I conjecture that paradigm-breaking photons caused by inverse Compton scattering from relativist jets explain the GZK paradox.
http://en/wikipedia.org/wiki/Greisen-Zatsepin-Kuzmin_limit
Consider Einstein's field equations: R(mu,nu) + (-1/2) * g(mu,nu) * R = - κ * T(mu,nu) - Λ * g(mu,nu) -- what might be wrong? Consider the possible correction R(mu,nu) + (-1/2) * g(mu,nu) * R =
- κ * (T(mu,nu) / equivalence-principle-failure-factor) - Λ * g(mu,nu), where
equivalence-principle-failure-factor = (1 - (T(mu,nu)/T(max))^2)^(1/2)
-- if T(max) = +∞ then Einstein's field equations are recovered. I conjecture that the preceding correction might provide a basis for understanding 2 things: (1) how photons can acquire incredibly large kinetic energy from relativistic jets and (2) Lestone's theory of virtual cross sections.
https://arxiv.org/abs/physics/0703151 "Physics based calculation of the fine structure constant" by John P. Lestone, 2009
http://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-UR-16-27659 Los Alamos Report LA-UR-16-27659 "Semi-classical Electrodynamics: A Short Note" by John Paul Lestone, issued 2016-10-05
http://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-UR-16-22121 J. P. Lestone, "Possible path for the calculation of the fine structure constant", Los Alamos Report LA-UR-16-22121, April 2016, Los Alamos National Laboratory
http://www.worldscientific.com/doi/abs/10.1142/S0217732308027199?journalCode=mpla Lestone, J. P. "Black-Body Photon Clustering by Semiclassical Means." Modern Physics Letters A 23, no. 15 (2008): 1067-1077.
According to Wikipedia, "Several remarkable properties of j have to do with its q-expansion (Fourier series expansion), written as a Laurent series in terms of q = exp(2πiτ), which begins:
j(τ) = 1/q + 744 + 196884 * q + ..."
http://en.wikipedia.org/wiki/j-invariant
Note that 6! = 1 * 2 * 3 * 4 * 5 * 6 = 720 and 744 - 720 = 24. Does 744 - 720 = 24 have some profound meaning in the foundations of physics?
Is spacetime 4-dimensional? Is spacetime 26-dimensional? Measurements of spacetime using clocks and surveying instruments demonstrate that spacetime is 4-dimensional. I say that, from one point of view, spacetime is 26-dimensional. 26 dimensions = 1 dimension of matter time + 1 dimension of antimatter time + 24 dimensions of (±, ±, ± )-space. What is (±, ±, ±)-space? For the measurement of space, employ 6 particle beams consisting of 3 electron beams and 3 positron beams. For each dimension of space, employ all 3-tuples of beams selected from the 6 beams. By definition, (±, ±, ±)-space consists of 3 dimensions of ordinary space, each of which is measured in 8 different ways by using all of the possible 3-tuples of the 6 beams. The 24 dimensions of (±, ±, ±)-space reduce to the 3 dimensions of ordinary space because quantum field theory is empirically valid -- however, (±, ±, ±)-space might be useful for representational redundancy (because of the role that the Leech lattice plays in the foundations of physics.)
Note that the order of the monster group is
2^46 * 3^20 * 5^9 * 7^6 * 11^2 * 13^3 * 17 * 19 * 23 * 29 * 31 * 41 * 47 * 59 * 71 --
observe that 2^46 * 3^20 * 5^9 / 720^9 = 9216 = 2 * 72 * 64 -- does the preceding numerology suggest that the number of permutations of 6 basic quarks with 3 quark colors (for both matter and antimatter) might involve matter-time, antimatter-time, a 72-ball, and 64 fundamental particles in free space? (Add the axion, the graviton, and the inflation to the 61 fundamental particles of the Standard Model.)