http://www.feynmanlectures.caltech.edu/II_42.html#Ch42-S6

paragraph 6 at the end.

Feynman's POV is very different from the LEV OKUN's point of view on GRAVITATION PHOTONS AND CLOCKS. LEV OKUN denies the possibility of any gravitational potential energy of photons. Feynman's lecture is not compliant with the results of Gravity Probe A experiment.

It is a big mistake Einstein did first, but sort of corrected, Feynman did last but didn't correct it because he thought he was right. No gravitational attraction is exerted on photons which can possibly justify any Redshift.

The energy associated with photons is supposed to have an associated gravitational effect ... IF that energy can be localised.

So if you have two identical internally-mirrored boxes, one containing a complex of light-energy and the other not, then if we place both boxes on sets of scales, the box containing light should give a (fractionally) greater weight reading.

We can work this out from the gravitational shift effect -- light starting at the top of the box arrives at the box floor blueshifted, with a greater energy and momentum than the light starting at the box floor and arriving at the top with a redshift. So while the trapped light exerts a pressure on all of the box walls, the radiation pressure on the box floor is higher than that on the box roof, and pushes the box down harder against the scales, producing a larger reading. So the energy contained in trapped light gives additional weight to the body within which it is trapped.

We can also calculate the radiation-pressure difference without knowing about gravitational shifts, directly from Eotvos' principle. If the two boxes are in freefall, and are falling at exactly the same rate regardless of their contents, then we know that the gravitational field has to be deflecting any contained horizontally-aimed light downwards at the same rate that it deflects the boxes. If the light fell faster in a gravitational field than the boxes, then the deflected light would apply a greater pressure on the floor of the light-filled box, making the "filled" box fall faster than its neighbour.

On the other hand, if light fell more slowly than matter in a gravitational field, (or wasn't deflected at all by gravity), then the falling light-filled box would experience a net upwards force on its internal surfaces, and would be "buoyed up", making it fall more slowly.

So Eotvos' principle tells us that gravity has to deflect light, and that an object containing light should weight more than one that doesn't.

Next, if we believe that gravitation is a mutual effect between two masses (mediated by curvature or fields or whatever), then we require the box containing light to also have a greater gravitational attraction itself due to the extra contained energy. The box containing light, if placed in deep space, should attract more strongly because of its contents (or else we'd need more complex equations that distinguished between different categories of massenergy).

Lastly, since the structure of the container doesn't seem to matter to these arguments, we should be able to increase the inertial and gravitational mass of a black hole by shining light into it, and we can even conceive of a black hole entirely composed of self-trapped light (a "Kugelblitz")

There's also a couple of papers out there somewhere that discuss the situation of a pair of constant parallel lightbeams mutually attracting each other.

----

Generally, if you confine lightenergy to a location or to a state of motion that is compatible with the state of motion of a piece of matter, then the associated energy should show gravitational properties equivalent to a speck of matter with that same state of motion.

Note that although these results are popularly associated with general relativity, none of these arguments actually require general relativity.

@ Aleksei and @Eric: time is Always relative as far as RG is valid since clock rate is determined by the stress-energy tensor, different point to point in the SPACE-TIME. No priviledged coordinate system exists and should not be used. Gravitation is the mutual interaction between "massive objects", confined energy . Light is not massive, or at least not influenced by gravitational attraction during its propagation, does not gravitate. Only when it's detected through a quantum mechanically process, it makes the detector gain mass. Unfortunately any consideration or theory against a well performed experiment fall, this is physics not math...

The deflection of light regards the direct relation of the curved SPACE-TIME with photons. Radiant energy doesn't curve space, the confined energy does it, this is composed of fermions and every field bind to them. The energy and momentum regards the confined energy not radiant energy. Sir. Eddington in his book said: "we still don't have the possibility to demonstrate if radiant energy gravitates" because such experiments were not performed yet. Reports the example of the box in which radiations bounces back and forth, and wonders if this can be a demonstration that light has a weight, but he knows he cannot draw any conclusion with the data he had access at that time.

Dear Aleksei, the only theory which has to be used is RG for sure. But at the time when Eddington lived (til 1950's), nor Pound and Rebka, nor atomic clocks, nor Shapiro Delay experimento nor Vessot and Levine experiments were performed. These experiments proved that:

1) Gravitational Redshift is an existing phenomenon (P&R)

2) Clock Hypothesys is valid, UCR is confirmed (Hafele and Keating)

3) The speed of light varies with gravitational potential (Shapiro)

4) No energy loss or gain occurs in a gravitational potential for photons. The reason why the frequency shift exists is due to the proper time difference or local variation of speed of light due to the curvature of the SPACE-TIME (Gravity probe A, Vessot and Levine)

These are facts.

The kernel of the question becomes: does radiant energy curve space? Can be the electromagnetic radiant energy included in the Einstein stress tensor or not? I would say no, according to the experiments. You say yes.

Albert Einstein in his General Relativity book says that in a weak gravitational field the Schwartzshild metric is a very good approximation of the general metric. This approximation which is widely used, is based on newtonian gravitational potential which is a scalar, while the potential in GR is a tensor (Einstein's words).

From this metric we can easily derive proper time differences of two clocks in a curved space time, globally curved by a mass M. The proper times derived from such metric depend on a "gravitational term" and on a "intertial term", (Lorenz factor). Two clocks result to have the same clock rate if it's valid a particular relation between the difference of potential and the speed differences of the two clocks. Well during the experiment of Gravity Probe A, there was an instant in which the two clocks had the same clock rate, according to GR. Right in these moments (cancelling the doppler frequency shift of the first order due to the relative speed), no frequency variation between the photons falling from the rocket and the one produced by the ground base was detected. No energy variation whatsoever occured if we exclude the energy transfer performed by the doppler effect. This is a very strong experiment which states that photons do not Exchange energy with the SPACE-TIME, or rather, no gravitational potential energy exists.

For me it's enough to show experimentally that light doesn't behave like a "massive object" in the Earth gravitational field, let's say in a weak field in general with and approximation of 2*10^-4. The purpose of my question was to point out Feynman's POV about free energy, his POV wasn't correct, light doesn't posess a gravitational potential energy in a weak gravitational field. What happens with a strong curvature might be different.

OKUN: "If the explanation in terms of gravitational attraction of a photon to the Earth were correct, one should expect red-shift doubling in an experiment Pound-Rebka type.." light does not gravitate in the term that it is subjected to gravitational force. It interacts directly with the space time, without the mediation of the gravitational force.

Ok Aleksei, let's put it another way. What causes curvature is the direct interaction between mass and space-time. The curvature becomes an interaction only when there is another curvature, gravitational interaction. If light in itself is a source of curvature which I doubt, then it gravitatates, interacting gravitationally modifiying the curvature around other objects, with energy Exchange.

The opposite thesis is that light is not a source of curvature but it follows it without altering it. Let's say the space time reacts as a Whole (like an infinite massive and rigid object) when light passes, bending its trajectory but no alteration of the curvature is allowed.

Or, more briefly: Einstein's GR equations, modified by omitting the energy-momentum tensor of electromagnetism, imply that there is no exchange of energy and momentum between photons and matter (!!)

Maybe I was not so clear about it. First Einstein himself wrote it in his book. Second the tensor does not include the radiant energy which is not the electromagnetic field in itself but only a part of it. Third, everything that can't be localized can't give birth to something massive. Fourth the photon does not have time, how can it possibly give contribuition to time, which is the norm of the stress tensor. if you think about the quantum property of photons, and the fact that the wave function can be divided and the photon detected at two completely different places according to the detector, what can be the contribuition to the stess tensor of the radiant energy guys and where???

"...if you think about the quantum property of photons..."

Stephano, what you are saying raises the spectre that has haunted physicists for a century: Tmunu should be constructed from quantum fields, but nobody knows how to quantise Einstein's gravitational field. What I said was in the context of classical physics, because GR is still, as of now, a classical theory.

I know, but it's not a matter of classical or non classical, phenomena are detected and have to be considered thoroughly. If the EM radiant energy wasn't considered in the tensor by Albert Einstein and wasn't put back later, there should be a more profound reason, beside the fact that he considered  it negligible in comparison with the other contribuitions.

So what if they have energy??? Only when they are detected though

 Einstein neglected such contributions in his theory "THE MEANING OF RELATIVITY", maybe, not only because they were negligible compared to the energies at stake, but because he was probably aware that, with his theory, it was impossible or maybe unproper to treat the contribution of light. If you think about the non locality of the wave function, of light, (PENROSE "the quantum particle") which once divided, it can be detected only once but in completely different places, where is the energy as it travels? It's not localised  until It is detected, it belongs to space-time but where?? How can I compute any stress-tensor calculation which is local with such not nlocal feature of a quantum physical verified phenomenon?

The proper time is strictly connected to tied energy and is totally absent from radiant energy.

Stefano ~

Energy-momentum conservation in quantum mecanics is problematic, because of non-locality. As you say, “where is the energy as it travels? It is not defined until it is detected”. It is worth recalling that Einstein’s gravitational theory also has its own “non-locality” problems: the “energy-momentum density of the gravitational field” remains undefined. At one time there were various unsatisfactory attempts to overcome this problem by defining energy-momentum “pseudotensors”. Your suggestion of omitting the energy-momentum tensor of radiation from Einstein’s field equations will not work either, for the reason mentioned by Alexei and myself.

It is conceivable that these two non-locality puzzles are related, but until we have a unified theory that combines gravitation and quantum mechanics, we are in the dark.

Dear Aleksiei,

maybe I was not clear in what I was taliking about before with Eric. In such case infact

1) What I was talking about regards photons,  never seen a fermion being divided in  parts and then detected somewhere else according to the position of the observer.

2)  I will be able to select zones in which the TENSOR has a value in the present only if the quantum in the future will be detected in that area rather than in another.

The "Spooky action at a distance" which scared Einstein (regards the quanglement though) prevented him to make mistakes about it. Maybe "some man" as you say like though Einstein writing such theory was aware of something he could not include in the theory.

I know we went out ot the initial argument I presented.

Just to refocus I wrote an article one moth ago about it.

It is difficult to think about "quantum averaging" in GR.

Maybe Space-time averaging if exists or we change theory.

Article "SPEED OF CLOCKS IN A GRAVITATIONAL FIELD" A FEYNMAN’S LECTU...

In order to conclude...

 I just learned from the Feynman's lectures owners that what Feynman wrote was mistakenly written by the ones who wrote the lectures and he didn't review such part.

Infact he would have never thought about a massive photon and his point of view is explained in his lectures on gravitation.

So I was right, what was written in the Lectures of physics about gravitational potential energy of photons or massive photons was wrong and what he wrote in his Lecutures on gravitation corresponds exactly to the idea I have about the gravitational Redshift.