# Could mass also experience a form of gravitational redshift?

Main question

Gravitational redshift for photons are a wellknown phenomena where the electromagnetic radiation is reduced in frequency and thus the wavelenght is increased.

The wave–particle duality is also a wellknown phenomena, even though harder to explain. Particles poses Compton wavelength and the momentum is calculated by taking the derivative of the wavefunction.

A quick analys suggests that it means particles would become "heavier" when near to a massive body (stronger gravitational field). In other words it means that the mass of a particle would increase as it gets closer to e.g. a black hole.

If photons are subjected to gravitational redshift, why aren't all particles subjected to gravitational redshift?

As r approaches infinity, the redshift, expressed as the fractional change of waveleght, varies with the distance R from the center of mass the photon is emitted: $$z(r)=\dfrac{1}{\sqrt{1-\dfrac{2GM}{c^2R}}}-1$$

In the Newtonian limit this becomes: $$z(r)=\dfrac{GM}{c^2R}$$

From e.g. Compton wavelength we can imagine that if the waveleght is changed then the mass also has to change. Using an approximation of circular orbits, the velocity of a star in a galaxy would in the Newtonian limit take the form: $$\dfrac{GMm}{r^2}=ma=\dfrac{mv^2}{r}$$

But if the mass is dependent on the radius, it would look like this: $$\dfrac{GM}{r^2}=\dfrac{kv^2}{r^2}$$ with constant k describing the relation between earth postion in the galaxy and the mass.

In other words, we interestingly enough have more mass in the galaxy then we thougt and a flat rotation curve which is the reason dark matter was invented in the first place.

I want to be clear that I am not suggesting that I in any way solved the dark matter problem. I just wanted to bring up the subject.

• Why do you imagine that if the wavelength changes the mass also changes? Mass is a scalar, momentum and energy change. – Javier Jul 12 '18 at 16:33
• If you take a look at the Compton wavelength, you see that the only two variables are wavelength and mass. Since I suggest that the wavelength depends on the gravitational field, the mass should also do that. – W.E. Jul 12 '18 at 17:06