Roger Penrose’s new book The Road to Reality is being released in the U.S. in a week or so. I’d been intending to write something about the book ever since I got a copy of the British edition a couple months ago, but this is quite a daunting task. The book is nearly 1100 pages long and actually comes close to living up to its subtitle: “A Complete Guide to the Laws of the Universe”. It certainly is the most wide-ranging book on theoretical physics that I can think of, offering not just a summary of a lot of material, but an in-depth treatment of many of the more sophisticated ideas of the subject.
Penrose’s point of view is that of a relativist, so his treatment of geometry, general relativity and classical field equations is the deepest and most detailed part of the book. But he also discusses quantum theory extensively as well as the various attempts to quantize gravity. Compared to the general relativity parts, his treatment of particle physics and quantum field theory is rather sketchy, but quite original.
One of the unique aspects of the book is its extensive use of drawings to illustrate mathematical, geometrical and physical concepts. In this respect it is unparalleled by any other mathematically sophisticated text I’ve ever seen. One of Penrose’s main fascinations is the crucial role that complex numbers play, both in quantization and in the geometry of spinors. He has always been motivated by the idea that complex structures provide an important link between these two subjects, one that is still poorly understood. I very much agree with him about this. Related to this issue, some of the topics covered in the book that aren’t in any non-technical reference that I know of are his discussions of hyperfunctions and the Fourier transform, the geometry of spinors and twistors, and the use of complex structures in quantization and quantum field theory.
Penrose also carefully lays out areas in which his point of view differs from the general consensus of most theoretical physicists. An example is his emphasis on the importance for cosmology of understanding why the universe had such low entropy at the Big Bang. For more about this, see a posting by Sean Carroll.
A second area where Penrose is less than orthodox is his belief that quantum gravity somehow modifies quantum theory and resolves its measurement paradoxes. He explains an experimental set-up that could in principle test whether gravity plays a role in quantum state reduction, but he doesn’t have a concrete proposal for how standard quantum mechanics is to be modified.
Finally, there’s a remarkable chapter on supersymmetry, extra dimensions, and string theory. Penrose is very skeptical of the whole idea of introducing more that 4 space-time dimensions. One reason is that the beautiful spinor and twistor geometry that fascinates him is special to 4 dimensions. Another reason he gives is the classical instability of higher-dimensional space-times. Under a small perturbation, such space-times should collapse and form singularities. The difficulties in stabilizing extra dimensions are at the heart of the problems of string theory, with the only known way of doing it leading to the “Landscape” picture and ruining any ability to get predictions out of the theory.
Penrose is critical of the supposed calculation of black hole entropy from string theory, noting: ” As appears to be usual with such string-theoretic proclamations, this conclusion is very considerably overblown.” He has quite a few other very critical comments about string theory and the way in which research in the field has been pursued. As you might guess, I’m very much in agreement with his point of view and glad to see it in print. I’d be very curious to know whether recent ideas about strings in twistor space and Yang-Mills theory have changed his views much on the whole topic of string theory.
Update: A commenter pointed out that Science magazine has a review of Penrose’s book by Frank Wilczek (subscription required). Wilczek is right that there isn’t very much about particle physics in the book and Penrose gets something wrong about neutral K-meson mixing. Wilczek also says Penrose makes incorrect statements about electroweak symmetry breaking, but in a quick look at the book I couldn’t find what he was objecting to. He seems to object strongly to the speculative later parts of the book, but I don’t quite understand why. Penrose is up-front about what is speculation (e.g. relations between twistor theory and QM) and what is solid science, and Wilczek’s comment that “at present twistor ideas appear more as the desire for a physical theory than the embodiment of one”, could equally be applied to string theory, leaving one wondering why he doesn’t write strongly critical reviews of books on that subject.
If you want to read Lubos Motl’s comments on a book he hasn’t read, they’re here.
Hi Matti,
I’ve been deleting comments that seem to me off topic, repetitive, and purely designed to promote the interests of the writer. This has nothing to do with censorship of unpopular scientific ideas, I’d do the same if someone tries to promote their mainstream work on string theory or anything else here this way.
If I allow you to continually post long comments promoting TGD, I also end up with long, multiple comments from Quantoken promoting GUITAR, and others promoting their favorite ideas, together with many hostile comments from other people who are annoyed that the comment section is being taken over by this kind of thing.
If you want to write in detail about TGD, please do it on your own weblog, not on mine. If something I’ve posted seems to you really relevant to TGD, it would be best if you write a short comment here with a link to a longer discussion on your own weblog. I won’t delete such short comments and links, as long as there is not an excessive number of them, and they do have some kind of relation to the topics I’m posting about.
I am one of the quite of many physicists who have been labelled crackpots after the establishment of M theory hegemony. In particular, it has not been possible to post anything to Archive-Org.
Therefore the The Road to Reality was of special significance to me since it gives a clear signal for Paul Ginsparg and those responsible for this scandalous black-listing and also contains a reference to p-adic TGD. It is difficult to imagine that physicists like Roger Penrose would refer to the work of a crackpot.
Roger Penrose’s book The Road to Reality comes in two editions:
UK edition (ISBN: 0224044478, Publisher: Jonathan Cape, July 29, 2004)
and
USA edition (ISBN: 0679454438, Publisher: Knopf, February 22, 2005).
The two editions are NOT identical.
For example:
The UK edition on page 1050 says in part:
“… Bibliography There is one major breakthrough in 20th century physics that I have yet to touch upon, but which is nevertheless among the most important of all! This is the introduction of arXiv.org, an online repository where physicists … can publish preprints (or ‘e-prints’) of their work before (or even instead of!) submitting it to journals. …as a consequence the pace of research activity has accelerated to unheard of heights. … … In fact, Paul Ginsparg, who developed arXiv.org, recently won a MacArthur ‘genius’ fellowship for his innovation. …”
but
The USA edition on its corresponding page (also page 1050) says in part: “… Bibliography … modern technology and innovation have vastly improved the capabilities for disseminating and retrieving information on a global scale. Specifically, there is the introduction of arXiv.org, an online repository where physicists … can publish preprints (or ‘e-prints’) of their work before (or even instead of!) submitting it to journals. …as a consequence the pace of research activity has accelerated to an unprecedented (or, as some might consider, an alarming) degree. …”.
However, the USA edition omits the laudatory reference to Paul Ginsparg that is found in the UK edition.
For another example:
The USA edition adds some additional references, including (at page 1077): “… Pitkanen, M. (1994). p-Adic description of Higgs mechanism I: p-Adic square root and p-adic light cone. [hep-th/9410058] …”.
I hope that this would serve as some kind of a signal also to Peter Woit, who has been continually censoring out my messages. This just to help the raise the level of discussion from what it is now.
Matti Pitkanen
http://www.physics.helsinki.fi/~matpitka/
http://matpitka.blogspot.com/
Roger Penrose’s book The Road to Reality comes in two editions:
UK edition (ISBN: 0224044478, Publisher: Jonathan Cape, July 29, 2004)
and
USA edition (ISBN: 0679454438, Publisher: Knopf, February 22, 2005).
The two editions are NOT identical.
For example:
The UK edition on page 1050 says in part:
“… Bibliography
There is one major breakthrough in 20th century physics thatI have yet to touch upon, but which is nevertheless among the most important of all! This is the introduction of arXiv.org, an online repository where physicists … can publish preprints (or ‘e-prints’) of their work before (or even instead of!) submitting it to journals. …as a consequence the pace of research activity has accelerated to unheard of heights. … In fact, Paul Ginsparg, who developed arXiv.org, recently won a MacArthur ‘genius’ fellowship for his innovation. …”
but
the USA edition on its corresponding page (also page 1050) says in part:
“… Bibliography
… modern technology and innovation have vastly improved the capabilities for disseminating and retrieving information on a global scale. Specifically, there is the introduction of arXiv.org, an online repository where physicists … can publish preprints (or ‘e-prints’) of their work before (or even instead of!) submitting it to journals. …as a consequence the pace of research activity has accelerated to an unprecedented (or, as some might consider, an alarming) degree. …”.
However,
the USA edition omits the laudatory reference to Paul Ginsparg that is found in the UK edition.
For another example:
The USA edition adds some additional references, including (at page 1077):
“… Pitkanen, M. (1994). p-Adic description of Higgs mechanism I: p-Adic square root and p-adic light cone. [hep-th/9410058] …”.
Note that Matti Pitkanen was in 1994 allowed to post papers on the e-print archives now known as arXiv(obviously including the paper
referenced immediately above), but that since that time Matti Pitkanen has been blacklisted by arXiv and is now barred from posting his work there. His web page account of being blacklisted is at http://www.physics.helsinki.fi/~matpitka/blacklist.html
It seems to me that it is likely that the omission of praise of arXiv’s Paul Ginsparg and the inclusion of a reference to the work of now-blacklisted physicist Matti Pitkanen are deliberate editorial decisions.
Also,
since the same phrase “… physicists … can publish preprints (or ‘e-prints’) of their work before (or even instead of!) submitting it to journals. …” appears in both editions, it seems to me that Roger Penrose favors the option of posting on arXiv without the delay (and sometimes page-charge expense) of journal publication with its refereeing system.
Therefore,
a question presented by these facts seems to me to be:
What events between UK publication on July 29, 2004 and USA publication on February 22, 2005 might have influenced Roger Penrose to make the above-described changes in the USA edition ?
There are two possibly relevant events in that time frame of which I am aware:
1 – The appearance around November 2004 of the ArchiveFreedom web site at http://www.physics.helsinki.fi/~matpitka/blacklist.html which web site documents some cases of arXiv blacklisting etc;
2 – According to a CERN web page at http://documents.cern.ch/EDS/current/access/action.php?doctypes=NCP “… CERN’s Scientific Information Policy Board decided, at its meeting on the 8th October 2004, to close the EXT-series. …”. Note that the CERN EXT-series had been used as a public repository for their work by some people (including me) who had been blacklisted by arXiv .
Maybe either or both of those two events influenced Roger Penrose in making the above-described changes in the USA edition.
If anyone has any other ideas as to why those changes were made, I would welcome being informed about them.
Tony Smith http://valdostamuseum.org/hamsmith/
I got the book on Saturday, it should be in every physicist’s library. It reminds me of Klein’s various “Vorlesungen” – lectures, literally “readings”. One thing Peter may not have mentioned is the clever prologue, which I assume takes place in Atlantis 🙂 This book appeals on many levels, including the very “tominess” of it!
-drl
Anyone who has purchased the Penrose book, will no doubt be daunted at ‘not only’ its size (the road to reality is a big one!), but must be prepared to journey across domains that alter the readers perspective about certain physical laws, I quote form the book:The spacetime singularities laying at cores of blackholes are among the known(or presumed)objects in the universe about which the most profound mysteries remain–and which our present-day theories are powerless to describe. As we have seen&&34.5,7,8,particularly, there are other deeply mysterious issues about which we have very little comprehension. It is quite likely that the 21st century will reveal even more wonderful insights than those that we have been blessed with in the 20th. But for this to happen,we shall need powerful new ideas,which will take us in directions significantly different from those currently being pursued. Perhaps what we mainly need is some subtle change in perspective-something that we have all missed…
Now correct me if I am wrong, or if I am not even right?..but Penrose clearly leaves the doors and windows open for ‘a breath of fresh air’, a humble way to entice the reader, whatever her/his previous thoughts were, you cannot help but wonder and reason?
I think it is a shame that Wilzeck seems to be riding the ”BIG-NOBEL-WAVE”, as his current joint undertaking in gravitational anomilies clearly shows?..would he have stepped into this arena previous to his ‘nobel-prize’?..I think not, quantum-waves have more energy, and can travel further 😉
Lubos would never read such a book, but if the Epilogue is anything to go by, then he would definatly not understand the experience of…
Thomas , see for example the panel debate on extra
dimensions at the Kavli conference on
http://www.phys.cwru.edu/events/cerca_video_archive.php
See the session on gravity and in particular the
panel debate on extra demisions (in that panel
wilczek argues against extra dimensions.)
See also http://mitworld.mit.edu/video/204/
and in particular his answer to scott hughes question about extra demisions.
However wilczek does believe in supersymmetry.
see also page 5 of astro-ph/0401347
Thomas asked:
“Where did Wilczek say that he doesn’t believe in extra-dimensions? …”
Posted by: Thomas Larsson at February 17, 2005 03:47 AM
I dont know what Wilczek thinks or what he has said about extra dimensions. But here is something that could help round out the picture. Wilczek is evidently interested in quantum gravity and has just posted this paper with Sean Robinson
http://arxiv.org/abs/gr-qc/0502074
A Relationship Between Hawking Radiation and Gravitational Anomalies
—exerpt from Wilczek/Robinson introduction—
Hawking radiation from black holes is one of the most striking effects that is known, or at least widely agreed, to arise from the combination of quantum mechanics and general relativity…
…The literature contains several derivations of Hawking radiation, each with strengths and weaknesses. …
…Derivations based on string theory have a logically consistent foundation, but they only apply to special solutions in unrealistic world models, and they do not explain the simplicity and generality of the results inferred from the other methods[4, 5]…
—endquote—
to draw the obvious conclusion, Wilczek seems willing to entertain reservations about current attempts to join quantum mechanics and general relativity and to go out on his own looking for new ones, as in the case of this paper.
Hope this helps, even though not directly responding to the question.
Where did Wilczek say that he doesn’t believe in extra-dimensions? I know that he has worked a lot on supersymmetry and axions, which seems about as speculative as twistors, but maybe less so than strings.
Incidently Wilczek and Penrose are in the same boat
as regards their opinions on extra-dimensions
(in other words both belive that they cannot be present.)
Peter,
Yes, that is the whole point, and is addressed by Weyl’s ansatz. Hence, to make progress, one needs a way to introduce the gauge group in the context of conformal weight, which is just what I am trying to do.
-drl
Peter,
Sorry for that; perhaps the time of day (1:17 AM) had something to do with the manic state I was in when I posted. The articles in question aren’t as far off-topic as one might think, but I won’t push my luck by attempting to explain this assertion now. Thanks for indulging me and leaving the comment in place, if only as an example of misbehavior.
Hi Stephen,
I’ll try and think if I can sensibly say more about this, but of course the underlying problem is that I don’t have a good idea about how to control the dynamics of the metric degrees of freedom. In the Standard model the Yang-Mills + Dirac actions beautifully determine the dynmamics of the connections and spinor fields (leaving only scalar fields problematic). The Einstein-Hilbert action doesn’t do the same for the metric degrees of freedom so one needs a new idea. LQG? TQFT? R^2 actions, twistors???
You should be trying to figure out how to use symmetries to gain control of the space-time degrees of freedom, not throwing out the gauge symmetry, creating a higher dimensional mess whose dynamics you don’t understand, then hoping to recover gauge symmetry as an effective low energy phenomenon.
Posted by Peter at February 15, 2005 01:52 PM
Maybe at a later time you will speak to this in more detail? This clarifies to me the essence of your resistance to other theoretical approaches and helps to point towards more information to be look at. This is good.
Thank you
Chris and others,
Please do resist the temptation to post here about unrelated topics. Once one of you starts this, others join in and this starts to become like sci.physics again. I’ve deleted some comments and will delete any more that aren’t about Penrose’s book.
Sorry for the shift of topic, but I couldn’t resist mentioning some interesting new and recent papers:
Supersymmetry and the Lorentz Fine Tuning Problem
This work was in response to the following, posted last March and last updated on 10/30/04:
Lorentz invariance and quantum gravity: an additional fine-tuning problem?
In January, none other than Seth Lloyd weighed in with an initial proposal (submitted to Science) for an approach to quantum gravity, starting with general notions of quantum computation theory, and with strong correspondences to causal set theory (Sorkin, Dowker, and others):
The Computational Universe: Quantum gravity from quantum computation
Finally, I’ll draw these threads together more tightly by citing the following paper by Dowker, Henson, and Sorkin:
Quantum Gravity Phenomenology, Lorentz Invariance and Discreteness
I’ll suppress my enthusiasm (and some thoughts begging to be expressed) and stop here.
Hi Lubos,
Thanks for plugging my “educational low-dimensional blog”, I like that. From the picture I see I was completely wrong about Lane’s lack of enthusiasm for string theory.
Actually I’ll be up at Harvard next month for the conference there. If you want I could pose in front of the NYT article too, right next to the part where Lawrence Krauss makes his “colossal failure” comment…
Hi Peter!
I hope that your next article will also be celebrating 20 years of strings! See my blog – Kenneth Lane has already celebrated.
It’s a matter of days before Shelly Glashow and others join! 🙂
Happy birthday 🙂
Lubos
Hi Z,
Anyone who wants to can look at what Penrose has to say about this stability issue, and then debate whether it makes sense or not. I’m just not interested enough in the question to spend time on this.
The problem with not fixing the moduli is that then your theory has massless scalar fields that couple to matter, producing long-range forces. We have very strong experimental bounds that these things don’t exist. So such a theory is simply wrong.
I don’t quite understand your last comment. If it’s about the general landscape philosophy, which I see very good reasons to believe is inherently incapable of predicting anything, all someone has to do to prove me wrong is come up with a prediction. That hasn’t happened yet.
Peter Woit said:
”
Penrose’s comments about higher dimensional theories were made in the context of a criticism of string theory, so I don’t think it is unreasonable for me to discuss them in that context. If you have another context in which you want to discuss these issues, you’ll have to make it explicit.
”
I think it was fairly obvious that the anonymous poster was talking about Penrose’s claims on the classical stability of KK spacetimes encountered in the string theory literature. I think it is legitimite to dwell on what the precise objection here is. I don’t think it is acceptable to show a tendency to sweep the issue under the rug if it turns out that this particular objection of Penrose’s turns out not to be so well-founded, but put flashing banners if there is the slightest possibility that it might be a valid objection. This is not how scientists should work, though unfortunately similar tendencies prevail in both the string theory camp and the anti-string theory camp. (Penrose’s objection *might* be well founded, I still don’t understand what the precise objection here is.)
Peter also said:
”
If you don’t like my commenting on string theory, just ignore it, or go somewhere else. I’m not going to stop. The situation with string theory is not, as you say, “almost the opposite of what you describe”, it is precisely as I described it. The fact of the matter is that at the linearized level, you have a flat potential for moduli to deal with, and this leads to the disaster of predicting unobserved massless particles. Until recently, most proposals for getting a non-zero potential for the moduli lead to the disaster of moduli running off to infinity. Lately, the flux vacua proposals fix the moduli, but lead to the landscape disaster. Saying that “there is no known theoretical reason to fix the moduli” is absurd.
”
and concluded
”
The theoretical reason is that the theory is supposed to be a theory of the real world.
”
This sonuds to me like a strong claim about what a candidate “fundamental theory” (if such a thing exists) *must* be able to explain. (I am not saying that you believe in the existence of such a theory, but rather pointing out what you seem to be demanding from a candidate.)
Here is a fundamental objection of mine (which I think is a fairly obvious one) to the main theme in many of your posts againsts string theory (I am not a string theorist, by the way):
Little scientist bugs that live on a magnet might come up with a candidate microscopic theory of ferromagnetism. It might turn out that their theory cannot explain the mean magnetization that they so clearly observe. They might run around trying to invent schemes that would stabilize the “magnetisation modulus” thinking it is a fundamental thing that must be predicted by the “correct” microscopic theory. They might fail in doing so. Their friends might criticise them for working on a theory that has not shown the slightest possibility of coming up with the observed magnetisation. Despite all this, the bugs’ theory might be correct.
Why not entertain a similar possibility for the issues about the “observed” gauge groups, etc.? Do you really think such a point of view would render a theory based on the latter totally unpredictive?
I don’t think going after the quark masses etc. is the only way string theory can be tested.
z
To whoever you are who keeps posting hostile comments. First of all, unless you have a really good reason, I think you should put your name to your comments. At least pick a pseudonym, so I know when I’m having a back and forth exchange with the same person. At this point, the only way I can identify that the comments belong to you is that they generally contain some sort of criticism of me for publicly complaining about what is going on in string theory. When I want to be sure it is you I can go into the Movable Type software and check that the comment came from an IP in Ontario, but that is pretty tedious.
Penrose’s comments about higher dimensional theories were made in the context of a criticism of string theory, so I don’t think it is unreasonable for me to discuss them in that context. If you have another context in which you want to discuss these issues, you’ll have to make it explicit.
If you don’t like my commenting on string theory, just ignore it, or go somewhere else. I’m not going to stop. The situation with string theory is not, as you say, “almost the opposite of what you describe”, it is precisely as I described it. The fact of the matter is that at the linearized level, you have a flat potential for moduli to deal with, and this leads to the disaster of predicting unobserved massless particles. Until recently, most proposals for getting a non-zero potential for the moduli lead to the disaster of moduli running off to infinity. Lately, the flux vacua proposals fix the moduli, but lead to the landscape disaster. Saying that “there is no known theoretical reason to fix the moduli” is absurd. The theoretical reason is that the theory is supposed to be a theory of the real world.
By the way, I notice you didn’t take your argument that only an obtuse string theory hater would not believe that finiteness of superstring amplitudes has been demonstrated over to Jacques Distler’s weblog, where he has written about this extensively. You really should; I think you and he would get along very well.
Hi!
I have been following this discussion with interest.
I am shocked at what I have heared from the post after Peter’s. Linearised stability theory was trashed in mathematical circles years ago as TOTALLY misleading. There have been Field Medals in mathematic given just for small advances in higher dimension stablity theory!
This is my interpretation of Penrose statement. Essentially, these states have large numbers of symmetries aka Solitons. The normally postion of the mathematical community regarding highly symmetric spaces is that they are essential CHAOTIC! This is because of problems of embedding conformal manifolds into real spaces.
Now, (my addition I apologise) recent research has confirmed this in admitted a low dimension setting. 3 dim constrained water waves have been show to have UNIVERSAL chaotic motions.
http://www-staff.lboro.ac.uk/~mamdg
/MarkGroves/Resources/spatialdynamics.pdf
Now, I should not have to tell you that if you had applied LINEAR analysis to this problem, you would have had never of found these CHAOTIC solutions!!!
Unfortunately, this analysis is effectly at the forfront of modern analysis and to write the sort of papers that is being asked is beyound anyone on the planet at this moment in time.
Is it really true that the Physic community believes in the stability of symmetric spaces due to Linear analysis?
I believe that it is time for a Hard Nosed mathematician to have a look at this problem and provide some help to the Physic community!
An amateur mathematician.
General points of philosophy and arguments of authority are just a matter of taste. The facts are that the question of linearized stability of KK spacetime, to the extent that it is a mathematically precise question, was settled long ago by precise calcualtions. I suggest that if Penrose had something concrete to say about it, he would publish a paper on the subject, which would then be subjected to the usual scrutiny. In the absence of that there is really nothing to agree or disagree with. Just relying on his authority is unfair to many talented and devoted people who actually worked on the subject. Similar words can be said about Hawking and the fiasco of the information paradox resolution.
Now, the situation about string theory is almost the opposite of what you describe. There is no known theoretical reasons to fix the moduli, nothing is inconsistent or unstable in theories that have those moduli, not at the linearized level or any other level. This is a huge problem for string theory because we live in a world that does not have them. If Pensrose had some concrete way to kill these highly symmetric KK spacetimes, nobody will be happier than string theorists.
I really think you could understand everything I say if you actually read complete sentences instead of just look for points for
or against string theory.
Peter, that was extremely well said!
Penrose essentially claims that his and Hawking’s singularity theorems also apply in this higher dimensional case. If you want the details, you have to take a look at the book, although Tony Smith just posted a relevant abstract.
I was just reporting what Penrose says, and I’m not interested enough in this issue to spend my time on the details of this. In any case I don’t think Penrose has an air-tight argument against extra dimensions, because you can always claim that quantization solves the problem.
I’m certainly fond of true statements, In this case we have one of the world’s leading experts on singularity theorems in classical GR making a claim about them in print. I strongly suspect that he knows what he is talking about here and is making true statements, that’s why I reported on them. As for mathematically precise statements, they have their place, but in many contexts they’re either not possible, not appropriate or not worth the investment of time and energy needed to get them.
In the case of string theory, there are much less subtle instability problems with extra dimensions than the ones you need Penrose’s singularity theorems to see. You already have a huge problem at the linearized level. I’m referring to the well-known problems fixing the moduli parameters that describe the size and shape of the extra dimensions. Unless you first solve that problem, worrying about more subtle problems seems to me a waste of time. The only “solution” to this problem I know of leads to the “Landscape” and a completely useless theory.
As a general matter of philosophy though, I very much agree with Penrose’s point of view about Kaluza-Klein. You’ve got enough trouble dealing with the metric degrees of freedom of space-time. You’re just making things worse when you add in a dynamical metric for the fibers of your principal bundle or for some internal space.
Another way of saying it is that in the standard model you have an SU(3)xSU(2)xU(1) principal bundle, and the geometry of the fibers is tightly constrained by the gauge symmetry, which is why the theory works so beautifully. You should be trying to figure out how to use symmetries to gain control of the space-time degrees of freedom, not throwing out the gauge symmetry, creating a higher dimensional mess whose dynamics you don’t understand, then hoping to recover gauge symmetry as an effective low energy phenomenon.
Is there any scientific paper, peer-reviewed and published, which supports the claim that (some) spacetimes of the KK form are classically unstable to small perturbations?
This stability is a well-formulated question that can be answered precisely, there is no place to hide. Of course, it was answered precisely already for many such spacetimes, but some people don’t like the answers. However, I thought the owner of this blog was fond of true and mathematically precise statements.
Roger Penrose, in the UK edition of The Road to Reality, says at pages 905-907: “… 31.12 Classical instability of extra dimensions … a classical M x Y universe – subject to Ricci flatness – is highly unstable against small perturbations. If Y is compact of of a Planck size, then spacetime singularities … are to be expected to result within a tiny fraction of a second! … Let us first consider perturbations of M x Y that disturb only the Y geometry … That is to say, we examine a ‘generic’ ricci-flat (1 + [dimension(Y)]) spacetime Z ([Z is] the perturbed evolution of Y) … [and] E1 x Y …[is]… the (unchanging) ‘time-evolution’ … of Y … a singularity theorem … shows that we must expect Z to be singular. … As one of this theorem’s consequences, any Ricci-flat spacetime that (like E1 x Y or Z) contains a compact spacelike hypersurface, and that is ‘generic’ in a certain specific sense … (and free of closed timelike curves … ), must indeed be singular! The original E1 x Y escapes from being singular because the generic condition fails in this case. But the generically perturbed Z has to be singular. … If the perturbation away from Y is the same general scale as Y itself (i.e. Planck scale), then we must expect the singularities in Z to occur in a comparable timescale ( about 10^(-43) s), but this timescale cold become somewhat longer if the perturbations are of a proportionally smaller size than Y itself. … the large Planck-sclae curvatures … that are likely to be present in Y will spill over into ordinary space, in gross conflict with observation, and will result in spacetime singularities in very short order. …”.
Richard Feynman, in his book QED The Strange Theory of Light and Matter (corrected 7th printing, Princeton 1988), says in a footnote at page 129: “… perhaps the idea that two points can be infinitely close together is wrong – the assumption that we can use geometry down to the last notch is false. If we make the minimum possible distance between two points as small as 10^(-100) centimeters (the smallest distance involved in any experiment today is around 10^(-16) centimeters), the infinities disappear, all right – but other inconsistencies arise, such as the total probablility of an event adds up to slightly more or less than 100%, or we get negative energies in infinitesimal amounts. …”.
Taken together, the Penrose and Feynman quotes seem to me to indicate that at the Planck scale spacetime (of any dimension) is probably discrete. It seems to me that a discrete spacetime is substantially consistent with a spacetime foam / LQG approach, and that it is consistent with physics models in which the M of M x Y is discrete (such as a Feynman Checkerboard) and the Y of M x Y is a compact manifold (such as my Clifford algebra model and perhaps Matti Pitkanen’s p-adic model), but I am not sure that a discrete spacetime is consistent with conventional string theory (perhaps Lubos could comment on that).
Tony Smith – new web site URL at http://www.tony5m17h.net/
The following might have been missed by the readers due to it having been posted a couple of days ago, but here it is (to humble ST people)
“…I do feel strongly that this is nonsense! …I think all this superstring stuff is crazy and is in the wrong direction. … I don’t like it that they’re not calculating anything. …why are the masses of the various particles such as quarks what they are? All these numbers … have no explanations in these string theories – absolutely none! … ”
–Richard Feynman: in Davies and Brown, Superstrings, Cambridge 1988, pp. 194-195.
The proceedings are published in a book format, knock yourself out, I only found words there.
BTW, nobody stands to profit more from some mysterious inconsistency of most (but not all) compactifications than string theorists, that used to be their holy grail.
I am not convinced either of what Penrose is saying but what I briefly read about it (a few remarks in a preprint intro) sounded interesting and it stuck in my mind. Since I was’nt actually at the conference and since there seems to be no paper from him, one cannot really comment on it or really know what he has in mind. I agree that a solid argument from someone like Penrose for classical instability of higher-dimensional spacetime would be of considerable interest. If he was really serious though and had thought it
through then one might have expected it to appear by now in J.Class Quant Grav say.
Steve M,
Even allowing for mights and mays, especially from such an accomplished scientist, it is hard to find an argument there. The usual singularity theorems, valid in 4dim asysmptotically flat space, are usually not taken to mean instability of flat space, or exclude it’s existence. Even if there is some hypothetical singularity thm. in higher dimesnion, why would it imply the non-existence of higher dimensional gravitational theory?
A solid argument for a classical instability of higher dimensional space, especially coming from an authority like Penrose, would become immediately an extremely hot topic for research by at least 2 scientific communities, probably more. Alas, in this case it is hard to find some flesh behind the words. Maybe someone else here had better success.
Of course, Penrose himself is a hero for myself and many of my generation, but this is no reason to treat his assertions differently. I
Speaking of book reviews, try http://schwinger.harvard.edu/~motl/rovelli.html
Something on Penrose and string theory here:
http://www.digitalmediatree.com/sallymckay/pageback/30638/
Refers to Penrose lectures at:
http://www.princeton.edu/WebMedia/lectures/
Steve M,
For sheer fun, find and read Penrose’s early paper on the appearence of a moving relativistic object.
I ordered the book as well.
Though it’s not generally mentioned AFAIK, twistors go all the way back to Pluecker’s “change of space element”, i.e. homogeneous line geometry. I would be interested to know if he mentions that in this new book.
-drl
I know Penrose has suggested (Talk given at Cambridge conference in honour of Steven Hawkings 60th birthday) that a variation of the singularity theorems might rule out the existence of compact extra dimensions ala KK. The idea is that wrapping of light rays around compact dimensions would create an effect analogous to trapped surfaces in gravitational collapse. I can’t find a published article though giving the details unless the proceedings have been published. Penrose is always interesting and original though and his new book certainly seems to be worth getting.
I too would like to read an elaboration of this instability issue. Does he mean N space + 1 time or N space + M time, or both? Does he mean the same thing that originally did in Einstein’s cosmology (thought of as say deSitter space)?
-drl
I got the book last july, it’s *very* impressive from a mathematical point of view (I can’t comment on the physics).
I find that the book explains the geometric concepts of fibre bundles and spinors perfectly well (certainly better than I would have thought they could be explained).
I’m not convinced that his exposition of fourier analysis would be easily graspible for the beginner, but I sure as hell enjoyed it!
One weird thing is that he *completely* skips over basic calculus – I guess that’s ok though – it leaves more time for fun stuff.
Still though, it’s remarkable, and it will, if it’s commercially successful bring up a whole generation of young intellectuals with a grasp of some concepts (mainly geometrical) that were previously viewed as very advanced…because, let’s face it, not many of the useful concepts of modern mainstream mathematics have been brought down to the popular level (“topology is rubber-sheet geometry” isn’t a useful concept, it’s an unmotivated generalization (well…locale theory is a pointless generalization…)).
Anyway, it’ll be a good thing if it’s successful
(mathematically anyway)
Under a small perturbation, such space-times should collapse and form singularities.
care to elaborate? for the usual compactification on CY, or torus, etc., this statement is just false with the usual interpretation of all the words appearing there. All such solutions are stable (tachyon free) classical solutions of supergravity.
Not that this is necessarily what Pensrose means when he talks about collapse, though it is hard to tell precisely what he does mean.
In my mind Penrose has more problems with higher dimensions than string theory specifically, but again he is perfectly capable in providing a tight mathematical argument, if he had one.
Article in the Times – a philosophical inquiry into bullshit!
http://nytimes.com/2005/02/14/books/14bull.html
Thesis: Bullshit is worse than outright lies, because lying presumes a truth, while bullshitting is an end in itself that disposes of truth altogether.
-drl
My text about the book is at
http://motls.blogspot.com/2005/02/frank-wilczek-about-penroses-new-book.html
To complain about the ‘objectivity’ is just below the belt… and, in fact, it’s a ‘meta statement’ in itself. I explain: Once “anonymous” is such an objective person, would you please do yourself (first and foremost) and ourselves the favor of checking out the reviews that the Lubos have on Amazon? Reviews of books like “PCT, Spin, Statistics and all that”, “Local Quantum Physics”, etc.
To me, at least, it sounds very awkward when a theoretical (hep-th or math-ph) physicist dismisses math as much STheorists do nowadays… and, before this last comment starts a flame war, let me just say that i only read about Donaldson Polynomials, Knot theory, gerbes and so forth on books either by the AMS (on QFT!) or by Kauffman or Baez. Personally, i never saw a single STheorist (mainly the ‘pop’ ones) talking about those topics; in fact, in more than one occasion i have been condemned for ‘breaking up a discussion’ with such ‘mathematics’ topics.
That’s what you get for objectivity.
Besides, please, have and show (!) some respect for Penrose: He did more in a lifetime than most of us combined and/or put together will ever do! Or are you telling me that if Newton were alive you’d walk all over his ass because he ‘was wrong’?!!! (Sorry, Peter, for the language; it’s just too soon in the morning to read gigantic loads of crap… add that to a bit of Napolitan blood and you have a recipe for a (flame-)war! >;-)
Note that i’m not – nor do i intend to – defending Penrose or anyone else for that matter. I have the same opinion of folks like Witten (and others whose names decided to runaway just now, while i looked at the door). It’s just hard to find, nowadays, people who are honest about what they know and about what they do not know. Then again, the market is kindda tight so, i guess this makes it all very understandable, does it not?! Afterall, we’re all fighting to survive… and, as a good reductionist would deduct, in the end we are just trying to pass our genes forward… ðŸ™
Meaning Penrose is untrustworthy. But surely Emperor’s New Mind has already proven that. Interested in why the Lunsfords, Voits haven’t lumped him in with the celebrity stringies they so detest. So much for objectivity I guess.
If you cared to look, e.g. in this thread, you would find that I have been quite critical of LQG in the past, for pretty much the same reason that I critized string theory: in order to quantize a constrained Hamiltonian system, like general relativity or the bosonic string, you must first understand its constraint algebra. As Urs Schreiber noticed in the link above, an infinite-dimensional constraint algebra is generically anomalous. In particular, GR has many constraint subalgebras isomorphic to infinite conformal symmetry in 2D, and most of these subalgebras should thus have conformal anomalies.
As for objectivity, I notice that people like Schreiber, Helling, Motl and Distler criticize LQGists essentially for missing conformal anomalies (this is a clear symptom if not the cause of the problem), but they have no interest in trying to understand why 4D diff anomalies do not arise in string theory. Note here that anomalies are physical effects seen in any reasonable quantization scheme – path integral quantization of the Polyakov action also singles out 26D, i.e. the conformal anomaly does not only arise in canonical quantizion.
Moreover, the string hype is without comparison, whereas LQG somehow reminds me of the description of earth in the Hitchhiker’s Guide: “Mostly harmless”.
” very interesting and challenging for beginners”
Perhaps the commonest response I’ve heard to this book, from working scientists (not neccessarily theoreticians) in the UK, is that of wishing it had been available to the reader when he/she was a beginning undergraduate. The exercises, friendly logos etc, sketches (by the author, not an illustrator) establish an intimate relationship with the reader not sought in the the Emperor’s New Mind etc. It’s hard not to see the whole thing as a textbook for the little Penrose – whose arrival is celebrated in rather extreme terms in the introduction – for use in later life.
RE: but flawed at the highest level
Meaning Penrose is untrustworthy. But surely Emperor’s New Mind has already proven that. Interested in why the Lunsfords, Voits haven’t lumped him in with the celebrity stringies they so detest. So much for objectivity I guess.
Real good review of Penrose’s book by Frank Wilczek in current (Feb 11) Science. Not Free, unfortunately. Says book is very interesting and challenging for beginners, but flawed at the highest level.
Best,
Jim Graber
Lubos,
I have a gedanken experiment for you, which anyone with any familiarity with Penrose’s work or indeed any real understanding of spinors will be able to immediately answer.
Just before a total eclipse of the Sun, the Moon is given a large velocity tangential to its orbit at mid-eclipse. Do the effects of relativity prevent the eclipse? Explain.
-drl
Thank you Lubos for sharing your vacuous thoughts on a book you have not seen.
Geez.
Penrose is a great and highly original guy, because of his contributions to GR, twistors, his triangle, his tiling, and so forth, but this kind of prayer is really bizarre. I have not seen the book.
Many of us have been fascinated with the complex numbers. But is this really a state-of-the-art fascination? I don’t think so. The complex numbers are very important in advanced contexts – such as SUSY. Penrose’s ideas about the relations between the interpretations of QM, quantum gravity, and collapses inside the brain would … well, let me not say anything because whatever I would say would be viewed as impolite.
Twistors are fun as a method to find solutions of various systems in 4D Minkowski spacetime, but the speculations that they could be related to quantum gravity or theory of everything just don’t seem terribly promising right now (and they have not seemed promising for 30 years). Moreover, many recent gauge-theory calculations have been reduced back to the language of spinors, so that the idea of twistors plays less role than initially.
My guess is that the criticism of black hole string theory calculations is nothing more than misunderstanding. We’ve been told about his strange lecture in which he argued that string theory had some “problem” because of some singularities – he probably meant the singularities in the moduli space of Calabi-Yaus, or something like that. This is *exactly* the physical question that has been understood in detail by the string theorists. It seems that no one has explained him this stuff, which is sad.
But still, I admire him, don’t get me wrong.
You’re right that a lot of the book is quite technical, but it evidently did sell quite well in England. But even if most people could understand only half of it, they’re getting 500 or more pages of interesting material to chew on, maybe they consider that a bargain at the price.
I also purchase a UK version of the book a few months back. It’s definitely an interesting read (making up, perhaps, for “Shadows of the Mind” which I thought wasn’t so great.) But the question I have is who exactly is going to read this book? I mean, for physicists who want a little easy and enlightening reading it’s really a nice book, but I can’t imagine the lay reader understanding more than half the book.
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