Mathematics – Logic
Scientific paper
Jan 2011
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011aas...21723107b&link_type=abstract
American Astronomical Society, AAS Meeting #217, #231.07; 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 continues: "It seems hardly possible to surmount these difficulties on the basis of Newtonian theory. We may ask ourselves the question whether they 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 κ ρ
where κ denotes a universal constant. If ρ be the uniform density of a distribution of mass, then φ=-4π κρ/λ is a solution." Einstein discarded this foil because it is not compatible with his famed equation for general relativity.
In 2004 I proposed a graviton of imaginary mass and a photon of real mass, both equal to 10 -25 eV. Classically this graviton satisfies Einstein's first equation with an empirical value of 2 π/√-λ=Ro/20 = 400 pc. I now suggest an equivalent absolute value -λ= (1/2)EH4 2 π G. where EH is the Hartree energy 2 × 13.6 eV and c=(h/2π) = 1. I will show why this choice and Einstein's second equation gives 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 I approximate is shown in Hartnett and Hirano (2008). The talk is 3 slides. There will be time for questions.
References- "Analogies between electricity and gravity", Metrologia 41(2004)S115-S124. books: Laughlin (2005), Feynman(1995), Weinberg (1977), Lorentz, Einstein, Minkowski, and Weyl (English) (1923).
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