Photons lose energy but not speed as they get red shifted by gravity or otherwise. Remember Einstein showed how they get bent in a gravitational field. Electrons lose both energy and speed as they get "red shifted" by gravity. This should be visible in a plain De Broglie wavelength / frequency shift!

Dear Anders, I really think that for photons is the opposite as you said.. the light bending doesn't depend on photon's attraction or work against the gravitational field. Read the paper below regarding photons.

Article Gravitation, photons, clocks

The law says that the wavelength of the emitted photon at coordinate r (in the vicinity of a large mass M) is the wavelength measured by an observer at a large distance from M, divided by the square root of 1-2k(r), where k(r) equals the gravitational radius divided by r. The coordinate r of the emitting particle has the origin at the center of mass M.

Solving the conjugate problem (space-time is conjugate to momentum-energy) one recovers the geometry of curved space time.

Furthermore if instead of a photon we consider a "slow" electron the redshift should refer to the de Broglie wave length. Note also that the factor 2 in front of k(r) takes care of the proper shift in both the photon and the electron case.

Erkki. What you are affirming is also the result of the Schwarzschild metric regarding time dilation between two reference systems (1-2k(r1))-1/2/(1-2k(r2))-1/2 which is also the Redshift of photons. This depends exclusively on the different measurement of energy at different gravitaitonal potential. Detectors atoms at different gravitational potential vibrate differently. I don't really know if you can use it for massive particles.

Stefano,

It could be tested by comparing an Auger electron produced in a strong gravitational field and its wavelength had it been ejected in a weaker field. 

I came to the conclusion that the frequency shift of slow electrons is double the Redshift of photons between the same gravitational potentials of emitter and observer. Electrons lose energy in a gravitational field (real effect)  and the detectors  above, being faster for the clock hypothesys, will detect a further decrease (apparent effect) of the frequency of electrons.

If the redshift (energy) law for photons and non-zero restmass particles would be different in gravitational fields would that not create problems to understand the perihelion motion of planet Mercury?

I don't really think so because only non zero rest mass particles are involved in the perihelion motion of Mercury, (unless you count the solar wind).

Well, the information of the perihelion comes via photons.

Ok the info of the position of the planet system point to point comes from EM waves, but this is not taken in consideration in the equation of motion of Mercury.

I think there is a deeper thing here. If you apply special relativity to the problem above, using consistently the relation between the force and the energy law for the material particles, you get only half the perihelion. General relativity imparts different force laws between zero restmass and material particles but the same energy law. I have written about this in my Kepler paper, see my RG page.

Erkki, for sure. But it does not depend on the fact that GR imparts different forces on zero rest mass particles, it depends instead on the fact that the Newton's law is only a first approximation of what really comes out of the Curvature of the Space time in terms of force.

Stefano,

What I mean is that different force laws that predominantly brought fame to Einstein will of course play no measurable role in the photon trajectories revealing the perihelion of planet Mercury. However the energy laws, being the same for zero- and non-zero restmass particles gives not only the correct perihelion motion but will also suggest that the redshift law should be the same for both photons and material particles.

MISNER THORNE WHEELER on the argument treating General Relativity Theory for example at page 659 paragraph "Gravitational Redshift" reports:

___________________________________________________________

"The conservation law |goo|1/2 *ELocal = constant, which is valid in this form for any time-independent metric with goj=0 and for particles with both zero and non-zero rest mass, is sometimes called the "law of energy red-shift". It describes how the locally measured energy of any particle or photon, changes (is "red-shifted" or "blue-shifted") as it climbs out of or falls into a static gravitational field. For a particle of zero rest mass (photon or neutrino), the locally measured energy Elocal and wavelength lamdalocal (not to be confused with affine parameter!), are related by ElOCaI = h/ lamdalocal  where h is Planck's constant. Consequently, the law of energy red-shift can be rewritten as  lamdalocal * |goo|-1/2 = constant.

______________________________________________

First we have to account for the energy distortion measurement of the space-time due to curvature, and the light responds only to it.

Then we account for other local interaction with massive particles which changes the energy of the system of the particle-massive object.

Stefano,

The account proposed makes me a bit schizophrenic. Arguing that we have separately local interactions as well as space time curvature and that these two corrections somehow should be added, does not abide well with the principle of equivalence. Either gravity should be formulated as a force law or mutatis mutandis in terms of  space time geometry. I do not think it is logically consistent to "add" separate contributions to get sensible results.

Erkki, I might be a generator of Schizofrenia...

the curvature anyway acts on material particles (non zero rest mass) exerting what we call a force, determined in the weak field by the Newton law.  The curvature acts on proper time too but in a completely different way.

The Stress tensor is low, far from masses, and it gets  bigger approaching the center of mass. Going under the Earth's surface the stress tensor increases, and the clocks go slower, though the force exerted by the gravitational field gets weaker till 0, the local curvature does not exert the same force.

Both phenomenologies are explained by General Relativity, curvature giving birth to a force and curvature slowing down clocks.

The local proper time which is determined by the local curvature, affects  the measurement of the energy. If I measure the energy in terms of h*v with one same atom, in regions with different proper times or gravitational potential, I don't posess the same way to measure the same energy.

Some fixed quantity of energy will be seen different if measured in a gravitational potential rather than another, and it is a funcion of the gravitational potential difference between the two considered points in the space-time.

This is why the energy of the photon which remains constant, crossing different gravitational potentials remains the same but is seen differently.

Dear Stefano, I am not sure why we need to go "under the Earth's surface" to discuss what happens to (i) a photon and (ii) to non-zero-mass particle. Would it not be simpler to compare the frequency v close to a heavy mass (or black hole) with v0 seen at an "infinite" distance for both the cases (i) and (ii)?

Yes Erkki, it was only to make clear that what changes is the way the energy is measured and this depends on the clock hypothesys. And such thing is not necessarily related to gravitational attraction though are both a consequence of the curvature of the space time.

Dear Erkki,

since you wrote papers on gravitation too, I would like to ask you a question:

the tidal locking is the phenomeon according to which an orbiting planet locks its rotation frequency to its revolution frequency.

THe name suggests that the deformation of the planets drive the phenomeon, which is incredibly slow and is due to different momenta which make the planet turn..

From a certain extent it is convincing, but I think it is not the only reason for the locking.

An orbiting planet around a massive one has a volume and it is bounded to have the speed relevant to the orbit passing through its centre of mass.

 The closest point to the massive one  would have a higher speed, while the farthest a lower speed.

Disintegrating the planet, the farthest dust would go slower the closest would go faster.

This tendency creates for sure a couple of forces which tries to equate the instant speed of the closest point to its proper orbit speed.

What do you think About it??

Dear Stefano,

Your argument appears to be correct to me, although I see no equations that details the magnitudes of the various forces and their effects on the trajectory.

My own approach concerns more the interplay between classical theories and the corrections one might expect from quantum effects. This naturally makes the models investigated more idealised.

I would advice you to contact also Robert Shuler, who is investigating these types of problems in his publications available at his RG page.