<<Is there a reasonable alternative to the theory of the expanding universe?>>
(1) The question itself is not reasonable because, Einstein had already abandoned his alternative concept of a static universe. Einstein used a cosmological constant Λ to represent the constants of the universe. He modelled the universe on the basis that the universe is stationary, isotropic and homogeneous.
The theory of the expansion of the universe developed from the observed redshift of celestial objects, the space between which galaxies are increasing, so that the relevant galaxies appear to be moving away from us at a speed that increases with their distance. Hubble's brilliant observation that the redshift of galaxies, announced in 1929, was directly proportional to the galaxy's distance from Earth.
Therefore, Einstein's cosmological constant was abandoned after Edwin Hubble's confirmation that the universe was expanding. Einstein called the idea of cosmic repulsion 'the biggest blunder of my life'. Thus, the only reasonable alternative to the theory of an expanding universe was a static universe. Reply @ResearchGate
<<We know that our star, the Sun loses about 10⁻¹⁴ (unit?) of its mass per year as a result of electromagnetic radiation and particle emission. That reduction in mass should show up as a decreasing gravitational red shift. Same thing should happen to entire galaxies.>>
(2) It is not a valid statement that mass loss should show up as a decreasing gravitational redshift. The mass loss of stars and galaxies does not affect the known gravitational redshift.
The reasons:
As we know that the gravitational redshift, also known as Einstein shift, is the phenomenon that electromagnetic waves or photons traveling out of a gravitational well lose energy. While the energy of a photon, at emission form a star, corresponds to its frequency, which are the same for from any stars, regardless from the Sun or from a star in any galaxy. This loss of energy corresponds to a decrease in the wave frequency and increase in the wavelength, generally known as a redshift.
Gravitational redshift can be explained as a consequence of the equivalence principle that gravity and acceleration are equivalent and the redshift is due to the Doppler effect. The relativistic Doppler effect is a change in the frequency, wavelength, and amplitude of light caused by the relative motion of the source and observer, as in the classical Doppler effect, when considering the effects described by the special theory of relativity. Where, relative Doppler effect = λᵣ/λₛ = fₛ/fᵣ = Doppler factor = √{(1-β)/(1-β)}, where β = v/c > 0. The initial energy of an emitted photon from any star is (E) = 4.0 × 10⁻¹⁹ J. Hence the corresponding frequency of an emitted photon is (f) = 6.0368 × 10¹⁴ Hz.
From the above explanations, we can see that the Doppler factor (fₛ/fᵣ) causes the red shift due to the speed of the (photon) wave, because the emission frequency of the photon is the source frequency (fₛ) which is always 6.0368 × 10¹⁴ Hz and the received frequency (fᵣ) is the corresponding distance's speed, causes red shift. The photon loses energy (ΔE) due to the gravitational effect of the photon source, which corresponds to a change in frequency (Δf) = (fₛ - fᵣ), a corresponding redshift due to the increase in photon wavelength (λᵣ/λₛ). The photon is massless, its interaction with the gravitational source or the emission source, remains the same regardless of gravitational intensity. Doppler redshift depends more on the distance between the source and the receiver. Reply @ResearchGate
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