Charlie Stromeyer Jr.
Jun24-04, 08:49 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>Today, there is a new paper on hep-th by T.G. Erler and D.J. Gross\nabout causality, locality etc. in OSFT [hep-th/0406199] which reminds\nme of something:\n\nThe comments I made earlier in this newsgroup in the message below\nabout non-causality are still true for both theoretical and\nexperimetal reasons, i.e. various non-causal phenomena have already\nbeen detected by experimentalists.\n\n[Moderator\'s note: It sounds very exciting, Charlie. ;-)\nCould you please be more specific about the\n"experimentally proved violations of causality"? Is it the Optics\nletter article? Incidentally, the Gross + Erler\npaper, on the contrary, seems to prove the causality of SFT by going\nto the light cone frame - which would explain why the S-matrix\nsatisfies the rules expected from causal and local theories. LM]\n\nHowever, I now want to warn the readers of this newsgroup that my\ndifferent comments below about acausality may or may not be true. This\nis simply because I have discovered since I made these comments that\nthere is even further likely relevant literature which I have not even\nlooked at yet.\n\nFor instance, QED is the most overall accurate scientific theory ever.\nIn a paper about acausality in QED [quant-ph/9802056], the author\nproves in section 5 that photons can exhibit acausal behavior in both\ntime-like and/or space-like (superluminal speed) directions.\n\nAt first, one might suspect that such a result might rule out certain\nideas within string theory such as some ideas about large extra\ndimensions. However, I myself would not make such a hypothesis for\nvarious reasons, e.g. I have not yet looked at any of the recent\npapers about photon propagation in noncommutative QED which of course\nis a different and perhaps more fundamental environment than the usual\ncontext for QED.\n\nSince I don\'t know enough about questions of acausality (at least\nyet), I will now finish what I am saying by reminding you of something\nAlbert Einstein once said which is that "No one really understands the\nnature of the photon". Richard Feynman also said or implied multiple\ntimes that no one really seems to understand QT.\n\nAlthough I do not have enough understanding in this area, perhaps\nthese two great physicists are still correct because, as just one\nexample, it seems (to me at least) that the field of quantum optics is\nstill an active area of research, both theoretically and\nexperimentally, and this field is even having a major conference this\nsummer.\n\nbaez@galaxy.ucr.edu (John Baez) wrote in message news:\n\n> >1) How are such approaches to be made compatible with vector\n> >supersymmetry (or vsusy) which is a topological type of symmetry that\n> >appears in both gravity and topological gauge theories [1].\n>\n> This "vector supersymmetry" is a mathematical feature of certain\n> field theories - not something that anyone has observed experimentally.\n\nOkay, but note that vsusy is an inherent aspect of your type of\napproach to spin foam models of BF theory and quantum gravity as well\nas the Ashtekar action. I discuss this some in post [1].\n\n(Btw, there is also a newer paper about the role of vsusy in a general\nsupergauge which is more general than WZ gauge and here there does not\nneed to be a metric which is nonsingular at every space-time point,\ni.e. the vielbein matrix doesn\'t have to be invertible in superspace\n[2].)\n\n> Nobody has yet constructed a background-free quantum theory that has\n> general relativity as its limit at large distance scales. The Ambjorn-\n> Jurkiewicz-Loll model is the closest anyone has come. If they succeed,\n> this will be of interest regardless of whether their model displays\n> mathematical features that appear in certain other theories!\n>\n> >2) How are such approaches to be made compatible with Bell-like\n> >correlations, non-locality and non-causality which are each present in\n> >the experiment described in this brief four page paper [2].\n>\n> As a quantum theory, the Ambjorn-Jurkiewicz-Loll model automatically\n> has Bell-like "entanglement" and all that jazz.\n\nAt first, I thought that the AJL model must be flawed for reasons\nmentioned in post [1], however, this may no longer be the case because\nthere are two recent papers which argue for separate reasons that\nsuperluminal signals may actually be compatible with GTR [3].\n\nAs I told Tony Smith in another thread, it will take me some time to\nread more literature and try to understand these issues better, and I\nhave never even read any of the Smolin or Magueiro papers on VSL and\nDSR and so this may take me a few weeks or even two months.\n\n> >3) To paraphrase a sentence that Stephen Hawking once wrote, to not\n> >believe in the beauty and unity of the dualities of M-theory is like\n> >believing that evolution did not occur because instead God placed by\n> >hand all the fossils in the Earth just to play a joke on the\n> >paleontologists :-)\n>\n> We resort to theological arguments in physics only when better arguments\n> are lacking. If a scintilla of experimental evidence for M-theory is\n> ever found, people will instantly stop making arguments of the sort\n> you mention here.\n\nActually, Hawking and I were making an argument which you have also\nmade before, but which is not really an argument so much as a truism:\n\nThousands of years of the history of mathematics have taught us that\nnew and non-trivial math which is beautiful and profound never turns\nout to be completely useless. Why is it that M-theory has contributed\nto or inspired so much variety of important new mathematics? Is this\nmerely some kind of fluke or joke that Nature is fooling people with?\n\nHere is another important point about this issue for critics of string\ntheory such as Peter Woit:\n\nDuring the 1990s, I would occasionally take courses at the Harvard\nExtension School. I was once seeing what a particular course would be\nlike by sitting in the classroom of a mathematical logic course taught\nby the famous logician Gerald Sacks who is now at MIT.\n\nOne student asked a question about the mathematical rigor of\nstring/M-theory. I don\'t remember what her question was but Sacks\nexplained why it is that string theorists have to make things up as\nthey go along, i.e. that there is an unavoidable degree of uncertainty\nand speculation involved in such an ongoing endeavor.\n\n[Moderator\'s note: such a general comment can be equally said\nabout any intellectual activity beyond pure math. It is always\npartly true, and always partly wrong, and it never proves that\nthe speaker knows the subject that he wants to talk about. LM]\n\nI also would guess that Sacks realized something that I realized later\nwhich is that it took about 2,100 years until Hilbert and others\nshowed that classical Euclidean geometry was logically incomplete.\n\n[Moderator\'s note: Peter Woit apparently does not intend to\ndistinguish mathematics and physics. In physics, we don\'t care\nwhether a set of "axioms" is overcomplete. What we care about\nis a sufficient set of rules that can describe Nature, the\nworld around us, and we are slowly getting a better\nunderstanding of the theory underlying Nature as proposed by\nstring theory, much like we were improving our understanding\nof theoretical physics before the age of string theory. LM]\n\nIf string theory turns out to be correct then mathematicians will\nprobably investigate the degree of consistency and completeness of\nstring theory\'s mathematical foundations. In the meantime, it does not\nmake sense to demand too much rigor before the time is ready.\n\n[Moderator\'s note: It will never be a task for physics itself to\ninvestigate some axioms with mathematical rigor - this task\nis strictly dedicated to mathematicians. In mathematical physics,\none can prove that Feynman\'s Minkowski path integral cannot exist\nin the context of the Lebesgue measure...\nThis theorem does not change anything about the fact that the\nphysicists use Feynman\'s path integrals as a complete and\ncompletely satisfactory box of tools to describe many theories,\nfor example QCD. We have the same complete understanding of\nperturbative string theory and non-perturbative string theory\naround certain backgrounds, and we are trying to improve this\nsituation further. LM]\n\nOtherwise, to use Lubos\' analogy, theorists risk being like\nhypothetical 19th century physicists trying to use Newton\'s equations\nto calculate the expansion of the universe.\n\n[Moderator\'s note: I don\'t remember this analogy, but one must\ncertainly be careful and avoid being picky about some details\nin a theory that may be conceptually incomplete. Being picky\nis something that people could have been 3000 years ago - yet,\nit is clear that they were missing something important - well,\nmany important things - and their rigor was nearly worthless,\nmuch like the current attempts to be rigorous can look in the\neyes of a physicist in 2050 who already knows some formerly\nunknown ideas. LM]\n\nFor more on this topic, also see my post in sci.physics.strings in\nreply to the question about "what is OPE?".\n\n> I\'m not saying that M-theory is "wrong" or that the Ambjorn-Jurkiewicz-Loll\n> model is "right". M-theory makes too few definite predictions to be wrong.\n\nThis point is not necessarily true, but I won\'t go on a long spiel\nabout it right now because Lubos, others and I have already discussed\nthis issue in more detail in s.p.s. and there are also plenty of\npapers in the Arxiv about potential tests of QG, including potential\ntests of string theory.\n\n> The AJL model does not include matter, so it cannot be right. But the\n> AJL model is *interesting*, because it represents the best attempt so far\n> to find a background-free quantum theory that reduces to general relativity\n> in the large-scale limit!\n\nOkay, I accept that their model might be interesting and I will now\neven read their paper !-) Btw, the distinction between discrete and\ncontinuous have a variety of different meanings in physics and math,\nand e.g. it was even the great polymath genius, von Neumann, who\ninvented the field of math known as continuous geometry from\nconsidering a series of discrete instances of projective geometry, and\nthis field has since been more generalized.\n\nMy point is that some of the distinctions between discrete vs.\ncontinous may turn out to be somewhat trivial, and this is one reason\nwhy I asked if Ashetkar\'s action might be compatible with the AJL\nmodel in post [1], but I will now also read the AJL paper.\n\n\n[1]\n\nThomas Larsson wrote:\n\n"In the AJL model, the gauge is already fixed;they formulate the\naction in terms of diff-invariant edge lengths rather than the\nmetric, there is a privileged time direction, etc. Since their\nmodel only contains gauge-invariant quantities, there are no\ndiffeomorphism constraints left, and thus no need for ghosts."\n\nHi Thomas, I think you have misunderstood what I wrote and so before I\nread the AJL or Bert Schroer papers let us try to clarify what we are\ntalking about and to make sure that we are considering the same\nconcepts.\n\nDespite the particularities of the specific BV approach to vsusy, it\nis the case that vsusy is an essential part of the origin of\nperturbative finiteness of BF theory, and it helps with the algebraic\nrenormalization of topological YM theory, and vsusy may have a role in\nconstructing physical observables in addition to perhaps being the\nsymmetric origin for the IR safety of topologically massive YM theory\nin Landau gauge.\n\nWell, at least this is more established for CS theory defined on an\narbitrary space-time three-manifold for Landau gauge choice in which\nvsusy is a renormalizable local supersymmetry which derives\nperturbative (UV) finiteness at all orders [1].\n\nIt is also interesting to note that YM field configurations on 3 and 4\ndimensional manifolds generate an effective Riemann-Cartan (in certain\nmodels, Riemann) geometry on a space (or spacetime) and vice versa,\ni.e geometry can yield YM gauge fields. The YM equations can\nperhaps be written without the use of any metric on an arbitrary\nsmooth manifold [2].\n\nHowever, the new AJL paper may also be intriguing because coframe\nmodels can have the problem of allowing the existence of non-physical\nmodes such as ghosts or tachyons [e.g. references 18 and 19 in\nhttp://www.arxiv.org/abs/gr-qc/0111087].\n\nAnyways, the first question I would like to ask before reading this\nnew AJL paper is if their approach is compatible with the Ashtekar\naction?\n\nI ask because the vsusy of 4d Einstein gravity (in the Palantini first\norder formalism) is compatible with the Ashtekar action and may be\ncompatible with any other actions if such actions have the vierbein\nand connection as independent variables and have invariance under\n_active_ diffeomorphisms, i.e. diffeos which act on dynamical fields\nonly, IOW, act quantum mechanically on field operators - the vierbein,\nconnection and matter fields\n[http://www.arxiv.org/abs/hep-th/0005011].\n\n"Causality seems to be the whole point with the AJL approach -\nlack of causality, i.e. singular metrics, is explicitly thrown\nout."\n\nHere we are thinking of different notions of "causality" which I will\nnow start attempting to clarify. Also, before discussing the AJL paper\nfurther we might want to consider the important conundrum I ask about\nat the bottom of this post.\n\n1) For some as yet unknown and hypothetical reason, it might turn out\nto be the case that theorists, e.g. either string theorists, LQG\ntheorists or discretized gravity theorists, will uncover what seems to\nbe a reasonable theory of QG but then for decades not be able to\nfigure out how to make the theory compatible with what we already know\nto exist here at the everyday low energy scale.\n\nHowever, let us presume, for this discussion at least, that a good\ntheory of QG should be inherently compatible with various low energy\nphenomena and then consider the following:\n\n1) Various quantum phenomena have already been demonstrated to be\n"noncausal" both theoretically and sometimes even experimentally. I\nhave been looking at some of this literature recently and so far,\nexcept for the one very important conundrum I ask about below, the\nterm\n"noncausal" means only that there is no discernable and meaningful\ndependence upon causality which is different from the idea that there\nis some kind of explicit violation of Einstein causality via\nsuperluminal signals.\n\nFor instance, experiments with TmYAG crystals have shown that\nstimulated photon ehoes (SPEs) can exist in the noncausal direction\n[3], and separate experiments have shown that the phase and energy of\na photon pulse can travel faster than c, the speed of light in a\nvacuum, but there does not (yet, anyways) seem to be meaningful\ninformation transmitted via superluminal signals due to cancellation\nof such potential superluminal signals because of complicated\ndiffraction and diffusion effects [4].\n\n3) However, now consider the important conundrum:\n\nSuppose that one definition of the presence of "acausality" would be\nthe existence of uncertainty which is clearly non-statistical (or\nnon-probabilistic). Well, this is what happens in the photon\nexperiment decsribed in this brief four page paper\n[http://www.arxiv.org/abs/quant-ph/0102109],\nyet there are no superluminal communications necssarily entailed !\n\nFurthermore, also consider this paper\n[http://www.arxiv.org/abs/quant-ph/9802056] about\nacausality in QED which shows that it is theoretically possible for\nthere to be acausal behavior for photons in both time-like\nspace-like directions.\n\nThomas, since you are from Scandinavia you should heed what the Prince\nof Denmark once said and also do not forget about ghosts :-)\n\n"I will tell you why; so shall my anticipation precede your discovery,\n....."\n\nHamlet, Act II, Scene 3\n\nI will post more later about noncausality and acausality, but in the\nmeantime I will demonstrate the existence of acausality by correctly\nanticipating what you, Thomas, will write in reply to this post before\nyou have even started typing on your keyboard !-)\n\n\n[1] "Local Supersymmetry of the Chern-Simons theory and finiteness",\nC. Lucchesi, O. Piguet, Nucl Phys B 381 (1992) .\n\n[2] "Induced Geometry: Riemann-Cartan from Yang-Mills", Y. Obukhov,\nD. Ivaneko Festschrift, JMS, v5 (1995) .\n\n[3] "Nutational Stimulated Photon Echoes", Optics Letters, v27(iss\n13) (2002), pp..\n\n[4] J.J. Carey et al., Phys Rev Lett, v84(no7) (2000), p.1431.\n\n\n---------- end of post [1] -------------\n\n\n[2] http://arxiv.org/abs/http://www.arx...s/gr-qc/0402036\n\n[3] http://arxiv.org/abs/http://www.arx...s/gr-qc/0304059\n\nhttp://arxiv.org/abs/http://www.arx...s/gr-qc/0403121\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>Today, there is a new paper on hep-th by T.G. Erler and D.J. Gross
about causality, locality etc. in OSFT [http://www.arxiv.org/abs/hep-th/0406199] which reminds
me of something:
The comments I made earlier in this newsgroup in the message below
about non-causality are still true for both theoretical and
experimetal reasons, i.e. various non-causal phenomena have already
been detected by experimentalists.
[Moderator's note: It sounds very exciting, Charlie. ;-)
Could you please be more specific about the
"experimentally proved violations of causality"? Is it the Optics
letter article? Incidentally, the Gross + Erler
paper, on the contrary, seems to prove the causality of SFT by going
to the light cone frame - which would explain why the S-matrix
satisfies the rules expected from causal and local theories. LM]
However, I now want to warn the readers of this newsgroup that my
different comments below about acausality may or may not be true. This
is simply because I have discovered since I made these comments that
there is even further likely relevant literature which I have not even
looked at yet.
For instance, QED is the most overall accurate scientific theory ever.
In a paper about acausality in QED [http://www.arxiv.org/abs/quant-ph/9802056], the author
proves in section 5 that photons can exhibit acausal behavior in both
time-like and/or space-like (superluminal speed) directions.
At first, one might suspect that such a result might rule out certain
ideas within string theory such as some ideas about large extra
dimensions. However, I myself would not make such a hypothesis for
various reasons, e.g. I have not yet looked at any of the recent
papers about photon propagation in noncommutative QED which of course
is a different and perhaps more fundamental environment than the usual
context for QED.
Since I don't know enough about questions of acausality (at least
yet), I will now finish what I am saying by reminding you of something
Albert Einstein once said which is that "No one really understands the
nature of the photon". Richard Feynman also said or implied multiple
times that no one really seems to understand QT.
Although I do not have enough understanding in this area, perhaps
these two great physicists are still correct because, as just one
example, it seems (to me at least) that the field of quantum optics is
still an active area of research, both theoretically and
experimentally, and this field is even having a major conference this
summer.
baez@galaxy.ucr.edu (John Baez) wrote in message news:
> >1) How are such approaches to be made compatible with vector
> >supersymmetry (or vsusy) which is a topological type of symmetry that
> >appears in both gravity and topological gauge theories [1].
>
> This "vector supersymmetry" is a mathematical feature of certain
> field theories - not something that anyone has observed experimentally.
Okay, but note that vsusy is an inherent aspect of your type of
approach to spin foam models of BF theory and quantum gravity as well
as the Ashtekar action. I discuss this some in post [1].
(Btw, there is also a newer paper about the role of vsusy in a general
supergauge which is more general than WZ gauge and here there does not
need to be a metric which is nonsingular at every space-time point,
i.e. the vielbein matrix doesn't have to be invertible in superspace
[2].)
> Nobody has yet constructed a background-free quantum theory that has
> general relativity as its limit at large distance scales. The Ambjorn-
> Jurkiewicz-Loll model is the closest anyone has come. If they succeed,
> this will be of interest regardless of whether their model displays
> mathematical features that appear in certain other theories!
>
> >2) How are such approaches to be made compatible with Bell-like
> >correlations, non-locality and non-causality which are each present in
> >the experiment described in this brief four page paper [2].
>
> As a quantum theory, the Ambjorn-Jurkiewicz-Loll model automatically
> has Bell-like "entanglement" and all that jazz.
At first, I thought that the AJL model must be flawed for reasons
mentioned in post [1], however, this may no longer be the case because
there are two recent papers which argue for separate reasons that
superluminal signals may actually be compatible with GTR [3].
As I told Tony Smith in another thread, it will take me some time to
read more literature and try to understand these issues better, and I
have never even read any of the Smolin or Magueiro papers on VSL and
DSR and so this may take me a few weeks or even two months.
> >3) To paraphrase a sentence that Stephen Hawking once wrote, to not
> >believe in the beauty and unity of the dualities of M-theory is like
> >believing that evolution did not occur because instead God placed by
> >hand all the fossils in the Earth just to play a joke on the
> >paleontologists :-)
>
> We resort to theological arguments in physics only when better arguments
> are lacking. If a scintilla of experimental evidence for M-theory is
> ever found, people will instantly stop making arguments of the sort
> you mention here.
Actually, Hawking and I were making an argument which you have also
made before, but which is not really an argument so much as a truism:
Thousands of years of the history of mathematics have taught us that
new and non-trivial math which is beautiful and profound never turns
out to be completely useless. Why is it that M-theory has contributed
to or inspired so much variety of important new mathematics? Is this
merely some kind of fluke or joke that Nature is fooling people with?
Here is another important point about this issue for critics of string
theory such as Peter Woit:
During the 1990s, I would occasionally take courses at the Harvard
Extension School. I was once seeing what a particular course would be
like by sitting in the classroom of a mathematical logic course taught
by the famous logician Gerald Sacks who is now at MIT.
One student asked a question about the mathematical rigor of
string/M-theory. I don't remember what her question was but Sacks
explained why it is that string theorists have to make things up as
they go along, i.e. that there is an unavoidable degree of uncertainty
and speculation involved in such an ongoing endeavor.
[Moderator's note: such a general comment can be equally said
about any intellectual activity beyond pure math. It is always
partly true, and always partly wrong, and it never proves that
the speaker knows the subject that he wants to talk about. LM]
I also would guess that Sacks realized something that I realized later
which is that it took about 2,100 years until Hilbert and others
showed that classical Euclidean geometry was logically incomplete.
[Moderator's note: Peter Woit apparently does not intend to
distinguish mathematics and physics. In physics, we don't care
whether a set of "axioms" is overcomplete. What we care about
is a sufficient set of rules that can describe Nature, the
world around us, and we are slowly getting a better
understanding of the theory underlying Nature as proposed by
string theory, much like we were improving our understanding
of theoretical physics before the age of string theory. LM]
If string theory turns out to be correct then mathematicians will
probably investigate the degree of consistency and completeness of
string theory's mathematical foundations. In the meantime, it does not
make sense to demand too much rigor before the time is ready.
[Moderator's note: It will never be a task for physics itself to
investigate some axioms with mathematical rigor - this task
is strictly dedicated to mathematicians. In mathematical physics,
one can prove that Feynman's Minkowski path integral cannot exist
in the context of the Lebesgue measure...
This theorem does not change anything about the fact that the
physicists use Feynman's path integrals as a complete and
completely satisfactory box of tools to describe many theories,
for example QCD. We have the same complete understanding of
perturbative string theory and non-perturbative string theory
around certain backgrounds, and we are trying to improve this
situation further. LM]
Otherwise, to use Lubos' analogy, theorists risk being like
hypothetical 19th century physicists trying to use Newton's equations
to calculate the expansion of the universe.
[Moderator's note: I don't remember this analogy, but one must
certainly be careful and avoid being picky about some details
in a theory that may be conceptually incomplete. Being picky
is something that people could have been 3000 years ago - yet,
it is clear that they were missing something important - well,
many important things - and their rigor was nearly worthless,
much like the current attempts to be rigorous can look in the
eyes of a physicist in 2050 who already knows some formerly
unknown ideas. LM]
For more on this topic, also see my post in sci.physics.strings in
reply to the question about "what is OPE?".
> I'm not saying that M-theory is "wrong" or that the Ambjorn-Jurkiewicz-Loll
> model is "right". M-theory makes too few definite predictions to be wrong.
This point is not necessarily true, but I won't go on a long spiel
about it right now because Lubos, others and I have already discussed
this issue in more detail in s.p.s. and there are also plenty of
papers in the Arxiv about potential tests of QG, including potential
tests of string theory.
> The AJL model does not include matter, so it cannot be right. But the
> AJL model is *interesting*, because it represents the best attempt so far
> to find a background-free quantum theory that reduces to general relativity
> in the large-scale limit!
Okay, I accept that their model might be interesting and I will now
even read their paper !-) Btw, the distinction between discrete and
continuous have a variety of different meanings in physics and math,
and e.g. it was even the great polymath genius, von Neumann, who
invented the field of math known as continuous geometry from
considering a series of discrete instances of projective geometry, and
this field has since been more generalized.
My point is that some of the distinctions between discrete vs.
continous may turn out to be somewhat trivial, and this is one reason
why I asked if Ashetkar's action might be compatible with the AJL
model in post [1], but I will now also read the AJL paper.
[1]
Thomas Larsson wrote:
"In the AJL model, the gauge is already fixed;they formulate the
action in terms of diff-invariant edge lengths rather than the
metric, there is a privileged time direction, etc. Since their
model only contains gauge-invariant quantities, there are no
diffeomorphism constraints left, and thus no need for ghosts."
Hi Thomas, I think you have misunderstood what I wrote and so before I
read the AJL or Bert Schroer papers let us try to clarify what we are
talking about and to make sure that we are considering the same
concepts.
Despite the particularities of the specific BV approach to vsusy, it
is the case that vsusy is an essential part of the origin of
perturbative finiteness of BF theory, and it helps with the algebraic
renormalization of topological YM theory, and vsusy may have a role in
constructing physical observables in addition to perhaps being the
symmetric origin for the IR safety of topologically massive YM theory
in Landau gauge.
Well, at least this is more established for CS theory defined on an
arbitrary space-time three-manifold for Landau gauge choice in which
vsusy is a renormalizable local supersymmetry which derives
perturbative (UV) finiteness at all orders [1].
It is also interesting to note that YM field configurations on 3 and 4
dimensional manifolds generate an effective Riemann-Cartan (in certain
models, Riemann) geometry on a space (or spacetime) and vice versa,
i.e geometry can yield YM gauge fields. The YM equations can
perhaps be written without the use of any metric on an arbitrary
smooth manifold [2].
However, the new AJL paper may also be intriguing because coframe
models can have the problem of allowing the existence of non-physical
modes such as ghosts or tachyons [e.g. references 18 and 19 in
http://www.arxiv.org/abs/http://www.arxiv.org/abs/gr-qc/0111087].
Anyways, the first question I would like to ask before reading this
new AJL paper is if their approach is compatible with the Ashtekar
action?
I ask because the vsusy of 4d Einstein gravity (in the Palantini first
order formalism) is compatible with the Ashtekar action and may be
compatible with any other actions if such actions have the vierbein
and connection as independent variables and have invariance under
_active_ diffeomorphisms, i.e. diffeos which act on dynamical fields
only, IOW, act quantum mechanically on field operators - the vierbein,
connection and matter fields
[http://www.arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0005011].
"Causality seems to be the whole point with the AJL approach -
lack of causality, i.e. singular metrics, is explicitly thrown
out."
Here we are thinking of different notions of "causality" which I will
now start attempting to clarify. Also, before discussing the AJL paper
further we might want to consider the important conundrum I ask about
at the bottom of this post.
1) For some as yet unknown and hypothetical reason, it might turn out
to be the case that theorists, e.g. either string theorists, LQG
theorists or discretized gravity theorists, will uncover what seems to
be a reasonable theory of QG but then for decades not be able to
figure out how to make the theory compatible with what we already know
to exist here at the everyday low energy scale.
However, let us presume, for this discussion at least, that a good
theory of QG should be inherently compatible with various low energy
phenomena and then consider the following:
1) Various quantum phenomena have already been demonstrated to be
"noncausal" both theoretically and sometimes even experimentally. I
have been looking at some of this literature recently and so far,
except for the one very important conundrum I ask about below, the
term
"noncausal" means only that there is no discernable and meaningful
dependence upon causality which is different from the idea that there
is some kind of explicit violation of Einstein causality via
superluminal signals.
For instance, experiments with TmYAG crystals have shown that
stimulated photon ehoes (SPEs) can exist in the noncausal direction
[3], and separate experiments have shown that the phase and energy of
a photon pulse can travel faster than c, the speed of light in a
vacuum, but there does not (yet, anyways) seem to be meaningful
information transmitted via superluminal signals due to cancellation
of such potential superluminal signals because of complicated
diffraction and diffusion effects [4].
3) However, now consider the important conundrum:
Suppose that one definition of the presence of "acausality" would be
the existence of uncertainty which is clearly non-statistical (or
non-probabilistic). Well, this is what happens in the photon
experiment decsribed in this brief four page paper
[http://www.arxiv.org/abs/http://www.arxiv.org/abs/quant-ph/0102109],
yet there are no superluminal communications necssarily entailed !
Furthermore, also consider this paper
[http://www.arxiv.org/abs/http://www.arxiv.org/abs/quant-ph/9802056] about
acausality in QED which shows that it is theoretically possible for
there to be acausal behavior for photons in both time-like
space-like directions.
Thomas, since you are from Scandinavia you should heed what the Prince
of Denmark once said and also do not forget about ghosts :-)
"I will tell you why; so shall my anticipation precede your discovery,
....."
Hamlet, Act II, Scene 3
I will post more later about noncausality and acausality, but in the
meantime I will demonstrate the existence of acausality by correctly
anticipating what you, Thomas, will write in reply to this post before
you have even started typing on your keyboard !-)
[1] "Local Supersymmetry of the Chern-Simons theory and finiteness",
C. Lucchesi, O. Piguet, Nucl Phys B 381 (1992) .
[2] "Induced Geometry: Riemann-Cartan from Yang-Mills", Y. Obukhov,
D. Ivaneko Festschrift, JMS, v5 (1995) .
[3] "Nutational Stimulated Photon Echoes", Optics Letters, v27(iss
13) (2002), pp..
[4] J.J. Carey et al., Phys Rev Lett, v84(no7) (2000), p.1431.
---------- end of post [1] -------------
[2] http://arxiv.org/abs/http://www.arx...s/http://www.arxiv.org/abs/gr-qc/0402036
[3] http://arxiv.org/abs/http://www.arx...s/http://www.arxiv.org/abs/gr-qc/0304059
http://arxiv.org/abs/http://www.arx...s/http://www.arxiv.org/abs/gr-qc/0403121
about causality, locality etc. in OSFT [http://www.arxiv.org/abs/hep-th/0406199] which reminds
me of something:
The comments I made earlier in this newsgroup in the message below
about non-causality are still true for both theoretical and
experimetal reasons, i.e. various non-causal phenomena have already
been detected by experimentalists.
[Moderator's note: It sounds very exciting, Charlie. ;-)
Could you please be more specific about the
"experimentally proved violations of causality"? Is it the Optics
letter article? Incidentally, the Gross + Erler
paper, on the contrary, seems to prove the causality of SFT by going
to the light cone frame - which would explain why the S-matrix
satisfies the rules expected from causal and local theories. LM]
However, I now want to warn the readers of this newsgroup that my
different comments below about acausality may or may not be true. This
is simply because I have discovered since I made these comments that
there is even further likely relevant literature which I have not even
looked at yet.
For instance, QED is the most overall accurate scientific theory ever.
In a paper about acausality in QED [http://www.arxiv.org/abs/quant-ph/9802056], the author
proves in section 5 that photons can exhibit acausal behavior in both
time-like and/or space-like (superluminal speed) directions.
At first, one might suspect that such a result might rule out certain
ideas within string theory such as some ideas about large extra
dimensions. However, I myself would not make such a hypothesis for
various reasons, e.g. I have not yet looked at any of the recent
papers about photon propagation in noncommutative QED which of course
is a different and perhaps more fundamental environment than the usual
context for QED.
Since I don't know enough about questions of acausality (at least
yet), I will now finish what I am saying by reminding you of something
Albert Einstein once said which is that "No one really understands the
nature of the photon". Richard Feynman also said or implied multiple
times that no one really seems to understand QT.
Although I do not have enough understanding in this area, perhaps
these two great physicists are still correct because, as just one
example, it seems (to me at least) that the field of quantum optics is
still an active area of research, both theoretically and
experimentally, and this field is even having a major conference this
summer.
baez@galaxy.ucr.edu (John Baez) wrote in message news:
> >1) How are such approaches to be made compatible with vector
> >supersymmetry (or vsusy) which is a topological type of symmetry that
> >appears in both gravity and topological gauge theories [1].
>
> This "vector supersymmetry" is a mathematical feature of certain
> field theories - not something that anyone has observed experimentally.
Okay, but note that vsusy is an inherent aspect of your type of
approach to spin foam models of BF theory and quantum gravity as well
as the Ashtekar action. I discuss this some in post [1].
(Btw, there is also a newer paper about the role of vsusy in a general
supergauge which is more general than WZ gauge and here there does not
need to be a metric which is nonsingular at every space-time point,
i.e. the vielbein matrix doesn't have to be invertible in superspace
[2].)
> Nobody has yet constructed a background-free quantum theory that has
> general relativity as its limit at large distance scales. The Ambjorn-
> Jurkiewicz-Loll model is the closest anyone has come. If they succeed,
> this will be of interest regardless of whether their model displays
> mathematical features that appear in certain other theories!
>
> >2) How are such approaches to be made compatible with Bell-like
> >correlations, non-locality and non-causality which are each present in
> >the experiment described in this brief four page paper [2].
>
> As a quantum theory, the Ambjorn-Jurkiewicz-Loll model automatically
> has Bell-like "entanglement" and all that jazz.
At first, I thought that the AJL model must be flawed for reasons
mentioned in post [1], however, this may no longer be the case because
there are two recent papers which argue for separate reasons that
superluminal signals may actually be compatible with GTR [3].
As I told Tony Smith in another thread, it will take me some time to
read more literature and try to understand these issues better, and I
have never even read any of the Smolin or Magueiro papers on VSL and
DSR and so this may take me a few weeks or even two months.
> >3) To paraphrase a sentence that Stephen Hawking once wrote, to not
> >believe in the beauty and unity of the dualities of M-theory is like
> >believing that evolution did not occur because instead God placed by
> >hand all the fossils in the Earth just to play a joke on the
> >paleontologists :-)
>
> We resort to theological arguments in physics only when better arguments
> are lacking. If a scintilla of experimental evidence for M-theory is
> ever found, people will instantly stop making arguments of the sort
> you mention here.
Actually, Hawking and I were making an argument which you have also
made before, but which is not really an argument so much as a truism:
Thousands of years of the history of mathematics have taught us that
new and non-trivial math which is beautiful and profound never turns
out to be completely useless. Why is it that M-theory has contributed
to or inspired so much variety of important new mathematics? Is this
merely some kind of fluke or joke that Nature is fooling people with?
Here is another important point about this issue for critics of string
theory such as Peter Woit:
During the 1990s, I would occasionally take courses at the Harvard
Extension School. I was once seeing what a particular course would be
like by sitting in the classroom of a mathematical logic course taught
by the famous logician Gerald Sacks who is now at MIT.
One student asked a question about the mathematical rigor of
string/M-theory. I don't remember what her question was but Sacks
explained why it is that string theorists have to make things up as
they go along, i.e. that there is an unavoidable degree of uncertainty
and speculation involved in such an ongoing endeavor.
[Moderator's note: such a general comment can be equally said
about any intellectual activity beyond pure math. It is always
partly true, and always partly wrong, and it never proves that
the speaker knows the subject that he wants to talk about. LM]
I also would guess that Sacks realized something that I realized later
which is that it took about 2,100 years until Hilbert and others
showed that classical Euclidean geometry was logically incomplete.
[Moderator's note: Peter Woit apparently does not intend to
distinguish mathematics and physics. In physics, we don't care
whether a set of "axioms" is overcomplete. What we care about
is a sufficient set of rules that can describe Nature, the
world around us, and we are slowly getting a better
understanding of the theory underlying Nature as proposed by
string theory, much like we were improving our understanding
of theoretical physics before the age of string theory. LM]
If string theory turns out to be correct then mathematicians will
probably investigate the degree of consistency and completeness of
string theory's mathematical foundations. In the meantime, it does not
make sense to demand too much rigor before the time is ready.
[Moderator's note: It will never be a task for physics itself to
investigate some axioms with mathematical rigor - this task
is strictly dedicated to mathematicians. In mathematical physics,
one can prove that Feynman's Minkowski path integral cannot exist
in the context of the Lebesgue measure...
This theorem does not change anything about the fact that the
physicists use Feynman's path integrals as a complete and
completely satisfactory box of tools to describe many theories,
for example QCD. We have the same complete understanding of
perturbative string theory and non-perturbative string theory
around certain backgrounds, and we are trying to improve this
situation further. LM]
Otherwise, to use Lubos' analogy, theorists risk being like
hypothetical 19th century physicists trying to use Newton's equations
to calculate the expansion of the universe.
[Moderator's note: I don't remember this analogy, but one must
certainly be careful and avoid being picky about some details
in a theory that may be conceptually incomplete. Being picky
is something that people could have been 3000 years ago - yet,
it is clear that they were missing something important - well,
many important things - and their rigor was nearly worthless,
much like the current attempts to be rigorous can look in the
eyes of a physicist in 2050 who already knows some formerly
unknown ideas. LM]
For more on this topic, also see my post in sci.physics.strings in
reply to the question about "what is OPE?".
> I'm not saying that M-theory is "wrong" or that the Ambjorn-Jurkiewicz-Loll
> model is "right". M-theory makes too few definite predictions to be wrong.
This point is not necessarily true, but I won't go on a long spiel
about it right now because Lubos, others and I have already discussed
this issue in more detail in s.p.s. and there are also plenty of
papers in the Arxiv about potential tests of QG, including potential
tests of string theory.
> The AJL model does not include matter, so it cannot be right. But the
> AJL model is *interesting*, because it represents the best attempt so far
> to find a background-free quantum theory that reduces to general relativity
> in the large-scale limit!
Okay, I accept that their model might be interesting and I will now
even read their paper !-) Btw, the distinction between discrete and
continuous have a variety of different meanings in physics and math,
and e.g. it was even the great polymath genius, von Neumann, who
invented the field of math known as continuous geometry from
considering a series of discrete instances of projective geometry, and
this field has since been more generalized.
My point is that some of the distinctions between discrete vs.
continous may turn out to be somewhat trivial, and this is one reason
why I asked if Ashetkar's action might be compatible with the AJL
model in post [1], but I will now also read the AJL paper.
[1]
Thomas Larsson wrote:
"In the AJL model, the gauge is already fixed;they formulate the
action in terms of diff-invariant edge lengths rather than the
metric, there is a privileged time direction, etc. Since their
model only contains gauge-invariant quantities, there are no
diffeomorphism constraints left, and thus no need for ghosts."
Hi Thomas, I think you have misunderstood what I wrote and so before I
read the AJL or Bert Schroer papers let us try to clarify what we are
talking about and to make sure that we are considering the same
concepts.
Despite the particularities of the specific BV approach to vsusy, it
is the case that vsusy is an essential part of the origin of
perturbative finiteness of BF theory, and it helps with the algebraic
renormalization of topological YM theory, and vsusy may have a role in
constructing physical observables in addition to perhaps being the
symmetric origin for the IR safety of topologically massive YM theory
in Landau gauge.
Well, at least this is more established for CS theory defined on an
arbitrary space-time three-manifold for Landau gauge choice in which
vsusy is a renormalizable local supersymmetry which derives
perturbative (UV) finiteness at all orders [1].
It is also interesting to note that YM field configurations on 3 and 4
dimensional manifolds generate an effective Riemann-Cartan (in certain
models, Riemann) geometry on a space (or spacetime) and vice versa,
i.e geometry can yield YM gauge fields. The YM equations can
perhaps be written without the use of any metric on an arbitrary
smooth manifold [2].
However, the new AJL paper may also be intriguing because coframe
models can have the problem of allowing the existence of non-physical
modes such as ghosts or tachyons [e.g. references 18 and 19 in
http://www.arxiv.org/abs/http://www.arxiv.org/abs/gr-qc/0111087].
Anyways, the first question I would like to ask before reading this
new AJL paper is if their approach is compatible with the Ashtekar
action?
I ask because the vsusy of 4d Einstein gravity (in the Palantini first
order formalism) is compatible with the Ashtekar action and may be
compatible with any other actions if such actions have the vierbein
and connection as independent variables and have invariance under
_active_ diffeomorphisms, i.e. diffeos which act on dynamical fields
only, IOW, act quantum mechanically on field operators - the vierbein,
connection and matter fields
[http://www.arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0005011].
"Causality seems to be the whole point with the AJL approach -
lack of causality, i.e. singular metrics, is explicitly thrown
out."
Here we are thinking of different notions of "causality" which I will
now start attempting to clarify. Also, before discussing the AJL paper
further we might want to consider the important conundrum I ask about
at the bottom of this post.
1) For some as yet unknown and hypothetical reason, it might turn out
to be the case that theorists, e.g. either string theorists, LQG
theorists or discretized gravity theorists, will uncover what seems to
be a reasonable theory of QG but then for decades not be able to
figure out how to make the theory compatible with what we already know
to exist here at the everyday low energy scale.
However, let us presume, for this discussion at least, that a good
theory of QG should be inherently compatible with various low energy
phenomena and then consider the following:
1) Various quantum phenomena have already been demonstrated to be
"noncausal" both theoretically and sometimes even experimentally. I
have been looking at some of this literature recently and so far,
except for the one very important conundrum I ask about below, the
term
"noncausal" means only that there is no discernable and meaningful
dependence upon causality which is different from the idea that there
is some kind of explicit violation of Einstein causality via
superluminal signals.
For instance, experiments with TmYAG crystals have shown that
stimulated photon ehoes (SPEs) can exist in the noncausal direction
[3], and separate experiments have shown that the phase and energy of
a photon pulse can travel faster than c, the speed of light in a
vacuum, but there does not (yet, anyways) seem to be meaningful
information transmitted via superluminal signals due to cancellation
of such potential superluminal signals because of complicated
diffraction and diffusion effects [4].
3) However, now consider the important conundrum:
Suppose that one definition of the presence of "acausality" would be
the existence of uncertainty which is clearly non-statistical (or
non-probabilistic). Well, this is what happens in the photon
experiment decsribed in this brief four page paper
[http://www.arxiv.org/abs/http://www.arxiv.org/abs/quant-ph/0102109],
yet there are no superluminal communications necssarily entailed !
Furthermore, also consider this paper
[http://www.arxiv.org/abs/http://www.arxiv.org/abs/quant-ph/9802056] about
acausality in QED which shows that it is theoretically possible for
there to be acausal behavior for photons in both time-like
space-like directions.
Thomas, since you are from Scandinavia you should heed what the Prince
of Denmark once said and also do not forget about ghosts :-)
"I will tell you why; so shall my anticipation precede your discovery,
....."
Hamlet, Act II, Scene 3
I will post more later about noncausality and acausality, but in the
meantime I will demonstrate the existence of acausality by correctly
anticipating what you, Thomas, will write in reply to this post before
you have even started typing on your keyboard !-)
[1] "Local Supersymmetry of the Chern-Simons theory and finiteness",
C. Lucchesi, O. Piguet, Nucl Phys B 381 (1992) .
[2] "Induced Geometry: Riemann-Cartan from Yang-Mills", Y. Obukhov,
D. Ivaneko Festschrift, JMS, v5 (1995) .
[3] "Nutational Stimulated Photon Echoes", Optics Letters, v27(iss
13) (2002), pp..
[4] J.J. Carey et al., Phys Rev Lett, v84(no7) (2000), p.1431.
---------- end of post [1] -------------
[2] http://arxiv.org/abs/http://www.arx...s/http://www.arxiv.org/abs/gr-qc/0402036
[3] http://arxiv.org/abs/http://www.arx...s/http://www.arxiv.org/abs/gr-qc/0304059
http://arxiv.org/abs/http://www.arx...s/http://www.arxiv.org/abs/gr-qc/0403121