John Brockman’s Edge web-site has an annual feature where he asks a wide array of scientists and others how they would answer a hopefully thought-provoking question. Last year the question was What Do You Believe Is True Even Though You Cannot Prove It? This year it’s What Is Your Dangerous Idea?

There are responses to this question from 117 different people, a large fraction of them psychologists or cognitive scientists. Among the responses from physicists, several deal with the Landscape as a dangerous idea. Susskind takes credit for it, noting “I have been accused of advocating an extremely dangerous idea”, and that some of his colleagues believe it will lead to the end of science, leaving no way to defend physics as a truer path to knowledge than religion. He proudly describes the anthropic Landscape idea as “spreading like a cancer.”

On the opposite side of the issue, Brian Greene emphasizes the dangers of the Landscape philosophy:

*When faced with seemingly inexplicable observations, researchers may invoke the framework of the multiverse prematurely — proclaiming some or other phenomenon to merely reflect conditions in our bubble universe — thereby failing to discover the deeper understanding that awaits us.*

Paul Steinhardt is more emphatic about these dangers:

*I think it leads inevitably to a depressing end to science. What is the point of exploring further the randomly chosen physical properties in our tiny corner of the multiverse if most of the multiverse is so different. I think it is far too early to be so desperate. This is a dangerous idea that I am simply unwilling to contemplate.*

He also has his own “dangerous idea”, about a cyclic model of the universe explaining the small size of the cosmological constant. Lawrence Krauss gives his own version of an explanation of the danger that the Landscape will lead to an end-point for theoretical physics:

*… all so-called fundamental theories that might describe nature would be purely “phenomenological”, that is, they would be derivable from observational phenomena, but would not reflect any underlying grand mathematical structure of the universe that would allow a basic understanding of why the universe is the way it is.*

Some other interesting contributions from physicists come from Philip Anderson, who has some speculative comments about dark matter and dark energy, Lee Smolin, who discusses the possibility of natural selection having something to do with fundamental laws, and Carlo Rovelli, who remarks that we have still not completely absorbed the revolutionary ideas of 20th century physics:

*I think that seen from 200 years in the future, the dangerous scientific idea that was around at the beginning of the 20th century, and that everybody was afraid to accept, will simply be that the world is completely different from our simple minded picture of it. As the physics of the 20th century had already shown.*

*What makes me smile is that even many of todays “audacious scientific speculations” about things like extra-dimensions, multi-universes, and the likely, are not only completely unsupported experimentally, but are even always formulated within world view that, at a close look, has not yet digested quantum mechanics and relativity!*

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I think Carlo Rovelli is right on the money. Physics moved ahead too quickly in the last century, without properly understanding the mathematics of quantum mechanics. The big advances in understanding QM came after 1960 when QFT had more or less been finalised. Parables about building on quicksand come to mind.

Happy New Year

posted today

[url]http://arxiv.org/abs/hep-th/0601001[/url]

[b]The String Landscape, Black Holes and Gravity as the Weakest Force[/b]

Nima Arkani-Hamed, Lubos Motl, Alberto Nicolis, Cumrun Vafa

20 pages, 5 figures

ionesco’s rhinoceros

et tu Lube?

The String Landscape, Black Holes and Gravity as the Weakest ForceNima Arkani-Hamed, Lubos Motl, Alberto Nicolis, Cumrun Vafa

20 pages, 5 figures (hep-th/0601001)

Susskind offers this curious remark:

I say curious inasmuch as this remark suggests that Susskind has been concealing his motivations. Perhaps he anticipates being deemed not crazy, but rather crazy-like-a-fox, at some point in the not-too-distant future. More precisely, perhaps he has decided that the best way to promote the intellectual independence of the post-1990 generation of theoretical physicists in the face of these deep problems is to convince them that their erstwhile mentors have become depressed, foolish, demented, or outright raving lunatics.

Adrian quoted Rovelli as of saying:

This is a really odd statement; you cannot blame physics for moving too fast, but maybe rather Rovelli for not having understood quantum mechanics; what math is it which is so complicated? Hilbert spaces? Linear equations? Or matrices?

“But as we know, the ambition of all young scientists is to make fools of their elders.”

Susskind is an old scientist, who wishes to be forever young, therefore it is his ambition to make a fool of himself.

Mission accomplished!

It’s interesting the see Carroll go apoplectic over a supposed attack on the holy balance of gender, while he calmly entertains the most absurd and twisted physical ideas.

Here’s my “dangerous idea” (what a load of dung for a topic) – Western man is committing intellectual suicide by allowing the entire estate to be tended by such hysterical stewards.

-drl

Bravo KO!

-drl

Greene, Steinhardt, and Krauss all make reasonable arguments against Susskind’s Landscape idea, or similar ideas associated with any concept of a “multiverse”, eternal inflation, etc. The arguments are generally of the form: It’s a cop-out to accept that the important physical constants are simply random variables. It would discourage continuing efforts to find fundamental principles that explain the values of these constants. And it’s not a testable or refutable idea anyhow.

But then I’m reminded of another theory which posited that fundamental aspects of reality are random variables — quantum theory. That has turned out OK, even though Einstein didn’t like it.

And further, I don’t see how the idea that there are basic principles determining the fundamental constants (as Einstein and many others have supposed) is refutable either. The idea that there really is a scientifically sound “theory of everything” may be testable if/when we have a candidate to test — but not before.

And what if we did happen to find a satisfactory theory that fully determined all the fundamental constants, as Einstein expected? Then we would have to face a rather striking conclusion — that the fundamental principle(s) together with pure mathematics require that all the physical constants have specific values which just happen to allow our kind of life to exist. Wouldn’t that itself be a conclusion which demands an explanation?

Just asking.

I wonder what exactly Susskind expects young researchers to make of this?

Currently, the academic system rewards obedience and punishes independent thought, unless the thinker in question is already well established (Susskind or Weinberg, for example). Young researchers who are prepared to snub their noses to the fashionable trains of thought do not tend to last more than a year or two, unless they have obtained a permanent job by some fluke. Even then, they will be ostracised. Although elderly gentlemen like Susskind may say that they relish the prospect of being proved wrong by some 24-year-old, they are in fact conveniently forgetting that the hierarchical structure they sit on will silence most dissenting voices long before they get a chance to be heard.

Kaspar said

”what math is it which is so complicated? Hilbert spaces? Linear equations? Or matrices?”

Unbounded self-adjoint operators with their domain restrictions (see Reed and Simon vol 1); State spaces of operator algebras (see Alfsen and Schultz, 2 volumes); Hyperfinite Factors; Gleason-Kochen-Specker proofs; C^* Algebras and Information theory; etc.

Time to update beyond your Dirac or von Neumann texts from the 1930s. A lot has happened. (The Copenhagen interpretation really did chloroform the physics community! I think that is what Rovelli is complaining about.)

Chris Oakley et al quoted Susskind as saying that “… if the young generation of scientists is really that spineless …[as to]… give up looking for the “true” reason for things, the beautiful mathematical principle … then science is doomed anyway … “.

Since Susskind himself is, by advocating his Landscape, “… … giv[ing] up looking for the “true” reason for things, the beautiful mathematical principle … “,

it seems to me that he himself is advocating that “science” be “doomed”, and

that his comment seems to be an attempt to shift the blame for any resulting Dark Age from himself to the “spineless … young generation”.

As one who has a model that does allow calculation of the fundamental constants, which model is therefore testable, I find the questions of Charles Daney:

“… what if we did happen to find a satisfactory theory that fully determined all the fundamental constants, as Einstein expected? Then we would have to face a rather striking conclusion – that the fundamental principle(s) together with pure mathematics require that all the physical constants have specific values which just happen to allow our kind of life to exist. Wouldn’t that itself be a conclusion which demands an explanation? …”

to be interesting.

Tony Smith

htttp://www.valdostamuseum.org/hamsmith/

Unbounded Ignorance…Ups! This is of course something which I should have known about, sorry. But I’m sure Adrian will help me. For starters: what is an unbounded operator? One without boundaries? (It’s hard for me to imagine what this could mean). How can such an OP have domain restrictions when it is unbounded? What is a state space of OP algebras? (I’ve never heard about an operator being in some specific “state”). And C^* algebras? What does the C stand for – and more interestingly the * – is it ultimatively related to cosmology? And Information Theory? Does that apply both to modern quantum mechaincs and the media? Seems like I’ve go a lot to learn…

Hi Kaspar

Yes, it looks like it’s going to be a long winter over those books. Enjoy! 🙂

A.H.

Kasper said

“what is an unbounded operator? One without boundaries? (It’s hard for me to imagine what this could mean). How can such an OP have domain restrictions when it is unbounded? What is a state space of OP algebras? (I’ve never heard about an operator being in some specific “state”). And C^* algebras? What does the C stand for – and more interestingly the * ”

An unbounded linear operator on a normed vector space (e.g. Hilbert or Banach space) is a _not necessarily continuous_ linear operator that is _not necessarily_ defined on the whole space! Bounded (= continuous) linear operators are then (confusingly) a special case of unbounded linear operators! Domain restrictions are a big thorn in the analysis of unbounded operators, which is why some mathematicians feel physicists are a bit dodgy in their calculations. See the nice paper:

F. Gieres, Mathematical surprises and Dirac’s formalism in quantum mechanics (quant-ph/9907069)

for a discussion of the sutleties of unbounded ops in QM.

For a more basic general discussion see the Wikipedia article:

http://en.wikipedia.org/wiki/Unbounded_operator

As for C*-algebras, see: http://en.wikipedia.org/wiki/C%2A-algebra

The * stands for the involution or “adjoint” operation on a C*-algebra (which plays the role of a generalized “conjugate transpose” from matrix theory). Physicists tend to use a “dagger” symbol for adjoints, while mathematicians use a “star” symbol. There is also the C*-identity: ||T*T|| = ||T||^2. Thus, a C*-algebra is a normed algebra, which is complete with respect to the induced norm topology, with an involution operation * that happens to satisfy the C*-identity.

A “state” on a C*-algebra A is a positive linear functional f : A -> C from A to the complex numbers C. (Thus, the “state space” of A is a subset of the dual space A* of all bounded linear functionals, but that is another use of *…) When A = B(H) is the C*-algebra of bounded linear operators on a Hilbert space H, every unit (= state) vector v gives a “state” for B(H) by the “expectation” formula:

f(T) = (T(v), v)

for T in B(H), where (v , w) denotes the inner product. By the Gelfand-Naimark-Segal (GNS) construction, every state on an abstract C*-algebra A can be (essentially) viewed in this way.

Hope this helps,

Jody

Sorry guys – but it was obviously a joke from begining to end 😉 Of course I know these things very well indeed.

The point here is, that for many applications of quantum mechanics (for example if you are doing atomic physics) you don’t need to know what an unbounded self-adjoint operator is. Or what a C^* algebra is. Or what Information Theory is.

So, it was not

unbounded ignorancefrom *my* side…HI everyone.

Carlo Rovelli did not say or imply that “Physics moved ahead too quickly in the last century, without properly understanding the mathematics of quantum mechanics.” Kasper, this comment was made by Adrian. Please read what he actually said, http://www.edge.org/q2006/q06_9.html#rovelli. Rovelli’s point was entirely different.

What Rovelli is complaining about is clear from his last sentence. It has nothing to do with the math, it is the extent to which string theory has become a study of cataloguing solutions to classical or at best semiclassical equations, ignoring both the background independence of general relativity and the challenges of understanding what a spacetime is within quantum mechanics. His point, with which I sadly have to agree, is that those who think of themselves as doing fundamental physics but have avoided wrestling with the implications of combining the principles of GR and QM have not appreciated the radical conceptual and technical innovations imposed on us just by those principles.

Best wishes to everyone for the new year, Lee

ps To avoid the inevitable misunderstanding, I do NOT imply here that the Einstein equations are fundamental, only that the principles of GR are.

And, yet, Rovelli was still condescending and wrong.

We must understand that Carlo has his own interpretation of quantum mechanics, the so-called relational interpretation, and his statement that others have not understood quantum mechanics simply means that others don’t share his interpretation.

(Incidentally, his interpretation is that which we should say that a thing is in one state “relative to” something else, rather than saying that a thing is in a particular state. He doesn’t answer the question: Can a cat be dead relative to one person and alive relative to somebody else? If the answer is yes, his interpretation is just many worlds, and if the answer is no then there’s nothing relational about it – the cat is absolutely alive or dead. Consequently, his interpretation is incoherent.)

The remarks about background independence are more widely known, and have more justification, although the appeals to Leibniz’s theory of space should not be made, since Leibnizian space was disproved by Kant in the 1780’s.

Aaron, would you care to say which of Rovelli’s statements you consider to be wrong and whether it is just your opinion or whether it’s an established fact?

Rovelli said:

What makes me smile is that even many of todays “audacious scientific speculations” about things like extra-dimensions, multi-universes, and the likely, are not only completely unsupported experimentally, but are even always formulated within world view that, at a close look, has not yet digested quantum mechanics and relativity!rof asks:

Aaron, would you care to say which of Rovelli’s statements you consider to be wrong and whether it is just your opinion or whether it’s an established fact?I don’t presume to speak for Aaron, but the quote above seems wrong to me, and it’s

Rovelliwho needs to justify the opinion. A perusal of the literature on extra dimensions, for instance, will reveal plenty of both relativity and quantum mechanics. It is, as Aaron said, condenscending of Rovelli to claim that other physicists do not understand these things. They are the bread and butter of all of high-energy physics.Aaron, would you care to say which of Rovelli’s statements you consider to be wrong and whether it is just your opinion or whether it’s an established fact?The idea that people don’t understand background independence, the lessons of general relativity, yadda, yadda, yadda. People are quite capable of understanding the metaphysics and still rejecting Rovelli’s favorite theory.

Has anyone of the “bigwigs” (a scientist of stature on the order of a Weinberg, say) proposed the dangerous idea that if quantum gravity theorists can’t figure out how to formulate a falsifiable theory, they should either make the ethical leap to mathematics*, where their imagination need not be fettered by external referents, or abandon quantum gravity models altogether for fields that contain problems which are testable, at least in principle?

(*This is not to denigrate mathematics, being perhaps the only worthy “philosophy”, to which the greatest human minds contribute, just to acknowledge there’s a difference, and that difference can be important.)

Aaron and Anonymous,

Let’s lower the temperature and discuss the substance of what we disagree about. You say, “People are quite capable of understanding the metaphysics and still rejecting Rovelli’s favorite theory.” But, as Carlo makes clear, his favorite theories are general relativity and quantum mechanics. He claims that the principles of these are ignored by approaches to unification that study only semiclasical effects in fixed classical spacetime backgrounds.

You make it clear that you disagree, i.e. you reject the view that a quantum theory of gravity should be background independent. This is a substantial disagreement. So lets discuss why we disagree.

Certainly, no insult is intended. But it is hard to avoid the impression that some people who reject the case for background independence have not thought carefully through the issues in the interpretation of general relativity that lead us to adopt it. Perhaps this is not true of Aaron, but it is true of many who confuse the methodlogy used to interpret very symmetric solutions to GR with the very different issue of describing observables for the generic solution.

The issue is not about knowing how to write the Einstein’s equations down or find simple solutions. It is about the interpretation of observables on the space of solutions. Untill one has struggled through the issues raised by the hole argument, or the problem of specifying diffeomorphism invariant observables, you cannot have absorbed the full meaning of general relativity. My impression is that once people have absorbed this it changes their taste as to what kinds of solutions to the problem of quantum gravity they are willing to entertain. Specifically it seems impossible to have understood these things and still to believe in the possible viability of any background dependent approach to quantum gravity.

Of course the equations of general relativity are used in Kaluza-Klein inspired higher dimensional unifications. But, because of these subtle interpretational issues, this is not the same thing as taking the princiiples of the theory seriously.

A related issue is that all the higher dimensional unifications require that some degrees of freedom be frozen. Otherwise, as Penrose argues in his recent book, there are instabilities that lead quickly to collapse to singularities. These are to some extent avoided by the flux compactifications but, as we know, the cost is the need to appeal to anthropic arguments.

But the point is that from a background independent point of view, any result that requires the specification of a specific solution rather than a generic prediction of the theory seems unreliable exactly because the symmetric solutions are in many ways non-generic.

Even Einstein saw this was a potential trap, when he commented, ““It is anomalous to replace the four dimensional continuum by a five dimensional one and then subsequently to tie up artificially one of those five dimensions in order to account for the fact that it does not manifest itself”

Thanks,

Lee

Dumb biologist,

There seems to be a misconception that if what string theorists are doing isn’t falsifiable and thus not physics, it must be mathematics. Not so. Some sorts of work in string theory involves non-trivial new mathematics that is of interest to mathematicians, and there already are some people doing this successfully working in mathematics departments. But most of the non-falsifiable stuff going on in string theory does not involve any new mathematics, and mathematicians want even less to do with this kind of thing than physicists.

Ah, I see.

Well, that’s kind of depressing…

Lee, back to that story. I believe you are talking about string perturbation theory when you claim we expand around a classical solution, which are very symmetric, and all the rest. I would call it lack of *manifest* BI., but never mind that.

\

Since it is already 2006 we don’t have to have that conversation. We have, since 1997, a background independent formulation of quantum gravity in spaces with negative cosmological constant. Yes, it is not quite as BI as you would like it to be, but as I mentioned before there are good reasons, independent of string theory, to believe that is the best one can do. Indeed, one of them is precisely the struggle to define diffeoemorphism invariant observables, which at least so far require one to have appropriate asymptotia.

\

Finally, not too get too deeply into that, but lowering the temperature seems like a good idea if one is to have a useful conversation, derogatory or misleading statements about each other’s research are not helpful in that.

Since I kind of started all this by posting the material from Rovelli, let me say a bit about why it struck a little bit of a chord with me and I included it. I suspect that my own ideas about this are quite different than Rovelli’s, but perhaps there is some overlap.

As everyone in the field is aware, combining QM and special relativity inescapably leads us to quantum field theory. My version of Rovelli’s comment that our picture of the world is too simple-minded and that we haven’t fully absorbed the implications of QM and special relativity would be not that physicists don’t understand the standard formalisms of these two subjects, but that the full implications of QFT have yet to be fathomed or absorbed. Starting in the late 1970s, people have found some very deep new mathematics by thinking about QFT, and I suspect there’s a lot more of this to be uncovered, with major implications both for mathematics and physics. 200 years from now, people may very well see the late 20th century as a period when we were just starting to get a clue about what QM+SR=QFT really was, with a large part of the field ignoring the very challenging issues posed by trying to get to the bottom of this, instead spending its time on ideas about multiverses and extra dimensions that turned out to be shallow and besides the point.

You make it clear that you disagree, i.e. you reject the view that a quantum theory of gravity should be background independent.I have made absolutely no such claim whatsoever. We’ve covered this ground

ad nauseumon Cosmic Variance, so I’m not going to repeat myself here.After all of that discussion, that you still don’t understand my position is inexplicable to me.

Dear Moshe,

Thanks. Two small points. You say, “there are good reasons, independent of string theory, to believe that is the best one can do.” No, we know that one can do much better and get results from genuinely background independent methods. This is shown by recent results in causal dynamical triangulations and LQG in both 2+1 and 3+1 dimensions. Indeed, the recent results are based on methods which deal successfully with the problems of diffeo invariant observables (read Rovelli’s papers leading up to the recent results on the graviton propagator-as that was their purpose.)

As for AdS/CFT, let me insist again that except for special cases where BPS symmetry is used, the evidence supports a weak form of the conjecture-which is the one in WItten’s 97 paper. This conjecture gives a map between CFT’s on the boundary and classical or semiclassial field threories on fixed backgrounds that are asymptotically AdS. Most of the very impressive results in this subject support this weaker form of the conjecture. This is far from sufficient to support the much bolder conjecture of Maldacena that there is an equivalence between a string theory in the bulk and the boundary CFT. Given that there is not even a complete formulation of free string propagation on AdS5 X S5 one cannot claim that there is strong evidence for Maldacena’s form of the conjecture-except again in very special cases where BPS symmetry allows constructions to be done that may not otherwise exist.

Given this, I see little support for the even stronger form of the conjecture that posits that results of the boundary CFT are equivalent to a fully background independent (except for asymptotic boundary conditions) quantum gravity theory in the bulk. There are many papers that assume that the conjecture is true and deduce consequences, but the only evidence I know of that supports a strong as opposed to a weak form of the AdS/CFT conjecture makes strong use of BPS symmetry, which means it may not be reliable outside of a tiny sector of the Hilbert space.

So I do not agree that “We have, since 1997, a background independent formulation of quantum gravity in spaces with negative cosmological constant.” I cannot object if you personally believe this strong form of the conjecture, but I do object if you write as if it is an established fact.

thanks, and happy new year, Lee

Aaron, I’m sorry, but I looked on CV and you say there that: “… to say that any quantum theory of gravity must be background independent smacks of hubris….Nature is going to work how it’s going to work.” And, “If a nonperturbative formulation of string theory exists, we should find it. If it’s background independent, that’s great. … But, if the nonperturbative formulation isn’t background independent, then so be it.”

If these are representative then you appear to ” reject the view that a quantum theory of gravity SHOULD be background independent”. which is what I said.

Thanks, Lee

Again, Lee, look at the paper of Berenstein, Maldacena and Nastase and the

795papers the cite it.I reject there the idea that a quantum theory of gravity

needsto be background independent. But, as the whole rest of that thread points out, string theory looks background independent. Nobody’s rejecting the “case for background independence”. You continually set up this straw man, and it’s tiresome.Lee, Aaron reminds me there was a reason for my deja vu… Let me just say I strongly disagree with your characterization of AdS/CFT as applying just to the BPS sector, or only in the supergravity limit, this is just wrong. I also think a conjecture that faced thousands of attempts for refutation over 8 years is as established as we will ever acheive in this business, just my opinion. If you prefer we can refer to anything that was not rigorously proven as a conjecture…

\

Peter, interesting interpretation of Rovelli’s remarks, I am afraid though that he refers to general and not special relativity… I have to say that this struck a chord with me as well, the thing I find most useful about string theory is that it is a quantum mechanical model which naturally incorporates general relativity at large distances. So maybe we don’t fully incorporate the deep ideals of QM and GR, but at least we incorporate the theories themselves, that is a good start.

The pp waves studied by BMN are an extremal limit of the theory. While these are very impressive results they are special cases that rely on special structures and so do not prove the general conjecture.

And Aaron, please clairfy: you reject the idea that a quantum theory of gravity NEEDS to be background independent. But you say nobody rejects the case for background independence. Isn’t this a contradiction? My reading of the “case” is that it consists of arguments that REQUIRE background independence.

I am sorry if this is tiresome, but you claim that “string theory looks background independent.” What is meant by background indepedence is a formulation of the theory that makes no reference to any classical background geometry. Even granting the strong Maldacena conjecture, it would not do this because there is a fixed Minkowksi geometry on whcih the SYM theory is defined.

Were there in fact a backgound independent formulation of string theory it would have a Hilbert space and observable algebra whose specificaion made no reference to any classical metric. There simply is no such formulation of string theory. All the matrix models considered to be part of string thoery, including BMN and BFSS have a fixed metric in their Hamiltonian. There were a few attmepts to make a truly background independent formulation of string theory, but not enough is known about them to claim success.

Lee

Lee, you said “As for AdS/CFT, let me insist again that except for special cases where BPS symmetry is used, the evidence supports a weak form of the conjecture”. Now, when presented with such evidence, you say “they are special cases that rely on special structures and so do not prove the general conjecture”. This strikes me as goalpost shifting.

In general, I reject metaphysics. You can make all such arguments you want, but nature is the ultimate arbiter. I don’t think we can ever ultimately learn anything about nature except through experiment.

As for the rest, pretty much everything I want to say has already been said in the CV thread, but “Even granting the strong Maldacena conjecture, it would not do this because there is a fixed Minkowksi geometry on whcih the SYM theory is defined.” is really a very strange statement. You’re complaining about background independence for a nongravitational theory?

You know, there is always the possibility that quantum gravity

really doesdepend on asymptotics. Background independence will be nice, but we just don’t know for sure if it is a necessary feature of quantum gravity. I think Banks has argued that it cannot be a feature of quantum gravity, for instance.Lee, is the following true from your perspective? Every known attempt to start from background independence and construct a theory of quantum gravity relies on the

assumptionof a UV fixed point for gravity. It’s true of all the examples I know, but I know of no convincing reason for that underlying assumption.So if we have to choose a starting point, either a UV fixed point and background independence, or a lack of a UV fixed point and a lack of manifest background independence, I would go with the latter. But string theory, though lacking

manifestbackground independence, certainy appears to haveat least some degreeof background independence. It would certainly be nice to clarify the exact status of background independence in string theory, but the lack of manifest background independence is no reason to scrap string theory in favor of other approaches starting from much shakier foundations.Hi Peter

Since Kasper pulled my leg by asking me ”which new mathematics” for QM, can I ask you to ‘fess up and say what new maths for QFT you have in mind?

(I’ve long been curious what happened to the Glimm and Jaffe program. At a certain point I just no longer heard of it. Did it face some insurmountable problem or did people just drift on to other things? For a while there it looked like it was the bomb.)

happy new year to you

Adrian,

Some of my speculations about the kind of mathematics behind quantum gauge theory is in the paper about QFT and representation theory I wrote a few years ago that is on the arXiv.

I haven’t heard much in recent years about the kind of rigorous constructive QFT that Glimm and Jaffe were working on. Not sure whether there just are very few people working on it, or really insuperable problems. My own guess is that trying to rigorously construct very general classes of QFTs is too hard, you need more structure to make the theory tractable. If one really could better understand the relation between QFT and representation theory I was writing about, for certain specific QFTs one might be able to do much more in terms of understanding the theory rigorously.

Hi Anonymous,

Thanks, your statment about background independence and UV fixed points is interesting but does not agree with my understanding of the results. Ambjorn and Loll, who have good results which show the emergence of geometry from a background independent theory, SHOW in detail that fixed points exist, they don’t assume it. As for the LQG results, the theory is shown to be uv finite, in both the hamiltonian and path integral formulations. So there is no uv scale invariance at all.

As to the role of asymptotics: in GR, which is a background independent theory, the phase space splits into disconnected sectors, depending on the asymptotics. I see now reason the same should not be true in

the quantum theory. The evidence, for example, from 2+1, is that it is.

To Moshe, I don’t dispute there is an AdS/CFT relation, I am just trying to find out precisely which possible version is true. Don’t you agaree this is a good thing to do, given that there are different possible conjectures? I am following a basic rule of logic which is that if two conjectures explain some evidence, only the weaker of them can be considered to have support from that evidence. Especially in a subject that has been well explored, where, as you say, there have been thousands of papers over 8 years, isn’t it reasonable to believe the weakest conjecture that I need to explain the evidence in all those papers?

I can easily imagine results that would support a stronger conjecture, given the subject is well studied, their absence is also at least indicative.

But perhaps we should agree to disagree till there are fresh results,

Thanks, Lee

Lee, I am curious about your statement about the phase space of GR having disconnected pieces, do you regard that as evidence for weaker form of BI such that asymptotics are kept fixed?

\

As for AdS/CFT, all I am saying there is lots of evidence for much stronger form of the relation than the form you presented (only BPS objects in the supergravity limit).

\

I also think that the mode of operation of physicists tend to be taking whatever seems to work as a hint and try to apply it to further interesting problems (for example in the present case gravity in deSitter space), we don’t tend to stick around and sharpen and prove conjectures, maybe that is regrettable but this is the way things are.

I pretty much agree with Aaron about the tiresomeness of objections to superstring theory based on lack of background independence.

If you go back to the days of N=8 supergravity, IIRC the gravity sector got the Einstein-Hilbert action from a MacDowell-Mansouri process applied to the anti-deSitter group Sp(2) = Spin(2,3), and IIRC people back then were not attacking supergravity based on lack of background independence.

IIRC, the attacks back then were based on fears that UV finiteness would not be maintained at high orders.

Was the idea back then that somehow “enough” background independence for GR would probably “emerge” through the MacDowell-Mansouri process (a la Deser-type formulations)?

Since such supergravity might be a low-energy limit of some superstring formulations, could it be that a similar “emergence” of “enough” background independence for GR might occur?

Doesn’t that mean that, unless and until such an “emergence” is conclusively ruled out (which I do not think has been done or is likely to be done in the near future), it is silly to attack superstring theory on the basis of lack of background independence?

Tony Smith

http://www.valdostamuseum.org/hamsmith/

PS – If my recollections above (designated by IIRC) are seriously flawed, then, as Gilda Radner used to say, “Nevermind”.

Lee Smolin said:

The issue is not about knowing how to write the Einstein’s equations down or find simple solutions. It is about the interpretation of observables on the space of solutions.

This is absolutely not the issue! and it is flat wrong for you to annouce it as such. I think you people are not very bright – you completely miss the point about GR, which is how you end up abusing it so much.

The issue is the measurement problem without assuming an apparatus = a background. This does honor to both GR and QM. You will instantly understand if you think for 10 minutes that the entire ethos of the measurement problem is antithetical to the idea of background independence. Any attempt to go farther than this is doomed. You must either change one, or the other. Your crowd ignores the actual physical import of GR because it is easier to hide one’s canoe in the metaphyical tributaries of the of “interpretation”.

“Wave function of the universe” – case closed!

The only people who take both GR and QM seriously are Finkelstein, Dirac, Einstein, Pauli, and Schroedinger. The very people who get ingored now.

-drl

(..and the actual physical import of GR is…)

Are you saying that assuming a background is equivalent to assuming that measurement apparatuses are physical realizable, which is obviously an essential precondition for doing physics, hence the demand for background independence is self-defeating and pointless?

[correction:

physicallyrealizable]Lee,

OK, it sounds like we are in agreement that asymptotics are potentially important.

You say “Ambjorn and Loll, who have good results which show the emergence of geometry from a background independent theory, SHOW in detail that fixed points exist, they don’t assume it. As for the LQG results, the theory is shown to be uv finite, in both the hamiltonian and path integral formulations. So there is no uv scale invariance at all.”

I’m puzzled by the Ambjorn/Loll result, but I have to admit to only having skimmed the relevant papers. It doesn’t seem the lattice theory is known to have a good continuum limit, which is what I would think you mean by “SHOW” that fixed points exist. Are you saying they have definitively established such a limit? In which papers?

As for LQG: you’re saying the theory is UV finite but there is no UV fixed point? How does this mesh with the nonrenormalizability of GR? What’s the extra structure that fixes the infinitely many independent constants one naively expects in quantum GR?

One last question: in all of these non-string theoretic approaches, quantum gravity is proposed to be just a

quantum field theoryin the usual sense, yes? If so the claims conflict with my field-theoretic intuition, but if you can answer or give references for answers for my questions above it should help me understand exactly what you’re claiming. Maybe others have the same confusion? (I, for one, thought LQG was predicated on assuming a UV fixed point of some sort.)Thanks!

Hi Moshe,

Yes, GR satisfies a weak form of BI (background independence) in which several things are kept fixed including dimensions, topology and asymptotics. So hence does any direct quantization of GR. We might posit a deeper theory that dispenced with these background structures, which takes us beyond the strict quantization of GR. Several people in the BI quantum gravity world have advocated doing so, for example, Markopoulou and Freidel both advocated forms of spin foam models in which there is no fixed embedding space for the spin foams.

I agree also its regrettable that at least some people don’t dig in and sharpen and prove conjectures. We can certainly do something about this, for example make sure that people who do so, like Berkovits, are honored and rewarded.

Hi Anonymous, for Abjorn and Loll, you can see clearly the demonstration of a fixed point in their 1+1 dimensional case, hep-th/9805108. Another way to see it is in the paper of Ansari and Markopoulou, hep-th/0505165. There are results also in 3+1 but those are numerical, whereas in 1+1 they are analytic and clean. As for LQG I tried to explain in an intuitive way for quantum field theorists the basics in my review hep-th/0408048. It evades perturbative non-renormalizability because there simply are no excitations with wavelength below the planck scale.

But there was an intuitive idea which indeed was motivational for LQG at the very beginning, which is that one expected from the ideas of asymptotic safety that a uv fixed point would require a scaling dimension of 2. This suggested that when you probe to Planck scales you should see a distribution of 1+1 dimensional excitations on a background where the metric vanished. Crane and I studied this heuristically in 84-85. This suggested initially looking at states made by finitely distributed WIlson loops, which was adopted then to the Ashtekar connection. But the actual results indicated there is just a uv cutoff rather than a scaling with reduced dimension.

However it is interesting to note that both Amborn and Loll and recent works on asymptotic safety see evidence for a reduction in scaling dimension to 2.

Thanks,

Lee

DRL,

Can you elaborate a bit about GR and measurement? It is a project of mine to take GR as it is presented at the moment (namely, as an ontological theory – “There exists a manifold, with this and that tensor and these geometrical properties”) and reword it so that it makes mention only of experimental results and their relationships from the points of view of observers. Have you attempted something similar?

Lee, just to clarify my opinion, I think that proving conjectures is not a particualrly effiecient search startegy. Sure, once the correct language and issues are identified this should be done. I am glad for example that the people who developed the standard model did not stop to prove their points. Many of the ingredients going into that theory, such as confinement and the existence of chiral gauge theory, remain on shaky mathematical ground to this day. But, of course this is just a matter of judgement, though this view I think is wide-spread among theoretical physicists of all stripes.

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And about background independence, I am a fan of the weak form, which fixes the asymptotics, at least for now. I take it as another encouraging sign that Einstein’s classical gravity obeys precisely this form.

I would like to go back to what Rovelli said in the first place. I have heard him say something similar, and he also talks about it in his book : it’s the need to be conservative to open the way for a scientific revolution. What Rovelli says, and he’s surely right about it, is that finding a quantum theory of gravity is not just a very difficult technical problem but a conceptual one that will involving a complete reinterpretation of our old ideas about the world. Perhaps even the words “quantum theory of gravity” are inappropriate for what will come out. But that does not mean that new concepts need to be introduced by hand before solving this problem : Rovelli also argues in his book that it had never worked that way. The only thing we can do is taking seriously the theories we have, without any wild guess about additional structures, and follow the thread until something appears that need to be understood in a new way. This is exactly what Einstein did with special relativity : he took Mawxell theory and galilean relativity seriously, and follow the thread until the Lorentz transformations followed. What’s interesting is that these were already around, but no one understood them, no one took them really seriously. Einstein did because they followed logically from two well established facts : the invariance of c and the relativity of inertial motion. Thus he was compelled to take them seriously, and it led him to a new conceptual framework. Before that, wild theories about how the way aether interacted with matter had been made, but of course they couldn’t get anywhere. Now suppose string theory is the right direction to follow to quantize gravity. To what conceptual revolution does it hint to ? This is not only a rhetorical question, I am frankly curious about that. As far as I can see, Maldacena conjecture if it turns out to be true seems to me the only candidate for a change in concepts, but I don’t know enough to be sure about that. On the other hand, the disappearance of time in LQG does really sound like a conceptual revolution to me. But what makes the difference between a new concept and what is just a clever idea ? Can several very clever ideas lead to a new concept ? I don’t know for sure, but perhaps one could say that a clever idea is an answer to a specific question (how many dimensions does spacetime has ? what is the shape of the universe ? what do particles look like at very small scales ?), even one that has never been put forward, whereas a new concept does not answer any question but tells you what questions you are allowed to ask.