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/lP) ×lP2. 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 CP2 scale about 104 Planck lengths for the ordinary value of Planck constant. The naive scaling law for the the area of partonic 2-surfaces would be A ∝ heff2, heff=n×h. An alternative form of the scaling law would be as A ∝heff. CD size scale T would scale as heff and p-adic length scale as its square root ( diffused distance R satisfies R∼ Lp∝ T1/2 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 CP2 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 CP2 size is the fundamental length parameter.
- One could give up diffraction picture and begin directly from the formula Δ x= (lPL)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 lPL) 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 ⟨ r2⟩ = DT, D= c2tP, 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 fhigh of laser beam to the relatively low frequencies fl in the frequency range of noise would correspond to the values of Planck constant involved: heff= fhigh/fl? 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.