output" of your theory. Incidentally, if
you measure the 29 parameters of the \nu-Standard Model with precision of
11 digits per each parameter, then you get over 300 decimal digits of
information from the experiment - which means that even among 10^{300} of
discrete vacua, it is unlikely that one of the will work exactly, and if
it would, it would be a highly impressive, unlikely prediction. (And I
have not included the extra bits that describe the "discrete" properties
of the Standard Model, like the number of generations and the gauge
groups and representations.)

What I want to emphasize is that in theories with potentially infinite
accuracy, a discrete choice of the vacua - even if it is one vacuum from a
family of 10^{320} sibblings - is still much much smaller fine-tuning than
the fine-tuning of new continuous parameters, especially if the number of
such continuous parameters is infinite (like in nonrenormalizable
theories or loop quantum gravity coupled to general matter). When the
theory of everything is found, time will be playing for us - the
quantitative predictive power will increase as the accuracy of the
experiments gets better.

On the other hand, I agree that this is not a dogma - that discrete
choices are always more acceptable - and the border that decides whether
discrete or continuous parameters are more acceptable in a predictive
theory is determined by the accuracy of the predictions that a given
theory can offer. If the accuracy is rough and bad, there is not much
difference between continuous parameters and discrete choices from a large
ensemble. As the accuracy increases, the new continuous parameters become
much worse for predictivity.

I am still nearly sure that in this counting, string theory is the most
predictive theory of fundamental physics we have.
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Thomas Larsson

Sep28-04, 02:26 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Lubos Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0409241610490.8769-100000@feynman.harvard.edu>...\n\n> What I want to emphasize is that in theories with potentially infinite\n> accuracy, a discrete choice of the vacua - even if it is one vacuum from a\n> family of 10^{320} sibblings - is still much much smaller fine-tuning than\n> the fine-tuning of new continuous parameters, especially if the number of\n\n10^320 is a very big number. If the Planck length is 10^-35 m, and the\nobservable universe is < 10^45 m, and there is one quantum state per\n(Planck length)^4, then 10^320 is larger than the number of quantum states\nin the observable universe. If there are more theories than quantum states\nin the observable universe, how much predictive power have you left?\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Lubos Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0409241610490.8769-100000@feynman.harvard.edu>...

> What I want to emphasize is that in theories with potentially infinite
> accuracy, a discrete choice of the vacua - even if it is one vacuum from a
> family of 10^{320} sibblings - is still much much smaller fine-tuning than
> the fine-tuning of new continuous parameters, especially if the number of

10^320 is a very big number. If the Planck length is 10^-35 m, and the
observable universe is < 10^45 m, and there is one quantum state per
(Planck length)^4, then 10^320 is larger than the number of quantum states
in the observable universe. If there are more theories than quantum states
in the observable universe, how much predictive power have you left?

cragwolf

Sep29-04, 08:29 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Tue, 28 Sep 2004 07:26:17 +0000, Thomas Larsson wrote:\n\n> 10^320 is a very big number. If the Planck length is 10^-35 m, and the\n> observable universe is < 10^45 m, and there is one quantum state per\n> (Planck length)^4, then 10^320 is larger than the number of quantum states\n> in the observable universe. If there are more theories than quantum states\n> in the observable universe, how much predictive power have you left?\n\nInteresting. Why is it one quantum state per (Planck length)^4? Why the\nfactor of 4? Any simple way to explain this?\n\ncragwolf\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Tue, 28 Sep 2004 07:26:17 +0000, Thomas Larsson wrote:

> 10^320 is a very big number. If the Planck length is 10^-35 m, and the
> observable universe is < 10^45 m, and there is one quantum state per
> (Planck length)^4, then 10^320 is larger than the number of quantum states
> in the observable universe. If there are more theories than quantum states
> in the observable universe, how much predictive power have you left?

Interesting. Why is it one quantum state per (Planck length)^4? Why the
factor of 4? Any simple way to explain this?

cragwolf

Lubos Motl

Sep29-04, 08:29 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Tue, 28 Sep 2004, Thomas Larsson wrote:\n\n> 10^320 is a very big number. If the Planck length is 10^-35 m, and the\n> observable universe is < 10^45 m, and there is one quantum state per\n> (Planck length)^4, then 10^320 is larger than the number of quantum states\n> in the observable universe.\n\nYour error is a pretty simple one: the entropy of the Universe is\n10^{100}, and therefore the minimal dimension of the Hilbert space to\ndescribe the Universe is roughly 10^{10^{100}}, which is still "slightly"\nbigger than 10^{320}. ;-)\n\n10^{320} is a lot, but it is very little to kill the predictive power of a\ntheory. To pick one choice among 10^{320} options, you need roughly 1000\nbits - which is 128 bytes. It\'s the input, assuming that we will be able\nto locate the correct vacuum. Be sure that the experiments have been\nalready able to verify more than 128 bytes of physics\' predictions. ;-)\nFor example, I just transfered 250 MB to my gmail account in agreement\nwith the theory of transistors.\n____________________________________ __________________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Tue, 28 Sep 2004, Thomas Larsson wrote:

> 10^320 is a very big number. If the Planck length is 10^-35 m, and the
> observable universe is < 10^45 m, and there is one quantum state per
> (Planck length)^4, then 10^320 is larger than the number of quantum states
> in the observable universe.

Your error is a pretty simple one: the entropy of the Universe is
10^{100}, and therefore the minimal dimension of the Hilbert space to
describe the Universe is roughly 10^{10^{100}}, which is still "slightly"
bigger than 10^{320}. ;-)

10^{320} is a lot, but it is very little to kill the predictive power of a
theory. To pick one choice among 10^{320} options, you need roughly 1000
bits - which is 128 bytes. It's the input, assuming that we will be able
to locate the correct vacuum. Be sure that the experiments have been
already able to verify more than 128 bytes of physics' predictions. ;-)
For example, I just transfered 250 MB to my gmail account in agreement
with the theory of transistors.
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Lubos Motl

Sep29-04, 08:29 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Mon, 27 Sep 2004, Boris Borcic wrote:\n\n> Indeed Lubos you sound here rather like how the Church would sound, if it\n> claimed that time did not prove Giordano Bruno right, since Bruno (in 1600)\n> multiplied the equation stars="distant solar systems" by an *infinite*\n> quantity of stars in the Universe, while our current beliefs admit "only" a\n> *finite* number of them.\n\nI don\'t quite understand the analogy. The only modest statement I was\nsaying was that a theory that must fine-tune (or arbitrarily choose)\ninfinitely many important parameters is not predictive, while a theory\nthat only has a finite number of parameters - especially if they are\ndiscrete - can be very predictive. How is it related to these hypothetical\ndiscussions of Bruno and the Church about the number of stars?\n\nLet me mention that even if your analogy were meaningful - which I doubt -\nthe number of stars in this Universe remained finite after all,\nand therefore my original statements win against your criticism anyway. ;-)\n_______________________________________________ _______________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Mon, 27 Sep 2004, Boris Borcic wrote:

> Indeed Lubos you sound here rather like how the Church would sound, if it
> claimed that time did not prove Giordano Bruno right, since Bruno (in 1600)
> multiplied the equation stars="distant solar systems" by an *infinite*
> quantity of stars in the Universe, while our current beliefs admit "only" a
> *finite* number of them.

I don't quite understand the analogy. The only modest statement I was
saying was that a theory that must fine-tune (or arbitrarily choose)
infinitely many important parameters is not predictive, while a theory
that only has a finite number of parameters - especially if they are
discrete - can be very predictive. How is it related to these hypothetical
discussions of Bruno and the Church about the number of stars?

Let me mention that even if your analogy were meaningful - which I doubt -
the number of stars in this Universe remained finite after all,
and therefore my original statements win against your criticism anyway. ;-)
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Arnold Neumaier

Sep29-04, 12:18 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nLubos Motl wrote:\n> On Tue, 28 Sep 2004, Thomas Larsson wrote:\n>\n>>10^320 is a very big number. If the Planck length is 10^-35 m, and the\n>>observable universe is < 10^45 m, and there is one quantum state per\n>>(Planck length)^4, then 10^320 is larger than the number of quantum states\n>>in the observable universe.\n>\n> 10^{320} is a lot, but it is very little to kill the predictive power of a\n> theory. To pick one choice among 10^{320} options, you need roughly 1000\n> bits - which is 128 bytes. It\'s the input, assuming that we will be able\n> to locate the correct vacuum. Be sure that the experiments have been\n> already able to verify more than 128 bytes of physics\' predictions. ;-)\n\nBut the current standard model + GR explains all currently observable\nphysics; thus it already reduced the \'more than 128 bytes of physics\'\npredictions\' to the number of bits needed to describe the standard model\nat the current accuracy of the parameters defining it. These are less\nthan half of the 1000 bits.\n\nThus, from the point of the informational contents, a better theory\nmust predict these on the basis of choices amounting to even fewer bits.\n\n\nArnold Neumaier\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Lubos Motl wrote:
> On Tue, 28 Sep 2004, Thomas Larsson wrote:
>
>>10^320 is a very big number. If the Planck length is 10^-35 m, and the
>>observable universe is < 10^45 m, and there is one quantum state per
>>(Planck length)^4, then 10^320 is larger than the number of quantum states
>>in the observable universe.
>
> 10^{320} is a lot, but it is very little to kill the predictive power of a
> theory. To pick one choice among 10^{320} options, you need roughly 1000
> bits - which is 128 bytes. It's the input, assuming that we will be able
> to locate the correct vacuum. Be sure that the experiments have been
> already able to verify more than 128 bytes of physics' predictions. ;-)

But the current standard model + GR explains all currently observable
physics; thus it already reduced the 'more than 128 bytes of physics'
predictions' to the number of bits needed to describe the standard model
at the current accuracy of the parameters defining it. These are less
than half of the 1000 bits.

Thus, from the point of the informational contents, a better theory
must predict these on the basis of choices amounting to even fewer bits.

Arnold Neumaier

Creighton Hogg

Sep29-04, 12:18 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nOn Wed, 29 Sep 2004, Lubos Motl wrote:\n\n> On Tue, 28 Sep 2004, Thomas Larsson wrote:\n>\n> > 10^320 is a very big number. If the Planck length is 10^-35 m, and the\n> > observable universe is < 10^45 m, and there is one quantum state per\n> > (Planck length)^4, then 10^320 is larger than the number of quantum states\n> > in the observable universe.\n>\n> Your error is a pretty simple one: the entropy of the Universe is\n> 10^{100}, and therefore the minimal dimension of the Hilbert space to\n> describe the Universe is roughly 10^{10^{100}}, which is still "slightly"\n> bigger than 10^{320}. ;-)\n>\n> 10^{320} is a lot, but it is very little to kill the predictive power of a\n> theory. To pick one choice among 10^{320} options, you need roughly 1000\n> bits - which is 128 bytes. It\'s the input, assuming that we will be able\n> to locate the correct vacuum. Be sure that the experiments have been\n> already able to verify more than 128 bytes of physics\' predictions. ;-)\n> For example, I just transfered 250 MB to my gmail account in agreement\n> with the theory of transistors.\n\nSorry, but this seems somewhat misleading to me. The main thing I\'m\ncurious about is how string theory can be tested and possibly falsified.\nLet\'s say that we don\'t see any signs of string theory at the LHC. Okay,\nwell that elimates all the models that predicted signals visible at the\nLHC during its run, but there\'s still many, many more possible vacua and\nvalues of the string scale so string theory wouldn\'t have been falsified.\nWell then, what if we don\'t see anything at the upgraded LHC with center\nof mass energy ~50TeV. We still haven\'t falsified string theory. What\ncan we do that would actually prove string theory wrong? From what I\nunderstand of string pheno, the string scale is to be determined\nexperimentally, and so all experiments can do is put a lower bound on the\nscale.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Wed, 29 Sep 2004, Lubos Motl wrote:

> On Tue, 28 Sep 2004, Thomas Larsson wrote:
>
> > 10^320 is a very big number. If the Planck length is 10^-35 m, and the
> > observable universe is < 10^45 m, and there is one quantum state per
> > (Planck length)^4, then 10^320 is larger than the number of quantum states
> > in the observable universe.
>
> Your error is a pretty simple one: the entropy of the Universe is
> 10^{100}, and therefore the minimal dimension of the Hilbert space to
> describe the Universe is roughly 10^{10^{100}}, which is still "slightly"
> bigger than 10^{320}. ;-)
>
> 10^{320} is a lot, but it is very little to kill the predictive power of a
> theory. To pick one choice among 10^{320} options, you need roughly 1000
> bits - which is 128 bytes. It's the input, assuming that we will be able
> to locate the correct vacuum. Be sure that the experiments have been
> already able to verify more than 128 bytes of physics' predictions. ;-)
> For example, I just transfered 250 MB to my gmail account in agreement
> with the theory of transistors.

Sorry, but this seems somewhat misleading to me. The main thing I'm
curious about is how string theory can be tested and possibly falsified.
Let's say that we don't see any signs of string theory at the LHC. Okay,
well that elimates all the models that predicted signals visible at the
LHC during its run, but there's still many, many more possible vacua and
values of the string scale so string theory wouldn't have been falsified.
Well then, what if we don't see anything at the upgraded LHC with center
of mass energy ~50TeV. We still haven't falsified string theory. What
can we do that would actually prove string theory wrong? From what I
understand of string pheno, the string scale is to be determined
experimentally, and so all experiments can do is put a lower bound on the
scale.

Ralph Hartley

Sep30-04, 12:21 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nLubos Motl wrote:\n\n> We must refine your criterion\n> in such a way that we are not multiply-counting the same or very related\n> successful predictions, which is of course subtle. This decision requires\n> us to know which experiments are just minor copies of some previous\n> experiments, and which ones have the potential to give completely new\n> data. We need to be smart in order to make such decisions, and these\n> decisions will still depend on our models.\n\nThe relevant quantity is the (information theoretic) entropy of each new\nexperiment conditioned on the results of all previous experiments. And yes,\nit does depend on a model (i.e. something like a Bayesian prior). There are\nrules for constructing Bayesian priors so that with enough evidence, the\nprior (usually) doesn\'t matter too much (e.g. never assign probability 0 to\nanything).\n\n> On the other hand, I agree that this is not a dogma - that discrete\n> choices are always more acceptable - and the border that decides whether\n> discrete or continuous parameters are more acceptable in a predictive\n> theory is determined by the accuracy of the predictions that a given\n> theory can offer. If the accuracy is rough and bad, there is not much\n> difference between continuous parameters and discrete choices from a large\n> ensemble. As the accuracy increases, the new continuous parameters become\n> much worse for predictivity.\n\nI think it is less than "not a dogma", it isn\'t true at all.\n\nContinuous parameters don\'t necessarily make a theory less predictive (to\nsay nothing of "more acceptable") than discrete ones.\n\nConsider a theory like Newton\'s gravity. It has a continuous parameter, but\nis the very prototype of a predictive theory.\n\nIt is predictive because successive digits of the parameter make less and\nless difference. If you know G to 3 digits you can predict a lot. If you\nknow G to 30 digits you can predict almost anything. Knowing G to 500\ndigits will let you predict measurements of the first 500 digits of G, but\nnot much else.\n\nIt is *so* predictive, that we now know that it isn\'t quite right, but the\ntheories that replaced are all very predictive, despite having parameters.\n\nMultiple free parameters, or even infinitely many, can be qualitatively the\nsame, if successive parameters each matter less. You could combine them\ninto a single parameter anyway, since a (countable) set of continuous\nparameters have the same number of digits as a single real number.\n\nCompare that to a theory that has "only" 10^320 versions (by the way is\nthat a real estimate, or just a guess?), but each is as different as our\nuniverse is from Conway\'s game of "life". You could presumably narrow those\ndown to ones that resemble our universe, but there is no guarantee that you\ncan make *any* prediction at *all* until you have narrowed it down to one.\n\nThe *good* thing about such a theory is that there is no guarantee that\nthere will be even one. The *bad* thing is that there is also no guarantee\nthat there will be as few as 10^100. So the theory could be very\npredictive, or not at all, and there is no way to tell!\n\nI think your point is that eventually, we could *in* *principle* know the\nvalues of the discrete parameters exactly. Once we did, *then* the theory\nwould be *completely* predictive. I wouldn\'t call such a theory\n"predictive" until then. I would agree that it is *potentially* predictive.\n\nBut that isn\'t what counts; no one promised you a completely predictable\nuniverse! What\'s important is what checkable predictions it can make *now*\n(or in the *near* future). On that score theories of quantum gravity are\ntied at zero all.\n\n> I am still nearly sure that in this counting, string theory is the most\n> predictive theory of fundamental physics we have.\n\nYou keep saying that, without being able to exhibit even *one* prediction\nof the theory!\n\nOK, unlike most theories, it does predict the number of dimensions, instead\nof assuming a value. But that prediction didn\'t pan out so well! Yes, I\nknow the extra dimensions could be very small, so the bad prediction isn\'t\nfatal, but it isn\'t a victory either.\n\nIt does get the expected value for the black hole entropy, you could call\nthat a prediction, though not one we can check. It\'s more like a\nconsistency condition than a prediction, since we already knew the "right"\nanswer, on purely theoretical grounds.\n\nDoes string theory actually predict supersymetry? In the sense that without\nsupersymetry the theory is dead?\n\nNewton had a more predictive theory! The Standard Model is *much* more\npredictive. Note that both of those are extremely predictive, even though\nthey have continuous parameters.\n\nI will grant that it is as predictive as any theory of quantum gravity we\nhave, but that isn\'t saying too much, especially if as you claim, it is the\n*only* theory of quantum gravity we have.\n\nRalph Hartley\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Lubos Motl wrote:

> We must refine your criterion
> in such a way that we are not multiply-counting the same or very related
> successful predictions, which is of course subtle. This decision requires
> us to know which experiments are just minor copies of some previous
> experiments, and which ones have the potential to give completely new
> data. We need to be smart in order to make such decisions, and these
> decisions will still depend on our models.

The relevant quantity is the (information theoretic) entropy of each new
experiment conditioned on the results of all previous experiments. And yes,
it does depend on a model (i.e. something like a Bayesian prior). There are
rules for constructing Bayesian priors so that with enough evidence, the
prior (usually) doesn't matter too much (e.g. never assign probability to
anything).

> On the other hand, I agree that this is not a dogma - that discrete
> choices are always more acceptable - and the border that decides whether
> discrete or continuous parameters are more acceptable in a predictive
> theory is determined by the accuracy of the predictions that a given
> theory can offer. If the accuracy is rough and bad, there is not much
> difference between continuous parameters and discrete choices from a large
> ensemble. As the accuracy increases, the new continuous parameters become
> much worse for predictivity.

I think it is less than "not a dogma", it isn't true at all.

Continuous parameters don't necessarily make a theory less predictive (to
say nothing of "more acceptable") than discrete ones.

Consider a theory like Newton's gravity. It has a continuous parameter, but
is the very prototype of a predictive theory.

It is predictive because successive digits of the parameter make less and
less difference. If you know G to 3 digits you can predict a lot. If you
know G to 30 digits you can predict almost anything. Knowing G to 500
digits will let you predict measurements of the first 500 digits of G, but
not much else.

It is *so* predictive, that we now know that it isn't quite right, but the
theories that replaced are all very predictive, despite having parameters.

Multiple free parameters, or even infinitely many, can be qualitatively the
same, if successive parameters each matter less. You could combine them
into a single parameter anyway, since a (countable) set of continuous
parameters have the same number of digits as a single real number.

Compare that to a theory that has "only" 10^320 versions (by the way is
that a real estimate, or just a guess?), but each is as different as our
universe is from Conway's game of "life". You could presumably narrow those
down to ones that resemble our universe, but there is no guarantee that you
can make *any* prediction at *all* until you have narrowed it down to one.

The *good* thing about such a theory is that there is no guarantee that
there will be even one. The *bad* thing is that there is also no guarantee
that there will be as few as 10^100. So the theory could be very
predictive, or not at all, and there is no way to tell!

I think your point is that eventually, we could *in* *principle* know the
values of the discrete parameters exactly. Once we did, *then* the theory
would be *completely* predictive. I wouldn't call such a theory
"predictive" until then. I would agree that it is *potentially* predictive.

But that isn't what counts; no one promised you a completely predictable
universe! What's important is what checkable predictions it can make *now*
(or in the *near* future). On that score theories of quantum gravity are
tied at zero all.

> I am still nearly sure that in this counting, string theory is the most
> predictive theory of fundamental physics we have.

You keep saying that, without being able to exhibit even *one* prediction
of the theory!

OK, unlike most theories, it does predict the number of dimensions, instead
of assuming a value. But that prediction didn't pan out so well! Yes, I
know the extra dimensions could be very small, so the bad prediction isn't
fatal, but it isn't a victory either.

It does get the expected value for the black hole entropy, you could call
that a prediction, though not one we can check. It's more like a
consistency condition than a prediction, since we already knew the "right"
answer, on purely theoretical grounds.

Does string theory actually predict supersymetry? In the sense that without
supersymetry the theory is dead?

Newton had a more predictive theory! The Standard Model is *much* more
predictive. Note that both of those are extremely predictive, even though
they have continuous parameters.

I will grant that it is as predictive as any theory of quantum gravity we
have, but that isn't saying too much, especially if as you claim, it is the
*only* theory of quantum gravity we have.

Ralph Hartley

Lubos Motl

Oct1-04, 04:22 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nOn Thu, 30 Sep 2004, Ralph Hartley wrote:\n\n> There are rules for constructing Bayesian priors so that with enough\n> evidence, the prior (usually) doesn\'t matter too much (e.g. never\n> assign probability 0 to anything).\n\nThere are no Bayesian priors that could be universally useful for any open\nquestion in physics. This is the whole reason why Newton (or Bayes or\nanyone else) could not have found the theory of everything immediately.\n;-) If one wants to make extrapolations in physics - and estimate how far\nthe extrapolations can be trusted - she must, first of all, know physics -\nthe knowledge of Bayesian priors just can\'t help her.\n\nPeople are doing different extrapolations. For example, loop quantum\ngravity people are extrapolating the 100% experimental support of Lorentz\nsymmetry to the assumption that the symmetry is definitely violated. They\nextrapolate the omnipresent and verified scale-dependent corrections to\nall the physical laws and constants into the statement that (the minimal)\nEinstein\'s equations can\'t have any corrections. They extrapolate our\nexperience with the non-renormalizable theories (such as Fermi\'s theory,\nwhere the divergences clearly led to a deeper theory with new physics,\nwhich was later confirmed) to the statement that a non-renormalizable\ntheory (GR) should be treated as exact description despite of its obvious\ninconsistencies.\n\nWhile all those who understand elementary particle physics know why these\nextrapolations are not qualified, this conclusion cannot be obtained just\nfrom some Bayesian priors - one must know physics!\n\n> I think it is less than "not a dogma", it isn\'t true at all.\n>\n> Continuous parameters don\'t necessarily make a theory less predictive (to\n> say nothing of "more acceptable") than discrete ones.\n\nOf course that they do, if it is a completely quantitative theory, but I\nam gonna read your stuff anyway.\n\n> Consider a theory like Newton\'s gravity. It has a continuous parameter, but\n> is the very prototype of a predictive theory.\n\nNewton\'s theory of gravity - as a union of mathematical laws and\nstructures - has no adjustable parameters that would change its behavior.\nThe only parameter is G which is dimensionful, and therefore depends on\nthe choice of units. A reasonable physicist can simply and always work in\nunits where G=1. The parameters you want to talk about are really the\nmasses and distances of the objects, which are properties of the\nenvironment.\n\n> It is predictive because successive digits of the parameter make less and\n> less difference.\n\nWell, this is why we make successively more accurate experiments to be\nable to "scale" this decreasing difference and extract the information\nanyway.\n\n> If you know G to 3 digits you can predict a lot. If you know G to 30\n> digits you can predict almost anything. Knowing G to 500 digits will\n> let you predict measurements of the first 500 digits of G, but not\n> much else.\n\nRight.\n\n> It is *so* predictive,\n\nThe classical theory has no dimensionless parameters, and therefore it is\n"maximally" predictive in this sense.\n\n> that we now know that it isn\'t quite right,\n\nThe fact that it is not right has nothing to do with the number of\nparameters. The theory of everything has no parameters, and it *is* quite\nright, for example. ;-) On the other hand, loop quantum gravity is\ncompletely wrong, even though it has infinitely many adjustable parameters\n(the coefficients of all conceivable interactions, including the\nnonrenormalizable ones - recall that Rovelli et al. claim that LQG\nregularizes all of them). ;-)\n\n> but the theories that replaced are all very predictive, despite having\n> parameters.\n\nNope. The theory that replaced Newton\'s theory is general relativity, and\n(the minimal) general relativity has no dimensionless parameters either.\nIts G_{newton} is the same constant as in Newton\'s theory. The speed of\nlight is another dimensionful quantity - it reduced the number of\nindependent "units", but it is not a parameter either.\n\nIt\'s only the Standard Model that has new dimensionless parameters, but\nneither of these new parameters is useful for gravitational experiments.\n\n> Multiple free parameters, or even infinitely many, can be qualitatively the\n> same, if successive parameters each matter less.\n\nThis is very vague language. What matters is how exactly we can measure\nsomething, and if we *are* able to measure something with a given\naccuracy, it is simply wrong to say that the last digits don\'t affect\nphysics. Small corrections may be uninteresting for someone, but if they\ncan be measured, they can certainly be enough to rule out a theory.\n\n> You could combine them into a single parameter anyway, since a\n> (countable) set of continuous parameters have the same number of\n> digits as a single real number.\n\nIt does not really matter much whether you have 2 or 3 parameters, but it\nmatters what\'s the total number of digits in these parameters that you\nmust adjust to describe everything that you can measure. The more digits\nyou must adjust, the more arbitrary (and less predictive) your theory is.\n\n> Compare that to a theory that has "only" 10^320 versions (by the way\n> is that a real estimate, or just a guess?), but each is as different\n> as our universe is from Conway\'s game of "life". You could presumably\n> narrow those down to ones that resemble our universe, but there is no\n> guarantee that you can make *any* prediction at *all* until you have\n> narrowed it down to one.\n\nRight.\n\n> The *good* thing about such a theory is that there is no guarantee that\n> there will be even one. The *bad* thing is that there is also no guarantee\n> that there will be as few as 10^100. So the theory could be very\n> predictive, or not at all, and there is no way to tell!\n\nRight. We just don\'t know which option is correct. Is the realistic\nbackground essentially unique? Will there be 10^{100} of them that we\nwon\'t be able to distinguish for centuries? I agree, all these things are\nopen questions.\n\nBut you are mixing the adjective "predictive" with the adjective\n"correct". If I discuss the predictive power of a theory, I separate this\nquestion from another question whether the predictions are actually exact.\n\n> I think your point is that eventually, we could *in* *principle* know the\n> values of the discrete parameters exactly. Once we did, *then* the theory\n> would be *completely* predictive. I wouldn\'t call such a theory\n> "predictive" until then. I would agree that it is *potentially* predictive.\n\nRight.\n\n> But that isn\'t what counts; no one promised you a completely predictable\n> universe!\n\nI know, but I happen not to be the only one who still believes that there\nare all good reasons to believe that all dimensionless, repeatedly\nmeasurable numbers in this Universe are predictable. This is David Gross\'s\nbig question number one.\n\n> What\'s important is what checkable predictions it can make *now*\n> (or in the *near* future).\n\nI totally disagree. I believe that what we are doing has a much\nlonger-term goal than baking the bread for this week, and this is in fact\nwhat makes this enterprise important.\n\nAnother important thing is that if you don\'t have any final complete\nnon-string-theoretical predictions "now or in the near future", and of\ncourse you can\'t have such predictions because it is a nonsense - then\nyour argument has absolutely no value.\n\nWe are doing realistic physics - the more formal a theorist is, the more\nlong-term goals should she solve - and we just seem to "know" today that\nit is unlikely that the final answers will be found today or this year -\nand nevertheless, that it is not a reason to stop doing physics. When a\ntotally new toolkit of exciting ideas is found, no doubt, our estimates\nhow quickly we will be able to solve "everything" will speed up\nconsiderably.\n\nIn 1984-85, the estimates were that it would take a couple of weeks before\nthe masses of all elementary particles etc. are calculated from\nsuperstring theory. They were reasonable estimates, based on the situation\nthen - they just turned out to be wrong. ;-) We are much less\nself-confident about the speed today, but we may be proved wrong, too.\n\n> On that score theories of quantum gravity are\n> tied at zero all.\n\nIf you scale your criteria in physics in such a way that you assign "zero"\nimportance to everything, then it may be a legitimate viewpoint that can\nlead to correct ratios - assuming that you know how much is 0/0 - but the\nrelevance of your viewpoint for physics is zero, too.\n\nThe physicists have much more refined criteria than you, and they get\nmeaningful "numbers" and conclusions, not just zero as you.\n\n> > I am still nearly sure that in this counting, string theory is the most\n> > predictive theory of fundamental physics we have.\n>\n> You keep saying that, without being able to exhibit even *one* prediction\n> of the theory!\n\nString theory predicts gravity. If you were interested in other\npredictions of string theory and these issues, you could be given a lot of\nthem, but you would probably first have to replace your exclamation marks\n- a bad starting point for you to learn anything - by the much more\nappropriate question marks.\n\n> OK, unlike most theories, it does predict the number of dimensions, instead\n> of assuming a value. But that prediction didn\'t pan out so well! Yes, I\n> know the extra dimensions could be very small, so the bad prediction isn\'t\n> fatal, but it isn\'t a victory either.\n\nIt\'s a huge victory in specific models - for heterotic strings on\nCalabi-Yaus these 6 dimensions is exactly what is necessary to get\na realistic matter spectrum.\n\n> It does get the expected value for the black hole entropy, you could call\n> that a prediction, though not one we can check. It\'s more like a\n> consistency condition than a prediction, since we already knew the "right"\n> answer, on purely theoretical grounds.\n\nThat\'s right: the correct BH formula is a consistency check, and string\ntheory has the only [known, but perhaps the only plausible] microscopic\nderivation of the exact value of the entropy in a quantum gravitational\ntheory in d>=4.\n\n> Does string theory actually predict supersymetry? In the sense that without\n> supersymetry the theory is dead?\n\nThe nice vacua that most people like to study definitely require and\npredict supersymmetry, and there are non-supersymmetric vacua which can\nhowever be described as spontaneously broken supersymmetry. Whether\nsupersymmetry always emerges at some level - or whether even all non-SUSY\nvacua can roll to another supersymmetric ground state - is an open\nquestion.\n\nWell, it is also an open question for experiments whether SUSY is relevant\nfor our world - so as you can see, there is an agreement between\nthe experiments and string theory again. ;-)\n\n> Newton had a more predictive theory! The Standard Model is *much* more\n> predictive.\n\nBut the Standard Model cannot agree with (Newton\'s) gravity. ;-)\n\n> Note that both of those are extremely predictive, even though\n> they have continuous parameters.\n\nWe know that (and why) they cannot predict all phenomena in the Universe,\neven with these parameters.\n\n> I will grant that it is as predictive as any theory of quantum gravity we\n> have, but that isn\'t saying too much, especially if as you claim, it is the\n> *only* theory of quantum gravity we have.\n\nYou are really misunderstanding the main point completely. Being the\n*only* theory is definitely a reason to take a theory much *more*\nseriously, not *less* seriously!\n______________________________________ ________________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Thu, 30 Sep 2004, Ralph Hartley wrote:

> There are rules for constructing Bayesian priors so that with enough
> evidence, the prior (usually) doesn't matter too much (e.g. never
> assign probability to anything).

There are no Bayesian priors that could be universally useful for any open
question in physics. This is the whole reason why Newton (or Bayes or
anyone else) could not have found the theory of everything immediately.
;-) If one wants to make extrapolations in physics - and estimate how far
the extrapolations can be trusted - she must, first of all, know physics -
the knowledge of Bayesian priors just can't help her.

People are doing different extrapolations. For example, loop quantum
gravity people are extrapolating the 100% experimental support of Lorentz
symmetry to the assumption that the symmetry is definitely violated. They
extrapolate the omnipresent and verified scale-dependent corrections to
all the physical laws and constants into the statement that (the minimal)
Einstein's equations can't have any corrections. They extrapolate our
experience with the non-renormalizable theories (such as Fermi's theory,
where the divergences clearly led to a deeper theory with new physics,
which was later confirmed) to the statement that a non-renormalizable
theory (GR) should be treated as exact description despite of its obvious
inconsistencies.

While all those who understand elementary particle physics know why these
extrapolations are not qualified, this conclusion cannot be obtained just
from some Bayesian priors - one must know physics!

> I think it is less than "not a dogma", it isn't true at all.
>
> Continuous parameters don't necessarily make a theory less predictive (to
> say nothing of "more acceptable") than discrete ones.

Of course that they do, if it is a completely quantitative theory, but I
am gonna read your stuff anyway.

> Consider a theory like Newton's gravity. It has a continuous parameter, but
> is the very prototype of a predictive theory.

Newton's theory of gravity - as a union of mathematical laws and
structures - has no adjustable parameters that would change its behavior.
The only parameter is G which is dimensionful, and therefore depends on
the choice of units. A reasonable physicist can simply and always work in
units where G=1. The parameters you want to talk about are really the
masses and distances of the objects, which are properties of the
environment.

> It is predictive because successive digits of the parameter make less and
> less difference.

Well, this is why we make successively more accurate experiments to be
able to "scale" this decreasing difference and extract the information
anyway.

> If you know G to 3 digits you can predict a lot. If you know G to 30
> digits you can predict almost anything. Knowing G to 500 digits will
> let you predict measurements of the first 500 digits of G, but not
> much else.

Right.

> It is *so* predictive,

The classical theory has no dimensionless parameters, and therefore it is
"maximally" predictive in this sense.

> that we now know that it isn't quite right,

The fact that it is not right has nothing to do with the number of
parameters. The theory of everything has no parameters, and it *is* quite
right, for example. ;-) On the other hand, loop quantum gravity is
completely wrong, even though it has infinitely many adjustable parameters
(the coefficients of all conceivable interactions, including the
nonrenormalizable ones - recall that Rovelli et al. claim that LQG
regularizes all of them). ;-)

> but the theories that replaced are all very predictive, despite having
> parameters.

Nope. The theory that replaced Newton's theory is general relativity, and
(the minimal) general relativity has no dimensionless parameters either.
Its G_{newton} is the same constant as in Newton's theory. The speed of
light is another dimensionful quantity - it reduced the number of
independent "units", but it is not a parameter either.

It's only the Standard Model that has new dimensionless parameters, but
neither of these new parameters is useful for gravitational experiments.

> Multiple free parameters, or even infinitely many, can be qualitatively the
> same, if successive parameters each matter less.

This is very vague language. What matters is how exactly we can measure
something, and if we *are* able to measure something with a given
accuracy, it is simply wrong to say that the last digits don't affect
physics. Small corrections may be uninteresting for someone, but if they
can be measured, they can certainly be enough to rule out a theory.

> You could combine them into a single parameter anyway, since a
> (countable) set of continuous parameters have the same number of
> digits as a single real number.

It does not really matter much whether you have 2 or 3 parameters, but it
matters what's the total number of digits in these parameters that you
must adjust to describe everything that you can measure. The more digits
you must adjust, the more arbitrary (and less predictive) your theory is.

> Compare that to a theory that has "only" 10^320 versions (by the way
> is that a real estimate, or just a guess?), but each is as different
> as our universe is from Conway's game of "life". You could presumably
> narrow those down to ones that resemble our universe, but there is no
> guarantee that you can make *any* prediction at *all* until you have
> narrowed it down to one.

Right.

> The *good* thing about such a theory is that there is no guarantee that
> there will be even one. The *bad* thing is that there is also no guarantee
> that there will be as few as 10^100. So the theory could be very
> predictive, or not at all, and there is no way to tell!

Right. We just don't know which option is correct. Is the realistic
background essentially unique? Will there be 10^{100} of them that we
won't be able to distinguish for centuries? I agree, all these things are
open questions.

But you are mixing the adjective "predictive" with the adjective
"correct". If I discuss the predictive power of a theory, I separate this
question from another question whether the predictions are actually exact.

> I think your point is that eventually, we could *in* *principle* know the
> values of the discrete parameters exactly. Once we did, *then* the theory
> would be *completely* predictive. I wouldn't call such a theory
> "predictive" until then. I would agree that it is *potentially* predictive.

Right.

> But that isn't what counts; no one promised you a completely predictable
> universe!

I know, but I happen not to be the only one who still believes that there
are all good reasons to believe that all dimensionless, repeatedly
measurable numbers in this Universe are predictable. This is David Gross's
big question number one.

> What's important is what checkable predictions it can make *now*
> (or in the *near* future).

I totally disagree. I believe that what we are doing has a much
longer-term goal than baking the bread for this week, and this is in fact
what makes this enterprise important.

Another important thing is that if you don't have any final complete
non-string-theoretical predictions "now or in the near future", and of
course you can't have such predictions because it is a nonsense - then
your argument has absolutely no value.

We are doing realistic physics - the more formal a theorist is, the more
long-term goals should she solve - and we just seem to "know" today that
it is unlikely that the final answers will be found today or this year -
and nevertheless, that it is not a reason to stop doing physics. When a
totally new toolkit of exciting ideas is found, no doubt, our estimates
how quickly we will be able to solve "everything" will speed up
considerably.

In 1984-85, the estimates were that it would take a couple of weeks before
the masses of all elementary particles etc. are calculated from
superstring theory. They were reasonable estimates, based on the situation
then - they just turned out to be wrong. ;-) We are much less
self-confident about the speed today, but we may be proved wrong, too.

> On that score theories of quantum gravity are
> tied at zero all.

If you scale your criteria in physics in such a way that you assign "zero"
importance to everything, then it may be a legitimate viewpoint that can
lead to correct ratios - assuming that you know how much is 0/0 - but the
relevance of your viewpoint for physics is zero, too.

The physicists have much more refined criteria than you, and they get
meaningful "numbers" and conclusions, not just zero as you.

> > I am still nearly sure that in this counting, string theory is the most
> > predictive theory of fundamental physics we have.
>
> You keep saying that, without being able to exhibit even *one* prediction
> of the theory!

String theory predicts gravity. If you were interested in other
predictions of string theory and these issues, you could be given a lot of
them, but you would probably first have to replace your exclamation marks
- a bad starting point for you to learn anything - by the much more
appropriate question marks.

> OK, unlike most theories, it does predict the number of dimensions, instead
> of assuming a value. But that prediction didn't pan out so well! Yes, I
> know the extra dimensions could be very small, so the bad prediction isn't
> fatal, but it isn't a victory either.

It's a huge victory in specific models - for heterotic strings on
Calabi-Yaus these 6 dimensions is exactly what is necessary to get
a realistic matter spectrum.

> It does get the expected value for the black hole entropy, you could call
> that a prediction, though not one we can check. It's more like a
> consistency condition than a prediction, since we already knew the "right"
> answer, on purely theoretical grounds.

That's right: the correct BH formula is a consistency check, and string
theory has the only [known, but perhaps the only plausible] microscopic
derivation of the exact value of the entropy in a quantum gravitational
theory in d>=4.

> Does string theory actually predict supersymetry? In the sense that without
> supersymetry the theory is dead?

The nice vacua that most people like to study definitely require and
predict supersymmetry, and there are non-supersymmetric vacua which can
however be described as spontaneously broken supersymmetry. Whether
supersymmetry always emerges at some level - or whether even all non-SUSY
vacua can roll to another supersymmetric ground state - is an open
question.

Well, it is also an open question for experiments whether SUSY is relevant
for our world - so as you can see, there is an agreement between
the experiments and string theory again. ;-)

> Newton had a more predictive theory! The Standard Model is *much* more
> predictive.

But the Standard Model cannot agree with (Newton's) gravity. ;-)

> Note that both of those are extremely predictive, even though
> they have continuous parameters.

We know that (and why) they cannot predict all phenomena in the Universe,
even with these parameters.

> I will grant that it is as predictive as any theory of quantum gravity we
> have, but that isn't saying too much, especially if as you claim, it is the
> *only* theory of quantum gravity we have.

You are really misunderstanding the main point completely. Being the
*only* theory is definitely a reason to take a theory much *more*
seriously, not *less* seriously!
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Lubos Motl

Oct1-04, 04:22 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nOn Wed, 29 Sep 2004, Creighton Hogg wrote:\n\n> Sorry, but this seems somewhat misleading to me. The main thing I\'m\n> curious about is how string theory can be tested and possibly falsified.\n> Let\'s say that we don\'t see any signs of string theory at the LHC.\n\nIf we see no signs of string theory at the LHC - not even remote signs of\nsupersymmetry, for example - string theory\'s stocks (funding, excitement,\nand interests of the students) will go down. No doubts about that. But it\nwould be unreasonable to conclude that string theory is definitely wrong.\nAs Glashow correctly says, it is possible that we will not know for\ndecades or centuries whether string theory is wrong or correct.\n\n> Okay, well that elimates all the models that predicted signals visible\n> at the LHC during its run, but there\'s still many, many more possible\n> vacua and values of the string scale so string theory wouldn\'t have\n> been falsified. Well then, what if we don\'t see anything at the\n> upgraded LHC with center of mass energy ~50TeV. We still haven\'t\n> falsified string theory.\n\nIt\'s not our job to focus on "falsifying string theory". Our job is more\ngeneral in the broad goal - to look for the best theory that is able to\ndescribe the observed Universe - but the goal is also more detailed in the\neveryday aspects of the work. An explicit experiment can rule out a very\nconcrete, detailed model about some particular properties of some system.\nIt is totally clear that at least 80% of the phenomenological models -\nincluding the string-inspired models - will be ruled out 1 year after the\nLHC starts. Well, it\'s because at least 80% of the published\nphenomenological models predict new physics to be seen at a few TeVs, and\nvirtually all of them will be proved wrong (at least in details), of\ncourse.\n\nBut string theory is today much more than a specific model of a feature of\nreality. It is a new underlying framework to organize theoretical physics.\nIt is the only known meaningful and predictive structure that reproduces\nthe good features of quantum field theories as well as classical general\nrelativity, but is able to go beyond them without introducing\ninconsistencies.\n\n> What can we do that would actually prove string theory wrong?\n\nBecause of the facts above, I just totally agree with you that it is *very\ndifficult* to prove the whole string theory wrong. To some extent, the\ngeneral framework called "string theory" is becoming a tautology.\n\nYou will be able to disprove string theory (or something similar) only if\none of three types of events is going to occur:\n\nIf you show that the probability of some events can be negative or greater\nthan one; gravity does not attract the apples; QFT does not work at low\nenergies - string theory will be dead. Of course this won\'t happen -\nstring theory has already passed these observational tests. You just\ncannot "undo" string theory completely.\n\nThe second possibility is that our understanding of string theory will\nbecome much more accurate, and we will be able to make definite\npredictions that will contradict observations. I am sure that even if this\nhappened, people would not believe that the "contradiction" was derived\nproperly - at least for a decade - simply because there are other reasons\nto take string theory seriously.\n\nThe third possibility does not really rule out string theory - but it\nwould make it obsolete. The third possibility is that a better, completely\nnon-stringy underlying framework for physics will be found. In that case,\nstring theory won\'t really be proved wrong, but it will become a less\nimportant topic of research. Well, as you know, I think that this is an\neven much less likely scenario than the previous two.\n\nOne might say that the situation is analogous to "disproving the evolution\ntheory". The evolution theory is not too quantitatively verified theory\neither. However, what do you need to do to rule out the theory of\nevolution? I don\'t know. You would probably have to prove that the\nUniverse is 6000 years old, and/or that the organisms don\'t evolve and the\ndaughters are always identical with the mother. Or, perhaps, you would\nhave to prove that having advantages does not increase your chances to\nsurvive.\n\nSure, it\'s not terribly likely. Does it mean that Darwin\'s theory is not\nscience? No. It mostly means that Darwin\'s theory is more or less a direct\nconsequence of the basic rational reasoning about the world. At a general\nlevel, it just works. It\'s just pretty obvious today. String theory is\nanalogous. Much like it is not the best strategy in science to try to rule\nout the whole evolutionary framework, it is also a pretty bad idea to try\nto disprove the whole string-theoretical framework. Both frameworks more\nor less contain all good ideas in the respective fields. If you want to\ndisprove something, you should probably try to choose a more realistic\ngoal than "disproving whole string theory".\n\nIt\'s clear that only some tools of string theory will be relevant for the\nultimate explanation of the Universe around us, and a task for the\nphenomenologists is to decide which of them are the correct ones (and\nwhich of them are missing). On the theoretical, conceptual front, the\nstring-theoretical research mostly follows the rules of math, and you can\nonly prove that something is wrong if you find an error in the argument or\nthe calculation.\n____________________________________ __________________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Wed, 29 Sep 2004, Creighton Hogg wrote:

> Sorry, but this seems somewhat misleading to me. The main thing I'm
> curious about is how string theory can be tested and possibly falsified.
> Let's say that we don't see any signs of string theory at the LHC.

If we see no signs of string theory at the LHC - not even remote signs of
supersymmetry, for example - string theory's stocks (funding, excitement,
and interests of the students) will go down. No doubts about that. But it
would be unreasonable to conclude that string theory is definitely wrong.
As Glashow correctly says, it is possible that we will not know for
decades or centuries whether string theory is wrong or correct.

> Okay, well that elimates all the models that predicted signals visible
> at the LHC during its run, but there's still many, many more possible
> vacua and values of the string scale so string theory wouldn't have
> been falsified. Well then, what if we don't see anything at the
> upgraded LHC with center of mass energy ~50TeV. We still haven't
> falsified string theory.

It's not our job to focus on "falsifying string theory". Our job is more
general in the broad goal - to look for the best theory that is able to
describe the observed Universe - but the goal is also more detailed in the
everyday aspects of the work. An explicit experiment can rule out a very
concrete, detailed model about some particular properties of some system.
It is totally clear that at least 80% of the phenomenological models -
including the string-inspired models - will be ruled out 1 year after the
LHC starts. Well, it's because at least 80% of the published
phenomenological models predict new physics to be seen at a few TeVs, and
virtually all of them will be proved wrong (at least in details), of
course.

But string theory is today much more than a specific model of a feature of
reality. It is a new underlying framework to organize theoretical physics.
It is the only known meaningful and predictive structure that reproduces
the good features of quantum field theories as well as classical general
relativity, but is able to go beyond them without introducing
inconsistencies.

> What can we do that would actually prove string theory wrong?

Because of the facts above, I just totally agree with you that it is *very
difficult* to prove the whole string theory wrong. To some extent, the
general framework called "string theory" is becoming a tautology.

You will be able to disprove string theory (or something similar) only if
one of three types of events is going to occur:

If you show that the probability of some events can be negative or greater
than one; gravity does not attract the apples; QFT does not work at low
energies - string theory will be dead. Of course this won't happen -
string theory has already passed these observational tests. You just
cannot "undo" string theory completely.

The second possibility is that our understanding of string theory will
become much more accurate, and we will be able to make definite
predictions that will contradict observations. I am sure that even if this
happened, people would not believe that the "contradiction" was derived
properly - at least for a decade - simply because there are other reasons
to take string theory seriously.

The third possibility does not really rule out string theory - but it
would make it obsolete. The third possibility is that a better, completely
non-stringy underlying framework for physics will be found. In that case,
string theory won't really be proved wrong, but it will become a less
important topic of research. Well, as you know, I think that this is an
even much less likely scenario than the previous two.

One might say that the situation is analogous to "disproving the evolution
theory". The evolution theory is not too quantitatively verified theory
either. However, what do you need to do to rule out the theory of
evolution? I don't know. You would probably have to prove that the
Universe is 6000 years old, and/or that the organisms don't evolve and the
daughters are always identical with the mother. Or, perhaps, you would
have to prove that having advantages does not increase your chances to
survive.

Sure, it's not terribly likely. Does it mean that Darwin's theory is not
science? No. It mostly means that Darwin's theory is more or less a direct
consequence of the basic rational reasoning about the world. At a general
level, it just works. It's just pretty obvious today. String theory is
analogous. Much like it is not the best strategy in science to try to rule
out the whole evolutionary framework, it is also a pretty bad idea to try
to disprove the whole string-theoretical framework. Both frameworks more
or less contain all good ideas in the respective fields. If you want to
disprove something, you should probably try to choose a more realistic
goal than "disproving whole string theory".

It's clear that only some tools of string theory will be relevant for the
ultimate explanation of the Universe around us, and a task for the
phenomenologists is to decide which of them are the correct ones (and
which of them are missing). On the theoretical, conceptual front, the
string-theoretical research mostly follows the rules of math, and you can
only prove that something is wrong if you find an error in the argument or
the calculation.
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Lubos Motl

Oct1-04, 04:22 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nOn Wed, 29 Sep 2004, Arnold Neumaier wrote:\n\n> But the current standard model + GR explains all currently observable\n> physics; thus it already reduced the \'more than 128 bytes of physics\'\n> predictions\' to the number of bits needed to describe the standard model\n> at the current accuracy of the parameters defining it. These are less\n> than half of the 1000 bits.\n>\n> Thus, from the point of the informational contents, a better theory\n> must predict these on the basis of choices amounting to even fewer bits.\n\nWhat you say sounds fine, indeed. But SM+GR have roughly 29 parameters (if\nyou include neutrino masses), and because most of them are known with a\nmany-digit accuracy, be sure that we need hundreds of decimal digits -\ni.e. at least 300 bits - to parameterize the continuous input of the\nStandard Model. This number "300" will increase - these numbers of bits\nare therefore not too far from being able to rule out string theory.\n\nAmong these "10^{300}" vacua, a rather small part describes physics with\nthe same "discrete" choices as the Standard Model, and - assuming that we\nlearn how to calculate physics of all of them exactly - it makes it very\nuncertain whether at least one of them can reproduce the known SM physics\nwith the desired precision.\n\nThese will become very scientific questions as soon as we (or some future\nscientists) will be able to list all the vacua and calculate their\nproperties accurately enough.\n--\n________________________________________________ ______________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Wed, 29 Sep 2004, Arnold Neumaier wrote:

> But the current standard model + GR explains all currently observable
> physics; thus it already reduced the 'more than 128 bytes of physics'
> predictions' to the number of bits needed to describe the standard model
> at the current accuracy of the parameters defining it. These are less
> than half of the 1000 bits.
>
> Thus, from the point of the informational contents, a better theory
> must predict these on the basis of choices amounting to even fewer bits.

What you say sounds fine, indeed. But SM+GR have roughly 29 parameters (if
you include neutrino masses), and because most of them are known with a
many-digit accuracy, be sure that we need hundreds of decimal digits -
i.e. at least 300 bits - to parameterize the continuous input of the
Standard Model. This number "300" will increase - these numbers of bits
are therefore not too far from being able to rule out string theory.

Among these "10^{300}" vacua, a rather small part describes physics with
the same "discrete" choices as the Standard Model, and - assuming that we
learn how to calculate physics of all of them exactly - it makes it very
uncertain whether at least one of them can reproduce the known SM physics
with the desired precision.

These will become very scientific questions as soon as we (or some future
scientists) will be able to list all the vacua and calculate their
properties accurately enough.
--
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Arnold Neumaier

Oct1-04, 04:22 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nRalph Hartley wrote:\n\n> Does string theory actually predict supersymetry? In the sense that without\n> supersymmetry the theory is dead?\n>\n> Newton had a more predictive theory! The Standard Model is *much* more\n> predictive. Note that both of those are extremely predictive, even though\n> they have continuous parameters.\n>\n> I will grant that it is as predictive as any theory of quantum gravity we\n> have, but that isn\'t saying too much, especially if as you claim, it is the\n> *only* theory of quantum gravity we have.\n\n\nAs a healthy contrast to the speculations of string theory, I\'d like\nto draw attention to the fact that there _is_ a theory of quantum gravity\nwhich quantitatively predicts the leading quantum corrections to the\nSchwarzschild, Kerr-Newman, and Reisner-Nordstroem metrics.\n\nThe theory that can do this is canonical quantum gravity, regarded as an\neffective field theory. Only a few new parameters arise at each loop\norder, in particular only one (the coefficient of curvature^2) at one\nloop. See, e.g.,\nCliff P. Burgess\nQuantum Gravity in Everyday Life:\nGeneral Relativity as an Effective Field Theory\nhttp://relativity.livingreviews.org/Articles/lrr-2004-5/\n\nIn particular, at one loop, Newton\'s constant of gravitation becomes\na running coupling constant with\nG(r) = G - 167/30pi G^2/r^2 + ...\nin terms of a renormalization length scale r.\nThis is taken from Section 4.1 of this paper, where it is concluded:\n\n\'\' Numerically, the quantum corrections are so miniscule as to be\nunobservable within the solar system for the forseeable future.\nClearly the quantum-gravitational correction is numerically extremely\nsmall when evaluated for garden-variety gravitational fields in the\nsolar system, and would remain so right down to the event horizon even\nif the sun were a black hole. At face value it is only for separations\ncomparable to the Planck length that quantum gravity effects become\nimportant. To the extent that these estimates carry over to quantum\neffects right down to the event horizon on curved black hole\ngeometries (more about this below) this makes quantum corrections\nirrelevant for physics outside of the event horizon, unless the\nblack hole mass is as small as the Planck mass\'\'\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Ralph Hartley wrote:

> Does string theory actually predict supersymetry? In the sense that without
> supersymmetry the theory is dead?
>
> Newton had a more predictive theory! The Standard Model is *much* more
> predictive. Note that both of those are extremely predictive, even though
> they have continuous parameters.
>
> I will grant that it is as predictive as any theory of quantum gravity we
> have, but that isn't saying too much, especially if as you claim, it is the
> *only* theory of quantum gravity we have.

As a healthy contrast to the speculations of string theory, I'd like
to draw attention to the fact that there _is_ a theory of quantum gravity
which quantitatively predicts the leading quantum corrections to the
Schwarzschild, Kerr-Newman, and Reisner-Nordstroem metrics.

The theory that can do this is canonical quantum gravity, regarded as an
effective field theory. Only a few new parameters arise at each loop
order, in particular only one (the coefficient of curvature^2) at one
loop. See, e.g.,
Cliff P. Burgess
Quantum Gravity in Everyday Life:
General Relativity as an Effective Field Theory
http://relativity.livingreviews.org/Articles/lrr-2004-5/

In particular, at one loop, Newton's constant of gravitation becomes
a running coupling constant with
G(r) = G - 167/30pi G^2/r^2 + ...
in terms of a renormalization length scale r.
This is taken from Section 4.1 of this paper, where it is concluded:

'' Numerically, the quantum corrections are so miniscule as to be
unobservable within the solar system for the forseeable future.
Clearly the quantum-gravitational correction is numerically extremely
small when evaluated for garden-variety gravitational fields in the
solar system, and would remain so right down to the event horizon even
if the sun were a black hole. At face value it is only for separations
comparable to the Planck length that quantum gravity effects become
important. To the extent that these estimates carry over to quantum
effects right down to the event horizon on curved black hole
geometries (more about this below) this makes quantum corrections
irrelevant for physics outside of the event horizon, unless the
black hole mass is as small as the Planck mass''

Arnold Neumaier

Ralph Hartley

Oct4-04, 12:22 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Lubos Motl wrote:\n> On Thu, 30 Sep 2004, Ralph Hartley wrote:\n>\n>>There are rules for constructing Bayesian priors so that with enough\n>>evidence, the prior (usually) doesn\'t matter too much (e.g. never\n>>assign probability 0 to anything).\n>\n> There are no Bayesian priors that could be universally useful for any open\n> question in physics. This is the whole reason why Newton (or Bayes or\n> anyone else) could not have found the theory of everything immediately.\n\nJust so. The trick with Bayesian priors is to pick a set that doesn\'t\n*hurt* you.\n\nThe main thing is never to assign probabilities of zero.\n\nAn example of a bad one from history: "The Earth absolutely does not move,\nnothing could convince me otherwise." It would have saved physics a world\nof hurt if they (The Church) had used instead "I\'m pretty sure the Earth\ndoes not move, only overwhelming evidence could convince me otherwise."\n\n>>Consider a theory like Newton\'s gravity. It has a continuous parameter, but\n>>is the very prototype of a predictive theory.\n>\n> Newton\'s theory of gravity - as a union of mathematical laws and\n> structures - has no adjustable parameters that would change its behavior.\n> The only parameter is G which is dimensionful, and therefore depends on\n> the choice of units. A reasonable physicist can simply and always work in\n> units where G=1. The parameters you want to talk about are really the\n> masses and distances of the objects, which are properties of the\n> environment.\n\nI know that, but it doesn\'t matter. To predict where Mercury will be next\nTuesday, I need to know either G, or if that is set to 1, the conversion\nfactors from units I can measure.\n\nYou can push the parameter around, so that it is outside of the theory, but\nyou still need to know it to make predictions. So there is still a free\nparameter *somewhere*.\n\nOf course, Newtonian gravity makes predictions even if you don\'t know G (or\nthe mass of anything in G=1 units). For example, it predicts that orbits\nwill be conics.\n\nAnyway, I shouldn\'t push the point, since I could just choose another\npredictive theory that has dimensionless parameters, like QED or the\nstandard model.\n\n>>If you know G to 3 digits you can predict a lot. If you know G to 30\n>>digits you can predict almost anything. Knowing G to 500 digits will\n>>let you predict measurements of the first 500 digits of G, but not\n>>much else.\n>\n> Right.\n\n\n>>Multiple free parameters, or even infinitely many, can be qualitatively the\n>>same, if successive parameters each matter less.\n>\n> This is very vague language.\n\nIndeed it is, and making it precise would be more trouble than it\'s worth,\nand would distract from the real point.\n\nPerhaps I should give (rather contrived I will admit) example of what I mean.\n\nSuppose we have a theory T with exactly one free parameter alpha (say\nbetween 0 and 1).\n\nConstruct the numbers alpha_n as follows. Let alpha_1 be the real number\nproduced by concatenating the odd numbered digits of alpha. Let alpha_2 be\nthe number produced by concatenating the even numbered digits who\'s\nposition is not divisible by 4, etc.. alpha_n contains every other digit\nnot included in alpha_{n-1}.\n\nSo if alpha = 0.12345678901234567890123456789...\nthen\nalpha_1 = 0.135791357913579...\nalpha_2 = 0.2604826...\nalpha_3 = 0.4208...\nalpha_4 = 0.84...\netc.\n\nNow from T we can construct a theory T\' which has as free parameters the\nalpha_n. T\' has infinitely many parameters, but it is just as predictive as\nT, since it is the same theory.\n\nSo it is possible for a theory with infinitely many free parameters to be\nas predictive as any theory with just one.\n\n> What matters is how exactly we can measure\n> something, and if we *are* able to measure something with a given\n> accuracy, it is simply wrong to say that the last digits don\'t affect\n> physics.\n\nMy point is not that they don\'t affect physics, but that not knowing them\ndoesn\'t prevent the theory from making predictions.\n\n> It does not really matter much whether you have 2 or 3 parameters\n\nor infinitely many,\n\n> but it\n> matters what\'s the total number of digits in these parameters that you\n> must adjust to describe everything that you can measure. The more digits\n> you must adjust, the more arbitrary (and less predictive) your theory is.\n\nWhat matters is how many digits you must adjust before you can describe\nsomething else besides the digits. Clearly, if you can always measure more\ndigits, you can never describe everything you can measure.\n\n>>The *bad* thing is that there is also no guarantee\n>>that there will be as few as 10^100. So the theory could be very\n>>predictive, or not at all, and there is no way to tell!\n>\n> But you are mixing the adjective "predictive" with the adjective\n> "correct".\n\nNo, it could still be correct and completely non-predictive. My point is\nthat whether it is predictive or not is just as much an open question as\nwhether it is correct.\n\nSo far as I know, none of these possibilities have been ruled out:\n(A) 0 - predictive, inconsistent with observations, incorrect.\n(B) 1 - predictive, consistent with observations, but incorrect anyway.\n(C) 1 - predictive, correct.\n(D) 10^100 - not predictive, and incorrect.\n(E) 10^100 - not predictive, and correct.\n\nI admit I would be a bit bothered by (B), and wouldn\'t consider it as\nlikely as the others :-)\n\n>>But that isn\'t what counts; no one promised you a completely predictable\n>>universe!\n>\n> I know, but I happen not to be the only one who still believes that there\n> are all good reasons to believe that all dimensionless, repeatedly\n> measurable numbers in this Universe are predictable.\n\nWhat are those reasons?\n\n>>What\'s important is what checkable predictions it can make *now*\n>>(or in the *near* future).\n....\n> We are doing realistic physics - the more formal a theorist is, the more\n> long-term goals should she solve - and we just seem to "know" today that\n> it is unlikely that the final answers will be found today or this year -\n> and nevertheless, that it is not a reason to stop doing physics.\n\nI don\'t think I ever suggested that we should. I was only suggesting that\ncalling string theory "the most predictive theory of fundamental physics we\nhave" is counting your chickens before they\'re hatched.\n\nI don\'t think *I* was the one suggesting that a field of inquiry should be\ndropped because we lack mathematical tools to get any predictions out of it\n(or in the case of LQG to tell if it makes any sense at all, I know you\nthink it doesn\'t, but I am not convinced either way).\n\n>>Does string theory actually predict supersymetry? In the sense that without\n>>supersymetry the theory is dead?\n>\n> The nice vacua that most people like to study definitely require and\n> predict supersymmetry, and there are non-supersymmetric vacua which can\n> however be described as spontaneously broken supersymmetry. Whether\n> supersymmetry always emerges at some level - or whether even all non-SUSY\n> vacua can roll to another supersymmetric ground state - is an open\n> question.\n\nThat\'s what I thought.\n\n>>Newton had a more predictive theory! The Standard Model is *much* more\n>>predictive.\n>\n> But the Standard Model cannot agree with (Newton\'s) gravity. ;-)\n\nAs you point out, being predictive is independent of being correct.\n\nThe Standard Model has more parameters than Newton\'s Gravity (be that one\nor zero), but predicts more. (OK, technically they are incomparable,\nbecause they don\'t overlap.)\n\nRalph Hartley\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Lubos Motl wrote:
> On Thu, 30 Sep 2004, Ralph Hartley wrote:
>
>>There are rules for constructing Bayesian priors so that with enough
>>evidence, the prior (usually) doesn't matter too much (e.g. never
>>assign probability to anything).
>
> There are no Bayesian priors that could be universally useful for any open
> question in physics. This is the whole reason why Newton (or Bayes or
> anyone else) could not have found the theory of everything immediately.

Just so. The trick with Bayesian priors is to pick a set that doesn't
*hurt* you.

The main thing is never to assign probabilities of zero.

An example of a bad one from history: "The Earth absolutely does not move,
nothing could convince me otherwise." It would have saved physics a world
of hurt if they (The Church) had used instead "I'm pretty sure the Earth
does not move, only overwhelming evidence could convince me otherwise."

>>Consider a theory like Newton's gravity. It has a continuous parameter, but
>>is the very prototype of a predictive theory.
>
> Newton's theory of gravity - as a union of mathematical laws and
> structures - has no adjustable parameters that would change its behavior.
> The only parameter is G which is dimensionful, and therefore depends on
> the choice of units. A reasonable physicist can simply and always work in
> units where G=1. The parameters you want to talk about are really the
> masses and distances of the objects, which are properties of the
> environment.

I know that, but it doesn't matter. To predict where Mercury will be next
Tuesday, I need to know either G, or if that is set to 1, the conversion
factors from units I can measure.

You can push the parameter around, so that it is outside of the theory, but
you still need to know it to make predictions. So there is still a free
parameter *somewhere*.

Of course, Newtonian gravity makes predictions even if you don't know G (or
the mass of anything in G=1 units). For example, it predicts that orbits
will be conics.

Anyway, I shouldn't push the point, since I could just choose another
predictive theory that has dimensionless parameters, like QED or the
standard model.

>>If you know G to 3 digits you can predict a lot. If you know G to 30
>>digits you can predict almost anything. Knowing G to 500 digits will
>>let you predict measurements of the first 500 digits of G, but not
>>much else.
>
> Right.

>>Multiple free parameters, or even infinitely many, can be qualitatively the
>>same, if successive parameters each matter less.
>
> This is very vague language.

Indeed it is, and making it precise would be more trouble than it's worth,
and would distract from the real point.

Perhaps I should give (rather contrived I will admit) example of what I mean.

Suppose we have a theory T with exactly one free parameter \alpha (say
between and 1).

Construct the numbers \alpha_n as follows. Let \alpha_1 be the real number
produced by concatenating the odd numbered digits of \alpha. Let \alpha_2 be
the number produced by concatenating the even numbered digits who's
position is not divisible by 4, etc.. \alpha_n contains every other digit
not included in \alpha_{n-1}.

So if \alpha = .12345678901234567890123456789...
then
\alpha_1 = .135791357913579...
\alpha_2 = .2604826...
\alpha_3 = .4208...
\alpha_4 = .84...
etc.

Now from T we can construct a theory T' which has as free parameters the
\alpha_n. T' has infinitely many parameters, but it is just as predictive as
T, since it is the same theory.

So it is possible for a theory with infinitely many free parameters to be
as predictive as any theory with just one.

> What matters is how exactly we can measure
> something, and if we *are* able to measure something with a given
> accuracy, it is simply wrong to say that the last digits don't affect
> physics.

My point is not that they don't affect physics, but that not knowing them
doesn't prevent the theory from making predictions.

> It does not really matter much whether you have 2 or 3 parameters

or infinitely many,

> but it
> matters what's the total number of digits in these parameters that you
> must adjust to describe everything that you can measure. The more digits
> you must adjust, the more arbitrary (and less predictive) your theory is.

What matters is how many digits you must adjust before you can describe
something else besides the digits. Clearly, if you can always measure more
digits, you can never describe everything you can measure.

>>The *bad* thing is that there is also no guarantee
>>that there will be as few as 10^100. So the theory could be very
>>predictive, or not at all, and there is no way to tell!
>
> But you are mixing the adjective "predictive" with the adjective
> "correct".

No, it could still be correct and completely non-predictive. My point is
that whether it is predictive or not is just as much an open question as
whether it is correct.

So far as I know, none of these possibilities have been ruled out:
(A) - predictive, inconsistent with observations, incorrect.
(B) 1 - predictive, consistent with observations, but incorrect anyway.
(C) 1 - predictive, correct.
(D) 10^100 - not predictive, and incorrect.
(E) 10^100 - not predictive, and correct.

I admit I would be a bit bothered by (B), and wouldn't consider it as
likely as the others :-)

>>But that isn't what counts; no one promised you a completely predictable
>>universe!
>
> I know, but I happen not to be the only one who still believes that there
> are all good reasons to believe that all dimensionless, repeatedly
> measurable numbers in this Universe are predictable.

What are those reasons?

>>What's important is what checkable predictions it can make *now*
>>(or in the *near* future).
....
> We are doing realistic physics - the more formal a theorist is, the more
> long-term goals should she solve - and we just seem to "know" today that
> it is unlikely that the final answers will be found today or this year -
> and nevertheless, that it is not a reason to stop doing physics.

I don't think I ever suggested that we should. I was only suggesting that
calling string theory "the most predictive theory of fundamental physics we
have" is counting your chickens before they're hatched.

I don't think *I* was the one suggesting that a field of inquiry should be
dropped because we lack mathematical tools to get any predictions out of it
(or in the case of LQG to tell if it makes any sense at all, I know you
think it doesn't, but I am not convinced either way).

>>Does string theory actually predict supersymetry? In the sense that without
>>supersymetry the theory is dead?
>
> The nice vacua that most people like to study definitely require and
> predict supersymmetry, and there are non-supersymmetric vacua which can
> however be described as spontaneously broken supersymmetry. Whether
> supersymmetry always emerges at some level - or whether even all non-SUSY
> vacua can roll to another supersymmetric ground state - is an open
> question.

That's what I thought.

>>Newton had a more predictive theory! The Standard Model is *much* more
>>predictive.
>
> But the Standard Model cannot agree with (Newton's) gravity. ;-)

As you point out, being predictive is independent of being correct.

The Standard Model has more parameters than Newton's Gravity (be that one
or zero), but predicts more. (OK, technically they are incomparable,
because they don't overlap.)

Ralph Hartley

Ralph Hartley

Oct5-04, 06:42 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Lubos Motl wrote:\n\n> One might say that the situation is analogous to "disproving the evolution\n> theory". The evolution theory is not too quantitatively verified theory\n> either.\n\nActually, it is. Compared to string theory it certainly is.\n\nThe status of the theory of evolution is roughly on a par with that of the\n"round Earth theory".\n\nDo you really think that string theory is verified to that level?\n\nWould you really take the same odds in a bet that the world is flat as you\nwould that string theory is wrong? (I do not propose such a bet)\n\nNo reasoning biologist would seriously doubt evolution. No reasoning\ngeologist would seriously doubt that the world is round. Are you claiming\nthat *no* reasoning physicist would doubt string theory?\n\nIf you are, you need a much stronger argument than "It is the only theory\nwe have." There have been times in history when the only consistent theory\nanyone could think of was dead wrong.\n\n> It mostly means that Darwin\'s theory is more or less a direct\n> consequence of the basic rational reasoning about the world.\n\nI\'ve heard it argued that Darwinian evolution is self evident, but I don\'t\nbelieve it. There are other theories that *could* be true, it\'s just that\nthey aren\'t.\n\nI\'ve heard claims that physics as it is known today could be derived from\npure thought, with no need for experiment, and I don\'t believe that ether.\n\nSorry if this sounds as if you have hit a nerve, because you have. I have\ntalked to creationists - people who wouldn\'t believe the evidence of reason\nor their own senses, if it didn\'t agree with The Book. If you *really*\nintended to paint other physicists with the same brush ...\n\nI will assume you did not.\n\nRalph Hartley\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Lubos Motl wrote:

> One might say that the situation is analogous to "disproving the evolution
> theory". The evolution theory is not too quantitatively verified theory
> either.

Actually, it is. Compared to string theory it certainly is.

The status of the theory of evolution is roughly on a par with that of the
"round Earth theory".

Do you really think that string theory is verified to that level?

Would you really take the same odds in a bet that the world is flat as you
would that string theory is wrong? (I do not propose such a bet)

No reasoning biologist would seriously doubt evolution. No reasoning
geologist would seriously doubt that the world is round. Are you claiming
that *no* reasoning physicist would doubt string theory?

If you are, you need a much stronger argument than "It is the only theory
we have." There have been times in history when the only consistent theory
anyone could think of was dead wrong.

> It mostly means that Darwin's theory is more or less a direct
> consequence of the basic rational reasoning about the world.

I've heard it argued that Darwinian evolution is self evident, but I don't
believe it. There are other theories that *could* be true, it's just that
they aren't.

I've heard claims that physics as it is known today could be derived from
pure thought, with no need for experiment, and I don't believe that ether.

Sorry if this sounds as if you have hit a nerve, because you have. I have
talked to creationists - people who wouldn't believe the evidence of reason
or their own senses, if it didn't agree with The Book. If you *really*
intended to paint other physicists with the same brush ...

I will assume you did not.

Ralph Hartley

Lubos Motl

Oct6-04, 08:03 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Mon, 4 Oct 2004, Ralph Hartley wrote:\n\n> Just so. The trick with Bayesian priors is to pick a set that doesn\'t\n> *hurt* you.\n\nThere is no set of assumptions that would guarantee not to hurt you.\n\n> The main thing is never to assign probabilities of zero.\n\nThat\'s not a very useful rule. If something had an infinitesimal\nprobability and you assigned a significantly nonzero probability to it,\nyou would get equally bad results as if you assigned a zero probability to\nsomething that can actually happen.\n\nIf ten independent questions have a 99.99% probability to be right, and\nyou only assign them the probability 90% or even less, then your\nprediction that at least one of them is not true will be more than 50%\neven though it is still infinitesimal - and it will certainly hurt you,\nespecially if this single thing is enough to destroy a consistent\n(and valid) theoretical structure. Such a wrong estimate would certainly\nblock you from thinking rationally.\n\nIf one assigns higher probabilities than appropriate, it can hurt her, and\nif she assigns lower probabilities, it can hurt her, too. Your simple\nrecipes just cannot be useful for anything.\n\n> An example of a bad one from history: "The Earth absolutely does not move,\n> nothing could convince me otherwise." It would have saved physics a world\n> of hurt if they (The Church) had used instead "I\'m pretty sure the Earth\n> does not move, only overwhelming evidence could convince me otherwise."\n\nIn current understanding, these two approaches are effectively equivalent\n(up to some completely superficial differences in rhetorical styles), and\nif they ever were inequivalent, the real problem was that the Church\nperhaps did not pay enough attention to the experiments - but the small\ndifference between your sentences was irrelevant and it could never\nhelped to speed up the scientific progress.\n\nIn science, various things are uncertain, and a scientist must be able to\nlive with this uncertainty. On the other hand, he must also be able to\nestimate the probabilities realistically (and scientifically), and if\nsomeone assigns all probabilities close to 50%, then he uses a strategy of\na person who knows nothing about anything, because the real probabilities\ncannot always be around 50%. In fact, one can easily derive contradictions\nfrom the assumption that all probabilities are close to 50%. Try to\ncombine them by "AND" or "OR". ;-)\n\n> I know that, but it doesn\'t matter. To predict where Mercury will be next\n> Tuesday, I need to know either G, or if that is set to 1, the conversion\n> factors from units I can measure.\n\nI don\'t understand what these statements are good for. I was just saying\nthat it is not technically true that Newton\'s theory has a parameter that\ncan change its mathematical structure. It only has environmental\nparameters and dimensionful parameters that only reflect a specific choice\nof units. Yes, you need to know not only physics, but also the question\n(which includes some initial conditions), before you find the physical\nanswer. Is this deep insight what you want to point out?\n\n> You can push the parameter around, so that it is outside of the theory, but\n> you still need to know it to make predictions. So there is still a free\n> parameter *somewhere*.\n\nHowever, it is essential that it is not a parameter that would deform the\ntheory. G is a parameter that only changes the map between the\nmathematical objects and reality. Two theories with different G are\nmathematically equivalent, unlike QED with two different fine-structure\nconstants.\n\n> Anyway, I shouldn\'t push the point, since I could just choose another\n> predictive theory that has dimensionless parameters, like QED or the\n> standard model.\n\nThat\'s right. But if you chose these theories, then it would be very\nimportant what I was saying before - that these theories *do* have a very\nsmall number of adjustable parameters. QED has one of them, and the pure\nQCD has no one, in fact. The Standard Model has some extra couplings,\nmaking up 19+10 parameters or so. It is critical that the number of\nparameters is finite, otherwise the theory could not be defined.\n\nI hope that I am not saying anything which would be so hard to understand:\nmy message is simply that it is very important for a theory to have a\nfinite input, and a finite number of parameters, otherwise it is not\npredictive - and a smaller number of such parameters always makes a theory\nsound (and be) more rigid and acceptable. It is probably the most\nimportant criterion to choose among two theories that otherwise look\nequally "true". Would you disagree?\n\n> Construct the numbers alpha_n as follows. Let alpha_1 be the real number\n> produced by concatenating the odd numbered digits of alpha. Let alpha_2 be\n> the number produced by concatenating the even numbered digits who\'s\n> position is not divisible by 4, etc.. alpha_n contains every other digit\n> not included in alpha_{n-1}.\n\nYour theory still has a *single* parameter alpha. You could make a\nperverse formulation of the theory that seems to depend on infinitely many\nparameters in a discontinuous way (by permuting your digits and dividing\nthem to the separate parameters according to some weird numerological\nalgorithm), but it does not prevent a thinking physicist from solving your\ntheory and concluding that it *has* a single parameter alpha and it\ndepends continuously on it. Your game is irrelevant, and even if you play\nit, you won\'t be able to hide anything about the difference between\n"more input" and "less input".\n\nYou can fool yourself by your tricks and think that your theory has many\nparameters, but a person who analyzes your theory more carefully will\nobtain the correct conclusion, namely that there is one parameter only.\n\nAll theories that physics has considered depend on its real parameters in\na continuous way. The space of the parameters is therefore a manifold, and\nwe can talk about its dimension. If the dimension is infinite, the theory\nis unpredictive and useless. Period.\n\n> Now from T we can construct a theory T\' which has as free parameters the\n> alpha_n. T\' has infinitely many parameters, but it is just as predictive as\n> T, since it is the same theory.\n\nRight, which is why this is a theory with a single parameter - by\nconstruction.\n\n> So it is possible for a theory with infinitely many free parameters to be\n> as predictive as any theory with just one.\n\nNo, it\'s not.\n\n> My point is not that they don\'t affect physics, but that not knowing them\n> doesn\'t prevent the theory from making predictions.\n\nI understood your point and explained why it\'s not correct. The theories\nwith infinitely many parameters simply can\'t make any predictions, and\nyour "counterexamples" had one (or a few) parameters only.\n\n> What matters is how many digits you must adjust before you can describe\n> something else besides the digits. Clearly, if you can always measure more\n> digits, you can never describe everything you can measure.\n\nIt is not enough that the output would be bigger. If the input carries an\ninfinite amount of physically relevant information, you will never be able\nto make predictions because you will never define your theory completely.\n\n> No, it could still be correct and completely non-predictive.\n\nA completely non-predictive theory cannot be correct; in fact, it should\nnot even be called a theory. The nonrenormalizable "theories", applied to\nthe full quantum regime, are examples. The theory "everything is\nuncertaint and must be fine-tuned in some arbitrary way" is not correct.\n\n> My point is that whether it is predictive or not is just as much an\n> open question as whether it is correct.\n\nWell, it is an open question until someone answers it. ;-) Is not it true\nabout every question? I am probably still missing your point. The\ndifference between the questions "is the theory predictive [in\nprinciple]?" and "is the theory correct?" is simply that the latter\nquestion requires experiments or observations to be done, while the\nformer question can be analyzed just by knowing its internal rules.\n\n> So far as I know, none of these possibilities have been ruled out:\n> (A) 0 - predictive, inconsistent with observations, incorrect.\n\nRight - say a theory with four light quark-lepton generations or pure\nSU(5) QCD. ;-)\n\n> (B) 1 - predictive, consistent with observations, but incorrect anyway.\n\nWell, I only know such theories if they are small enough modifications of\nthe correct theories so that the small difference is not visible. I am not\naware of any "true" representative of this class; if a theory is *really*\nincorrect, it can always be *clearly* seen by making right enough\nexperiments. What does the number 1 mean?\n\n> (C) 1 - predictive, correct.\n\nRight, that\'s probably string theory, once the details are clarified, and\napproximately also the Standard Model. ;-)\n\n> (D) 10^100 - not predictive, and incorrect.\n\nRight. Nonrenormalizable theories and loop quantum gravity.\n\n> (E) 10^100 - not predictive, and correct.\n\nI don\'t understand what it means. How can something in physics ever be\ncorrect if it cannot predict?\n\n> I admit I would be a bit bothered by (B), and wouldn\'t consider it as\n> likely as the others :-)\n\nI am bothered by (B) and (E).\n\n> > I know, but I happen not to be the only one who still believes that there\n> > are all good reasons to believe that all dimensionless, repeatedly\n> > measurable numbers in this Universe are predictable.\n>\n> What are those reasons?\n\nThe reasons are thousands of developments in theoretical physics that were\nsystematically reducing the number of unexplained parameters of Nature,\ndespite an exponentially growing amount of data from the experiments. The\noriginally independent millions of properties of individual materials etc.\nhave been reduced to 19 (+10 neutrino) parameters of the Standard Model,\nand explaining all parameters is the only truly natural final point of\nthis process.\n\n> I don\'t think I ever suggested that we should. I was only suggesting that\n> calling string theory "the most predictive theory of fundamental physics we\n> have" is counting your chickens before they\'re hatched.\n\nYou probably still misunderstand what the word "predictive" usually means.\nI am not deciding whether the predictions are correct. I am saying that\ngiven the (discrete) choice of the background, string theory - by its very\nnature - is able to predict everything (I am not saying whether we can\nactually make all these calculations) that can happen on this theoretical\nbackground, and all physical, convention-independent questions in such a\nvirtual (or real) Universe can be answered.\n\n> I don\'t think *I* was the one suggesting that a field of inquiry should be\n> dropped because we lack mathematical tools to get any predictions out of it\n\nWell, this is a question whose answer depends on the context. If we\nclearly can\'t have a chance to find the mathematical tools to study\nsomething, I think that no reasonable physicist would work on it. That\'s\nhowever *not* the main reason why I don\'t find the loop quantum gravity\nresearch too useful and motivated. The main reason is that it is an\napparently inconsistent theory that would be - even in the most optimistic\nscenario - unpredictive, and it is simply based on (too many) wrong\nassumptions.\n\nIt is certainly not true that we have no chance to find the right\nmathematical tools in string theory - and in fact, roughly 30% of the\ntools that the string theorists were dreaming about 20 years ago in string\ntheory have already been found, and no doubt, we will try to find the\nrest.\n\n> (or in the case of LQG to tell if it makes any sense at all, I know you\n> think it doesn\'t, but I am not convinced either way).\n\nThat\'s your problem. I am not getting any dividends from you being\nconvinced.\n\n> > But the Standard Model cannot agree with (Newton\'s) gravity. ;-)\n> As you point out, being predictive is independent of being correct.\n\nI would say that being predictive is not sufficient for being correct; I\nam not sure what a correct unpredictive theory means.\n\n> The Standard Model has more parameters than Newton\'s Gravity (be that one\n> or zero), but predicts more. (OK, technically they are incomparable,\n> because they don\'t overlap.)\n\nRight. All the best, Lubos\n___________________________________________ ___________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Mon, 4 Oct 2004, Ralph Hartley wrote:

> Just so. The trick with Bayesian priors is to pick a set that doesn't
> *hurt* you.

There is no set of assumptions that would guarantee not to hurt you.

> The main thing is never to assign probabilities of zero.

That's not a very useful rule. If something had an infinitesimal
probability and you assigned a significantly nonzero probability to it,
you would get equally bad results as if you assigned a zero probability to
something that can actually happen.

If ten independent questions have a 99.99% probability to be right, and
you only assign them the probability 90% or even less, then your
prediction that at least one of them is not true will be more than 50%
even though it is still infinitesimal - and it will certainly hurt you,
especially if this single thing is enough to destroy a consistent
(and valid) theoretical structure. Such a wrong estimate would certainly
block you from thinking rationally.

If one assigns higher probabilities than appropriate, it can hurt her, and
if she assigns lower probabilities, it can hurt her, too. Your simple
recipes just cannot be useful for anything.

> An example of a bad one from history: "The Earth absolutely does not move,
> nothing could convince me otherwise." It would have saved physics a world
> of hurt if they (The Church) had used instead "I'm pretty sure the Earth
> does not move, only overwhelming evidence could convince me otherwise."

In current understanding, these two approaches are effectively equivalent
(up to some completely superficial differences in rhetorical styles), and
if they ever were inequivalent, the real problem was that the Church
perhaps did not pay enough attention to the experiments - but the small
difference between your sentences was irrelevant and it could never
helped to speed up the scientific progress.

In science, various things are uncertain, and a scientist must be able to
live with this uncertainty. On the other hand, he must also be able to
estimate the probabilities realistically (and scientifically), and if
someone assigns all probabilities close to 50%, then he uses a strategy of
a person who knows nothing about anything, because the real probabilities
cannot always be around 50%. In fact, one can easily derive contradictions
from the assumption that all probabilities are close to 50%. Try to
combine them by "AND" or "OR". ;-)

> I know that, but it doesn't matter. To predict where Mercury will be next
> Tuesday, I need to know either G, or if that is set to 1, the conversion
> factors from units I can measure.

I don't understand what these statements are good for. I was just saying
that it is not technically true that Newton's theory has a parameter that
can change its mathematical structure. It only has environmental
parameters and dimensionful parameters that only reflect a specific choice
of units. Yes, you need to know not only physics, but also the question
(which includes some initial conditions), before you find the physical
answer. Is this deep insight what you want to point out?

> You can push the parameter around, so that it is outside of the theory, but
> you still need to know it to make predictions. So there is still a free
> parameter *somewhere*.

However, it is essential that it is not a parameter that would deform the
theory. G is a parameter that only changes the map between the
mathematical objects and reality. Two theories with different G are
mathematically equivalent, unlike QED with two different fine-structure
constants.

> Anyway, I shouldn't push the point, since I could just choose another
> predictive theory that has dimensionless parameters, like QED or the
> standard model.

That's right. But if you chose these theories, then it would be very
important what I was saying before - that these theories *do* have a very
small number of adjustable parameters. QED has one of them, and the pure
QCD has no one, in fact. The Standard Model has some extra couplings,
making up 19+10 parameters or so. It is critical that the number of
parameters is finite, otherwise the theory could not be defined.

I hope that I am not saying anything which would be so hard to understand:
my message is simply that it is very important for a theory to have a
finite input, and a finite number of parameters, otherwise it is not
predictive - and a smaller number of such parameters always makes a theory
sound (and be) more rigid and acceptable. It is probably the most
important criterion to choose among two theories that otherwise look
equally "true". Would you disagree?

> Construct the numbers \alpha_n as follows. Let \alpha_1 be the real number
> produced by concatenating the odd numbered digits of \alpha. Let \alpha_2 be
> the number produced by concatenating the even numbered digits who's
> position is not divisible by 4, etc.. \alpha_n contains every other digit
> not included in \alpha_{n-1}.

Your theory still has a *single* parameter \alpha. You could make a
perverse formulation of the theory that seems to depend on infinitely many
parameters in a discontinuous way (by permuting your digits and dividing
them to the separate parameters according to some weird numerological
algorithm), but it does not prevent a thinking physicist from solving your
theory and concluding that it *has* a single parameter \alpha and it
depends continuously on it. Your game is irrelevant, and even if you play
it, you won't be able to hide anything about the difference between
"more input" and "less input".

You can fool yourself by your tricks and think that your theory has many
parameters, but a person who analyzes your theory more carefully will
obtain the correct conclusion, namely that there is one parameter only.

All theories that physics has considered depend on its real parameters in
a continuous way. The space of the parameters is therefore a manifold, and
we can talk about its dimension. If the dimension is infinite, the theory
is unpredictive and useless. Period.

> Now from T we can construct a theory T' which has as free parameters the
> \alpha_n. T' has infinitely many parameters, but it is just as predictive as
> T, since it is the same theory.

Right, which is why this is a theory with a single parameter - by
construction.

> So it is possible for a theory with infinitely many free parameters to be
> as predictive as any theory with just one.

No, it's not.

> My point is not that they don't affect physics, but that not knowing them
> doesn't prevent the theory from making predictions.

I understood your point and explained why it's not correct. The theories
with infinitely many parameters simply can't make any predictions, and
your "counterexamples" had one (or a few) parameters only.

> What matters is how many digits you must adjust before you can describe
> something else besides the digits. Clearly, if you can always measure more
> digits, you can never describe everything you can measure.

It is not enough that the output would be bigger. If the input carries an
infinite amount of physically relevant information, you will never be able
to make predictions because you will never define your theory completely.

> No, it could still be correct and completely non-predictive.

A completely non-predictive theory cannot be correct; in fact, it should
not even be called a theory. The nonrenormalizable "theories", applied to
the full quantum regime, are examples. The theory "everything is
uncertaint and must be fine-tuned in some arbitrary way" is not correct.

> My point is that whether it is predictive or not is just as much an
> open question as whether it is correct.

Well, it is an open question until someone answers it. ;-) Is not it true
about every question? I am probably still missing your point. The
difference between the questions "is the theory predictive [in
principle]?" and "is the theory correct?" is simply that the latter
question requires experiments or observations to be done, while the
former question can be analyzed just by knowing its internal rules.

> So far as I know, none of these possibilities have been ruled out:
> (A) - predictive, inconsistent with observations, incorrect.

Right - say a theory with four light quark-lepton generations or pure
SU(5) QCD. ;-)

> (B) 1 - predictive, consistent with observations, but incorrect anyway.

Well, I only know such theories if they are small enough modifications of
the correct theories so that the small difference is not visible. I am not
aware of any "true" representative of this class; if a theory is *really*
incorrect, it can always be *clearly* seen by making right enough
experiments. What does the number 1 mean?

> (C) 1 - predictive, correct.

Right, that's probably string theory, once the details are clarified, and
approximately also the Standard Model. ;-)

> (D) 10^100 - not predictive, and incorrect.

Right. Nonrenormalizable theories and loop quantum gravity.

> (E) 10^100 - not predictive, and correct.

I don't understand what it means. How can something in physics ever be
correct if it cannot predict?

> I admit I would be a bit bothered by (B), and wouldn't consider it as
> likely as the others :-)

I am bothered by (B) and (E).

> > I know, but I happen not to be the only one who still believes that there
> > are all good reasons to believe that all dimensionless, repeatedly
> > measurable numbers in this Universe are predictable.
>
> What are those reasons?

The reasons are thousands of developments in theoretical physics that were
systematically reducing the number of unexplained parameters of Nature,
despite an exponentially growing amount of data from the experiments. The
originally independent millions of properties of individual materials etc.
have been reduced to 19 (+10 neutrino) parameters of the Standard Model,
and explaining all parameters is the only truly natural final point of
this process.

> I don't think I ever suggested that we should. I was only suggesting that
> calling string theory "the most predictive theory of fundamental physics we
> have" is counting your chickens before they're hatched.

You probably still misunderstand what the word "predictive" usually means.
I am not deciding whether the predictions are correct. I am saying that
given the (discrete) choice of the background, string theory - by its very
nature - is able to predict everything (I am not saying whether we can
actually make all these calculations) that can happen on this theoretical
background, and all physical, convention-independent questions in such a
virtual (or real) Universe can be answered.

> I don't think *I* was the one suggesting that a field of inquiry should be
> dropped because we lack mathematical tools to get any predictions out of it

Well, this is a question whose answer depends on the context. If we
clearly can't have a chance to find the mathematical tools to study
something, I think that no reasonable physicist would work on it. That's
however *not* the main reason why I don't find the loop quantum gravity
research too useful and motivated. The main reason is that it is an
apparently inconsistent theory that would be - even in the most optimistic
scenario - unpredictive, and it is simply based on (too many) wrong
assumptions.

It is certainly not true that we have no chance to find the right
mathematical tools in string theory - and in fact, roughly 30% of the
tools that the string theorists were dreaming about 20 years ago in string
theory have already been found, and no doubt, we will try to find the
rest.

> (or in the case of LQG to tell if it makes any sense at all, I know you
> think it doesn't, but I am not convinced either way).

That's your problem. I am not getting any dividends from you being
convinced.

> > But the Standard Model cannot agree with (Newton's) gravity. ;-)
> As you point out, being predictive is independent of being correct.

I would say that being predictive is not sufficient for being correct; I
am not sure what a correct unpredictive theory means.

> The Standard Model has more parameters than Newton's Gravity (be that one
> or zero), but predicts more. (OK, technically they are incomparable,
> because they don't overlap.)

Right. All the best, Lubos
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Italo Vecchi

Oct6-04, 08:03 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Boris Borcic <borcis@users.ch> wrote in message news:<41570746.1000905@users.ch>...\n......\n\n> Indeed Lubos you sound here rather like how the Church would sound, if it\n> claimed that time did not prove Giordano Bruno right, since Bruno (in 1600)\n> multiplied the equation stars="distant solar systems" by an *infinite*\n> quantity of stars in the Universe, while our current beliefs admit "only" a\n> *finite* number of them.\n>\n\nBruno\'s ideas ("horrida Nolana philosophia" in Kepler\'s words) are as\nunsettling now as they were on February 17, 1600. You may believe that\nthe number of stars is finite if you accept the proposal of a\nCatholic priest that the universe started with a big bang.\nThat most of the information we perceive gushed out of a white-holish\nsingularity can be argumented quite convincingly. But after reading\nBruno\'s "Dell\'infinito, universo et mondi" you may sneer at the claim\nthat the whole universe must have originated from there.\n\nIV\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Boris Borcic <borcis@users.ch> wrote in message news:<41570746.1000905@users.ch>...
......

> Indeed Lubos you sound here rather like how the Church would sound, if it
> claimed that time did not prove Giordano Bruno right, since Bruno (in 1600)
> multiplied the equation stars="distant solar systems" by an *infinite*
> quantity of stars in the Universe, while our current beliefs admit "only" a
> *finite* number of them.
>

Bruno's ideas ("horrida Nolana philosophia" in Kepler's words) are as
unsettling now as they were on February 17, 1600. You may believe that
the number of stars is finite if you accept the proposal of a
Catholic priest that the universe started with a big bang.
That most of the information we perceive gushed out of a white-holish
singularity can be argumented quite convincingly. But after reading
Bruno's "Dell'infinito, universo et mondi" you may sneer at the claim
that the whole universe must have originated from there.

IV

Lubos Motl

Oct7-04, 10:55 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Thu, 7 Oct 2004, Ralph Hartley wrote:\n\n> > LM: It is critical that the number of parameters is finite, otherwise\n> > the theory could not be defined.\n>\n> In the sense that a theory with one parameter can be defined, there are\n> theories with infinitely many that can also be defined.\n\nNo, it cannot. A theory is only fully defined once the parameters are set,\nand if there is an infinite number of them, it is impossible to determine\nall of them and define the theory.\n\n> A single real parameter is not a finite amount of information. It carries\n> the same amount of information as an infinite number.\n\nNo, it does not. For any theory that depends on its parameters in a\ncontinuous way - and virtually all meaningful theories in physics ever\nproposed fall into this category - one can simply count how many\nparameters it depends on, and two is always more than one. The\ndimensionality of the parameter space is a well-defined quantity. An\ninfinite number of yet-to-be-determined, physically relevant real\nparameters is unacceptable for a set of ideas to be called a "theory".\n\n> But you can\'t determine that just by counting parameters. A theory with\n> infinitely many can be more rigid than a theory with just one.\n\nNo, a theory with infinitely many parameters cannot be rigid at all, and\nit certainly cannot be more rigid than a theory with one parameter.\n\n> I could do it in a continuous way as well, but the formulation wouldn\'t be\n> any less perverse :-)\n\nShow us, I don\'t think that this would be possible, even in a perverse\nway. Would it be some continuous, but highly unsmooth dependence? ;-)\n\n> I\'m pretty sure I could prove that there exist theories for which no\n> physicist cold determine how many parameters there "really" are, or even if\n> there are finitely many.\n\nI\'m pretty sure that such "theories" are irrelevant for natural science.\nMaybe they are useful for religion?\n\n> Perhaps, but it is your game as well.\n\nI am not playing any games. I am talking about absolutely physical and\nessential physical theories - of the type that was awarded by the Nobel\nprize on Tuesday: pure QCD has no dimensionless parameters, for example,\nand this is what makes it really powerful, predictive, rigid, and\nconvincing.\n\nYou are probably talking about something very different, and I think that\nthis very different thing does not belong to science.\n\n> If you count alternate formulations as the same theory, I\'m not even\n> sure "number of parameters" is well defined, or is ever different from\n> 1.\n\nQCD has no dimensionless constants; QED has one; the Standard Model has\nroughly 19+10 of them. You should learn how to count them before you make\nnonsensical statements like "it is not possible to count". It\'s not that\nhard.\n\n> For example, consider a pertubative quantum gravity theory, which needs\n> infinitely many parameters to completely define.\n\nFirst of all, such a thing is not a "theory", and second of all, I really\ndon\'t intend to "consider" this kind of nonsense.\n\n> You have repeated that over and over, but you haven\'t proven it. I don\'t\n> see how you could, in light of the many predictions that *are* made by\n> theories that *do* have infinitely many parameters.\n\nNever. One can make an effective theory with a limited validity, and say\nthat there is a lot of new physics beyond it, but this physics is\nirrelevant for some category of questions that we want to ask (physics at\nlow energies), at least if the questions should only be answered with a\nlimited accuracy. But such a theory must still have a finite number of\nparameters that matter. If a set of ideas or rules has infinitely many\nadjustable parameters, then it is *not* a theory and it should not be\nconsidered by any scientist.\n\nWe are often using the word "theory" in different meanings. Above, I am\nusing the most frequent meaning - a set of rules and ideas that are able\nto predict phenomena. The theory of special relativity is called a\n"theory" but it is really a "metatheory" - a set of principles that every\n"theory" (in the previous sense) must satisfy.\n\n> A theory can make predictions without being defined *completely*. If it has\n> undetermined parts, it can\'t predict them by definition, but it can predict\n> other things.\n\nAn (incomplete) theory can only be used to predict a limited set of events\nAB, without claiming to predict other things such as CD, if the truncation\nto AB can be justified (or at least if it is true, at least in some\nsense). If it is so, then the parameters affecting CD do *not* belong to\nthis theory. Only the parameters affecting AB are a part of this theory,\nand the number of them must again be finite.\n\n> Note that your argument applies *equally* well to theories with a single\n> parameter, as those with infinitely many. Both carry an infinite amount of\n> "physically relevant information".\n\nNo. Nineteen real parameters is always more than one real parameter and\neveryone who is able to distinguish integers from each other must know\nwhy. An infinite number of physically relevant real continuous adjustable\nparameters makes a set of ideas useless and unacceptable as a scientific\ntheory.\n\n> I suspect that the only reason you want to make the distinction is that\n> otherwise you would have to reject theories with even one parameter, and\n> too many good theories are in that class.\n\nAll these ridiculous statements are based on your assumption that one\nequals infinity, which is not a correct assumption.\n\n> > A completely non-predictive theory cannot be correct; in fact, it should\n> > not even be called a theory.\n>\n> It would be useless, but there are lots of useless, but true, facts.\n\nNo, there are no *theories* like that. A single fact has no adjustable\nparameters either, otherwise it is not a fact. ;-) For example, if you say\nthat the Bush approval rate is X where X is adjustable, then it is not a\nfact but a vague combination of words without any information value.\n\n> You say, "String theory is the most predictive theory of fundamental\n> physics we have."\n>\n> I say, "Isn\'t that an open question?"\n\nI say "No, according to what we know, it is not an open question."\n\n> You seam to be trying to say, "Yes, but when we know the answer it won\'t be."\n\nNo, if it were an open question, I could not state it as a statement. It\nis only you who is trying to make an open question out of it. I\'ve\nexplained how predictivity is determined, and why the statement about\nstring theory is true.\n\n> I say, "Answers first, inferences from the answers later. Open questions\n> can go either way."\n\nYou\'re saying many things like that. Whatever.\n\n> The number of "realistic string vacua." Basically the number of different\n> "versions" of string theory\n\nThere are no "versions" of string theory. There is one theory only and it\nhas many states - even many superselection sectors (backgrounds) or\nclassical solutions.\n\n> You can claim that string theory is unique. But it doesn\'t make predictions\n> independent of the vacuum, so if you don\'t know which vacuum applies it\'s\n> just a mathematical structure, not a physical theory.\n\nYou would have to explain what you mean by a "physical theory", because\notherwise your sentence makes no sense. In normal language, a quantum\nphysical theory is a set consisting of a Hilbert space, operators with\namplitudes that can be calculated from a finite amount of input and\ninterpreted as results of (any) experiments, and string theory undoubtedly\nis a physical theory. The only (slightly) open question is whether it is a\ncorrect theory of our Universe.\n\n> No. I\'m talking about string theory in *all* these cases.\n\nThen you\'re incorrect in virtually *all* of these cases.\n\n> This is the case where lots of vacua are stable, and agree with all the\n> experiments we have done, or if you like with all that we could do. But\n> there are so many that you can\'t get any new predictions out of it.\n\nThat\'s simply not true. You could have said this untrue statement about\nany successful theory in history of science before the theory calculated\nthe answer for a given question - and it would be an equally wrong\nstatement in all these cases. You could say that Mendelejev\'s table was\nuseless because it had too many atoms and one cannot make anything with\nsuch a complicated table. Your current statement is comparably\nunjustified.\n\n> This is the case where string theory is completely wrong, has nothing to do\n> with our world, but doesn\'t make enough predictions for it to be proven wrong.\n\nString theory certainly cannot be "completely" wrong. As far as the rough\nscheme goes, string theory has already been proved correct.\n\n> > I don\'t understand what it means. How can something in physics ever be\n> > correct if it cannot predict?\n>\n> If you think you have been promised a completely predictable universe then\n> I suppose it can\'t.\n\nWhat can\'t? String theory certainly *can* predict, and it is the most\npredictive theory we ever had. The question is whether the really relevant\ndetailed predictions can be extracted with the tools we have and we will\nhave, and whether they are correct.\n\n> But there is certainly nothing incoherent in the possibility that the\n> universe really *is* constructed from the vibration modes of tiny strings\n> (etc.), but that knowing that fact is completely useless, because you can\n> never find out enough about the state of the vacuum to make any predictions.\n\nThat\'s just ridiculous. If the string scale were separated from the Planck\nscale by a lot - imagine near a couple of TeVs - we could actually produce\nthe strings, and their qualitative behavior would be independent of the\ndetails of the compactification. Be sure that this would convince all\nrationally thinking people that string theory is correct, and I don\'t care\nabout the rest (of the people).\n\n> I understand that part perfectly. I think being predictive and being\n> correct are even more independent of each other than you do.\n\nRight. It\'s because you think that a theory can be correct even if it\npredicts nothing, and you are wrong.\n\n> But if the answer to that question is "almost anything can happen, those\n> discrete choices cover the space of low energy theories very densely", then\n> you have tortured the term "prediction" beyond it\'s breaking point.\n\nThis is certainly not the type of predictions that string theory is\nproducing - or is designed to produce. String theory (has been and) is\nmaking bold and very specific predictions - so specific in fact that some\npeople are irritated by it and they prefer "theories" that don\'t make any\nnew predictions whatsoever. ;-) The predictions in the models that we\nstudy are very quantitative, and the predictions for the real world are\nbound to be equally quantitative once the correct background is found.\n\nAll the best\nLubos\n_____________________________________ _________________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Thu, 7 Oct 2004, Ralph Hartley wrote:

> > LM: It is critical that the number of parameters is finite, otherwise
> > the theory could not be defined.
>
> In the sense that a theory with one parameter can be defined, there are
> theories with infinitely many that can also be defined.

No, it cannot. A theory is only fully defined once the parameters are set,
and if there is an infinite number of them, it is impossible to determine
all of them and define the theory.

> A single real parameter is not a finite amount of information. It carries
> the same amount of information as an infinite number.

No, it does not. For any theory that depends on its parameters in a
continuous way - and virtually all meaningful theories in physics ever
proposed fall into this category - one can simply count how many
parameters it depends on, and two is always more than one. The
dimensionality of the parameter space is a well-defined quantity. An
infinite number of yet-to-be-determined, physically relevant real
parameters is unacceptable for a set of ideas to be called a "theory".

> But you can't determine that just by counting parameters. A theory with
> infinitely many can be more rigid than a theory with just one.

No, a theory with infinitely many parameters cannot be rigid at all, and
it certainly cannot be more rigid than a theory with one parameter.

> I could do it in a continuous way as well, but the formulation wouldn't be
> any less perverse :-)

Show us, I don't think that this would be possible, even in a perverse
way. Would it be some continuous, but highly unsmooth dependence? ;-)

> I'm pretty sure I could prove that there exist theories for which no
> physicist cold determine how many parameters there "really" are, or even if
> there are finitely many.

I'm pretty sure that such "theories" are irrelevant for natural science.
Maybe they are useful for religion?

> Perhaps, but it is your game as well.

I am not playing any games. I am talking about absolutely physical and
essential physical theories - of the type that was awarded by the Nobel
prize on Tuesday: pure QCD has no dimensionless parameters, for example,
and this is what makes it really powerful, predictive, rigid, and
convincing.

You are probably talking about something very different, and I think that
this very different thing does not belong to science.

> If you count alternate formulations as the same theory, I'm not even
> sure "number of parameters" is well defined, or is ever different from
> 1.

QCD has no dimensionless constants; QED has one; the Standard Model has
roughly 19+10 of them. You should learn how to count them before you make
nonsensical statements like "it is not possible to count". It's not that
hard.

> For example, consider a pertubative quantum gravity theory, which needs
> infinitely many parameters to completely define.

First of all, such a thing is not a "theory", and second of all, I really
don't intend to "consider" this kind of nonsense.

> You have repeated that over and over, but you haven't proven it. I don't
> see how you could, in light of the many predictions that *are* made by
> theories that *do* have infinitely many parameters.

Never. One can make an effective theory with a limited validity, and say
that there is a lot of new physics beyond it, but this physics is
irrelevant for some category of questions that we want to ask (physics at
low energies), at least if the questions should only be answered with a
limited accuracy. But such a theory must still have a finite number of
parameters that matter. If a set of ideas or rules has infinitely many
adjustable parameters, then it is *not* a theory and it should not be
considered by any scientist.

We are often using the word "theory" in different meanings. Above, I am
using the most frequent meaning - a set of rules and ideas that are able
to predict phenomena. The theory of special relativity is called a
"theory" but it is really a "metatheory" - a set of principles that every
"theory" (in the previous sense) must satisfy.

> A theory can make predictions without being defined *completely*. If it has
> undetermined parts, it can't predict them by definition, but it can predict
> other things.

An (incomplete) theory can only be used to predict a limited set of events
AB, without claiming to predict other things such as CD, if the truncation
to AB can be justified (or at least if it is true, at least in some
sense). If it is so, then the parameters affecting CD do *not* belong to
this theory. Only the parameters affecting AB are a part of this theory,
and the number of them must again be finite.

> Note that your argument applies *equally* well to theories with a single
> parameter, as those with infinitely many. Both carry an infinite amount of
> "physically relevant information".

No. Nineteen real parameters is always more than one real parameter and
everyone who is able to distinguish integers from each other must know
why. An infinite number of physically relevant real continuous adjustable
parameters makes a set of ideas useless and unacceptable as a scientific
theory.

> I suspect that the only reason you want to make the distinction is that
> otherwise you would have to reject theories with even one parameter, and
> too many good theories are in that class.

All these ridiculous statements are based on your assumption that one
equals infinity, which is not a correct assumption.

> > A completely non-predictive theory cannot be correct; in fact, it should
> > not even be called a theory.
>
> It would be useless, but there are lots of useless, but true, facts.

No, there are no *theories* like that. A single fact has no adjustable
parameters either, otherwise it is not a fact. ;-) For example, if you say
that the Bush approval rate is X where X is adjustable, then it is not a
fact but a vague combination of words without any information value.

> You say, "String theory is the most predictive theory of fundamental
> physics we have."
>
> I say, "Isn't that an open question?"

I say "No, according to what we know, it is not an open question."

> You seam to be trying to say, "Yes, but when we know the answer it won't be."

No, if it were an open question, I could not state it as a statement. It
is only you who is trying to make an open question out of it. I've
explained how predictivity is determined, and why the statement about
string theory is true.

> I say, "Answers first, inferences from the answers later. Open questions
> can go either way."

You're saying many things like that. Whatever.

> The number of "realistic string vacua." Basically the number of different
> "versions" of string theory

There are no "versions" of string theory. There is one theory only and it
has many states - even many superselection sectors (backgrounds) or
classical solutions.

> You can claim that string theory is unique. But it doesn't make predictions
> independent of the vacuum, so if you don't know which vacuum applies it's
> just a mathematical structure, not a physical theory.

You would have to explain what you mean by a "physical theory", because
otherwise your sentence makes no sense. In normal language, a quantum
physical theory is a set consisting of a Hilbert space, operators with
amplitudes that can be calculated from a finite amount of input and
interpreted as results of (any) experiments, and string theory undoubtedly
is a physical theory. The only (slightly) open question is whether it is a
correct theory of our Universe.

> No. I'm talking about string theory in *all* these cases.

Then you're incorrect in virtually *all* of these cases.

> This is the case where lots of vacua are stable, and agree with all the
> experiments we have done, or if you like with all that we could do. But
> there are so many that you can't get any new predictions out of it.

That's simply not true. You could have said this untrue statement about
any successful theory in history of science before the theory calculated
the answer for a given question - and it would be an equally wrong
statement in all these cases. You could say that Mendelejev's table was
useless because it had too many atoms and one cannot make anything with
such a complicated table. Your current statement is comparably
unjustified.

> This is the case where string theory is completely wrong, has nothing to do
> with our world, but doesn't make enough predictions for it to be proven wrong.

String theory certainly cannot be "completely" wrong. As far as the rough
scheme goes, string theory has already been proved correct.

> > I don't understand what it means. How can something in physics ever be
> > correct if it cannot predict?
>
> If you think you have been promised a completely predictable universe then
> I suppose it can't.

What can't? String theory certainly *can* predict, and it is the most
predictive theory we ever had. The question is whether the really relevant
detailed predictions can be extracted with the tools we have and we will
have, and whether they are correct.

> But there is certainly nothing incoherent in the possibility that the
> universe really *is* constructed from the vibration modes of tiny strings
> (etc.), but that knowing that fact is completely useless, because you can
> never find out enough about the state of the vacuum to make any predictions.

That's just ridiculous. If the string scale were separated from the Planck
scale by a lot - imagine near a couple of TeVs - we could actually produce
the strings, and their qualitative behavior would be independent of the
details of the compactification. Be sure that this would convince all
rationally thinking people that string theory is correct, and I don't care
about the rest (of the people).

> I understand that part perfectly. I think being predictive and being
> correct are even more independent of each other than you do.

Right. It's because you think that a theory can be correct even if it
predicts nothing, and you are wrong.

> But if the answer to that question is "almost anything can happen, those
> discrete choices cover the space of low energy theories very densely", then
> you have tortured the term "prediction" beyond it's breaking point.

This is certainly not the type of predictions that string theory is
producing - or is designed to produce. String theory (has been and) is
making bold and very specific predictions - so specific in fact that some
people are irritated by it and they prefer "theories" that don't make any
new predictions whatsoever. ;-) The predictions in the models that we
study are very quantitative, and the predictions for the real world are
bound to be equally quantitative once the correct background is found.

All the best
Lubos
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Ralph Hartley

Oct8-04, 06:20 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nLubos Motl wrote:\n> On Thu, 7 Oct 2004, Ralph Hartley wrote:\n>\n>>In the sense that a theory with one parameter can be defined, there are\n>>theories with infinitely many that can also be defined.\n>\n> No, it cannot. A theory is only fully defined once the parameters are set,\n> and if there is an infinite number of them, it is impossible to determine\n> all of them and define the theory.\n\nBut to define, in your sense, a theory with a single parameter would\nrequire setting the value for every digit, and there is an infinitele\nnumber of them, it is impossible to determine all of them and define the\ntheory.\n\n>>A single real parameter is not a finite amount of information. It carries\n>>the same amount of information as an infinite number.\n>\n> No, it does not.\n\nDo you deny that takes an infinite amount of information to determine the\nvalue of a single real number?\n\nThat would only be true if there were finitely many different real numbers.\n\n>>I could do it in a continuous way as well, but the formulation wouldn\'t be\n>>any less perverse :-)\n>\n> Show us, I don\'t think that this would be possible, even in a perverse\n> way. Would it be some continuous, but highly unsmooth dependence? ;-)\n\nYes, of course. It would involve Peano curves.\n\n>>If you count alternate formulations as the same theory, I\'m not even\n>>sure "number of parameters" is well defined, or is ever different from\n>>1.\n>\n> QCD has no dimensionless constants\n\nMy bad! Zero is also possible. (Zero is preferable too.)\n\n>>For example, consider a pertubative quantum gravity theory, which needs\n>>infinitely many parameters to completely define.\n>\n> First of all, such a thing is not a "theory", and second of all, I really\n> don\'t intend to "consider" this kind of nonsense.\n\nIt is a mathematical structure that predicts virtually every experiment we\nhave any realistic expectation of ever doing, but it isn\'t a theory? No\nscientist should ever consider something that does that?\n\nIts predictions could be wrong, e.g. if string theory is correct and have\nlow energy consequences, but we are agreeing (I think) that correctness is\na separate issue.\n\n> Above, I am\n> using the most frequent meaning - a set of rules and ideas that are able\n> to predict phenomena.\n\nI will accept that definition for the sake of the remainder of this\nargument, if I stray from it it will be by accident.\n\nBy that definition string theory could in principle *become* a theory, and\nperturbative gravity is one already.\n\n>>A theory can make predictions without being defined *completely*. If it has\n>>undetermined parts, it can\'t predict them by definition, but it can predict\n>>other things.\n>\n> An (incomplete) theory can only be used to predict a limited set of events\n> AB, without claiming to predict other things such as CD, if the truncation\n> to AB can be justified (or at least if it is true, at least in some\n> sense). If it is so, then the parameters affecting CD do *not* belong to\n> this theory. Only the parameters affecting AB are a part of this theory,\n> and the number of them must again be finite.\n\nIn that case perturbative gravity is an incomplete theory, where AB is low\nenergy phenomena, which are affected by only a few parameters, and the\ninfinitely many parameters that affect only CD (very high energy phenomena)\nare not part of the theory.\n\n> Nineteen real parameters is always more than one real parameter and\n> everyone who is able to distinguish integers from each other must know\n> why.\n\nDo you claim that there are more 19-tuples of reals than there are reals?\n\n>>I suspect that the only reason you want to make the distinction is that\n>>otherwise you would have to reject theories with even one parameter, and\n>>too many good theories are in that class.\n>\n> All these ridiculous statements are based on your assumption that one\n> equals infinity, which is not a correct assumption.\n\nNo. It only depends on the assumption that the number of (countably)\ninfinite sequences of reals is the same as the number of reals, which is an\nelementary fact about the real numbers.\n\n> There are no "versions" of string theory. There is one theory only and it\n> has many states - even many superselection sectors (backgrounds) or\n> classical solutions.\n>\n>>You can claim that string theory is unique. But it doesn\'t make predictions\n>>independent of the vacuum, so if you don\'t know which vacuum applies it\'s\n>>just a mathematical structure, not a physical theory.\n>\n> You would have to explain what you mean by a "physical theory", because\n> otherwise your sentence makes no sense. In normal language, a quantum\n> physical theory is a set consisting of a Hilbert space, operators with\n> amplitudes that can be calculated from a finite amount of input and\n> interpreted as results of (any) experiments,\n\nWhat I meant was "a set of rules and ideas that are able to predict\nphenomena". Your new definition (the second in one post) reduces to your\nfirst if the "finite amount of input" is also *obtainable*.\n\nThe "one true string theory" is not a theory at all by your first\ndefinition, only string theory combined with information about the "state"\nor "background" predicts phenomena.\n\nSo the question is how *much* added information is required? In other words\nhow *many* realistic backgrounds are there?\n\nIf you can show, with more than a dismissive remark, that there is only\none, or even a small number, then I would agree that string theory is a\n(predictive) theory.\n\nIf there are 10^100 then by the definition I am now using (at your request)\nit isn\'t a theory at all.\n\n100^10 realistic backgrounds is always more than one realistic background\nand everyone who is able to distinguish integers from each other must know\nwhy. :-)\n\nDo you contend that the number of realistic backgrounds is known?\n\n>>This is the case where lots of vacua are stable, and agree with all the\n>>experiments we have done, or if you like with all that we could do. But\n>>there are so many that you can\'t get any new predictions out of it.\n>\n> That\'s simply not true.\n\nOK. How many stable states that resemble our universe are there?\n\nIf there are only a few (I would count even 10^6 as "small" but not\n10^100), then my statement is false. My claim was *not* that it is true,\nbut only that it is one of a list of statements that havn\'t been ruled out.\n\nIf the there are *very* many, then it is true.\n\nIf the number of realistic backgrounds is unknown over a wide range, then\nit is an open question. It may be true or not, and saying "That is simply\nnot true" is incorrect.\n\n> String theory certainly cannot be "completely" wrong. As far as the rough\n> scheme goes, string theory has already been proved correct.\n\nI must have missed that part. :-)\n\n>>But there is certainly nothing incoherent in the possibility that the\n>>universe really *is* constructed from the vibration modes of tiny strings\n>>(etc.), but that knowing that fact is completely useless, because you can\n>>never find out enough about the state of the vacuum to make any predictions.\n>\n> That\'s just ridiculous. If the string scale were separated from the Planck\n> scale by a lot - imagine near a couple of TeVs - we could actually produce\n> the strings, and their qualitative behavior would be independent of the\n> details of the compactification. Be sure that this would convince all\n> rationally thinking people that string theory is correct, and I don\'t care\n> about the rest (of the people).\n\nIt would sure convince me! But if the string scale is *not* much larger\nthan the Planck scale (do you not agree that that is a logical\npossibility?), then that wouldn\'t be possible. Since we have no real idea\nof what the string scale *is*, it is unknown how predictive string theory is.\n\n>>I think being predictive and being\n>>correct are even more independent of each other than you do.\n>\n> Right. It\'s because you think that a theory can be correct even if it\n> predicts nothing, and you are wrong.\n\nBy the definition I am using now, it has to predict stuff to be a theory,\nand "right" or "wrong" only apply to theories. That makes it hard to talk\nabout something when you don\'t yet know if it is a theory or not, like the\nso called "string theory", but I guess I can live with that.\n\n> This is certainly not the type of predictions that string theory is\n> producing - or is designed to produce.\n\nDesigned? I thought it came from God! :-) I am *very* sorry, but how could\nI resist a setup like that? :-)\n\n> The predictions in the models that we\n> study are very quantitative, and the predictions for the real world are\n> bound to be equally quantitative once the correct background is found.\n\nIf it is unique.\n\nRalph Hartley\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Lubos Motl wrote:
> On Thu, 7 Oct 2004, Ralph Hartley wrote:
>
>>In the sense that a theory with one parameter can be defined, there are
>>theories with infinitely many that can also be defined.
>
> No, it cannot. A theory is only fully defined once the parameters are set,
> and if there is an infinite number of them, it is impossible to determine
> all of them and define the theory.

But to define, in your sense, a theory with a single parameter would
require setting the value for every digit, and there is an infinitele
number of them, it is impossible to determine all of them and define the
theory.

>>A single real parameter is not a finite amount of information. It carries
>>the same amount of information as an infinite number.
>
> No, it does not.

Do you deny that takes an infinite amount of information to determine the
value of a single real number?

That would only be true if there were finitely many different real numbers.

>>I could do it in a continuous way as well, but the formulation wouldn't be
>>any less perverse :-)
>
> Show us, I don't think that this would be possible, even in a perverse
> way. Would it be some continuous, but highly unsmooth dependence? ;-)

Yes, of course. It would involve Peano curves.

>>If you count alternate formulations as the same theory, I'm not even
>>sure "number of parameters" is well defined, or is ever different from
>>1.
>
> QCD has no dimensionless constants

My bad! Zero is also possible. (Zero is preferable too.)

>>For example, consider a pertubative quantum gravity theory, which needs
>>infinitely many parameters to completely define.
>
> First of all, such a thing is not a "theory", and second of all, I really
> don't intend to "consider" this kind of nonsense.

It is a mathematical structure that predicts virtually every experiment we
have any realistic expectation of ever doing, but it isn't a theory? No
scientist should ever consider something that does that?

Its predictions could be wrong, e.g. if string theory is correct and have
low energy consequences, but we are agreeing (I think) that correctness is
a separate issue.

> Above, I am
> using the most frequent meaning - a set of rules and ideas that are able
> to predict phenomena.

I will accept that definition for the sake of the remainder of this
argument, if I stray from it it will be by accident.

By that definition string theory could in principle *become* a theory, and
perturbative gravity is one already.

>>A theory can make predictions without being defined *completely*. If it has
>>undetermined parts, it can't predict them by definition, but it can predict
>>other things.
>
> An (incomplete) theory can only be used to predict a limited set of events
> AB, without claiming to predict other things such as CD, if the truncation
> to AB can be justified (or at least if it is true, at least in some
> sense). If it is so, then the parameters affecting CD do *not* belong to
> this theory. Only the parameters affecting AB are a part of this theory,
> and the number of them must again be finite.

In that case perturbative gravity is an incomplete theory, where AB is low
energy phenomena, which are affected by only a few parameters, and the
infinitely many parameters that affect only CD (very high energy phenomena)
are not part of the theory.

> Nineteen real parameters is always more than one real parameter and
> everyone who is able to distinguish integers from each other must know
> why.

Do you claim that there are more 19-tuples of reals than there are reals?

>>I suspect that the only reason you want to make the distinction is that
>>otherwise you would have to reject theories with even one parameter, and
>>too many good theories are in that class.
>
> All these ridiculous statements are based on your assumption that one
> equals infinity, which is not a correct assumption.

No. It only depends on the assumption that the number of (countably)
infinite sequences of reals is the same as the number of reals, which is an
elementary fact about the real numbers.

> There are no "versions" of string theory. There is one theory only and it
> has many states - even many superselection sectors (backgrounds) or
> classical solutions.
>
>>You can claim that string theory is unique. But it doesn't make predictions
>>independent of the vacuum, so if you don't know which vacuum applies it's
>>just a mathematical structure, not a physical theory.
>
> You would have to explain what you mean by a "physical theory", because
> otherwise your sentence makes no sense. In normal language, a quantum
> physical theory is a set consisting of a Hilbert space, operators with
> amplitudes that can be calculated from a finite amount of input and
> interpreted as results of (any) experiments,

What I meant was "a set of rules and ideas that are able to predict
phenomena". Your new definition (the second in one post) reduces to your
first if the "finite amount of input" is also *obtainable*.

The "one true string theory" is not a theory at all by your first
definition, only string theory combined with information about the "state"
or "background" predicts phenomena.

So the question is how *much* added information is required? In other words
how *many* realistic backgrounds are there?

If you can show, with more than a dismissive remark, that there is only
one, or even a small number, then I would agree that string theory is a
(predictive) theory.

If there are 10^100 then by the definition I am now using (at your request)
it isn't a theory at all.

100^10 realistic backgrounds is always more than one realistic background
and everyone who is able to distinguish integers from each other must know
why. :-)

Do you contend that the number of realistic backgrounds is known?

>>This is the case where lots of vacua are stable, and agree with all the
>>experiments we have done, or if you like with all that we could do. But
>>there are so many that you can't get any new predictions out of it.
>
> That's simply not true.

OK. How many stable states that resemble our universe are there?

If there are only a few (I would count even 10^6 as "small" but not
10^100), then my statement is false. My claim was *not* that it is true,
but only that it is one of a list of statements that havn't been ruled out.

If the there are *very* many, then it is true.

If the number of realistic backgrounds is unknown over a wide range, then
it is an open question. It may be true or not, and saying "That is simply
not true" is incorrect.

> String theory certainly cannot be "completely" wrong. As far as the rough
> scheme goes, string theory has already been proved correct.

I must have missed that part. :-)

>>But there is certainly nothing incoherent in the possibility that the
>>universe really *is* constructed from the vibration modes of tiny strings
>>(etc.), but that knowing that fact is completely useless, because you can
>>never find out enough about the state of the vacuum to make any predictions.
>
> That's just ridiculous. If the string scale were separated from the Planck
> scale by a lot - imagine near a couple of TeVs - we could actually produce
> the strings, and their qualitative behavior would be independent of the
> details of the compactification. Be sure that this would convince all
> rationally thinking people that string theory is correct, and I don't care
> about the rest (of the people).

It would sure convince me! But if the string scale is *not* much larger
than the Planck scale (do you not agree that that is a logical
possibility?), then that wouldn't be possible. Since we have no real idea
of what the string scale *is*, it is unknown how predictive string theory is.

>>I think being predictive and being
>>correct are even more independent of each other than you do.
>
> Right. It's because you think that a theory can be correct even if it
> predicts nothing, and you are wrong.

By the definition I am using now, it has to predict stuff to be a theory,
and "right" or "wrong" only apply to theories. That makes it hard to talk
about something when you don't yet know if it is a theory or not, like the
so called "string theory", but I guess I can live with that.

> This is certainly not the type of predictions that string theory is
> producing - or is designed to produce.

Designed? I thought it came from God! :-) I am *very* sorry, but how could
I resist a setup like that? :-)

> The predictions in the models that we
> study are very quantitative, and the predictions for the real world are
> bound to be equally quantitative once the correct background is found.

If it is unique.

Ralph Hartley

Arnold Neumaier

Oct8-04, 06:20 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nLubos Motl wrote:\n\n> An infinite number of yet-to-be-determined, physically relevant real\n> parameters is unacceptable for a set of ideas to be called a "theory".\n\nAny classical field theory depends on an unknown parameter vector\nfrom an infinite-dimensional manifold, namely through the initial\ncondition. A finite number of parameters in the defining differential\nequations could easily be absorbed into an additional dynamical\nvector s with the differential equation sdot=0. Thus any constant can be\nturned into an initial condition. Conversely, if there are constants of\nthe motion, these could be elevated to parameters of the theory,\nand the state space be reduced. Thus how many parameters a theory has\ndepends on how one formulates it, and is not a measure of predictivity\nor rigidity.\n\nThe informational freedom in a theory is therefore determined solely\nby the size of the state space. Because of finite limits on measurability,\nit depends of course very much on how accurate the initial conditions\nmust be known in order that sensible predictions are possible.\n\nThus Newton\'s laws are very predictive since the state of the solar\nsystem is fairly well determined by a few dozen of numbers to not\ntoo high accuracy. As we move away from simple systems, more and more\ninfomation is needed to predict details. Only gross features that\ndepend little on the state, or universal features that are independent\nof the state are well predicted. In particular, fluid mechanics\nneeds infinitely many degrees of freedom, but specifying the fields\nroughly is already useful (except in the turbulent regime).\nClassical statistical mechanics needs of the order of 10^23 bytes of\ninformation as initial conditions, and quantum physics again infinite\namounts, though often (and in particular near equlibrium) much less\ninformation suffices.\n\nString theory needs functions on function spaces, which is again\nmuch much more information. Thus its non-predictivity beyond what\nis known already is not a surprise. That it has no built-in parameters\nbut all parameters arise dynamically (and probably dependent on the\ninitial conditions) is not a consolation.\n\n\nArnold Neumaier\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Lubos Motl wrote:

> An infinite number of yet-to-be-determined, physically relevant real
> parameters is unacceptable for a set of ideas to be called a "theory".

Any classical field theory depends on an unknown parameter vector
from an infinite-dimensional manifold, namely through the initial
condition. A finite number of parameters in the defining differential
equations could easily be absorbed into an additional dynamical
vector s with the differential equation sdot=0. Thus any constant can be
turned into an initial condition. Conversely, if there are constants of
the motion, these could be elevated to parameters of the theory,
and the state space be reduced. Thus how many parameters a theory has
depends on how one formulates it, and is not a measure of predictivity
or rigidity.

The informational freedom in a theory is therefore determined solely
by the size of the state space. Because of finite limits on measurability,
it depends of course very much on how accurate the initial conditions
must be known in order that sensible predictions are possible.

Thus Newton's laws are very predictive since the state of the solar
system is fairly well determined by a few dozen of numbers to not
too high accuracy. As we move away from simple systems, more and more
infomation is needed to predict details. Only gross features that
depend little on the state, or universal features that are independent
of the state are well predicted. In particular, fluid mechanics
needs infinitely many degrees of freedom, but specifying the fields
roughly is already useful (except in the turbulent regime).
Classical statistical mechanics needs of the order of 10^23 bytes of
information as initial conditions, and quantum physics again infinite
amounts, though often (and in particular near equlibrium) much less
information suffices.

String theory needs functions on function spaces, which is again
much much more information. Thus its non-predictivity beyond what
is known already is not a surprise. That it has no built-in parameters
but all parameters arise dynamically (and probably dependent on the
initial conditions) is not a consolation.

Arnold Neumaier

Frank Hellmann

Oct8-04, 06:20 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nRalph Hartley <hartley@aic.nrl.navy.mil> wrote in message news:<ck1asi\\$a4h\\$1@ra.nrl.navy.mil>...\n\n> A single real parameter is not a finite amount of information. It carries\n> the same amount of information as an infinite number.\n>\n\nI take it the point is that each successive parameter needs to be\n"less important" in the sense that it doesn\'t influence the theory as\nstrongly as preceding ones, as is the case in nonrenormalizable\nperturbative theories where the successive parameters appear in later\nterms of the expansion.\nCorrect?\nThen the countably infinite real parameters are no worse then the\nparts of the one real parameter we don\'t know, where the fact that\nthose parts are the later decimals accounts for them being less\nimportant.\n\nThat\'s basically your argument isn\'t it?\nIf the infinitely many real parameters are actually all equally\nrelevant the argument fails, doesn\'t it?\n\n\n---\nfrank.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Ralph Hartley <hartley@aic.nrl.navy.mil> wrote in message news:<ck1asi$a4h$1@ra.nrl.navy.mil>...

> A single real parameter is not a finite amount of information. It carries
> the same amount of information as an infinite number.
>

I take it the point is that each successive parameter needs to be
"less important" in the sense that it doesn't influence the theory as
strongly as preceding ones, as is the case in nonrenormalizable
perturbative theories where the successive parameters appear in later
terms of the expansion.
Correct?
Then the countably infinite real parameters are no worse then the
parts of the one real parameter we don't know, where the fact that
those parts are the later decimals accounts for them being less
important.

That's basically your argument isn't it?
If the infinitely many real parameters are actually all equally
relevant the argument fails, doesn't it?

---
frank.

Ilja Schmelzer

Oct13-04, 03:45 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n"Frank Hellmann" <Certhas@gmail.com> schrieb\n> Ralph Hartley <hartley@aic.nrl.navy.mil> wrote\n> > A single real parameter is not a finite amount of information. It\ncarries\n> > the same amount of information as an infinite number.\n\n> I take it the point is that each successive parameter needs to be\n> "less important" in the sense that it doesn\'t influence the theory as\n> strongly as preceding ones, as is the case in nonrenormalizable\n> perturbative theories where the successive parameters appear in later\n> terms of the expansion.\n> Correct?\n\nOf course, usually if we have y=f(x) in infinite-dimensional x we can\nsay that some of the parameters are in some sense less important.\nWhatever the coefficients of y = sum a_i x_i, or the a_i have to\ndescrease or the x_i, else the series is divergent.\n\n> If the infinitely many real parameters are actually all equally\n> relevant the argument fails, doesn\'t it?\n\nDepends on how you define "equally relevant". But if you are\nable to define functions on infinite-dimensional spaces so that\nall dimensions are "equally relevant" (whatever this means)\nat all, then I don\'t think the argument fails.\n\nTo derive a prediction from a theory with infinite number of\nparameters you need some function\n\nY = f(X) X=(x_0,x_1,...) in L\n\nfor some infinite-dimensional space L. Then you need some\nexperimental restrictions on L. These experimental\nrestrictions are usually obtained by bounds for other\nmeasurements:\n\nY_i = f_i(X), Y_i in [Y_min,Y_max]=U_i\n\nThis gives the restrictions\n\nX in V_i = f_i^{-1}(U_i)\n\nThus, we obtain the prediction: Y in f(/\\ V_i). Nothing prevent this\nrestriction from being highly nontrivial.\n\nA nice example: The theory tells that some function is holomorph.\nThus, f(z)=sum c_i z^i with an infinite set of parameters c_i.\nWe observe a single value: max_{|z|=C} |f(z)| = Y_0. The theory\npredicts |f(z)|< Y_0 for all |z|<C.\n\nLooking at f(z)=sum c_i z^i I would not say that c_n with\nlarger n is less relevant for the value of f(z), at least if |z|>1.\n\nIlja\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Frank Hellmann" <Certhas@gmail.com> schrieb
> Ralph Hartley <hartley@aic.nrl.navy.mil> wrote
> > A single real parameter is not a finite amount of information. It
carries
> > the same amount of information as an infinite number.

> I take it the point is that each successive parameter needs to be
> "less important" in the sense that it doesn't influence the theory as
> strongly as preceding ones, as is the case in nonrenormalizable
> perturbative theories where the successive parameters appear in later
> terms of the expansion.
> Correct?

Of course, usually if we have y=f(x) in infinite-dimensional x we can
say that some of the parameters are in some sense less important.
Whatever the coefficients of y = sum a_i x_i, or the a_i have to
descrease or the x_i, else the series is divergent.

> If the infinitely many real parameters are actually all equally
> relevant the argument fails, doesn't it?

Depends on how you define "equally relevant". But if you are
able to define functions on infinite-dimensional spaces so that
all dimensions are "equally relevant" (whatever this means)
at all, then I don't think the argument fails.

To derive a prediction from a theory with infinite number of
parameters you need some function

Y = f(X) X=(x_0,x_1,...)[/itex] in L

for some infinite-dimensional space L. Then you need some
experimental restrictions on L. These experimental
restrictions are usually obtained by bounds for other
measurements:

Y_i = f_i(X), Y_i in [itex][Y_{min},Y_{max}]=U_i

This gives the restrictions

X in V_i = f_i^{-1}(U_i)

Thus, we obtain the prediction: Y in f(/\ V_i). Nothing prevent this
restriction from being highly nontrivial.

A nice example: The theory tells that some function is holomorph.
Thus, f(z)=sum c_i z^i with an infinite set of parameters c_i.
We observe a single value: max_{|z|=C} |f(z)| = Y_0. The theory
predicts |f(z)|< Y_0 for all |z|<C.

Looking at f(z)=sum c_i z^i I would not say that c_n with
larger n is less relevant for the value of f(z), at least if |z|>1.

Ilja

Lubos Motl

Oct13-04, 03:45 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nOn Tue, 12 Oct 2004, Ralph Hartley wrote:\n\n> That\'s because there exists a continuous function from the unit interval\n> onto the Hilbert Cube (the product of countably many copies of the unit\n\nThat\'s exactly what I expected. ;-) Well, let me say that physics theories\ndon\'t depend on the parameters just continuously, but also smoothly almost\neverywhere - which means that the derivative of the result with respect to\nthe parameters is well-defined and finite everywhere except for a set of\nmeasure zero. I hope that this will stop your unphysical attempts that\nhave really nothing to do with our discussions about the predictive power\nof physical theories.\n_______________________________________ _______________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\nWebs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Tue, 12 Oct 2004, Ralph Hartley wrote:

> That's because there exists a continuous function from the unit interval
> onto the Hilbert Cube (the product of countably many copies of the unit

That's exactly what I expected. ;-) Well, let me say that physics theories
don't depend on the parameters just continuously, but also smoothly almost
everywhere - which means that the derivative of the result with respect to
the parameters is well-defined and finite everywhere except for a set of
measure zero. I hope that this will stop your unphysical attempts that
have really nothing to do with our discussions about the predictive power
of physical theories.
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
Webs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Lubos Motl

Oct13-04, 03:45 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nOn Tue, 12 Oct 2004, Peter Shor wrote:\n\n> May I point out that this is wrong, even thought it appears to be\n> dogma among particle physicists. One can imagine a theory (and I\n> suspect they exist in the engineering disciplines) which has as\n> one of its parameters a continous function defined on the interval\n> [0,1]. This clearly contains an infinite number of free parameters,\n> but a reasonable approximation to this function could be derived by...\n\nDear Peter, thanks for your response;\n\nsuch things are definitely possible, and the point is that you can for\nexample Fourier-expand the function on [0,1], and the increasingly high\nFourier modes are increasingly less important for most approximate\ncalculations - calculations that involve quantities associated with the\nlow-lying Fourier modes only. Ever higher modes in the parameters cause\never smaller errors.\n\nBut all these procedures are just about vague approximations. These\n"engineering theories" are simply not the type of stuff that can and\nshould appear in fundamental physics. Fundamental physics is meant - and\nso far it has been able to - produce theories that can, in principle, lead\nto arbitrarily precise new predictions once you make a finite number of\nexperiments. And this is simply not possible if the parameters are\nfunctions on [0,1].\n\nThe higher and higher Fourier modes can be compared to something in\ntheoretical physics - namely the knowledge of physics at increasingly\nhigher energy scales. But it is still true that if you want to describe\nphysics at *some* energy scale, you need to know the parameters that\naffect physics at this scale (and lower scales), and the number of such\nparameters must be finite.\n\nIf I apply this language to your functions on [0,1]: if your function is\nknown/measured approximately, you should view it as an effective theory\nthat is only valid for all other quantities being e.g. sufficiently smooth\nfunctions so that the Fourier modes "n" and higher can be neglected. This\nis a legitimate (and given your uncertainties, necessary) truncation of\nyour "theory", changing it into an effective theory. I repeat that you\njust can\'t trust your randomly measured function on [0,1] for arbitrarily\nquickly changing processes, and therefore the language of effective theory\nis inevitable.\n\nHowever, the effective theory only depends on the first "n" Fourier modes,\nand it has therefore a finite number of parameters. Having an infinite\nnumber of parameters such that all of them would matter would be a\ndisaster for a physics theory, but also for an engineering theory - the\nonly disclaimer here is that you must carefully realize that an effective\ntheory does not really depend on everything about your function, but just\na finite number of numbers.\n\nOf course, if someone just draws random graphs copied from her aparatus\nwithout realizing which sort of information she uses, which information\nshe does not use, and so on, then she can reach incorrect conclusions\nabout the number of parameters of the "real" theory relevant for her\nproblem. But that does not mean that you should be reproducing her naive\nerrors, Peter.\n\n> experiments, and could give excellent predictive results in practice.\n> More relevant to this discussion is t\'Hooft\'s work, which I saw him\n> give a talk on, in which he works with a perturbative expansion of\n> quantum gravity. He showed that low order expansions of perturbative\n> quantum gravity had only a very small number of extra free parameters\n> per order. If we can get by with fifth order expansions in the\n> standard model, and fifth-order perturbative quantum gravity has fewer\n> free parameters than the standard model, why should one be considered\n> predictive and the other not? (I ignore here the small consideration\n> of experimentally reaching the predictive domain of the theory :-) )\n\nIt\'s a question of principle. If they have the same number of parameters\nup to some precision, it is fine, and anyone can use them - but the most\nimportant fact continues to be that the full Standard Model is consistent\nto all orders and it has a finite number of parameters to all orders,\nWell, it\'s very paradoxical that you mention \'t Hooft as a sort of support\nfor your strange statement; it is paradoxical because \'t Hooft got his\nNobel prize EXACTLY for having proved that the number of parameters in the\nStandard Model that you need up to any order is finite. This is an\nextremely important feature of the Standard Model, which distinguishes it\nfrom quantized general relativity, and the proof of this feature brought\n\'t Hooft and Veltman their Nobel prize.\n\nOn the other hand, the quantized general relativity does not a finite\nnumber of parameters to each order. If you look at the situation with\nlimited precision, in a very pragmatic, engineering way, you can make an\nincorrect conclusion that both theories are equally predictive. If you\nlook at the theories with the exact eyes of a particle physicist, you will\nconclude that quantized GR is nonrenormalizable, therefore it requires an\ninfinite number of parameters, and therefore it is not a theory.\n\nI think that \'t Hooft\'s Nobel prize should convince you that if you don\'t\nsee the huge difference between a renormalizable and a nonrenormalizable\ntheory, you are missing something very important!\n\nIt does not really matter that the existing experiment cannot measure\nthings beyond the 5th order (well, they cannot measure general relativity\neven beyond the tree level). The important thing is that - by pure thought\n- we know that in principle one can create experiments that test higher\norders, and a nonrenormalizable theory simply can\'t predict what happens\nunless it is given an infinite number of parameters.\n\nIt is the very difference between a consistent and complete theory on one\nside, and an inconsistent or inevitably incomplete theory on the other\nhand. A cook (and perhaps many engineers) perhaps do not care about the\ndifference, but this difference is absolutely critical for a theoretical\nphysicist.\n\n> Forget Hartley\'s contrived example. I think my first example, with\n> a continuous function as a parameter, shows that infinitely many\n> free parameters (can a continuous function be treated as anything\n> but infinitely many free parameters?) can in some cases be considered\n> predictive.\n\nIt\'s only a truly quantitative theory once you parameterize your idealized\nfunction by some explicit Ansatz. For example, experimentally you see\n(measure) that the function looks as a bulge, and you decide that it is\nsin(pi.x). If you write sin(pi.x) just in this form, it has no parameters\nin it. Well, this is what kids from the basic school could say.\n\nBut that\'s not the whole story in particle physics. If we have any\nmotivated theory, we must allow to deform the theory in all possible ways\nthat spoil neither the consistency nor the required symmetries of the\ntheory. Otherwise we would be just guessing, and guessing is not enough in\nphysics. If there exists no symmetry reason why sin(pi.x)+sin(3.pi.x)/5 is\nworse than sin(pi.x), then you must consider it as a possibility -\nGell-Mann\'s totalitarian principle. Consequently, your engineering theory,\nif extrapolated into a complete theory, has infinitely many parameters -\nwhich is what you admitted at the very beginning - and from a fundamental\nphysics point of view, it is not a predictive theory.\n\nThis example is a bit misleading simply because one can imagine that with\nthe parameters being organized into the function, there are still many\npredictions that are more or less independent of the function (or at least\nof its short distance details). This is not the case for typical\nnon-predictive theories of this kind in physics - like for\nnonrenormalizable theories. In that case, the infinite number of\nparameters is typically such that the theory can give you virtually any\nprediction for the parameteric dependence of a quantity on a variable.\n\n> A breakthrough meta-theory, which gave the form of the\n> continuous function, would be very intersting theoretically, but if\n> the form had too many continous parameters describing it, this\n> meta-theory might paradoxically still be less predictive than the\n> original theory.\n\nSorry but such an approach can never be correct in theoretical physics. If\nyour exact form of the function is justified by any rational underlying\nmechanism or argument - even if it is difficult to comprehend it - and if\nit is also tested experimentally, then it is always a more complete and\nmore predictive theory than the theory with the randomly extracted graph.\nI am sure that you don\'t need to go to quantum field theory and string\ntheory to see examples. Epicycles are an older example.\n\nPeople originally saw some curves that the planets move along on the\nskies. That\'s your "engineering predictive function" that was copied from\nexperiment. Then they described these functions as "circles upon circles"\nand used all these epicycles, which was certainly a progress, because they\nknew what sort of result was waiting for a physics explanation. It was not\nthe explanation yet. The final progress was made by Kepler and Newton when\nthey parameterized the curves correctly as ellipses and derived them from\nNewton\'s equations. Einstein gave more fundamental laws that predict\nNewton\'s results plus some corrections. Would you have doubts about my\nstatement that each step in this historical sequence was progress that\nmade astronomy or physics more predictive?\n\nThere are a plenty of confusing statements of non-physicists that the\nepicycles were "more accurate" than Newton\'s laws, and so forth. I hope\nthat you personally don\'t believe that Newton\'s laws were ever failing to\ndescribe the motion of planets! ;-)\n\nIt\'s just completely essential in physics to distinguish a description of\nobservation - phenomenology in the primitive sense - from having an actual\ntheory. What you\'re talking about is a description of observations, not\nyet a theory, and no doubt, a correct theory is always more complete and\nmore predictive than a set of observations!\n\n> In fact, I think this example is analogous to the\n> relationship between string theory (playing the role of the\n> theoretically nice but experimentally useless meta-model) and the\n> Standard Model (playing the role of the engineer\'s more practical\n> concrete model), ...\n\nI agree that this is the correct analogy. The Standard Model is closer to\nthe "engineer\'s description" while string theory is like the real theory\nthat replaces graphs and curves by quantitative explanation. I just don\'t\nunderstand how can you say that the former can be more predictive than the\nlatter (assuming that both of them agree with reality). Even most of the\npeople who work on the Standard Model and ignore string theory would agree\nwith me that having a quantitative justification for a function on the\ninterval [0,1], leading to results that agree with reality, is always more\nsatisfying and predictive than to copy the function from some\nobservations! Do you really have doubts about it? This is the whole\npurpose of theoretical physics, to be reducing the number of independent\ningredients that are necessary to describe an increasing body of\nobservations! To copy a graph is not the same thing as to understand it!\nNo one before Planck understood the black body curve, for example.\n\nOf course, the people who don\'t like reductionism and propose religious or\nphilosophical prejudices instead of reductionism would disagree with me,\nbut I don\'t really think that sci.physics.research is the place where the\nopinion of these people should be taken into account.\n\nBest\nLubos\n_________________________ __________________________________________________ ___\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\nWebs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Tue, 12 Oct 2004, Peter Shor wrote:

> May I point out that this is wrong, even thought it appears to be
> dogma among particle physicists. One can imagine a theory (and I
> suspect they exist in the engineering disciplines) which has as
> one of its parameters a continous function defined on the interval
> [0,1]. This clearly contains an infinite number of free parameters,
> but a reasonable approximation to this function could be derived by...

Dear Peter, thanks for your response;

such things are definitely possible, and the point is that you can for
example Fourier-expand the function on [0,1], and the increasingly high
Fourier modes are increasingly less important for most approximate
calculations - calculations that involve quantities associated with the
low-lying Fourier modes only. Ever higher modes in the parameters cause
ever smaller errors.

But all these procedures are just about vague approximations. These
"engineering theories" are simply not the type of stuff that can and
should appear in fundamental physics. Fundamental physics is meant - and
so far it has been able to - produce theories that can, in principle, lead
to arbitrarily precise new predictions once you make a finite number of
experiments. And this is simply not possible if the parameters are
functions on [0,1].

The higher and higher Fourier modes can be compared to something in
theoretical physics - namely the knowledge of physics at increasingly
higher energy scales. But it is still true that if you want to describe
physics at *some* energy scale, you need to know the parameters that
affect physics at this scale (and lower scales), and the number of such
parameters must be finite.

If I apply this language to your functions on [0,1]: if your function is
known/measured approximately, you should view it as an effective theory
that is only valid for all other quantities being e.g. sufficiently smooth
functions so that the Fourier modes "n" and higher can be neglected. This
is a legitimate (and given your uncertainties, necessary) truncation of
your "theory", changing it into an effective theory. I repeat that you
just can't trust your randomly measured function on [0,1] for arbitrarily
quickly changing processes, and therefore the language of effective theory
is inevitable.

However, the effective theory only depends on the first "n" Fourier modes,
and it has therefore a finite number of parameters. Having an infinite
number of parameters such that all of them would matter would be a
disaster for a physics theory, but also for an engineering theory - the
only disclaimer here is that you must carefully realize that an effective
theory does not really depend on everything about your function, but just
a finite number of numbers.

Of course, if someone just draws random graphs copied from her aparatus
without realizing which sort of information she uses, which information
she does not use, and so on, then she can reach incorrect conclusions
about the number of parameters of the "real" theory relevant for her
problem. But that does not mean that you should be reproducing her naive
errors, Peter.

> experiments, and could give excellent predictive results in practice.
> More relevant to this discussion is t'Hooft's work, which I saw him
> give a talk on, in which he works with a perturbative expansion of
> quantum gravity. He showed that low order expansions of perturbative
> quantum gravity had only a very small number of extra free parameters
> per order. If we can get by with fifth order expansions in the
> standard model, and fifth-order perturbative quantum gravity has fewer
> free parameters than the standard model, why should one be considered
> predictive and the other not? (I ignore here the small consideration
> of experimentally reaching the predictive domain of the theory :-) )

It's a question of principle. If they have the same number of parameters
up to some precision, it is fine, and anyone can use them - but the most
important fact continues to be that the full Standard Model is consistent
to all orders and it has a finite number of parameters to all orders,
Well, it's very paradoxical that you mention 't Hooft as a sort of support
for your strange statement; it is paradoxical because 't Hooft got his
Nobel prize EXACTLY for having proved that the number of parameters in the
Standard Model that you need up to any order is finite. This is an
extremely important feature of the Standard Model, which distinguishes it
from quantized general relativity, and the proof of this feature brought
't Hooft and Veltman their Nobel prize.

On the other hand, the quantized general relativity does not a finite
number of parameters to each order. If you look at the situation with
limited precision, in a very pragmatic, engineering way, you can make an
incorrect conclusion that both theories are equally predictive. If you
look at the theories with the exact eyes of a particle physicist, you will
conclude that quantized GR is nonrenormalizable, therefore it requires an
infinite number of parameters, and therefore it is not a theory.

I think that 't Hooft's Nobel prize should convince you that if you don't
see the huge difference between a renormalizable and a nonrenormalizable
theory, you are missing something very important!

It does not really matter that the existing experiment cannot measure
things beyond the 5th order (well, they cannot measure general relativity
even beyond the tree level). The important thing is that - by pure thought
- we know that in principle one can create experiments that test higher
orders, and a nonrenormalizable theory simply can't predict what happens
unless it is given an infinite number of parameters.

It is the very difference between a consistent and complete theory on one
side, and an inconsistent or inevitably incomplete theory on the other
hand. A cook (and perhaps many engineers) perhaps do not care about the
difference, but this difference is absolutely critical for a theoretical
physicist.

> Forget Hartley's contrived example. I think my first example, with
> a continuous function as a parameter, shows that infinitely many
> free parameters (can a continuous function be treated as anything
> but infinitely many free parameters?) can in some cases be considered
> predictive.

It's only a truly quantitative theory once you parameterize your idealized
function by some explicit Ansatz. For example, experimentally you see
(measure) that the function looks as a bulge, and you decide that it is
sin(\pi.x). If you write sin(\pi.x) just in this form, it has no parameters
in it. Well, this is what kids from the basic school could say.

But that's not the whole story in particle physics. If we have any
motivated theory, we must allow to deform the theory in all possible ways
that spoil neither the consistency nor the required symmetries of the
theory. Otherwise we would be just guessing, and guessing is not enough in
physics. If there exists no symmetry reason why sin(\pi.x)+sin(3.\pi.x)/5 is
worse than sin(\pi.x), then you must consider it as a possibility -
Gell-Mann's totalitarian principle. Consequently, your engineering theory,
if extrapolated into a complete theory, has infinitely many parameters -
which is what you admitted at the very beginning - and from a fundamental
physics point of view, it is not a predictive theory.

This example is a bit misleading simply because one can imagine that with
the parameters being organized into the function, there are still many
predictions that are more or less independent of the function (or at least
of its short distance details). This is not the case for typical
non-predictive theories of this kind in physics - like for
nonrenormalizable theories. In that case, the infinite number of
parameters is typically such that the theory can give you virtually any
prediction for the parameteric dependence of a quantity on a variable.

> A breakthrough meta-theory, which gave the form of the
> continuous function, would be very intersting theoretically, but if
> the form had too many continous parameters describing it, this
> meta-theory might paradoxically still be less predictive than the
> original theory.

Sorry but such an approach can never be correct in theoretical physics. If
your exact form of the function is justified by any rational underlying
mechanism or argument - even if it is difficult to comprehend it - and if
it is also tested experimentally, then it is always a more complete and
more predictive theory than the theory with the randomly extracted graph.
I am sure that you don't need to go to quantum field theory and string
theory to see examples. Epicycles are an older example.

People originally saw some curves that the planets move along on the
skies. That's your "engineering predictive function" that was copied from
experiment. Then they described these functions as "circles upon circles"
and used all these epicycles, which was certainly a progress, because they
knew what sort of result was waiting for a physics explanation. It was not
the explanation yet. The final progress was made by Kepler and Newton when
they parameterized the curves correctly as ellipses and derived them from
Newton's equations. Einstein gave more fundamental laws that predict
Newton's results plus some corrections. Would you have doubts about my
statement that each step in this historical sequence was progress that
made astronomy or physics more predictive?

There are a plenty of confusing statements of non-physicists that the
epicycles were "more accurate" than Newton's laws, and so forth. I hope
that you personally don't believe that Newton's laws were ever failing to
describe the motion of planets! ;-)

It's just completely essential in physics to distinguish a description of
observation - phenomenology in the primitive sense - from having an actual
theory. What you're talking about is a description of observations, not
yet a theory, and no doubt, a correct theory is always more complete and
more predictive than a set of observations!

> In fact, I think this example is analogous to the
> relationship between string theory (playing the role of the
> theoretically nice but experimentally useless meta-model) and the
> Standard Model (playing the role of the engineer's more practical
> concrete model), ...

I agree that this is the correct analogy. The Standard Model is closer to
the "engineer's description" while string theory is like the real theory
that replaces graphs and curves by quantitative explanation. I just don't
understand how can you say that the former can be more predictive than the
latter (assuming that both of them agree with reality). Even most of the
people who work on the Standard Model and ignore string theory would agree
with me that having a quantitative justification for a function on the
interval [0,1], leading to results that agree with reality, is always more
satisfying and predictive than to copy the function from some
observations! Do you really have doubts about it? This is the whole
purpose of theoretical physics, to be reducing the number of independent
ingredients that are necessary to describe an increasing body of
observations! To copy a graph is not the same thing as to understand it!
No one before Planck understood the black body curve, for example.

Of course, the people who don't like reductionism and propose religious or
philosophical prejudices instead of reductionism would disagree with me,
but I don't really think that sci.physics.research is the place where the
opinion of these people should be taken into account.

Best
Lubos
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)
Webs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Peter Shor

Oct15-04, 01:55 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nLubos Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0410121849250.11136-100000@feynman.harvard.edu>...\n> On Tue, 12 Oct 2004, Peter Shor wrote:\n>\n> > May I point out that this is wrong, even thought it appears to be\n> > dogma among particle physicists. One can imagine a theory (and I\n> > suspect they exist in the engineering disciplines) which has as\n> > one of its parameters a continous function defined on the interval\n> > [0,1]. This clearly contains an infinite number of free parameters,\n> > but a reasonable approximation to this function could be derived by...\n>\n> Dear Peter, thanks for your response;\n>\n> such things are definitely possible, and the point is that you can for\n> example Fourier-expand the function on [0,1], and the increasingly high\n> Fourier modes are increasingly less important for most approximate\n> calculations - calculations that involve quantities associated with the\n> low-lying Fourier modes only. Ever higher modes in the parameters cause\n> ever smaller errors.\n>\n> But all these procedures are just about vague approximations. These\n> "engineering theories" are simply not the type of stuff that can and\n> should appear in fundamental physics. Fundamental physics is meant - and\n> so far it has been able to - produce theories that can, in principle, lead\n> to arbitrarily precise new predictions once you make a finite number of\n> experiments. And this is simply not possible if the parameters are\n> functions on [0,1].\n\nThis isn\'t possible unless you have a theory with no free parameters.\nThis is an ultimate hope of string theorists, but nobody has yet\nachieved it (in a theory that describes the universe) and I\'m not\nconvinced it\'s possible.\n\n> The higher and higher Fourier modes can be compared to something in\n> theoretical physics - namely the knowledge of physics at increasingly\n> higher energy scales. But it is still true that if you want to describe\n> physics at *some* energy scale, you need to know the parameters that\n> affect physics at this scale (and lower scales), and the number of such\n> parameters must be finite.\n\nWe\'re essentially in agreement here.\n\n> > More relevant to this discussion is t\'Hooft\'s work, which I saw him\n> > give a talk on, in which he works with a perturbative expansion of\n> > quantum gravity. He showed that low order expansions of perturbative\n> > quantum gravity had only a very small number of extra free parameters\n> > per order. If we can get by with fifth order expansions in the\n> > standard model, and fifth-order perturbative quantum gravity has fewer\n> > free parameters than the standard model, why should one be considered\n> > predictive and the other not? (I ignore here the small consideration\n> > of experimentally reaching the predictive domain of the theory :-) )\n>\n> It\'s a question of principle. If they have the same number of parameters\n> up to some precision, it is fine, and anyone can use them - but the most\n> important fact continues to be that the full Standard Model is consistent\n> to all orders and it has a finite number of parameters to all orders,\n> Well, it\'s very paradoxical that you mention \'t Hooft as a sort of support\n> for your strange statement; it is paradoxical because \'t Hooft got his\n> Nobel prize EXACTLY for having proved that the number of parameters in the\n> Standard Model that you need up to any order is finite. This is an\n> extremely important feature of the Standard Model, which distinguishes it\n> from quantized general relativity, and the proof of this feature brought\n> \'t Hooft and Veltman their Nobel prize.\n\nBut after seeing \'t Hooft\'s talk, I think one of his points was that\neven non-renormalizable theories with an infinite number of free\nparameters, like perturbative quantum gravity, actually have some\npredictive power, and that physicists shouldn\'t dismiss them\nout-of-hand as unworthy of consideration, because they could actually\nlead to some insight.\n\n> I think that \'t Hooft\'s Nobel prize should convince you that if you don\'t\n> see the huge difference between a renormalizable and a nonrenormalizable\n> theory, you are missing something very important!\n\nI do see the difference.\n\n> Consequently, your engineering theory,\n> if extrapolated into a complete theory, has infinitely many parameters -\n> which is what you admitted at the very beginning - and from a fundamental\n> physics point of view, it is not a predictive theory.\n\nI don\'t know what you mean by predictive here. This theory, once\nrefined by enough experiments, will predict the results of other\nexperiments, and the difference between this and a finite-parameter\ntheory is how much refinement is needed before predictions can be\nmade. There\'s also the question you bring up of how well experiments\nmade in one experimental domain of the theory will predict results\nfrom another experimental domain of the theory. I feel sure that one\ncan come up with a version of my toy model where they will, so I don\'t\nthink this is a fundamental distinction between finite-parameter and\ninfinite-parameter theories.\n\n> This is the whole\n> purpose of theoretical physics, to be reducing the number of independent\n> ingredients that are necessary to describe an increasing body of\n> observations!\n\nI would disagree. The whole purpose of theoretical physics is to come\nup with models that better and better describe and predict behavior\nof the real physical world. The discovery of the Standard Model was a\nremarkable scientific advance. That it simultaneously greatly\nreduced the number of free parameters in our theories and greatly\nincreased the accuracy of our experimental predictions is due to the\namazing fact that all of our experiments back then (and nearly\nall of our experiments even now) can be almost exactly described by a\nquantum field theory with 19 free parameters. The belief that all\nof physics can be described by a theory having even fewer parameters\nis a profound (and probably philosophically unjustifiable) faith in\nthe simplicity of the laws of physics.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Lubos Motl <motl@feynman.harvard.edu> wrote in message news:<Pine.LNX.4.31.0410121849250.11136-100000@feynman.harvard.edu>...
> On Tue, 12 Oct 2004, Peter Shor wrote:
>
> > May I point out that this is wrong, even thought it appears to be
> > dogma among particle physicists. One can imagine a theory (and I
> > suspect they exist in the engineering disciplines) which has as
> > one of its parameters a continous function defined on the interval
> > [0,1]. This clearly contains an infinite number of free parameters,
> > but a reasonable approximation to this function could be derived by...
>
> Dear Peter, thanks for your response;
>
> such things are definitely possible, and the point is that you can for
> example Fourier-expand the function on [0,1], and the increasingly high
> Fourier modes are increasingly less important for most approximate
> calculations - calculations that involve quantities associated with the
> low-lying Fourier modes only. Ever higher modes in the parameters cause
> ever smaller errors.
>
> But all these procedures are just about vague approximations. These
> "engineering theories" are simply not the type of stuff that can and
> should appear in fundamental physics. Fundamental physics is meant - and
> so far it has been able to - produce theories that can, in principle, lead
> to arbitrarily precise new predictions once you make a finite number of
> experiments. And this is simply not possible if the parameters are
> functions on [0,1].

This isn't possible unless you have a theory with no free parameters.
This is an ultimate hope of string theorists, but nobody has yet
achieved it (in a theory that describes the universe) and I'm not
convinced it's possible.

> The higher and higher Fourier modes can be compared to something in
> theoretical physics - namely the knowledge of physics at increasingly
> higher energy scales. But it is still true that if you want to describe
> physics at *some* energy scale, you need to know the parameters that
> affect physics at this scale (and lower scales), and the number of such
> parameters must be finite.

We're essentially in agreement here.

> > More relevant to this discussion is t'Hooft's work, which I saw him
> > give a talk on, in which he works with a perturbative expansion of
> > quantum gravity. He showed that low order expansions of perturbative
> > quantum gravity had only a very small number of extra free parameters
> > per order. If we can get by with fifth order expansions in the
> > standard model, and fifth-order perturbative quantum gravity has fewer
> > free parameters than the standard model, why should one be considered
> > predictive and the other not? (I ignore here the small consideration
> > of experimentally reaching the predictive domain of the theory :-) )
>
> It's a question of principle. If they have the same number of parameters
> up to some precision, it is fine, and anyone can use them - but the most
> important fact continues to be that the full Standard Model is consistent
> to all orders and it has a finite number of parameters to all orders,
> Well, it's very paradoxical that you mention 't Hooft as a sort of support
> for your strange statement; it is paradoxical because 't Hooft got his
> Nobel prize EXACTLY for having proved that the number of parameters in the
> Standard Model that you need up to any order is finite. This is an
> extremely important feature of the Standard Model, which distinguishes it
> from quantized general relativity, and the proof of this feature brought
> 't Hooft and Veltman their Nobel prize.

But after seeing 't Hooft's talk, I think one of his points was that
even non-renormalizable theories with an infinite number of free
parameters, like perturbative quantum gravity, actually have some
predictive power, and that physicists shouldn't dismiss them
out-of-hand as unworthy of consideration, because they could actually
lead to some insight.

> I think that 't Hooft's Nobel prize should convince you that if you don't
> see the huge difference between a renormalizable and a nonrenormalizable
> theory, you are missing something very important!

I do see the difference.

> Consequently, your engineering theory,
> if extrapolated into a complete theory, has infinitely many parameters -
> which is what you admitted at the very beginning - and from a fundamental
> physics point of view, it is not a predictive theory.

I don't know what you mean by predictive here. This theory, once
refined by enough experiments, will predict the results of other
experiments, and the difference between this and a finite-parameter
theory is how much refinement is needed before predictions can be
made. There's also the question you bring up of how well experiments
made in one experimental domain of the theory will predict results
from another experimental domain of the theory. I feel sure that one
can come up with a version of my toy model where they will, so I don't
think this is a fundamental distinction between finite-parameter and
infinite-parameter theories.

> This is the whole
> purpose of theoretical physics, to be reducing the number of independent
> ingredients that are necessary to describe an increasing body of
> observations!

I would disagree. The whole purpose of theoretical physics is to come
up with models that better and better describe and predict behavior
of the real physical world. The discovery of the Standard Model was a
remarkable scientific advance. That it simultaneously greatly
reduced the number of free parameters in our theories and greatly
increased the accuracy of our experimental predictions is due to the
amazing fact that all of our experiments back then (and nearly
all of our experiments even now) can be almost exactly described by a
quantum field theory with 19 free parameters. The belief that all
of physics can be described by a theory having even fewer parameters
is a profound (and probably philosophically unjustifiable) faith in
the simplicity of the laws of physics.