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# Verification of Gravitational Redshift by the Mass Defect

The gravitational redshift is a simple consequence of Einstein’s equivalence principle (“all bodies fall with the same acceleration independent of their composition”) and was found by Einstein eight years before the full theory of relativity. Observing the gravitational redshift in the solar system is one of the classical tests of relativity. Gravitational redshift is an important effect in satellite-based navigation systems such as GPS.

According to the theory of gravitational redshift, if the wavelength of the sodium d1 line is ¥, then in the presence of a heavy mass the wavelength should be shifted towards the red end. Let in presence of a heavy mass of mass M and radius R, the wavelength of sodium d1 line becomes ¥'(¥’>¥). So, the amount of redshift Δ¥ = ¥’- ¥

Now, according to the theory of gravitational redshift Δ¥/¥ = GM/(RC^2), Where G is the Gravitational constant, C is the velocity of light in free space.

Now, I try to verify this theory with the help of my won theory name as “Reason Behind Gravitational Energy” which is published on the journal name as IJNRD in volume 4. According to this theory, the origin of gravitational energy is the mass defect of interacting objects. According to this theory mass of a particle is not constant but it changes with the corresponding change in Gravitational interaction. The mass defect of interacting objects converted into the gravitation interaction energy between them following the equation E = ΔmC^2 i.e in present case ΔmC^2 = GM1M2/r………1

Where r is the center to center distance between interacting objects and Δm is the mass defect.

According to this theory within the gravitational field mass of an electron is not constant, it depends on the strength of gravitational interaction. Let the mass of electron in sodium in the absence of other mass is m(e). Now, on the surface of a heavy star, the mass becomes m'(e) = m(e) – Δm.

Δm ~ GMm(e)/(RC^2) from equation 1

Where R is the radius of the star and M is the mass of the star.

Now, in absence of any other mass, the frequency of sodium d1 line can be expressed by

£ = Km(e){1/n1^2 -1/n2^2}

Now, the frequency of sodium d1 line on the surface of the star is

£’= K{m(e)-Δm}{1/n1^2 -1/n2^2}

=> £’= £ – KΔm{1/n1^2 – 1/n2^2}

=> £’ = £ – (KGMm(e))/(RC^2){1/n1^2 – 1/n2^2}

=> £’ = £ -GM£/(RC^2)

Now, £ > £’

=> £-£’ = GM£/RC^2

=> Δ£/£ = GM/RC^2 eqn2. [where Δ£ = £-£’]

Now, £ = C/¥ where ¥ is the wavelength of light.

=> Δ£ = -CΔ¥/¥^2. eqn3

So, from equation 2 and 3 we get

Δ¥/¥ = GM/RC^2. eqn4

Where Δ¥ = ¥’-¥, as ¥’>¥

Equation 4 is the equation for gravitational redshift which is predicted by Einstein.

So, the equation for a gravitational redshift can be derived from the mass defect of electron mass due to gravitational interaction.