# Mathematical way of testing this statement?

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i dare say i will be jumped on from a great hight for this statement but here goes anyway
if spacetime has structure as predicted in LQG then anything traveling
through this structure should have a different speed than in a pure vacuum without gravitational effects, the problem i see is unless one can construct a perfect vacuum without gravitational effects how can it be tested?
is there a mathmatical way of testing this statement?

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Originally posted by wolram
i dare say i will be jumped on from a great hight for this statement but here goes anyway
if spacetime has structure as predicted in LQG then anything traveling
through this structure should have a different speed than in a pure vacuum without gravitational effects, the problem i see is unless one can construct a perfect vacuum without gravitational effects how can it be tested?
is there a mathmatical way of testing this statement?

It seems to me that your questions are often both intuitive and very much on target, or anyway agree with my own notions of what is interesting.

It sounds like what you are describing is "dispersion relations" which are variations in the speed of light based, e.g., on energy.
This is actually a place where at least some version of LQG could be shot down.

There is a short June 2003 paper on this
"Comments on Challenges for Quantum Gravity"
Perez and Sudarsky
arxiv.org/gr-qc/0306113

In an odd way, one wants a theory to be vulnerable to disproof by experimental evidence, and is always looking for predictions that might be shown false. Because a physical theory that has no chance of being proven false is meaningless! The guts of a theory are in the falsifiable predictions and a model that makes no such predictions is mere mathematical fantasy and thumb-twiddling.

LQG has in fact recently begun to face observational tests in the area of dispersion relations. Perez Sudarsky have this two-page paper and the first sentence is eerily in line with what you said.

"There has been recently a great deal of interest in possible modifications of the dispersion relations for ordinary particles that might be the result of quantum gravitational effects."

They mean to include light, and the first case they consider is photons of light. And "dispersion relations" means a spread in speeds related to energy.

It is a complicated issue, or so it seems to me, and there is no simple answer. There is a related issue of LQG's "energy-momentum relation". Whatever version of the theory passes the "dispersion relations" test will then meet a test of its energy momentum relation. I have seen hopes expressed that this part of testing could be feasible sometimes within the next 5 years.

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planned experimental tests

Wolram you've raised a really crucial issue. I found a relevant passage about this on pages 17, 18 of a recent paper ("How far are we from a quantum theory of gravity?") by Smolin, posted March 2003.

It is a nitty-gritty point of disagreement between LQG and string
http://arxiv.org/hep-th/0303185 [Broken]

The two theories can be expected to duke it out around the issue of "lorentz", or "poincare" (basically they mean special relativity-type) symmetry at very small scale. String bets are placed on perfect special-rel symmetry down to the smallest scale---LQG bets are on deviating from that perfect flatness or evenness at some point down near Planck scale.

He gives numbered references to planned experimental tests.
The equation here is the famed "energy-momentum relation"
that goes back to Einstein 1905. Energy is E and momentum is p.
And a couple of miniscule correction terms are stuck in which some people hope turn out to be flat zero and others wouldn't mind if arent quite:

<<...Loop quantum gravity makes specific predictions ...

It turns out that this has consequences for the question of whether special relativity, and lorentz invariance, is exactly true in nature, or is only an approximation which holds on scales
much longer than the Planck scale[28]-[40]. Several recent calculations, done with different methods[36]-[38], yield predictions for modifications to the energy momentum relations for elementary particles. These are of the form,

E2= p2 + M2+ &alpha; lPl E + &beta; lPl2 E4 + ...

where predictions have been found for the leading coefficients &alpha;, which generally depend on spin and helicity[36]-[38].

This is then an area of disagreement with string theory. Further, these modifications appear to be testable with planned experiments[28, 30, 39, 40].

Hence the different predictions of string theory and loop quantum gravity concerning the fate of lorentz invariance offer a
possibility of experimentally distinguishing the theories in the near future...>>

Wolram as you may know or guess, in a perfect special relativity flat Minkowsky world the alpha and beta in the equation up there would be naughts. The suspected corrections are extremely small because, as you can see in the formula, they have the Planck length (lPl) in them. But apparently some people expect they are there and have plans to look for them.

There is an curious paper by a string theorist Tom Banks where he says perfect "poincare" invariance cannot be realistic (because space is known to be curved, bumpy, not flat) and he sounds kind of frustrated with string theory because he doesn't see it evolving away from strict poincare invariance. I posted the first few paragraphs of Tom Banks paper recently in another thread. Rigid flat perfection and absolute zero in the energy-momentum relation could be good, could be bad. A cliff-hanger.

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what he says immediately after that

Here's a continuation of that, on page 18 of the paper. Hope not posting too much about this, it seems like a central issue:

<<4. The near term experimental situation

The most important development of the last few years in quantum gravity is the realization that it is now possible to probe Planck scale physics experimentally. Depending on dynamical assumptions there is now good experimental sensitivity to the &alpha; terms in [the energy-momentum relation] for photons, electrons and protons. Increased sensitivity is expected over the next few years from a number of other experiments so that it is not impossible that even if the leading order E3 terms are absent, it will be possible to put order unity bounds on &beta;, the coefficient of the E4 term.

However it is crucial to mention that to measure &alpha; and &beta; one has to specify how lorentz invariance is treated in the theory. There are two very different possibilities which must be distinguished.

• Scenario A) The relativity of inertial frames is broken and there exists a preferred frame. In this case the analysis has to be done in that preferred frame. The most likely assumption is that the preferred frame coincides with the rest frame of the cosmic microwave background. In such theories energy and momentum conservation are assumed to remain linear.

• Scenario B) The relativity of inertial frames is preserved, but the lorentz transformations are realized non-linearly when acting on the energy and momentum eigenstates of the theory. Such theories are called modified special relativity or doubly special relativity. Examples are given by some forms of non-commutative geometry, for example, &kappa; - Minkowski spacetime[32]. In all such theories energy and momentum conservation become non-linear which, of course, effects the analysis of the experiments. In some, but not all, cases of such theories, the geometry of spacetime becomes non-commutative.

Among the experiments which either already give sufficient sensitivity to measure &alpha; and &beta;, or are expected to by 2010 are...>>

He then gives 10 or so instances of near-term observational tests, some of which have already been made. Scenario B seems to survive but scenario A seems (as I would guess) pretty much ruled out.

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hi MARCUS, from my poit of view string theory is dead, i believe some
theorists are hanging on to M theory in the hope that it gives a result similar to QLT but from a different perspective
i was thinking, it is stated that gravity cannot be shielded,as
QLT deals with plank size loops, it seems to me that it would be imposible to shield against it because it is "everywhere"
i canot get to the link you gave "page not available"
iam hopfull that some solid data will soon be forthcomming from QLT
many thanks wolram

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Originally posted by wolram

i canot get to the link you gave "page not available"
iam hopfull that some solid data will soon be forthcomming from QLT
many thanks wolram

Thank you for pointing that out. I pasted it in wrong at first and believe it will work now.

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thanks for link MARCUS, its going to take me ages to digest this lot
there are things in it i do not understand yet but I am determined to
plod through it "wheeler dewitt equation"? think i will print it all
cheers...

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Originally posted by wolram
thanks for link MARCUS, its going to take me ages to digest this lot
there are things in it i do not understand yet but I am determined to
plod through it "wheeler dewitt equation"? think i will print it all
cheers...

I am a bit uneasy about your going to the trouble of printing out
that long paper. I am in a bind about giving links to papers---there are only a very few whole papers that I would actually RECOMMEND.
A lot of papers are just too long, with too many formulas.
Maybe I should try to make a short list of LQG papers that are short and to the point---and somehow mathematically efficient.
It would not be an easy list to make.

The worst LQG paper of all, I think, is Thiemann's 286-page "Introduction to Modern Canonical Quantum General Relativity".
Yet people go on recommending that other people read it.
Someone named "fando" here at PF was recently advised to go read Thiemann. IMHO Thiemann writes a lot of equations but does not seem as insightful as either Ashtekar or Rovelli. Or Smolin for that matter! So a whole telephone book of Thiemann is an awful thing to contemplate.

Just now in the case of Smolin's paper I sort of had to give a reference to it (although it's really too long to ever read thru) because of the clear explanation on pages 17 and 18 of that one issue.

I don't like to seem to state things on my own say-so! So if I assert something and can give a reference to something on line, I often will----even tho I wouldn't put the entire paper on my short list of goodies.

Or maybe I would. It is recent (2003) and has a lot of interesting stuff. But 90 pages! It seems like he could have condensed it down.

If this model of spacetime is not shot down by experimental evidence, the writing in it is going to get much more efficient and elegant in the next few years, I believe. This can happen in a new field when people begin to teach courses and get inspired to search for ways to explain things.

Well, the good thing is you can look at Smolin online and decide for yourself if it is worth printing out.

Best regards,

Marcus

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This contains interesting commentary!
post by jeff 5:38 or so

quote:
--------------------------------------------------------------------------------
Originally posted by wolram
if spacetime has structure as predicted in LQG then anything traveling
through this structure should have a different speed than in a pure vacuum without gravitational effects
--------------------------------------------------------------------------------

The cumulative effects of the scattering of light by the "nodes" of any discrete spacetime geometry - whether or not it's described by LQG - may be detectable in photons that have traveled over sufficiently great distances (of course other particles would be effected too, but the effect would be more difficult to observe than with cosmological photons). These are the dispersive effects mentioned by marcus (though the relation is between energy and momentum, not speed) and represent the violations of lorentz invariance expected in any theory which - like LQG - describes spacetime geometry as discrete.

quote:
--------------------------------------------------------------------------------
Originally posted by wolram
is there a mathmatical way of testing this statement?
--------------------------------------------------------------------------------

The only putative theory of discrete spacetime geometry we have is in fact LQG, and though numerous suggestions have been made, it's not yet known precisely how to include in it other particles so that calculations of the scattering effects mentioned above, for example, can at this point be performed only on a heuristic level with trust in them being guarded, as they should be.

Now, what was the raison d'etre of the Perez-Sudarsky paper marcus discusses? Well, we know that theories like strings and LQG must yield to approximation at lower energies by their LEEFTs (low energy effective field theories). For LQG to be correct, it's LEEFT must contain GR, however it's not yet known if this is the case. Speculation about the possible low energy behaviour of LQG has given rise to a number of conjectural LEEFTs. The thing is that in order to correspond to theories which like LQG describe spacetime geometry as discrete, the actions of these LEEFTs must include terms that - as mentioned above - break lorentz invariance. So any attempt to argue in general effective field theoretic terms that violations of lorentz invariance can always be suppressed throws into doubt any theory of discrete spacetime geometry like LQG. It was precisely to rebuff a specific such claim made in the paper given as ref[2] that the Perez-Sudarsky paper was written and in doing so they also increased the stringency of the bound on Lorentz violation.

Now I want to point out a somewhat subtle - from your point of view anyway - but relevant point made in Perez-Sudarsky. Firstly, when one realizes that it implies the existence of preferred frames of reference, lorentz noninvariance can seem a rather unlovely feature of theories like LQG. However, even though a theory's equations may not be lorentz invariant, it's conceivable that the physical spectrum can be constructed to consist of only lorentz invariant states (this can be viewed as a kind of converse of spontaneous symmetry breaking in gauge theories). This means that the failure to observe violations of lorentz invariance may not all by itself rule out theories like LQG.

quote:
--------------------------------------------------------------------------------
Originally posted by wolram
...from my poit of view string theory is dead...
--------------------------------------------------------------------------------

Do you honestly feel sufficiently confident in your knowledge of the string theory program to make that sort of blanket unqualified rejection?

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no preferred frame in "Scenario B"

Wolram, I want to repeat something from my post of 11 AM this morning, and emphasize it because it seems important---the no preferred frame idea, or preserving the "relativity of inertial frames" as he calls it. It seems to be connected with one possible way of handling the nonlinear modification in the energy-momentum relation that comes from microscopic discreteness:

However it is crucial to mention that to measure &alpha; and &beta; one has to specify how lorentz invariance is treated in the theory. There are two very different possibilities which must be distinguished.

• Scenario A) The relativity of inertial frames is broken and there exists a preferred frame. In this case the analysis has to be done in that preferred frame. The most likely assumption is that the preferred frame coincides with the rest frame of the cosmic microwave background. In such theories energy and momentum conservation are assumed to remain linear.

• Scenario B) The relativity of inertial frames is preserved, but the lorentz transformations are realized non-linearly when acting on the energy and momentum eigenstates of the theory. Such theories are called modified special relativity or doubly special relativity. Examples are given by some forms of non-commutative geometry, for example, &kappa; - Minkowski spacetime[32]. In all such theories energy and momentum conservation become non-linear which, of course, effects the analysis of the experiments. In some, but not all, cases of such theories, the geometry of spacetime becomes non-commutative.

Your expressing interest in the Smolin paper prompted me to re-read parts of it. I'm finding it better-written and more understandable than before. Earlier maybe I misjudged the paper's merits. Now I'm glad I printed it out.

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Originally posted by marcus
There is an curious paper by a string theorist Tom Banks where he says perfect "poincare" invariance cannot be realistic (because space is known to be curved, bumpy, not flat) and he sounds kind of frustrated with string theory because he doesn't see it evolving away from strict poincare invariance.

Okay, I think I've discovered the source of your conviction that strings admit only flat backgrounds. Consider the following two (appropriately parsed) quotations from page 1 of tom's paper:

"Traditional string phenomenology...[asks] for an exact solution of a purported theory of everything, which exhibits exact Poincare symmetry..."

"There are many...families of Poincare invariant solutions of string theory."

In both cases, tom is speaking only of the poincare invariant sector of the moduli space of possible backgrounds of string theory. As I've mentioned, the entire moduli space must include general curved spaces. If we make the "formal" identification "TOE = QFT+GR+?", then the above may be viewed as analogous to the way that although traditional particle phenomenology is studied using QFT on flat backgrounds, the gravitational field equations of GR still admit general curved solutions.

Also, consider - and you may have been aware of this but failed to make the connection - that the LEEFTs of strings are supergravity theories which of course could never arise from a theory whose backgrounds are all flat.

The balance of the paper reviews how the issues tom raises might be addressed.

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hi jeff, to answer your last comment, i have to say I am not qualified
to say anything as sutch to any learned person in away that discounts
there brilliant work, i think i have already said in other posts that" i am just a pleb", the only quality i can assign myself is good intuition, which tells me that string theorists have created a theory that only a few understand in its entirity and seems to me to be detatched from the real world, you may think i am stupid "i do myself somtimes", but to me the theory that will survive will be the one that explians our universe without the complexity of multiple dimentions,
if people as yourself have patience with people like me it may help to bring science to the masses and encourage better understanding.
cheers.

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Originally posted by wolram
hi jeff, to answer your last comment, i have to say I am not qualified
to say anything as sutch to any learned person in away that discounts
there brilliant work, i think i have already said in other posts that" i am just a pleb", the only quality i can assign myself is good intuition, which tells me that string theorists have created a theory that only a few understand in its entirity and seems to me to be detatched from the real world, you may think i am stupid "i do myself somtimes", but to me the theory that will survive will be the one that explians our universe without the complexity of multiple dimentions,
if people as yourself have patience with people like me it may help to bring science to the masses and encourage better understanding.
cheers.

I fully appreciate your sentiments. I haven't really discussed string theory much because people here are more interested in LQG and I think studying LQG provides good opportunities to learn about all kinds of physics in a very interesting and not too difficult to understand setting.

As time goes on, I'll introduce people here to various aspects of string theory which I think are also very interesting and as with LQG provide good opportunities to learn some pretty neat physics. Also, you'll come to understand better why most high energy theorists find string theory so compelling.

I hope to eventually address the half-truths in terms of which both string theory and LQG are portrayed by people like lee smolin.

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Tom Banks' paper in close agreement w/Smolin p.52

Banks' critique applies to string theory in general, not merely "traditional"---

"Balance" of paper (after the quote from page 1) not directed towards suggesting how to repair trouble. Critique still going strong on page 30.

Banks' critique bears out Smolin (e.g. page 52 of March 2003 paper).

Word "traditional" in second sentence does not apply to the rest---it is for historical perspective, why theory began the way it did. Note that in abstract his argument is not limited to traditional
but applies to "M theory" another name for general stringery:

-exerpts from Tom Banks' paper--------
June 9, 2003

A Critique of Pure String Theory: Heterodox Opinions of Diverse Dimensions
T. Banks
Department of Physics and Institute for Particle Physics
University of California, Santa Cruz, CA 95064
and
Department of Physics and Astronomy, NHETC
Rutgers University, Piscataway, NJ 08540
E-mail: banks@scipp.ucsc.edu

ABSTRACT
I present a point of view about what M Theory is and how it is related to the real world that departs in certain crucial respects from conventional wisdom. I argue against the possibility of a background independent formulation of the theory,...

1. Introduction: The Conventional Wisdom

String theory, although it is a theory of gravity, is a creation of particle physicists. Traditional string phenomenology shows its pedigree by asking for an exact solution of a purported theory of everything, which exhibits exact Poincare symmetry (a symmetry which is clearly only approximate in the real world). This theory is supposed to describe the scattering of particles in the real world, which is thus postulated to be insensitive to the cosmological nature of the universe.

The basis for this assumption is locality, a property that is evidently only approximately true of string theory at low energy. Super Planckian scattering is dominated by black hole production, and the spectrum and properties of black holes of sufficiently high energy are definitely affected by the global structure of the universe. By continuity, there are effects on low energy physics as well. The only question is how large they are.

At any rate, a principal defect of this approach is that it already postulates two mathematically consistent solutions of the theory of everything, namely the real, cosmological, world, and the exact Poincare invariant solution. In fact, as is well known, the situation is much worse than that. There are many disconnected continuous families of Poincare invariant solutions of string theory. They have various dimensions, low energy fields, and topologies, but they all share the property of exact SUSY. The program of string phenomenology is to find a SUSY violating, Poincare invariant solution of the theory, which describes low energy scattering in the real world. In [2] I expressed the opinion that no such solution exists.

...The theory of the real world has a finite number of states and can be neither Poincare invariant, nor supersymmetric. Since the number of states in the real world is exp(10120), it would not be surprising to find that some of the properties of the real world are well approximated...

...[later in the same section, on page 6]...
The above discussion, and [12] make it clear (to me at least) that the old dream of background independence in string theory is a chimera...

----------end of quotes from Tom Banks------

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key quote from Smolin, in line with Banks

[he is doing a side-by-side comparison of the situations of stringery and loopics and has finished discussing ways LQG could be disproved or fail to achieve a quantum theory of gravity, here he does the parallel thing with string theory]

----from Smolin paper page 52---

I ended the section on loop quantum gravity by indicating how the approach is most likely to fail. Some of the ways that string theory could fail, given present knowledge, include,

• String theory could fail if there turn out to be no consistent and stable string vacua consistent with all the observed features of our universe including complete super-symmetry breaking, the absence of massless scalar fields and a positive cosmological constant.

• Conversely, string theory could fail if it turns out that there are so many consistent and stable string vacua consistent with all observations to date that they populate the space of post-standard model physics densely enough that the theory makes no predictions for future experiments.

• String theory could also fail for theoretical reasons. For example, it may turn out that it lacks both a perturbative defintion, if perturbative finiteness fails past genus two, and a complete non-perturbative definition (if, for example, all attempts to construct non-perturbative regularizations of supersymmetric Yang-Mills and string theories are subject to fermion doubling problems that break supersymmetry.)

It is also possible that string theory could pass these tests, but one or more of the open conjectures could fail, leading to a different physical picture than is widely believed. For example, we may note that the present evidence is consistent with the following pessimistic conjecture...

-----end of quote----

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I'm not inclined to take what jeffery says at face value because
of tendency to misrepresent (eg recent characterization of Banks paper) and use obfuscation ("snow-job" replete with jargon and name-dropping) in the service of cant.

Also seems to understand things mostly on a superficial verbal level, as e.g. an English Lit/creative writing major might (if mimicking how he thinks real physicists sound). Impressive verbal intelligence. But no right to claim authority or to (as just now with wolram) play the bully----"do you really know enough to express an opinion, little man". A real physicist would not talk like that, only a phony pretending to be one. In my modest opinion anyway.

But that said, even tho string theory seems to be a dead horse (as wolram indicated) and not very interesting, it DOES seem interesting how closely Smolin March 2003 and Banks June 2003 papers agree on the main string troubles

A combination of no realistic theories and too many theories.

A key thing is a realistic theory must break supersymmetry (SUSY) at the everyday level because the real world does not exhibit supersymmetry. Both writers are concerned that the string groundstate (vacuum = basic ground state-----the model of plain "empty" space) seems unrealistic in this respect.

Another is that real nature has no massless scalar fields. Both writers appear concerned that string theories (there always seem to be a bunch of them) predict these, etc.

Another thing Banks is concerned with is the absence of a background independent non-perturbative theory (he says such a hoped-for thing is a "chimera"). the theories are based on
a perfectly flat conventional spacetime ("minkowski" space, with
"poincare" symmetry, what namedroppers we all are and I mean all not just stringers) which is then "perturbed" to put some realistic bumps in it. This "perturbative" approach worries Banks
and he is also worried by the dependence on perfect poincare symmetry which he says is not a feature of nature. He seems bothered by this way of starting off even if you put some bumps in later---rightly or wrongly he sees it as an unrealistic foundation.
Not something to be glossed over. The essential conservatism
(like Ptolemy, add more epicycles and force the old model to work) of that approach as opposed to trying for a fundamentally new model of space and time.

I will try to link up the two papers. Must say that Banks paper does shed light on what Smolin is talking about. Both know string from inside----Smolin's published string papers as well as LQG.

----from Smolin paper page 52---

• String theory could fail if there turn out to be no consistent and stable string vacua consistent with all the observed features of our universe including complete super-symmetry breaking, the absence of massless scalar fields and a positive cosmological constant.

• Conversely, string theory could fail if it turns out that there are so many consistent and stable string vacua consistent with all observations to date that they populate the space of post-standard model physics densely enough that the theory makes no predictions for future experiments.

• String theory could also fail for theoretical reasons. For example, it may turn out that it lacks both a perturbative defintion, if perturbative finiteness fails past genus two, and a complete non-perturbative definition (if, for example, all attempts to construct non-perturbative regularizations of supersymmetric Yang-Mills and string theories are subject to fermion doubling problems that break supersymmetry.)

It is also possible that string theory could pass these tests, but one or more of the open conjectures could fail, leading to a different physical picture than is widely believed. For example, we may note that the present evidence is consistent with the following pessimistic conjecture...

-----end of quote----

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Originally posted by marcus
Banks' critique applies to string theory in general, not merely "traditional"

You dropped the key word:

A theory and it's associated phenomenology are related but separate things. When you say phenomenology you're talking about the space of solutions to the equations of the theory, not the equations themselves. Some solutions will be poincare invariant and those are the ones we traditionally use since it's only in those cases that spin and mass are globally defined. But the rest of the solutions - in this case of string theories - are curved.

Just pick up a book on strings and have a look.

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My point is that you gave a distorted gloss of Banks paper in your post just now, with the emphasis on traditional which you added. Unreliable. Wastes time.

Originally posted by jeff
Okay, I think I've discovered the source of your conviction that strings admit only flat backgrounds. Consider the following two (appropriately parsed) quotations from page 1 of tom's paper:

"Traditional string phenomenology...[asks] for an exact solution of a purported theory of everything, which exhibits exact Poincare symmetry..."

"There are many...families of Poincare invariant solutions of string theory."

In both cases, tom is speaking only of the poincare invariant sector of the moduli space of possible backgrounds of string theory. As I've mentioned, the entire moduli space must include general curved spaces. If we make the "formal" identification "TOE = QFT+GR+?", then the above may be viewed as analogous to the way that although traditional particle phenomenology is studied using QFT on flat backgrounds, the gravitational field equations of GR still admit general curved solutions.

Also, consider - and you may have been aware of this but failed to make the connection - that the LEEFTs of strings are supergravity theories which of course could never arise from a theory whose backgrounds are all flat.

The balance of the paper reviews how the issues tom raises might be addressed.

Originally posted by marcus
My point is that you gave a distorted gloss of Banks paper in your post just now, with the emphasis on traditional which you added. Unreliable. Wastes time.

I didn't mean to distort or waste time, but do you see my point? Why is it that you're polite with everyone else, but with me you insist on being rude always reading the worst of intentions into my posts? I could have easily said that you're distorting things too, but I don't believe that you are, you're just posting what you believe to be true, which is fine with me. Why can't my posts be fine with you in this way?

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Okay, I think I've found the origin of your remarks about strings, time-dependent backgrounds and cosmology.

On page 48 of smolin's "How far are we from the quantum theory of gravity?" we find the following remark:

"So far no string theory background is known which is time dependent, as is our universe."

In theories like LQG which are based on a (3+1)-dimensional canonical decomposition of spacetime, we have the idea of a spatial hypersurface whose evolution is parametrized by a time coordinate. As you know, cosmological models are typically framed in terms of this sort of noncovariant picture. In string theory however, although moduli space runs over generally curved spacetimes, there is no generally accepted way of making this sort of decomposition so string cosmology cannot be studied in the traditional way.

Again, just pick up a book on string theory and you'll find it filled to the brim with curved spacetime.

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-exerpt from Tom Banks' paper----
ABSTRACT
I present a point of view about what M Theory is and how it is related to the real world that departs in certain crucial respects from conventional wisdom. I argue against the possibility of a background independent formulation of the theory,...
----end of exerpt-----

Also one of Smolin's concerns. Point of LQG and efforts in general to quantize GR is to start with a blank slate---no predetermined idea of spacetime..letting the geometry be free from the start.
this makes the theory independent of preconceived background spacetime.

-----another Banks quote (Im trying to link up the two papers---
...[later, on page 6]...
The above discussion, and [12] make it clear (to me at least) that the old dream of background independence in string theory is a chimera...
------end quote----

lack of background indenpendence major concern of Banks, not just a hangnail limited to some "sector". infects whole theory at level of foundations----tho can perturb to add realistic looking bumps never really get away from foundations

attempts to model black holes (calculate temp and entropy) done in flat space! must irk Banks since he likes black holes.

-----another Banks quote-----
String theory, although it is a theory of gravity, is a creation of particle physicists. Traditional string phenomenology shows its pedigree by asking for an exact solution of a purported theory of everything, which exhibits exact Poincare symmetry (a symmetry which is clearly only approximate in the real world). This theory is supposed to describe the scattering of particles in the real world, which is thus postulated to be insensitive to the cosmological nature of the universe.
-----end quote----

Comparing theory's predictions with real world phenomenon is absolutely essential. The subject implied by "This theory" is string theory----not some "sector". Try deleting the second sentence, which is about the historical roots of string theory (in particle theory rather than in general relativity---gravity---spacetime etc).

"String theory, although it is a theory of gravity, is a creation of particle physicists...This theory is supposed to describe the scattering of particles in the real world, which is thus postulated to be insensitive to the cosmological nature of the universe."

---further Banks quote---
At any rate, a principal defect of this approach is that it already postulates two mathematically consistent solutions of the theory of everything, namely the real, cosmological, world, and the exact Poincare invariant solution.
----end quote---

Too many "sectors" too many conflicting predictions. Real world on one hand, perfect flatspace Poincare symmetry on the other.

-------further Banks quote--------
In fact, as is well known, the situation is much worse than that. There are many disconnected continuous families of Poincare invariant solutions of string theory. They have various dimensions, low energy fields, and topologies, but they all share the property of exact SUSY.
------end of quote-----

Supersymmetry SUSY not shown in everyday real world. Goal is to find SOME version of string theory making reasonable testable predictions about real world phenomenon.

---further Banks quote-----
The program of string phenomenology is to find a SUSY violating, Poincare invariant solution of the theory, which describes low energy scattering in the real world. In [2] I expressed the opinion that no such solution exists.
-----end of quote----

Then the problem is if you have something with so many versions and so many tunable parameters that you can get SOME version to fit, what do you do with all the other versions? Too much flexibility can be an embarrassment. To be really testable---to have meaning----a theory must make inevitable predictions that can be falsified by observation. I.e. it cannot be so mushy that it predicts anything you want it to by going to another version or another sector or adding a few more branes. That is like Ptolemaic earth-centered model where you just have to add on more epicycles to get it to work in an ad hoc fashion.

Compare Smolin page 52:

-----quote from Smolin-----
I ended the section on loop quantum gravity by indicating how the approach is most likely to fail. Some of the ways that string theory could fail, given present knowledge, include,

• String theory could fail if there turn out to be no consistent and stable string vacua consistent with all the observed features of our universe including complete super-symmetry breaking, the absence of massless scalar fields and a positive cosmological constant.

• Conversely, string theory could fail if it turns out that there are so many consistent and stable string vacua consistent with all observations to date that they populate the space of post-standard model physics densely enough that the theory makes no predictions for future experiments.

• String theory could also fail for theoretical reasons. For example, it may turn out that it lacks both a perturbative defintion, if perturbative finiteness fails past genus two, and a complete non-perturbative definition (if, for example, all attempts to construct non-perturbative regularizations of supersymmetric Yang-Mills and string theories are subject to fermion doubling problems that break supersymmetry.)

It is also possible that string theory could pass these tests, but
one or more of the open conjectures could fail...

----end quote----

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Originally posted by jeff
Okay, I think I've found the origin of your remarks about strings, time-dependent backgrounds and cosmology.

On page 48 of smolin's "How far are we from the quantum theory of gravity?" we find the following remark:

"So far no string theory background is known which is time dependent, as is our universe."

My remarks, and understanding, not based on Smolin's paper. And no, you have not "found their origin". Can recommend papers by Ashtekar and Rovelli if you want.
Would be surprised if you did not understand idea of (spatial, not time) background independence. So basic. Thiemann LivingReviews article which you recommended someone read (!) is much more emphatic than Smolin about this and argues string invalid on the issue of failing to be background independent. Smolin more objective and balanced, or at least more polite, than the article of Thiemann you recommended.

But since you quote from Smolin's page 48 you prompted me to take a look at it. I don't like quoting out of context so that an isolated sentence often gets misinterpreted. Let's quote the whole Smolin passage (c. page 48) that you pulled the sentence out of:

6.5 Open issues of string theory

It is clear from the summary just given that there is very good reason to take string theory seriously. The theory appears to give a good perturbative description of quantum gravity through at least the two loop level and, even if this is true also of supergravity theories, this is still a very impressive fact. Many of the results are very impressive, including the ones which show that there exist analogous systems in string theory with the same entropies and temperatures of extremal and non-extremal black holes.

At the same time, there are a large number of open issues.

• There are a very large number of string theory backgrounds, labeled by both discrete topological classes and continuous parameters.

• So far, no string theory background is known which is consistent with all features of the observed universe. They all have one or more of the following features, which each
disagree with observation: no positive cosmological constant, unbroken supersymmetry, massless scalar fields.

• So far no string theory background is known which is time dependent, as is our universe. Further no stable string theory background is known which is consistent with recent
observations that strongly suggest that there is a positive cosmological constant[140].

• Further, we observe no massless scalar fields. Thus in any string background corresponding to nature there can be no such fields. This means that the compactified geometry must be a consistent background only for discrete values of its parameters. At the same time, those parameters must have very small ratios in them, to explain the hierarchy problem.

• Even if a string theory background is found which is also consistent with everything that is observed, does this tell us anything, given that there is an infinite space of possible string backgrounds to search? The theory would be predictive only if there were a unique string background consistent with what is observed. Is there any reason to believe this is the case, rather than there being a large or infinite number of such backgrounds?

So, we should ask, even if there is a unique string theory background consistent with what is observed, how would nature pick it out? One might hope that there were a principle of stability or lowest energy that would pick out a unique string theory background. However this is unfortunately unlikely. We have good reason to believe [ref. 41] that many of the supersymmetric vacua are stable. So it appears very unlikely that the observed background is the only stable one.

Thus, even if string theory is true, there is so far no reason to believe that nature has a unique choice as to low energy phenomenology. Whatever the hopes, present evidence from string theory is more compatible with the idea that the observed background is picked out from many possible consistent ones by some dynamical process, occurring in the early universe, or even before the big bang.

This circumstance suggests that perhaps some attention be given to what might be called the search question in string theory. Given what we know, it is likely that if string theory is true, the real world is described by one out of a very large number of local minima of some potential or energy functional. This may be either a function on the space of string backgrounds or the expectation value of a potential or Hamiltonian in some fundamental Hilbert space of string theory. In either case, we have to find the global minimum of a function on a high dimensional space, which parameterizes possible string backgrounds. Further, we expect that the function has many local extrema, corresponding to the perturbatively consistent string theories. How do we find its global extremum? Further, if the global minimum is to agree with observed physics, there can be no massless moduli fields. This means that the true minimum must be an isolated point in the space of consistent string theories. However, all known consistent string theories have massless scalar fields, this means that all the local minima that correspond to them live in continuous submanifolds of solutions.

How then are we to find the one true, isolated minima of a very complicated potential, which we know has lots of other minima, many of which have much more measure than the solution we seek?

It is fair to ask whether examining them one by one, as they are discovered by people putting together ever more complicated combinations of branes, orbifolds and complex manifolds is likely to hit on the true one. After all, the number of consistent backgrounds vastly outnumbers the number of people working in the field. Should we be concerned that picking out the true minimum of a complex potential with a large number of local minimum is known from results in the theory of computation to be a very hard problem?

A striking result of complexity theory is somewhat worrying in this regard. Called the “no free lunch theorem” this states that no specific search algorithm is likely to do better than random search in finding the global minimum of a randomly chosen complicated potential[168]. To do better than random search, a search procedure must be based on an algorithm which is crafted taking into account some properties of a given potential.

This suggests that if we are ever to find the string vacua that describes our world we need to craft a search algorithm based on some non-trivial property of string theory, rather than just studying more and more complicated string vacua as the tools are developed to define them.

• It must also be emphasized that string theory does not give a genuine quantum theory of gravity, in the sense that each consistent string theory is defined with respect to a fixed, classical, non-dynamical background.

So it is not background independent and it fails to address many of the questions that a quantum theory of gravity must answer...

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Marcus,

Firstly, string theory faces problems that are so incredibly difficult that I doubt I'll see their resolution in my lifetime. Believe me, I'm intimately familiar with the epidemiology of strings. You really don't need to convince me. Eventually, I'll discuss these problems in a way that will leave what few "supporters" of string theory there are here feeling a bit depressed (I get a bit down about this myself from time to time). I just think that strings are closer to the truth than LQG is, it's nothing personal.

Download this very brief introduction to string theory and begin on page 31 section 3.4 on strings in curved backgrounds. This is the perturbative bosonic theory and is not the most general case, but it should take you all of about 5 to 10 seconds to see that we are not restricted to minkowski space in string theory. Hopefully you'll reconsider my interpretation of banks's and smolin's remarks, but if not that's fine, just don't respond with something like "your distorting things on purpose" or "you're basically the anti-christ" etc.

http://xxx.lanl.gov/abs/hep-th/0207249

I appreciated your supportive remark about my answer to wolram's original question. I thought your answer to his question was really good and right on the money. I've edited my original post to reflect that and have added something else. You should take another look at it.

Anyways, in two weeks I'll be taking leave of this forum for about two months, so you have that much time to rally the gang around LQG before I return to "mess everything up" When I get back, I think maybe I'll try starting my own threads like you do, but I'm going to talk about QFT since that seems to be everyone's achilles heel here.

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Edited for diplomatic reasons

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Gold Member
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this post communicates a real person to me and if you start QFT threads as you say you might do later then I would (judging by this post alone) be enthusiastic about reading and maybe putting some questions into the mix in a non-critical way. this is a remarkably nice open-sounding post.

Regards,
Marcus

Originally posted by jeff
Marcus,

Firstly, string theory faces problems that are so incredibly difficult that I doubt I'll see their resolution in my lifetime. Believe me, I'm intimately familiar with the epidemiology of strings. You really don't need to convince me. Eventually, I'll discuss these problems in a way that will leave what few "supporters" of string theory there are here feeling a bit depressed (I get a bit down about this myself from time to time). I just think that strings are closer to the truth than LQG is, it's nothing personal.

Download this very brief introduction to string theory and begin on page 31 section 3.4 on strings in curved backgrounds. This is the perturbative bosonic theory and is not the most general case, but it should take you all of about 5 to 10 seconds to see that we are not restricted to minkowski space in string theory. Hopefully you'll reconsider my interpretation of banks's and smolin's remarks, but if not that's fine, just don't respond with something like "your distorting things on purpose" or "you're basically the anti-christ" etc.

http://xxx.lanl.gov/abs/hep-th/0207249

I appreciated your supportive remark about my answer to wolram's original question. I thought your answer to his question was really good and right on the money. I've edited my original post to reflect that and have added something else. You should take another look at it.

Anyways, in two weeks I'll be taking leave of this forum for about two months, so you have that much time to rally the gang around LQG before I return to "mess everything up" When I get back, I think maybe I'll try starting my own threads like you do, but I'm going to talk about QFT since that seems to be everyone's achilles heel here.

Originally posted by marcus
this post communicates a real person to me and if you start QFT threads as you say you might do later then I would (judging by this post alone) be enthusiastic about reading and maybe putting some questions into the mix in a non-critical way. this is a remarkably nice open-sounding post.

Regards,
Marcus

Sounds great. I'm happy I found a way to strike a positive chord with you. I'll be sure not to forget how while I'm away.

As ever
Jeff.

P.S. It's true that I avoid introducing mathematical notation in my posts. I actually regard papers overflowing with mathematical formalism accompanied by little exposition with suspiscion that the author's are hiding either the fact that their result is trivial or that their understanding of the material is spotty.

In any case, there's in general little need for a lot of symbology here. But if at any time for any reason you'd like to see a more mathematical treatment of a question, just let me know. In fact, you remember those unicode symbols I found. I made macros for all of them and am looking for a good excuse to use them. Unfortunately their use is rarely justified here and I don't think having that kind of fun at the expense of someone else's understanding makes sense (though I'm not sure about that).

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May I ask respectfully, why of this endless discussion about string theory on curved backgrounds? The question (the requirement put mainly by relativists to a quantum-gravity theory) is not flat or curved background, but background independence. Background dependence means to make use of any predefined solution (usually symmetric solution) of the Einstein Equations and to perturbate it, as done in the usual QFT. Of course string theory supports curved backgrounds in the same way as the usual QFT does (see e.g. the derivation of the Hawking radiation for a beatiful application). The question is whether it supports background independence as LQG does, I believe not. The more interesting question might be whether background independence is actually a necessary requirement. I (and may be also others) get more and more the impression that, although all your discussions could be highly interesting, they lead systematically to focus on the wrong issues, mainly due to personal attacks...what a pitty.

Regards.

Gold Member
Dearly Missed
Great clarification, thermonuclear, thank you!

Originally posted by thermonuclear
May I ask respectfully, why of this endless discussion about string theory on curved backgrounds? The question (the requirement put mainly by relativists to a quantum-gravity theory) is not flat or curved background, but background independence. Background dependence means to make use of any predefined solution (usually symmetric solution) of the Einstein Equations and to perturbate it, as done in the usual QFT. Of course string theory supports curved backgrounds in the same way as the usual QFT does (see e.g. the derivation of the Hawking radiation for a beatiful application). The question is whether it supports background independence as LQG does, I believe not. The more interesting question might be whether background independence is actually a necessary requirement. I (and may be also others) get more and more the impression that, although all your discussions could be highly interesting, they lead systematically to focus on the wrong issues, mainly due to personal attacks...what a pity.

Regards.

Actually I have started LQG threads to help me learn more about it and have valued other people's input focused on LQG (which does not distract but helps very much)

I am not looking for debate and regret the distraction it represents.

Various people at PF have helped me learn some LQG by working along with me in threads or making suggestions----Rutwig has stepped in, Chroot has helped, Hurkyl has pulled me out of the ditch several times, various people. You, wolram, somebody named Instanton early on gave a thumbnail sketch of LQG that was very helpful. Sauron obviously knows a lot about LQG.

It is hard enough to plow thru some of these papers without having distractions!

On the other hand if others want to start collective-learning threads about QFT or the Standard Model or M-theory or whatever that is great!

It sounds like Jeff might start a QFT thread further down the road.
I would very much respect and appreciate such an effort---tho could not promise participation---and it is clear that there are a halfdozen or so people here currently studying QFT, eg. Damgo, Tom, or knowledgeable about it, like you probably and Sauron. It could be an outstanding thread. Rutwig, you may have noticed, is savvy beyond any doubt.

I'll try to think about what you said, the substantive thing.
The value of backgr. indep seems obvious to me at the moment
as leading to the discrete spectr. of area and vol operators, and
removing the bigbang singularity, and getting some good black hole numbers and just generally triggering a bunch of progress on several fronts. Also it is an incredible challenge to construct a theory with backgr. indep---this also intrigues me: the fundamental newness and difficulty. But the fact that its value
"seems obvious" to me is also a sign that I should re-examine,
as you suggest. Never should take anything on faith.

Best regards

Originally posted by thermonuclear
The question is whether it [string theory] supports background independence as LQG does, I believe not.

I don't think anyone's arguing that string theory is background independent. The question is whether M-theory will turn out to be background independent. There are clues in string theory that M-theory will be a more intrinsically quantum theoretic framework than strings so that the answer could very well be yes, but nobody knows.

Originally posted by thermonuclear The more interesting question might be whether background independence is actually a necessary requirement.

No argument there, and I'm semi-blown away that you made that point because it seems that most peope here consider background independence a given, but in terms of pure logical possibility - as opposed to plausibility - it's really not.

Originally posted by thermonuclear I (and may be also others) get more and more the impression that, although all your discussions could be highly interesting, they lead systematically to focus on the wrong issues, mainly due to personal attacks...what a pitty.[/B]

You're right and I feel bad about that. Part of the difficulty for me is that I've already learned QFT, string theory, LQG, GR and just about everything else along with all the math so that the problem of how to contribute to the threads dedicated to a combined effort to learn about something without dampening the spirit of the thread has been a bit trickey. Unfortunately those are the threads that interest me most, but as a teacher not a student.

But what am I supposed to do? I don't think it makes sense for me to pretend that anyone here has anything to teach me (though they might). The only alternative is just to stay out of those threads. So either I start my own threads which was not something I initially had any interest in doing, or just leave. The truth is I'm not here to make a contribution. I'm here because I can keep my mind engaged in the kind of low level discussions of physics that help me stay creative in my own research while avoiding having to deal for the same self-serving reasons with students in person who end up taking too much of my time.

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Gold Member
Dearly Missed
with reverance to MARCUS and JEFF i find it difficult to define something if you don't know ALL of its properties, there seems to be
several ongoing arguments as to what gravity is and its properties
and or how it is conveyed
http://space.com/scienceastronamy/gravity-speed-030116html [Broken]
http://www.ldolphin.org/vanFlandern/gravityspeed.html
http://goodfelloweb.com/nature/cgbi/#b
the last link may be "iffy" but its worth a look
MARCUS ,JEFF are there still as many S theorists working on same as of a few years ago?
how about a poll to see who believes what the best theory is?
top link should be-------------gravity-speed-030116html its ok on original but won't post.

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Gold Member
Dearly Missed
Just occurred to me I should probably edit out my earlier post
because it was lacking in reserve and dignity. In fact I was
yakking like a moron. However I did enjoy this link, which I think
I got from you, to an item in "physics news update", about gravity.

http://www.aip.org/enews/physnews/1999/split/pnu454-1.htm [Broken]

I've been going over past physics news update (pnu) things today
and like that website very much. The science writers they have there, doing the short summary reports, are serious and don't waste words just being "journalistic". I see you have pointed to several pnu newsitems. Thanks for the lead.

Marcus

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Gold Member
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What is the simplest evidence that there are more than 4 dimensions?
There is none. All of the 'evidence' is of the theoretical kind, but none of it has been put to the test because...we don't know how! All we know is that our space-time is 4 dimensional to about a few parts per hundred billion based on how well gravity follows 4-D general relativity inside our solar system.

i found this quote by a respected scientist
--------------------------------------------------------------------------------

------------------------------------------------------------------------

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Gold Member
Dearly Missed
Originally posted by wolram
What is the simplest evidence that there are more than 4 dimensions?
There is none. All of the 'evidence' is of the theoretical kind, but none of it has been put to the test because...we don't know how! All we know is that our space-time is 4 dimensional to about a few parts per hundred billion based on how well gravity follows 4-D general relativity inside our solar system.

i found this quote by a respected scientist

That is an interesting quote. I'm curious to know who said it, as I would look them up on the web and see what other things they said. Sometimes I am amazed at how much the internet makes science better---that is, more fun and accessible to a wider audience. (Because one of the most fundamental things science ought to be is fun and accessible to a wider audience, if it is that, then it is better science.) If I hear of a person or an idea then it is highly probable that I can find out more about that idea within 3 minutes, and so on.

You have turned up some interesting stuff on the web, you know what I mean. Its great. And every serious "science watcher" has, I believe, a perfect right to express their opinion. You don't have to play football in order to know the teams and who's winning, just like you don't have to be a horse in order to know the odds.
In fact it probably helps if you are NOT a horse. Outsiders make good watchers. I am talking too much as usual. Well, my wife just came in and told me what I have to do for the next hour or so.
Be back later,

m

Gold Member
Dearly Missed
quote is by Dr Sten Odenwald, I am sorry i don't have a link, i downloaded this in the late nineties, i know i should keep urls