Criticisms from some physicists suggest that they misunderstand my analysis of the Koide formula. For me, the point is NOT that the Koide formula predicts some particular range of values for lepton masses -- the WHOLE POINT is that square-root(mass) has some kind of profound meaning in terms of physics. Conventional wisdom says that there exists a Planck time and a Planck length. Does there exist a Wolfram time and a Wolfram length? In other words, it is true that the wavelengths of photons and gravitons can be arbitrary long or is it true that there exists a maximum wavelength in the physical universe? How do physicists know the answer to the previous question? If there is a maximum length in the physical universe, then should there be a modification of Einstein's field equations (even after quantum averaging)?
According to Einstein's field equations and string theory with the infinite nature hypothesis, our universe expands forever. What is the explanation for the space roar? Does the Koide formula suggest that there might be a modification of Einstein's field equations? 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 * (1 - (R(min) / R)^2)^(1/2) = - κ * T(mu,nu) - Λ * g(mu,nu), if R(min) = 0 then Einstein's field equations are recovered.
EINSTEIN'S "THE MEANING OF RELATIVITY", 5TH EDITION, PAGES 83 AND 84
[edit note: for page 83, all except last paragraph of page 83 deleted]
If there is an analogue of Poisson's equation in the general theory of relativity, then this equation must be a tensor equation for the tensor g(mu,nu) of the gravitational potential; the energy tensor of matter must appear on the right-hand side of this equation. On the left-hand side of the equation there must be a differential tensor in the g(mu,nu). It is completely determined by the following three conditions:
1. It may contain no differential coefficients of the g(mu,nu) higher than the second.
2. It must be linear in these second differential coefficients.
3. Its divergence must vanish identically.
The first two of these conditions are naturally taken from Poisson's equation. Since it may be proved mathematically that all such differential tensors can be formed algebraically (i.e. without differentiation) from Riemann's tensor, our tensor must have the form
R(mu,nu) + a g(mu,nu) R
in which R(mu,nu) and R are defined by (88) and (89) [edit note: see page 77]. Further, it may be proved that the third condition requires a to have the value - 1/2 . For the law of the gravitational field we therefore get the equation
(96) R(mu,nu) - (1/2) g(mu,nu) R = - κ * T(mu,nu) .
Equation (95) [edit note: see deleted part of page 83] is a consequence of this equation. κ denotes a constant, which is connected with the Newtonian gravitational constant.
CRITICISM OF EINSTEIN'S ASSUMPTION for R
How do physicists know that there is not some law of nature that forces R ≥ R(min), always and everywhere? The Koide formula suggests that square-root(mass-energy) might somehow be construed as area. If so, the entire universe might undergo an instantaneous (i.e. one Planck time interval) collapse. If the universe collapses when the average temperature of the universe gets too cold, then Einstein was wrong. Therefore, there might be some modification involving R that changes the underlying physics basis for eternal cosmological expansion. Can physicists cite empirical evidence that proves that the preceding speculation is wrong? Theorists might cite theoretical reasons why the proposed modification is wrong, but CAN THEY CITE EMPIRICAL EVIDENCE WHICH CLEARLY DISCONFIRMS THE PROPOSED MODIFICATION?