Evidence for manysheeted spacetime from gamma ray flares
MAGIC collaboration has found evidence for a gamma ray anomaly.
Gamma rays are different energy ranges seem to arrive with
different velocities from Mkn 501 (see this). The delay in
arrival times is about 4 minutes. The proposed
explanation is in terms of broken Lorentz
invariance. TGD allows to explain the finding in
terms of manysheeted spacetime and there is no
need to invoke breaking of Lorentz invariance.
1. TGD based explanation at qualitative level
One of the oldest predictions of manysheeted spacetime is that the time for photons to propagate from point A to B along given spacetime sheet depends on spacetime sheet because photon travels along lightlike geodesic of spacetime sheet rather than lightlike geodesic of the imbedding space and thus increases so that the travel time is in general longer than using maximal signal velocity.
Manysheetedness predicts a spectrum of Hubble constants and gamma ray anomaly might be a demonstration for the manysheetedness. The spectroscopy of arrival times would give information about how many sheets are involved.
Before one can accept this explanation, one must have a good argument for why the spacetime sheet along which gamma rays travel depends on their energy and why higher energy gamma rays would move along spacetime sheet along which the distance is longer.
 Shorter wavelength means that that the wave oscillates faster. Spacetime sheet should reflect in its geometry the matter present at it. Could this mean that the spacetime sheet is more "wiggly" for higher energy gamma rays and therefore the distance travelled longer? A natural TGD inspired guess is that the padic length scales assignable to gamma ray energy defines the padic length scale assignable to the spacetime sheet of gamma ray connecting two systems so that effective velocities of propagation would correspond to padic length scales coming as half octaves. Note that there is no breaking of Lorentz invariance since gamma ray connects the two system and the rest system of receiver defines a unique coordinate system in which the energy of gamma ray has Lorentz invariant physical meaning.
 One can invent also an objection. In TGD classical radiation field decomposes into topological light rays ("massless extremals", MEs) which could quite well be characterized by a large Planck constant in which case the decay to ordinary photons would take place at the receiving end via decoherence (Allais effect discussed in previous posting is an application of this picture in the case of gravitonal interaction). Gamma rays could propagate very much like a laser beam along the ME. For the simplest MEs the velocity of propagation corresponds to the maximal signal velocity and there would be no variation of propagation time. One can imagine two manners to circumvent to the counter argument.
 Also topological light rays for which lightlike geodesics are replaced with lightlike curves of M^{4} are highly suggestive as solutions of field equations. For these MEs the distance travelled would be in general longer than for the simplest MEs.
 The gluing of ME to background spacetime by wormhole contacts (actually representation for photons!) could force the classical signal to propagate along a zigzag curve formed by simple MEs with maximal signal velocity. The length of each piece would be of order padic length scale. The zigzag character of the path of arrival would increase the distance between source and receiver.
2. Quantitative argument
A quantitative estimate runs as follows.
 The source in question is quasar Makarian 501 with redshift z= .034. Gamma flares of duration about 2 minutes were observed with energies in bands .25.6 TeV and 1.210 TeV. The gamma rays in the higher energy band were near to its upper end and were delayed by about Δ τ=4 min with respect to those in the lower band. Using Hubble law v=Hct with H= 71 km/Mparsec/s, one obtains the estimate Δτ/τ= 1.6×10^{14}.
 A simple model for the induced metric of the spacetime sheet along which gamma rays propagate is as a flat metric associated with the flat imbedding Φ= ωt, where Φ is the angle coordinate of the geodesic circle of CP_{2}. The time component of the metric is given by
g_{tt}=1R^{2}ω^{2}.
ω appears as a parameter in the model. Also the embeddings of ReissnerNorström and Schwartschild metrics contain frequency as free parameter and spacetime sheets are quite generally parametrized by frequencies and momentum or angular momentum like vacuum quantum numbers.
 ω is assumed to be expressible in terms of the padic prime characterizing the spacetime sheet. The parametrization to assumed in the following is
ω^{2}R^{2}=Kp^{r}.
It turns out that r=1/2 is the only option consistent with the padic length scale hypothesis. The naive expectation would have been r=1. The result suggests the formula
ω^{2} = m_{0}m_{p} with m_{0}= K/R
so that ω would be the geometric mean of a slowly varying large padic mass scale and padic mass scale.
The explanation for the padic length scale hypothesis leading also to a generalization of HawkingBekenstein formula assumes that for the strong form of padic length scale hypothesis stating p≈ 2^{k}, k prime, there are two padic length scales involved with a given elementary particle. L_{p} characterizes particle's Compton length and L_{k} the size of the wormhole contact or throat representing the elementary particle. The guess is that ω is proportional to the geometric mean of these two padic length scales:
ω^{2}R^{2} = x/[2^{k/2}k^{1/2}].
 A relatively weak form of the padic length scale hypothesis would be p≈ 2^{k}, k an odd integer. M_{127} corresponds to the mass scale m_{e}5^{1/2} in a reasonable approximation. Using m_{e}≈.5 MeV one finds that the mass scales m(k) for k=892n, n=0,1,2...,6 are m(k)/TeV= x, with x=0.12, 0.23, 0.47, 0.94, 1.88, 3.76, 7.50. The lower energy range contains the scales corresponding to k=87 and 85. The higher energy range contains the scales corresponding to k=83,81,79,77. In this case the proposed formula does not make sense.
 The strong form of padic length scale hypothesis allows only prime values for k. This would allow Mersenne prime M_{89} (intermediate gauge boson mass scale) for the lower energy range and k=83 and 79 for the upper energy range. A rough estimate is obtained by assuming that the two energy ranges correspond to k_{1}=89 and k_{2}=79.
 The expression for τ reads as τ= (g_{tt})^{1/2}t. The expression for Δτ/τ is given by
Δ τ/τ=(g_{tt})^{1/2}Δ g_{tt}/2≈ R^{2}Δ ω^{2} = x[(k_{2}p_{2})^{1/2}(k_{1}p_{1})^{1/2}] ≈x(k_{2}p_{2})^{1/2}= x×2^{79/2}(79)^{1/2}.
Using the experimental value for Δτ/τ one obtains x≈.45. x=1/2 is an attractive guess.
It seems that one can fairly well say that standard cosmology is making a crash down while TGD is making a breakthrough after breakthrough as the interpretation becomes more and more accurate. TGD is patiently waiting;). Interesting to see how long it still will take before sociology of science finally gives up and the unavoidable happens.
For details and background see the chapter The Relationship Between TGD and GRT.
