## Einstein's Key to Hubble Redshift

**Authors:** W.Q. Sumner

In 1907 Einstein discovered the key to understanding accelerating Hubble redshifts. By assuming that acceleration and gravity are equivalent (“The Happiest Thought of my Life”), he proved that Maxwell’s equations are the same in every acceler- ated reference frame but that vacuum permittivity depends on the acceleration. Vacuum permittivity is the scalar in Maxwell’s equations that determines the speed of light and the strength of electrical fields. Maxwell’s equations are valid in every coordinate sys- tem in general relativity. Vacuum permittivity depends on the spacetime curvature. For Friedmann spacetime, vacuum permittivity is proportional to the radius of the universe. When the radius changes, changing electrical fields in atoms change the wavelengths of emitted photons by about twice as much as photon wavelengths change. This is the key Einstein left us: The evolution of both photons and atoms must be used together to understand Hubble redshift. When this is done, the physics of Maxwell, Einstein, Bohr, and Friedmann fits modern Hubble redshift observations beautifully.

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### Submission history

[v1] 2017-05-23 19:58:32

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