The Japanese are getting in on the string theory hype business, with KEK issuing a press release today with the title: The mechanism that explains why our universe was born with 3 dimensions: a 40-year-old puzzle of superstring theory solved by supercomputer. As usual for this kind of press release, the claim is that researchers at the institution issuing the press release have finally solved the age-old problem of string theory predicting nothing. In this case the prediction is that there are 3 dimensions of space (I think that, technically, this is a “post-diction”). According to the press release:

A group of three researchers from KEK, Shizuoka University and Osaka University has for the first time revealed the way our universe was born with 3 spatial dimensions from 10-dimensional superstring theory in which spacetime has 9 spatial directions and 1 temporal direction. This result was obtained by numerical simulation on a supercomputer…

… it is expected that superstring theory allows the investigation of the birth of the universe. However, actual calculation has been intractable because the interaction between strings is strong, so all investigation thus far has been restricted to discussing various models or scenarios…

… It is almost 40 years since superstring theory was proposed as the theory of everything, extending the general theory of relativity to the scale of elementary particles. However, its validity and its usefulness remained unclear due to the difficulty of performing actual calculations. The newly obtained solution to the space-time dimensionality puzzle strongly supports the validity of the theory.

Furthermore, the establishment of a new method to analyze superstring theory using computers opens up the possibility of applying this theory to various problems. For instance, it should now be possible to provide a theoretical understanding of the inflation that is believed to have taken place in the early universe, and also the accelerating expansion of the universe, whose discovery earned the Nobel Prize in Physics this year. It is expected that superstring theory will develop further and play an important role in solving such puzzles in particle physics as the existence of the dark matter that is suggested by cosmological observations, and the Higgs particle, which is expected to be discovered by LHC experiments.

This goes back to the pre-arXiv days, before many of our current graduate students were even born, but some of us are old enough to remember similar claims being made back in the late 1980s. For example there’s the 1989 Brandenberger-Vafa paper claiming that string theory predicts 3 dimensions, using a “string gas” cosmology. I don’t remember if there was a “finally, physicists find a way to make a prediction based on string theory” press release back in 1989 or not.

and then there’s the Randall and Karch paper and the Momen and Rahman paper. And you know what? They all found we live in 3+1 dimensions!

I suppose a continuation of this pre-print?

http://arxiv.org/abs/1108.1540

“Expanding (3+1)-dimensional universe from a Lorentzian matrix model for superstring theory in (9+1)-dimensions

Sang-Woo Kim, Jun Nishimura, Asato Tsuchiya

(Submitted on 7 Aug 2011 (v1), last revised 7 Sep 2011 (this version, v2))

We reconsider the matrix model formulation of type IIB superstring theory in (9+1)-dimensional space-time. Unlike the previous proposal in which the Wick rotation was used to make the model well-defined, we regularize the Lorentzian model by introducing infrared cutoffs in both the spatial and temporal directions. Monte Carlo studies reveal that the two cutoffs can be removed in the large-N limit and that the theory thus obtained has no parameters other than one scale parameter. Moreover, we find that three out of nine spatial directions start to expand at some “critical time”, after which the space has SO(3) symmetry instead of SO(9). “

Here is a physics-trivia-type question to think about over the Holiday Season. Name the earliest possible scientific paper, written by a bona fide physicist, that aims to explain why we live in 3+1 dimensions.

Merry Christmas.

Ehrenfest 1918?

http://www.dwc.knaw.nl/DL/publications/PU00012213.pdf

Rather than say that such a result explains why space is 3-dimensional in some absolute sense, one should merely say that it explains how space can be 3-dimensional in this particular theory, which prima facie implies that it is n-dimensional with n ≠ 3 — that is, implies that the observed dimensionality must be a dynamical consequence of the theory, and may be highly contingent.

Of course we are not accustomed to theories in which the observed dimensionality must be a dynamical consequence of the theory — or rather, we are accustomed to having considerable difficulty recovering the observed 3-dimensionality of space in such theories, and therefore tend to be skeptical of all of them on this basis alone. From that point of view this is an interesting result, whatever its place in the sprawling and profligate theoretical mess that “string” theory has become.

If a result like this — and others that the authors would like to pursue* in this framework — turn out to be generic, it might point to a path out of the morass known as the string theory landscape. I admit that is a faint hope, but given prior experience it will always seem like a faint hope until the path is actually found.

(* See their conclusion: “The next step would be to show that the four fundamental interactions and the matter fields appear in our universe at later time. For that we need to change the scale from the Planck scale to the TeV scale, which may require constructing a framework similar to the renormalization group or the low energy effective theory.”)

Chris W.,

You can come up with string theory models with any large number of spatial dimensions from 1 to 9 (10 w/M-theory). A large number of people over the last 25 years have come up with “arguments” to pick out 3, Brandenberger-Vafa is one example, Bee gives some others. I don’t see what’s supposed to be interesting about finding yet another one, since there’s no more reason to take it seriously than any of the others.

As for their “The next step would be…”, that is just bizarre. What do they think thousands of very smart people have been trying to do for the past couple decades? Exactly this of course, with zero success. These authors write as if string theory were some new idea, and they’re the first to suggest that one should try and connect it to reality.

To be fair, the Brandenberger-Vafa paper is one of the most beautiful papers in the history of string theory. Its main results, including the 3d explanation, can be “explained to your grandmother”. There is very little in string theory, old or new, that meets this criterion.

Mitchell Porter,

That’s indeed the paper that I had in mind. I held it the original publication in my hands in a library many years ago, and I’m glad to know that it’s now available online. Thanks for that and best wishes on the Holiday Season.

Some 20 years ago I saw a paper where someone had measured the dimensionality of space, with the result D = 3+epsilon where |epsilon| is less than 10^-20 or so. What they did measure was the power in Coloumb’s law, but the result was phrased as a measurement of dimensionality.

@ Thomas Larsson

If you permit measuring Coulomb’s law exponent as a measurement of space dimensions, then you go to about 1769 or so:

http://en.wikipedia.org/wiki/John_Robison_%28physicist%29

Incidentally, you can make sense of non-integer dimensions: see “fractal dimension”. This arises in some triangulation models for quantum gravity.

Thanks alot for the post Peter, the research looks awesome, groundbreaking.

The article to be published is cited on PRL with the same title as the preprint linked to by Anonyrat:

http://arxiv.org/abs/1108.1540

They do not seem to have posted the official version, accepted november 21, 2011.

The conclusion is quite gripping: they propose investigating nonperturbatively the appearance of a local field theory on commutative 4-dimensional spacetime at low-energy (which is the only parameter of their simulation it seems), and then appearance of matter and the 4 fundamental forces, or some gauge theory at least I guess. That is: researching consequences of type IIB strings from nonperturbative simulations in the IKKT model -I think.

Perhaps the most exciting aspect is trying to explain these observations theoretically, mathematically. There is research into relating various models of quantum gravity (Rivasseau has a recent arXiv article), and these computational observations may definitely give us motivation to relate perturbative and nonperturbative formulations, to find limitations of perturbative string theory, and perhaps relate string theory to loop quantum gravity, and eventually understand something about quantum gravity. (We may optimistically take cues from lattice QCD to inspire us.)

Of course these are pipe-dreams, and I am pretty much ignorant of the little knowledge actual researchers may have of what I mention -I plan to learn. But this is honest work for theoretical physicists and mathematicians to do, and we could be grateful for that, in the current situation.

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Also see section 7 of Wikipedia’s article Spacetime for a discussion of spacetime’s dimensionality, with references to two papers by Ehrenfest and one by Tegmark. (The latter employs a partially anthropic argument.)

The PDF document linked in Mitchell Porter’s comment slightly misstates the title of Ehrenfest’s

Proceedings of the Amsterdam Academypaper.In

The Road To Reality, Penrose writes that classical N+1 GR spacetimes with N>3 are unstable under a theorem he proved together with Hawking. Taking this together with T-duality wouldn’t one then expect a spacetime with 3 large dimensions and 6 with Planck-scale ones to be dynamically stable?The classical instability would presumably cause one of the existing small dimensions to collapse in on itself if it spontaneously became much larger than the Planck length, and by T-duality one might expect a natural corollary of this to be that it can’t get much smaller than the Planck length either, as that would be dual to some other geometry with with more than 3 spacial dimensions and would likewise be classically unstable.

(One might further expect spacetimes with

fewerthan 3 large space dimensions to be vulnerable to the spontaneous expansion (or contraction) of one of their Planck-scale dimensions due to the absence of this instability.)Layman question:

Does anyone know whether this result, or its antecedents, would hold for all of the 10^500 false vacua? Or is that huge ambiguity just a perturbative artefact? If so, why so much dismay about the unscientific nature of the anthropic “landscape” if it will go away when when we do non-perturbative calculations?

abbyyorker,

The IKKT matrix model the authors are using dates back to 1996, one of a class of proposals for a fundamental non-perturbative definition of string theory from around that time. These proposals don’t seem to lead to low-energy physics that looks anything like the real world, so most people abandoned them after a few years.

The landscape models of the last decade use a different philosophy. They don’t start from a fundamental non-perturbative theory, but just assume the existence of such a thing, with various properties, and then try to construct “string vacua”, which are supposed to be consistent low-energy solutions to the unknown fundamental theory, whatever it is. One can certainly take the point of view (Gross and many others do), that until you actually find the fundamental theory, claims about the “landscape” of solutions to it shouldn’t be taken too seriously. The problem is though that if you take that point of view, you can no longer say much of anything at all about how string theory is supposed to connect to reality.

^^^ meant to write “a spacetime with 3 large dimensions and 6 Planck-scale ones”

About Kaku, funny response here: http://bigthink.com/ideas/41681

It has some gems, such as “or finding experimental deviations from Newton’s inverse square law which may prove the existence of parallel universes”.

Thanks Cesar,

I also like Kaku’s definition of a superpartner: “higher vibration of the string”.

Would be interesting to know who, according to Kaku, would win the bet if SUSY were discovered, since he seems to make no distinction between it and strings.

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