Lawrence Krauss and Leonard Susskind have a letter to the editor in this week’s New York Times Sunday Book Review, complaining about John Horgan’s NYT Book Review essay Einstein Has Left the Building of a couple weeks back. For some discussion of an earlier Susskind-Horgan exchange about another NYT piece of Horgan’s, see here and here.

Krauss and Susskind write that “Horgan evidently sees the two of us as being on opposite sides of an imagined controversy”, but that “the fact is that there is little of substance that we disagree about.” They accuse Horgan of thinking “that reconciling quantum mechanics with Einstein’s theory of gravity is a frivolous pursuit”, whereas “both of us feel that reconciling the conflict between gravity and quantum mechanics is one of the deepest problems in modern physics.” They comment about extra dimensions:

*As for Horgan’s bête noire of physics — higher dimensions, or what he refers to as “hyperspace theories” — he writes: “But pursuers of this ‘theory of everything’ have wandered into fantasy realms of higher dimensions with little or no empirical connection to our reality.” That both of the present writers recognize that additional degrees of freedom of one sort or another are needed to characterize the physics of elementary particles may come as a surprise to Horgan. What the two of us may disagree about is what may be the likely physical and mathematical basis of this fact. But we both recognize that the mathematical spaces that we already deal with in describing the quantum theory of matter are in a certain sense more mathematically exotic than simple possible extra physical dimensions.*

It seems to me that Krauss and Susskind are creating a straw man to attack here, not really dealing with Horgan’s actual criticisms, the full text of which was:

*Especially as represented by best sellers like “A Brief History of Time,” by Stephen Hawking, and “The Elegant Universe,” by Brian Greene, physics has also become increasingly esoteric, if not downright escapist. Many of physics’ best and brightest are obsessed with fulfilling a task that occupied Einstein’s latter years: finding a “unified theory” that fuses quantum physics and general relativity, which are as incompatible, conceptually and mathematically, as plaid and polka dots. But pursuers of this “theory of everything” have wandered into fantasy realms of higher dimensions with little or no empirical connection to our reality. In his new book “Hiding in the Mirror: The Mysterious Allure of Extra Dimensions, from Plato to String Theory and Beyond,” the physicist Lawrence Krauss frets that his colleagues’ belief in hyperspace theories in spite of the lack of evidence will encourage the insidious notion that science “is merely another kind of religion.”*

I don’t see Horgan here criticizing the attempt to quantize gravity as “frivolous”. His criticism of physicists as having “wandered into fantasy realms of higher dimensions with little or no empirical connection to our reality”, is a justifiable one that deserves to be seriously addressed. Krauss and Susskind’s comment that Horgan would be surprised that both of them think that new degrees of freedom will be needed to characterize elementary particle physics doesn’t seem to have any basis in fact. Horgan isn’t making broad claims that physicists shouldn’t look for new degrees of freedom, he is very specifically referring to the use of extra space-time dimensions.

Krauss and Susskind at least implicitly take Horgan to task for referrring to such extra dimensions as “hyperspace”. He may well have picked this up from Michio Kaku who wrote a book with this title. By the way, tonight Kaku will be appearing on the Art Bell “Coast to Coast” radio program, a program which is mostly concerned with UFOs and the like. If Krauss and Susskind want an example of the kind of theoretical physics research that Horgan is bothered by, they could check out this radio program.

I do see in this a thinly veiled exasperation on Horgan’s part with the belief—as expressed in research priorities—that such a unification is possible and worth pursuing. It seems to me that he has made fairly clear in his earlier writings that pursuit of this goal (and others, such as the nature and origin of consciousness) is likely to lead into a swamp of, as he calls it, ironic science.

In a way he’s right. We may become mired in just such a swamp. That risk has always existed when confronting difficult theoretical problems. Successfully facing the risk is what has distinguished great scientists from the much larger number of talented and competent practitioners who shy away from it, are defeated by it, or fall victim to it and lose their bearings.

Congratulations for having upgraded from Krauss’s silly opinions about extra dimensions to Horgan’s idiotic opinions about the whole modern science. What’s the next step? Defending Dembski against those who argue that more than a “click” by an intelligent creator is needed to create and explain the world? 😉

I find the letter by Sootkind and Krauss totally SLEAZY and DISHONEST. My opinion of Sootkind’s tactics in debating and politics was already very low, but my opinion of Krauss is now lower.

“That both of the present writers recognize that additional degrees of freedom of one sort or another are needed to characterize the physics of elementary particles may come as a surprise to Horgan.”

Really! Horgan would be surprised by that? Ever since Newton, physicists have used “additional degrees of freedom of one sort or another”. Any person of normal intelligence will have no problem realizing that by “hyperspace”, Horgan meant extra space-time dimensions. Only a genius String Theorist could misread that.

Krauss and Susskind write that “Horgan evidently sees the two of us as being on opposite sides of an imagined controversy”, but that “the fact is that there is little of substance that we disagree about.”

Does it mean that Krauss wanted to reverse his claim that String theory is a colossal failure?

maybe somebody has gotten to him.

I am amazed at the straw-man arguments Krauss(it was expected of Susskind) has used to attack Horgan. This is pathetic. The credibility of physicists, not just string theorists, is sinking like a stone. I think Krauss should retract his book since “there is little of substance that they disagree about” .

Who is going to be next? Et tu, Peter?

I do not read anything wrote by Horgan after i read his

End of Sciencebook.Reading that Peter Woit has wrote above, it appears that Horgan is just maintaining the RELEVANT and PURELY SCIENTIFIC point that he exposed in his book years ago about the (non)verificability of the exoteric ideas of string theory (such as tiny extradimensions).

In his interview to Witten, Horgan claimed that both extradimensions and Planck scale strings were really non-verifiable and therefore outside of science (physics).

Witten’s esxhasperation to lack of empirical evidence is well-reflected in the interview.

I would not use the word ‘idiotic’ other used in this blog, but i find particularly relevant Witten’s belief (exposed in the book) that aliens already discovered GR, supersimmetry, QFT, and string theory but not necesarily in that order 🙂

—

Juan R.

Center for CANONICAL |SCIENCE)

It is odd that one would bother to write an entire book about what “little of substance” there is to disagree about. I wonder what these extra degrees of freedom, if not extra spatial dimensions (compactified or otherwise) are supposed to be.

My understanding of Krauss’ thesis was that there’s some psychologically-bequiling quality posessed by “extra dimensions” that draws great minds into la-la land.

At any rate, is not testability the most pressing issue? Extra dimensions may be 100% real, but if it takes god-like technology to probe them, it seems throwing the bulk of theorists’ efforts into theorizing about them is putting the cart before the horse, and apparently discounting the possibility that the vast gulf of energy scales between what we can currently test and the Planckian realm may hold some big surprises.

For folks whose research must be mathematically consistent, it’s surprising to see this level of rhetorical incongruity.

mathjunkie,

Krauss has said that his “colossal failure” quote was taken out of context.

D.B.,

Not sure exactly what “extra degrees of freedom” Krauss and Susskind are talking about. One possibility is supersymmetry which is sometimes thought of as involving “extra (fermionic) dimensions”, another is gauge theory itself, which in some sense involves extra “internal” dimensions.

OK. Thanks!

It could also be that the “degrees of freedom” refer to the amount of Superstrings in the theory. Krauss is saying that unless this parameter is zero then the theory will be a “colossal failure”; Susskind is saying otherwise. The so-called “disagreement” – massively exaggerated by Horton – is only over this one unimportant parameter.

How’s this for off topic.

Peter, what ever happened with the trackback issue?

Juan:

Interesting to know that Witten has the belief that aliens have figured it all out: “aliens already discovered GR, supersimmetry, QFT, and string theory” How did Witten know. Did he belong to religious sect that happen to believe so? Or how could he be so certain that aliens study super string theory at all? Maybe the aliens never ever started the super string theory, but worked on something else instead? How could Witten know it is super string theory that the aliens studied, not something else?

I propose to Witten that we utilize some of those giant radio telescope dishes, and send out a telegraph to the space asking about questions in super string theory. Some where in the universe there must be advanced alien civilizations capable of intercepting our messages and they may be kind enough to response with some easy answers.

Or maybe we get no response at all, in which case the anthropic principle answer would be that these aliens, who are so advanced they figured everything out, figured out that those earthlines must be too stupid and too primitive that they are still wasting their time on super string research after two decades, and which we aliens know a long time ago is a deadend.

Quantoken and Juan,

Stop with the nonsense about Witten and aliens. This is just a reference to Witten’s speculating about the possibility of various ideas about theoretical physics being discovered in a different order.

ksh95,

Still don’t know what’s going on about this. Actually I couldn’t access trackbacks at all there for the few days, so I thought something was up. But it appears to have been a problem caused by some cookies my browser was using, deleting them returned things to normal.

A member of the arxiv advisory board tells me someone from the arXiv has promised to contact me this week and tell me what is going on. Will let you know what I hear.

Horgan’s book definitely tried to picture Edward Witten as a person who is confused by ideas about aliens.

If there are two possible explanations – Edward Witten being confused or John Horgan (with all people who endorse him) being a complete idiot, which explanation do you think is more likely?

http://motls.blogspot.com/2006/01/when-krauss-and-susskind-are-right.html

I wonder if the aliens have confused ideas about Witten? They seem to think the smart people live in trailer parks.

-drl

Does anyone know “for sure” where this term came from?

Slightly off topic. In an interesting paper (hep-th/0601162) Delia Schwartz-Perlov and Alexander Vilenkin conclude that the volume distribution for the cosmological constant is nonflat near the observed value, which seems to invalidate previous calculations based on the anthropic principle.

Idiots vs fanatics. I guess I’m a little in favour for idiots. It’s simply healthier to be too stupid to not believe in things that don’t exist. The same thing with sensitivity and paranormal awareness. It’s better to be a little too dumb to feel spooky phenomena.

Woit said:

Krauss has said that his “colossal failure” quote was taken out of context.

Sorry, Peter, my English is not very good as it is not my mother tongue. So, does it mean that Krauss was referring to something else that is a “colossal failure” but not to string theory?

Maybe he decided to order a latte one day at the physics department canteen instead of a capuccino. Not liking it as much, he then decided that this move was a “colossal failure”.

Actually, in string theory there is not such a big difference between degrees of freedom and space-time dimensions. Quantizing in Minkowski space for example, the space-time coordinates appear as fields in the worldsheet theory. In compactifications to 4 dimensions, what is required for consistency is not really to add 6 dimensions, but to add a conformal field theory on the worldsheet with the right central charge. Sometimes these fields can be interpreted as the coordinates of a compact manifold, and other times not.

Two examples of the latter are general Landau-Ginzburg models, and some interesting recent discoveries of nongeonetric flux compactifications: hep-th/0508133. It’s also important that in CFT moduli space, one can moove smoothly between geometric and nongeometric backgrounds. So in the context of compactification (as opposed to say intersecting brane models) it really is better to think in terms of degrees of freedom of a conformal field theory than extra dimensions.

This equivalence of degrees of freedom and extra compact dimensions is not unique to string theory. This is the essence of Kaluza–Klein theory – one can study a K-K expansion of any field theory on R^4\times S^1 for example and find a field theory just on R^4, in this case with an infinite number of fields.

Anyhow, we know for sure (from unitarity bounds) that there are new degrees of freedom to be found even at the weak scale – most likely a Higgs boson. The same sorts of arguments, applied to graviton scattering, require that new gravitational degrees of freedom appear at (or before) the Planck scale. I guess Susskind and Krauss are just saying that they disagree about what these might be – but not about whether they exist, and not about whether they will seem exotic (as they probably will) if they are ever discovered.

Maybe I’m being too general here for a group of theoretical physicists, but on the question of dimensions: I’ve mentioned before that you can always get a symmetry by adding dimensions. Also, suppose you are writing an algorithm to generate (compute) the world, you might use 100 dimensions (degrees of freedom) but the result, the output should only have 4. In real time targeting of tanks, for example, with the input signals from a sidelooking radar, you begin with 12 dimensions and compact them to 7 so you can do the calculations in real time, but the missile you fire and the tank you hit (?) exist in a world of 4 dimensions. In an even more practical example: the number of degrees of freedom of a diaper making machine are greater than the number of atoms in the universe but the product produced holds 3-D excrement. One last thing: the possible worlds of many dimensions and “the landscape” have the odor of Anselm’s ontological proof. Is physics entering another Dark Age?

Steve – if you have a specific, physical reason for introducing more dimensions, and a specific, physical ontology for them, then you are inside the boundary of science. When you introduce them to make an already wacky idea somewhat credible, you are close to the edge. When you introduce them in a way that had been discredited 30 years earlier by one of the great physicists, in order to make a wacky idea credible, and then you spend the next 25 years beating an unworkable strawman, you are over the fence into non-science.

-drl

Help for the ignorant, please:

“Degree of freedom” here seems to encompass just about any quantifiable or qualifiable property of a particle; what it both can do and be. Is that correct? I guess I have a primitive understanding of the term, more like “what’s the particle’s position, momentum, spin” and so forth. Would, say, the ability for a lepton to be a muon or an electron be considered a “degree of freedom” for a lepton? I thought a string theorist would answer that question by saying “because the string can vibrate at a certain frequency, wrap around compactified dimensions of a certain shape, and is so wrapped at a certain tension, it looks like a particular kind of lepton”. I.E., the ability to move around in a particular way gives the string its observed properties, and the extra dimensions provide the “degrees of freedom” to so move.

D.B.

Those are good questions. What is meant by degrees of freedom depends to some extent on the context, i.e. classical mechanics, field theory or string theory. Perhaps the following will help:

Classical particle mechanics:

– Here things are as you say – each component of position or momentum is a degree of freedom, i.e. the number of d.o.f. is how many numbers you have to give to specify the state of the system.

Nonrelativistic quantum (particle) mechanics:

– Here even a single particle is described by a wavefunction, which requires an infinitely many numbers to specify. So we often think of the number of d.o.f. as the number of generators of the Heisenberg algebra (esssentially positions and momenta). But very few discussions in particle physics take place in this context.

Classical field theory:

– There are classical systems with an infinite number of d.o.f. as defined above, e.g. the electric field. Formally, one can understand a field as a harmonic oscillator at each point in space–time. Here we think of a d.o.f. as an component of a field – see the next section for comments.

Quantum Field Theory:

– Here a degree of freedom refers to a component of a field. But there are many subtleties. Some of these are as follows:

– Gauge Theories – here some of the d.o.f. (i.e. some of the ways the field can change) are local symmetries of the action – thus the description of the system in terms of gauge fields is redundant, and there are fewer d.o.f. than there appear.

– On shell/Off shell – The equations of motion of the theory are extra constraints on the fields – further reducing the number of independent components. We call the ones left “on-shell d.o.f”. The full set are called the “off-shell d.o.f”.

– Propagating? – Sometimes (particularly in supersymmetric theories) it’s useful to have fields whose equations of motion are algebraic, i.e. not differential equations. So you don’t have to put in initial conditions to solve them. They can be solved and the solution substituted in to the action to eliminate them if we want. These are called “non-propagating d.o.f.” A non-supersymmetric example of this is general relativity in 2 dimensions.

String Theory:

One caveat: In an important sense it isn’t yet known what the fundamental d.o.f. of string theory really are. If we study perturbation theory about a fixed background, we get a quantum field theory with an infinite number of fields (although a finite number with masses less than the Planck scale) – corresponding as you say, to the different oscillations and winding modes of the string. But we know that the appearance of an infinite number of d.o.f. is misleading from the AdS/CFT correspondence. There, string theory in AdS is seen to be equivalent to a field theory with just a finite number of fields (N=4 SYM). Moreover, prior to the discovery of the AdS/CFT correspondence there were widely held expectations that something like this would happen – going under the general name “holography”.

One last comment: the reason why an extra dimension (a few extra degrees of freedom) can be replaced with an infinite number of fields in a K-K expansion, is that those infinitely many fields also come with infinitely many gauge redundancies. More details are in hep-th/9410046.

Wowza! OK, that will take some digestion, but I sincerely appreciate the effort to answer the question, and I guarantee I will put at least commensurate effort into understanding it (to the limits of my intellect, of course!).

Thanks!

D.B.

No problem. The posts above do assume some technical knowledge, and leave a lot unsaid, so don’t worry if they’re confusing – you can always ask more more questions!

I absolutely agree with you about Kaku. Here’s more from Art Bell:

“Kaku also forecast into the far distant future when our universe will be dying out. At such a time, a Type 3 or 4 civilization (capable of manipulating huge amounts of energy) might construct a massive machine that could make space and time unstable. With an atom smasher the size of a solar system, he hypothesized it might open up a bubble ten light years across, through which our civilization could escape into another universe.”

This is just a bad Star Trek episode. The man is an embarrassment to honest physicists. I stopped taking him seriously when he made a fool of himself campaigning against the launch of the magnificent Cassini probe.

Very well put post. It makes me wince every time I see someone who should know better make a logically weak argument against Horgan (the worst being ad hominem). It seems to have happened a lot in the last decade.

Awright…just blast this post, Dr. Woit, if you feel I’m being an annoying newb here. I’ll understand completely.

To Simon (or whoever cares to answer): This AdS/CFT thing. I read Maldacena’s article in SciAm, and while he didn’t mention “conformal field theories”, it was pretty clear that’s what he was describing. Hence, I know probably about as much as my brain can handle about “anti-de Sitter space”. Clearly, doing physics in this kind of space has had some exciting consequences.

Now I know some flat maps of the Earth are called “conformal” because, while distorted in some ways, they preserve some important features of an actual globe, and can even be more convenient in some ways (a straight line on a Mercator projection always has a constant heading, for instance, though it’s harder to find the shortest distance between two points than it is on a globe). That seems to be roughly analagous to what’s going in in modeling physics in one less dimension than usual. Apparently, out of this has come a rigorous demonstration of the idea that all you need to know about a volume can be represented on its surface, and this makes doing quantum gravity easier by turning it into a field theory something like QCD. You can talk about gravity in terms of stringly lines of gluons, or something like that.

Okaaay…So, not surprisingly, I’m at about my limit even attempting to grasp most of this, but here goes: What happens to all the compatified dimensions when all of space looks like a flattened image of negatively-curved hyperbolic solid?

D.B.

Ok, more good questions. Conformal symmetry is a very interesting subject, but it’s obscuring the important issues here. First, there are (at least) two conformal field theories in AdS/CFT. One is the theory on the worldsheet of the string in AdS (with some suitable extra dimensions). The other (eponymous) CFT is the `dual’ theory in some sense living on the boundary of AdS. The first is a 2d theory, the second is 4d.

Most importantly: whereas in the 2d theory, conformal symmetry is required for consistency, it is not so required in the 4d theory. What is meant by this is that theories without conformal symmetry are also (in a slightly different way) dual to string theories in AdS. This result which was expected because of a very general argument of ‘t Hooft in the 70s, has recently been fleshed out in more detail. And it lends hope to the idea that non-conformal field theories like QCD can be reformulated as string theories. It is expected that this duality would relate strongly coupled regions of one theory to weakly coupled regions of the other, so the eventual goal is to access the low energy bound states of QCD (which at present cannot be derived analytically because of the strength of the coupling) through the low energy excitations of string theory.

I haven’t said much about what conformal symmetry actually is – you can think of it as a generalization of `scale invariance’ – i.e. rescaling all the lengths in the system by a same amount, although it this isn’t really quite the same thing. Remembering that shorter lengths are equivalent to higher energies, and vice versa, you can see that a theory like QCD (or for that matter the rest of the standard model) where the strength of the coupling depends on the energy, cannot have conformal symmetry. (In that case it’s interesting that the classical QCD does in fact possess scale invariance, but it is broken by quantization).

It is ‘local’ scale invariance, meaning invariance under rescalings that differ from point to point. Equivalently. it means that only angles have an invariant meaning, not lengths.

There are a few things here one might want to have separate terms for. There are local scale transformations that act directly on the metric – these are called Weyl transformations. Changes of coordinates that happen to result in rescalings of the metric are conformal transformations. But surprisingly there are more ways to do this than you might think. You can rescale the coordinates – so called dilatations. But there are also `special conformal’ transformations, which roughly, invert the coordinates, translate them, and then invert them again.

The special conformal transformations have some interesting consequences. They can move any point in space-time out to infinity. As a result, in a conformal field theory it is not possible to localize interactions in a conformally invariant way. This is why many people say that it makes no sense to calculate scattering amplitudes in CFTs, and why people should just calculate correlation functions.

Simon said

As a result, in a conformal field theory it is not possible to localize interactions in a conformally invariant way. This is why many people say that it makes no sense to calculate scattering amplitudes in CFTs, and why people should just calculate correlation functions.

This doesn’t sound right. It’s certainly not right in Weyl conformal geometry. In fact the latter comes about precisely from thoroughly localizing metricity. Weyl therefore called it “pure infinitesimal geometry”.

-drl

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