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

(Before It's News)

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 x² ⟩ ∼ (R/l_P) ×l_P². 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.

1. 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.

2. 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 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.

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

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