Einstein, Schwinger, And The Sinusoidal Potential

Details Einstein, Schwinger, And The Sinusoidal Potential Einstein, Schwinger, And The Sinusoidal Potential

Apr 2011

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011dda....42.0402c&link_type=abstract

American Astronomical Society, DDA meeting #42, #4.02; Bulletin of the American Astronomical Society, Vol. 43, 2011

Mathematics

Logic

Scientific paper

Before introducing his cosmological constant, Einstein considered a difficulty with Newtonian theory: a steady-state, infinite Newtonian stellar system cannot exist at all. He wrote : "We may ask ourselves the question whether [this difficulty] can be removed by a modification of the Newtonian theory. First of all we will indicate a method which does not in itself claim to be taken seriously; it merely serves as a foil for what is to follow. In place of Poisson's equation we write Δφ - λ φ = 4 π Gρ, where G denotes a universal constant. If ρ be the uniform density of a distribution of mass, then φ=-4π Gρ/λ is a solution.” Einstein considered λ to be a positive number. Einstein discarded this foil because it is incompatible with his famed equation for general relativity.
In 2004 Bartlett proposed a graviton of imaginary mass and a photon of real mass both equal to 10-25eV.
Thus fg = -(GM/r)[cos(k0r)] and fe = (Q/r)[exp(-k0r)]. Classically, this graviton satisfies Einstein's first equation with k02 = -λ. Empirically, the value of k0 is 2 π/λ0 with wavelength λ0= Ro / 20 = 400 pc. An equivalent absolute value for k02 is (1/2)EH4 2 π G, where EH is the Hartree energy, 2 × 13.6 eV, with c=(h/2π) = 1. With this choice and Einstein's second equation we show an emergence of structure at a lookback Z=5.65 dex, a time between nucleosynthesis and recombination when the universe was a plasma of photons, protons, electrons, and helium nuclei. The particular strong structure that we approximate is shown in Hartnett and Hirano (2008).

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