### What Fermilab's Holometer experiment has to do with Quantum Gravity?

Bee told in rather critical tone about an article titled "Search for Space-Time Correlations from the Planck Scale with the Fermilab Holometer" reporting Fermilab experiment. The claim of Craig Hogan, who leads the experimental group, is that that the experiment is able to demonstrate the absence of quantum gravity effects. The claim is based on a dimensional estimate for transversal fluctuations of distances between mirrors reflecting light. The fluctuations of the distances between mirrors would be visible as a variation of interference pattern and the correlations of fluctuations between distant mirrors could be interpreted as correlations forced by gravitational holography. No correlations were detected and the brave conclusion was that predicted quantum gravitational effects are absent.

Although no quantitative theory for the effect exists, the effect is expected to be extremely small and non-detectable. Hogan has however different opinion based on his view about gravitational holography not shared by workers in the field (such as Lenny Susskind). Argument seems to go like follows (I am not a specialist so that there might be inaccuracies).

One has volume size R and the area of of its surface gives bound on entanglement entropy implying that fluctuations must be correlated. A very naive dimensional order of magnitude estimate would suggest that the transversal fluctuation of distance between mirrors (due to the fluctuations of space-time metric) would be given by ⟨ Δ x^{2} ⟩ ∼ (R/l_{P}) ×l_{P}^{2}. For macroscopic R this could be measurable number. This estimate is of course ad hoc, involves very special view about holography, and also Planck length scale mysticism is involved. There is no theory behind it as Bee correctly emphasizes. Therefore the correct conclusion of the experiments would have been that the formula used is very probably wrong.

Why I saw the trouble of writing about this was that I want to try to understand what is involved and maybe make some progress in understanding TGD based holography to the GRT inspired holography.

- The argument of Hogan involves an assumption, which seems to be made routinely by quantum holographists: the 2-D surface involved with holography is
*outer*boundary of macroscopic system and bulk corresponds to its interior. This would make the correlation effect large for large R if one takes seriously the dimensional estimate large for large R. The special role of outer boundaries is natural in AdS/CFT framework.

- In TGD framework outer boundaries do not have any special role. For strong form of holography (SH) the surfaces involved are string world sheets and partonic 2-surfaces serving as "genes" from which one can construct space-time surfaces as preferred extremals by using infinite number of conditions implying vanishing of classical Noether charges for sub-algebra of super-symplectic algebra.

For weak form of holography one would have 3-surfaces defined by the light-like orbits or partonic 2-surfaces: at these 3-surfaces the signature of the induced metric changes from Minkowskian to Euclidian and they have partonic 2-surfaces as their ends at the light-like boundaries of causal diamonds (CDs). For SH one has at the boundary of CD fermionic strings and partonic 2-surfaces. Strings serve as geometric correlates for entanglement and SH suggests a map between geometric parameters - say string length - and information theoretic parameters such as entanglement entropy.

- The typical size of the partonic 2-surfaces is CP
_{2}scale about 10^{4}Planck lengths for the ordinary value of Planck constant. The naive scaling law for the the area of partonic 2-surfaces would be A ∝ h_{eff}^{2}, h_{eff}=n×h. An alternative form of the scaling law would be as A ∝h_{eff}. CD size scale T would scale as h_{eff}and p-adic length scale as its square root ( diffused distance R satisfies R∼ L_{p}∝ T^{1/2}in diffusion; p-adic length scale would be analogous to R ).

- The most natural identification of entanglement entropy would be as entanglement entropy assignable with the
*union*of partonic 2-surfaces for which the light-like 3-surface representing generalized Feynman diagram is connected. Entanglement would be between ends of strings beginning from different partonic 2-surfaces. There is*no*bound on the entanglement entropy associated with a given Minkowski 3-volume coming from the area of its*outer*boundary since interior can contain very large number of partonic 2-surfaces contributing to the area and thus entropy. As a consequence, the correlations between fluctuations are expected to be weak.

- Just for fun one can feed numbers into the proposed dimensional estimate, which of course does not make sense now. For R about of order CP
_{2}size it would predict completely negligible effect for ordinary value of Planck constant: this entropy could be interpreted as entropy assignable to single partonic 2-surface. Same is true if R corresponds to Compton scale of elementary particle.

The difference between TGD based and GRT inspired holographies is forced by the new view about space-time allowing also Euclidian space-time regions and from new new view about General Coordinate Invariance implying SH. This brings in a natural identification of the 2-surfaces serving as holograms. In GRT framework these surfaces are identified in ad hoc manner as outer surfaces of arbtrarily chosen 3-volume.

After writing above comments I realized that around 2008 I have written about a proposal of Hogan. The motivation came from the email of Jack Sarfatti. I learned that gravitational detectors in GEO600 experiment have been plagued by unidentified noise) in the frequency range 300-1500 Hz. Craig J. Hogan had proposed an explanation in terms of holographic Universe. By reading the paper I learned that assumptions needed might be consistent with those of quantum TGD. Light-like 3-surfaces as basic objects, holography, effective 2-dimensionality, are some of the terms appearing repeatedly in the article. The model contained some unacceptable features such as Planck length as minimal wave length in obvious conflict with Lorentz invariance.

Having written the above comments I got again interested in the explanation of the reported noise. It might be real
although Hogan's explanation is not plausible to me. Within light of afterwisdom generated during 7 years it is clear that the diffraction analog serving as the starting point in Hogan's model cannot be justified in TGD framework. Fortunately, diffraction can be replaced by diffusion emerging very naturally in TGD framework and finally allows to understand how Planck length emerges from TGD framework, where CP_{2} size is the fundamental length parameter.

- One could give up diffraction picture and begin directly from the formula Δ x= (l
_{P}L)^{1/2}. This would allow also to avoid problems with Lorentz invariance generated by the idea about minimum wavelength. One would give up the interpretation of l_{P}L) as wavelength so that the formula would be just dimension analytic guess and therefore unsatisfactory.

- Could one assign Δ x to the randomness of the light-like orbit of wormhole contact/partonic 2-surface/fermionic line at it. Δ x would represent the randomness of the transversal coordinate for light-like parton orbit. This randomness could be also assigned to the light-like curves defining fermion lines at the orbits of partonic 2-surfaces. Diffusion would provide the physical analogy rather than diffraction.

T=L/c would correspond to time and Δ x would be analogous to the mean square distance ⟨ r

^{2}⟩ = DT, D= c^{2}t_{P}, diffused during time T. This would also conform qualitatively with the basic idea of p-adic thermodynamics. One would also find the long sought interpretation of Planck length as diffusion constant in TGD framework, where CP2 length scale is the fundamental length scale.

- Why the noise would appear at certain frequency range? A possible explanation is that large Planck constants are involved. The ratios of the frequency f
_{high}of laser beam to the relatively low frequencies f_{l}in the frequency range of noise would correspond to the values of Planck constant involved: h_{eff}= f_{high}/f_{l}? Maybe low frequencies could correspond to bunches of dark low energy photons with total energy equal to that of laser photon. Dark photons could relate to the long range correlations inside laser beam.

The presence of large values of Planck constants suggests strongly quantum criticality, which should relate to the long range coherence of the laser beam. Could one assign the long range correlations of laser beam with quantum criticality realized as spectrum of Planck constants?

I do not know whether the noise reported in the motivating article has been eliminated. I hope not! It is unclear whether how the model relates to the Hogan's later model proposing that the correlations implied by holography as he interprets it, are not found. Certainly the idea that Planck wave length waves would be amplified to observable noise does not make sense in TGD framework. It is diffusion of fermion lines in transversal degrees of freedom of light-like random orbits of partonic 2-surfaces serving as a signature of non-pointlikeness of fundamental objects, which would become visible as noise.

For TGD based view model for the noise claimed in GEO600 experiment see the article Quantum fluctuations in geometry as a new kind of noise? or the chapter More about TGD and Cosmology of "Physics in Many-Sheeted Space-time".

For a summary of earlier postings see Links to the latest progress in TGD.

## 5 Comments:

Any possible connection with sonoluminescence? https://en.wikipedia.org/wiki/Sonoluminescence

Could resolving this classically measurable mystery offer a way to the quantifiable theory in question in terms of TGD?

No : to my opinion.

I have considered sonoluminescence.

http://tgdtheory.fi/public_html/articles/geesink.pdf .

My guess is that Pollack's fourth phase of water modelled in terms of magnetic flux tubes to which part of protons goes and becomes dark explains the formation of highly negatively charged exclusions zones observed by Pollack.

This would be essentially formation dark nuclei as dark proton sequences but with binding energy of in biophoton range rather than MeV region. Spontaneous dark nuclear chain reaction, dark fusion is in question: dark nucleus is formed, emits binding energy which generates new fourth phase, etc...

Some fraction of these dark proton sequences could transform to ordinary nuclei and liberate ordinary nuclear energy and produce also the energy involved with sonoluminescence.

Sonoluminescence occurs also in other liquids, see e.g: http://gaw.bol.ucla.edu/sono.html

and

"The effect that different chemicals present in solution have to the velocity of the collapsing bubble has recently been studied. Nonvolatile liquids such as sulfuric and phosphoric acid have been shown to produce flashes of light several nanoseconds in duration with a much slower bubble wall velocity,[10] and producing several thousand-fold greater light emission. This effect is probably masked in SBSL in aqueous solutions by the absorption of light by water molecules and contaminants."

https://en.wikipedia.org/wiki/Mechanism_of_sonoluminescence

So, the effect cannot be explained by EZ molecules alone. The Wiki article says: "In order to understand the light emission mechanism, it is important to know what is happening in the bubble's interior and at the bubble's surface."

The holographic association comes from surface tensions etc. surface dynamics.

Interesting findings. I do not however see why water would the only liquid where the formation of EZs can take place. What is special is that water two water molecules would be hydrogen bonded and give up one proton which becomes dark. Does this mechanism have analog for the other liquids? The first thing to check is whether hydrogen bonds are present and whether molecule clusters are formed.

Concerning holography related to the work that I commented. I found that I have written 8 years ago comments about anomalous noise in gravitational detectors. I realised that although Hogan's modeller the anomalies is wrong it leads to a formula true in certain frequency range and the earlier findings and recent ones are consistent in TGD framework. What is nice that also the interpretation of Planck length in TGD framework, where it is not a fundamental constant, emerges. Plus experimental support for the hierarchy of Planck constants. The connections of TGD with empiria are evolving rapidly at many frontiers.

Still a little comment about Hogan's model. Hogan's model as such is wrong. The formula might be correct in certain frequency range and it would be important to not forget that the formula was inspired by an unidentified noise in experiment for detection of gravitational waves. It could be reasonable formula in the frequency range involved in earlier experiment and TGD can explain why so. The 8 year old experiment and the new experiment yield only apparently conflicting results. This should not be forgotten . But neither the team nor other realize it. This is sad and show how important it would be to have a real theory.

Similar loose thinking dominates in particle physics. The failure to find SUSY in standard sense was a great disappointment. Now evidence has been accumulating for totally unexpected particles: leptoquarks. Something that no-one wanted. But they are nothing but squarks in TGD framework. It would help enormously if "the only game in the town" thinking would be replaced with serious scientific approach.

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