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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?

Additional thought

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.

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  • $\begingroup$ Why do you imagine that if the wavelength changes the mass also changes? Mass is a scalar, momentum and energy change. $\endgroup$ – Javier Jul 12 '18 at 16:33
  • $\begingroup$ 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. $\endgroup$ – W.E. Jul 12 '18 at 17:06
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The Compton wavelength of a particle is equal to the wavelength of a photon whose energy is the same as the mass (see mass-energy equivalence) of that particle.

One cannot conclude from this alone that mass has wavelength, or that energy as mass is going to behave the same as photonic energy which is purely momentum.

If you asked about De Broglie wavelength, the answer might be more difficult.

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  • $\begingroup$ De Broglie wavelength demand a velocity of the particle which I don't like to add to the problem. But I would be happy if anyone could answer that question too. It is fairly easy to describe mass as the slope between a fixed number (planck's constant) and the wavelength. It works well in e.g. special relativity, the Dirac equation and De Broglie wavelength. Since the fixed number (or height it you like) is constant, the only way to change the slope (the mass) is to change the wavelength. This wavelength I believe has to change in a gravitational field since space itself changes. $\endgroup$ – W.E. Jul 13 '18 at 8:48

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