Fluorescence image of Bose-Einstein-Condensate. Image Credits: Stefan Kuhr and Immanuel Bloch, MPQ |

**String theory phenomenology and quantum many–body systems**

Sergio Gutiérrez, Abel Camacho, Héctor Hernández

arXiv:1707.07757 [gr-qc]

In the paper, the authors calculate how additional space-like dimensions affect a condensate of ultra-cold atoms, known as Bose-Einstein-Condensate. At such low temperatures, the atoms transition to a state where their quantum wave-function acts as one and the system begins to display quantum effects, such as interference, throughout.

In the presence of extra-dimensions, every particle’s wave-function has higher harmonics because the extra-dimensions have to close up, in the simplest case like circles. The particle’s wave-functions have to fit into the extra dimensions, meaning their wave-length must be an integer fraction of the radius.

Each of the additional dimensions has a radius of about a Planck length, which is 10

^{-35}m or 15 orders of magnitude smaller than what even the LHC can probe. To excite these higher harmonics, you correspondingly need an energy of 10

^{15}TeV, or 15 orders of magnitude higher than what the LHC can produce.

How do the extra-dimensions of string theory affect the ultra-cold condensate? They don’t. That’s because at those low temperatures there is no way you can excite any of the higher harmonics. Heck, even the

*total*energy of the condensates presently used isn’t high enough. There’s a reason string theory is famously detached from experiment – because it’s a damned high energy you must reach to see stringy effects!

So what’s the proposal in the paper then? There isn’t one. They simply ignore that the higher harmonics can’t be excited and make a calculation. Then they estimate that one needs a condensate of about a thousand particles to measure a discontinuity in the specific heat, which depends on the number of extra-dimensions.

It’s probably correct that this discontinuity depends on the number of extra-dimensions. Unfortunately the authors don’t go back and check what’s the mass per particle in the condensate that’s needed to make this work. I’ve put in the numbers and get something like a million tons. That gigantic mass becomes necessary because it has to combine with the miniscule temperature of about a nano-Kelvin to have a geometric mean that exceeds the Planck mass.

In summary: Sorry, but nobody’s going to test string theory with Bose-Einstein-Condensates.

## 17 comments:

"presence of additional dimensions of space, which is a prediction of string theory"Of course, this prediction is not unique to string theory.

By the way, the first hit returned by Google for "parakeet string theory" (without the quotes) returns an interesting article. Check it out.

I see that, along with Thomas Gold and Freeman Dyson, Lovelace is one of the few scientists one could truly call pioneers who doesn't have a doctorate.

I'm impressed Dr. H! Hope you are doing well. Thanks for the reality check

"

the presence of additional space-like dimension affects" afford additional thermodynamic degrees of freedom....1) Simple molecules’ vacuum rotational and vibrational spectra (microwave, IR, Raman, fluorescence; room temperature, supersonic vacuum expansion-cooled to ~1 kelvin). Monoisotopic iodine, I_2:

http://www.e-opthos.com/wavemeters.htm

...10^(-7) precision in 1978.

http://kb.osu.edu/dspace/handle/1811/30672

...2005

https://inspirehep.net/record/819093/plots

...2010

https://inspirehep.net/record/1317194/plots

...2015

...2) Specific enthalpies near zero kelvin.

...3) Blackbody radiation curves, cosmic microwave background.

...4) Etalons; hyper-reflection and zero-reflection optical stacks on mirrors and lenses, Casimir effect.

...5) Optical combs coupling atomic clocks to frequency measurements.

...6) The impedance of free space.

...7) Lamb shift, hydrogen atom and U(+91).

I’m no fan of string theory and I believe you aren’t either; yet there is a potential benefit I try to keep in mind when I think about the resources going into it. I am a big believer in learning a lot more from our failures than successes; with that in mind I try to remember string theory is going to teach us a an awful lot!

Although Dr. Hossenfelder is accused of being overly negative at times, her reviews of questionable theories serve to keep us grounded and sane in a time of increasing scientific hype and hyperbole. Her views on string theory and BE condensates are a perfect example of her tempered outlook, and she is to be commended for it.

Around 25 years ago I saw a paper that claimed to measure the number of spatial dimensions, which was found to equal 3 with one part in 10^20. What they really did was a precision measurement of the exponent in Coulomb's law, which equalled 2 within that error bar. Probably a solid but not terribly exciting experiment, but a somewhat unconventional way to state the result.

On reading the title of this post I was quite excited, and eagerly plunged into the article. The first few paragraphs had me riding on a crest of optimism, imagining of a major advance in our understanding of the universe. But, alas, a reality check, in the final sentences, intruded on such pleasant daydreams. Thank you, Bee, for bringing us down to earth on these inadequately thought out experimental proposals.

Exactly the kind of blog posts I love and come here for :-)

Keep up the good work.

Sadly, the authors probably achieved their purpose with the outlandish claim that they're testing for extra dimensions. Without it, you, and others, wouldn't have noticed the paper; or at least, you wouldn't have written about it. They're following the terrible, but somewhat true, maxim: "no publicity is bad publicity".

It seems to me that all the conditions required to show the hidden dimensions expected by string theory are meet in condensed matter physics using the bosonic quasiparticle called the Surface Plasmon Polariton (SPP). This boson can form non-equilibrium Bose-Einstein condensates at room temperature and beyond.

In “Oscillatory behavior of the specific heat at low temperature in quasiperiodic structures” E.L. Albuquerquea;∗, C.G. Bezerraa, P.W. Maurizb, M.S. Vasconcelos, a structure featuring 11 level discontinuity in specific heat as predicted by the Mexican paper is shown to exist.

The behavior of a variety of particles or quasi-particles (electrons, phonons, photons, polaritons, magnons, etc.) has been and is currently being studied in quasi-periodic systems. A fascinating feature of these quasi-periodic structures is that they exhibit collective properties not shared by their constituent parts.

Furthermore, the long-range correlations induced by the construction of these systems are expected to be reflected to some degree in their various spectra, designing a novel description of disorder. A common factor shared by all these excitations is a complex fractal energy spectrum.

Could this discontinuous fractal based specific heat spectrum of SPPs be exposing the higher dimensions of reality as predicted by the Mexicans?

"... the presence of extra dimensions of space, which is a prediction of string theory ..." I have conjectured that string theory with the infinite nature hypothesis implies supersymmetry, extra dimensions of space, and no MOND, while string theory with the finite nature hypothesis implies MOND, no supersymmetry, and no extra dimensions of space (i.e. the extra dimensions are involved in the description of Wolfram's automaton using the monster group, the 6 pariah groups, and 3 copies of the Leech lattice but the extra dimensions are entirely virtual). Google "witten milgrom" and "kroupa milgrom".

Thanks for this analysis! Unfortunately there are these papers with too much "sensation" and not enough "doing the math". Ideally these would be weeded out in the peer review process. In reality, what happens is the authors resubmit to other journals until a reviewer sleeps and the manuscript gets published.

@Axil DOI:10.1016/j.physa.2004.06.004

"thermodynamical properties of plasmon–polaritons that propagate in multiple semiconductor layers arranged in a quasi-periodical fashion of Fibonacci and Thue–Morse types." Support for String theory multiple dimensions then suggests anomalous "multiscale fractal energy spectra," No EM or massed anomalies are observed to the limits of measurement in a broad selection of venues I listed above.

Anomalous spacetime geometry detected within achievable boundary conditions can falsifying a physics postulate, e.g. Euclid versus non-Euclidean geometries. Physics furiously rejects experiments designed to violate Tommy Aquinas-invested existing theory lacking empirical validation.

@Uncle Al

In response to your request for data supporting theoretical predictions of discontinuity in the specific heat of polariton/plasmonic based Bose condensates, please consider this example of specific heat discontinuity in a family of solid state systems showing the associated onset of unconventional superconductivity.

http://iopscience.iop.org/article/10.1088/0953-8984/23/22/222201

Specific heat discontinuity, ΔC, at Tc in BaFe2(As0.7P0.3)2—consistent with unconventional superconductivity

Bose condensation is solid state systems might fill the need for use as a research tool to show string theory productions.

Hi everybody

We have read the criticisms and remarks about our work, and, of course, we should be granted the opportunity to answer them.

There is a huge difference in quantum gravity phenomenology when you switch from probes defined by one-particle and systems involving many particles. Indeed, for a one-particle system, the detection of extra dimensions requires, from the particle, to be in an energy eigenstate in which the contribution of the extra dimensions is not trivially zero. Why; answer: because, this is the only evidence upon the system of the existence of the extra dimensions. This kind of probes are the usual one in quantum gravity phenomenology. This is one of the shortcomings of phenomenology of systems with one particle, they must have a very large energy, in order to "see" the extra dimensions.

Is there a way out of this conundrum? We think so, the core point is to notice that in a many-body system, one in which the idea of thermodynamical equilibrium can be defined, an additional possibility exists. Indeed, all the thermodynamical properties emerge from the partition function, which is defined as a function of all the energy eigenstates available to the system, even those belonging to the excited states of the extra dimensions. What does this mean? Among other things, it implies that this physical parameter already includes the excited states of the compact dimensions. You use the partition function in order to derive the properties of the system, either at high or at low temperatures.

That is why a system with many-particles at very low temperatures (i.e., no particle has an energy similar to any of the excited states of the extra dimensiones) can have information of the extra dimensions, it has been included, from the very beginning.

Does this last argument imply that we would "see" the extra-dimensions in our daily life? Answer: NO. Why? I'll provide two different arguments.

1) Firstly, in order to "see" (what an ambiguous word) the extra dimensions you need to know two facts: (i) the structure of the physical parameters in a world without extra dimensions, and, (ii) the structure of the same parameter in a universe with extra dimensions. It is only through the comparison between these two results that we could obtain information about the number of dimensions, i. e., a single measuring process tells you nothing about the number of dimensions, you just measure a physical parameter without knowing how it depends new upon the geometry of space-time.

2) Secondly, if you take a look, for instance, to the number of particles that we have deduced, you' ll see that it's a function of the mass of the atoms, the number of non-compact dimensions, the radius of the compact dimensions, the condensation temperature, etc. Clearly, in an experiment you know "N, m, T_c", but not "R", or "l". In other words, given a certain experimental value for the number of particles (N) our expression accepts l=0, or l=1, etc., you cannot deduce two unknowns with just one mathematical expression, in this case these two unknowns are "l" and "R". To state that our work implies the possibility of "seeing" in our daily life the effects of the extra-dimensions is just a naive statement, thrown to the wind without any mathematical justification.

Best regards.

Sergio,

First, your point about going from one to many-particle systems is highly questionably, but really it's not relevant here. The system clearly can't occupy any state in phase-space with energy higher than even the system's total energy. If you'd maybe just write a sum rather than an integral and put boundary values on it you'd see that the only thing left of phase-space is the integral over the usual, four, dimensions.

Your paper is simply wrong, and you should either correct or withdraw it. If you doubt that what I say is correct, ask anyone who has worked on the phenomenology of extra dimensions.

Best,

B.

Another method that might be used in the exploration of string theory comes out of optics associated with the Bose Condensation of light.

Calorimetry of a Bose–Einstein-condensed photon gas

https://www.nature.com/articles/ncomms11340

Also see this article

https://phys.org/news/2016-04-capacity-condensed.html

"the temperature of a gas of light can not be measured with a thermometer; but that is also not necessary. "In order to determine the temperature of the gas, it is only necessary to know the different wavelengths of the light particles – the distribution of its colors", says Klärs. And this can be determined with extreme precision with the methods available today."

This level of extreme precision is just what the string theorist needs to test their ideas.

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