Dear professor Alfonso-Faus,

of course when you explicitly neglect the difference between photon and massive particle, then you get no difference :) 

I think it's inconsistent to insert relativistic expressions into Newton's law. M in that law is simply the mass not the energy. Photon has zero mass but nonzero energy. 

What you are actually discussing is the conservation of the energy inside the sphere. Since the total energy is conserved, you conclude that the gravitational field is unchanged. Thus, the real issue is the conservation of energy.

But if you really want to discuss gravitational field, you must consider general relativity, because in the Newtonian gravity only the mass is a source of gravitational field. There is no way how to treat gravitational field of photon in classical framework, for the photon is an ultrarelativistic object. Einstein's equations reduce to Newton's law only for small velocities. You can assume that the gravitational field of single photon is weak and treat it as a perturbation to flat space. However, what you get is not the Newton's law with m = E /c^2, because you have the retardation effects connected with the finite speed of gravitational propagation.

Hence, talking about gravitational field of a photon in the Newtonian framework is meaningless.

But even if this was not the case, remember that Newton's law in its simple form holds only for a point particle. The total gravitational field is a superposition of the field from all particles. And it is certainly a difference whether we have, say, massive particles at rest in the sphere (so that the field is static), or the same number of photons travelling with the speed of light inside the sphere (so that the field is only stationary and in the statistical sense only).

To conclude, if the question was whether the energy is conserved and whether there is energy associated with the mass, the answer is yes. If the question was whether gravitational field remains unchanged, the answer is definitely no.

The gravity field will not change. After the matter and antimatter particles annihilate, their rest masses are converted into electromagnetic energy, which is then trapped by your ideal mirrors inside the sphere. The total gravitational field of the sphere is the result of the total mass + energy of the sphere and its contents, not just the rest mass; you just converted some rest mass into electromagnetic field energy, but the total mass-energy of the sphere, hence its gravitational field, remained the same.

Very clear explanation V.T.Toth. May I add that in my opinion the source of gravity is energy, rather than mass. Then since there is no change in the total energy of the system, the gravity field will not change.

The idea is that the gravitational constant G must be proportional to c^4, for a " true constant" cosmological constant  lambda (see my last paper here, with M. Fullana,  on the conditions that have to be satisfied by a G(t) and c(t)). or if lambda is also variable, then G must be proportional to c^2 (see here my paper with J.A. Belinchón, "A theory of Time-Varying constants".

Then, in any case the product GM for the gravitational potential is proportional to the total relativistic energy, Mc^2, so that this is the energy source of the gravitational field, not just mass M.

I don't agree. The source of gravity is not only the energy, but the energy-momentum tensor. This object includes the flux of energy-momentum and the stress tensor (pressure). The photon gas satisfies different equation of state than massive particles, the energy-momentum tensor will be different and hence the gravitational field will be different.

Of course, we may argue whether in the case of the small sphere this is significant or not, but in principle the gravitational field will be different in both cases. But it certainly matters in cosmological models or in the models of stars.

Martin,

I am talking Newtonean gravitation: gravitational force = GMm/r^2 . Here, as always with G, The product GM is proportional to the total relativistic energy of the source Mc^2,  that is proportional to GM. Within this context, the proposed question is OK with the answer: the gravitational field will not change.

In General Relativity, and for large distances, this is another story. 

Martin I think you are right. Consider that Einstein in his "MEANING OF RELATIVITY" explicitly neglected the contribution of free energy in his calculation of the  energy momentum stress tensor.  Putting such contributions in the stress tensor would be arbitrary. Consider that light does not gravitate, as specified in the article attached,  hence it would be quite difficult for it to be a source of gravity.

Article Gravitation, photons, clocks

THe source of Gravity is not free energy (PHOTONS) but tied energy which is connected to time.

Dear professor Alfonso-Faus,

of course when you explicitly neglect the difference between photon and massive particle, then you get no difference :) 

I think it's inconsistent to insert relativistic expressions into Newton's law. M in that law is simply the mass not the energy. Photon has zero mass but nonzero energy. 

What you are actually discussing is the conservation of the energy inside the sphere. Since the total energy is conserved, you conclude that the gravitational field is unchanged. Thus, the real issue is the conservation of energy.

But if you really want to discuss gravitational field, you must consider general relativity, because in the Newtonian gravity only the mass is a source of gravitational field. There is no way how to treat gravitational field of photon in classical framework, for the photon is an ultrarelativistic object. Einstein's equations reduce to Newton's law only for small velocities. You can assume that the gravitational field of single photon is weak and treat it as a perturbation to flat space. However, what you get is not the Newton's law with m = E /c^2, because you have the retardation effects connected with the finite speed of gravitational propagation.

Hence, talking about gravitational field of a photon in the Newtonian framework is meaningless.

But even if this was not the case, remember that Newton's law in its simple form holds only for a point particle. The total gravitational field is a superposition of the field from all particles. And it is certainly a difference whether we have, say, massive particles at rest in the sphere (so that the field is static), or the same number of photons travelling with the speed of light inside the sphere (so that the field is only stationary and in the statistical sense only).

To conclude, if the question was whether the energy is conserved and whether there is energy associated with the mass, the answer is yes. If the question was whether gravitational field remains unchanged, the answer is definitely no.

The gravitational field is performed only on the surface of the container where the photons bounce, changing their momentum. I see it as  the only source for the stress tensor.

Dear Algidras,

it is not true that EM field does not generate the curvature. What you refer to is the scalar curvature, the trace of the Ricci tensor (or "spur" in German) and this vanishes for EM field, that's correct. But the scalar curvature is only one part of the Riemann tensor which describes the curvature. Even if the trace of the Ricci tensor is zero, the Ricci tensor itself is non-zero in the presence of EM field. 

As I said in my contribution above, you can find the gravitational field generated by a single photon. You simply assume that the background spacetime is flat (Minkowski) and then calculate the field of the photon as the perturbation of the flat spacetime and ou can get a reasonable answer.

Sephano ~

Your statement: "Consider that light does not gravitate, as specified in the article attached, hence it would be quite difficult for it to be a source of gravity." Is NOT correct. Light is electromagnetism. Electromagnetism has an energy-momentum tensor. Energy-momentum is the source of the gravitational field.

I don't know (or care) what it says in "the article attached".

Eric,

if you don't care about one of the reference articles written also by J.A Wheeler what can I say...

Electromagnetism includes tied fields to charges and currents and electromagnetic radiation. Einstein said the radiant part was anyway a negligible part, (you could say he neglected but It may not be negligible). The tied energy contributes to the stress tensor and affects gravitation, the free energy cannot because for it, the time does not exist. Only with quantum physics the radiation is absorbed and becomes matter and then the time for it comes to be defined and a source for the Einstein Stress Tensor for the space-time.

Dear Stefano, 

which paper do you mean? The one by Okun et al. is not accessible through ResearchGate (at least to me).

However, I am afraid that Eric Lord is correct. Even free electromagnetic field is definitely a source of gravitational field, because it has non-vanishing energy-momentum tensor. There is a simple example, an exact solution of EInstien's equations called Vaidya metric. It represents the so-called null dust. The energy-momentum tensor is similar to ordinary dust (perfect fluid without pressure), but instead of 4-velocity there is a null 4-vector which plays the role of the wave vector k. This is pure electromagnetic radiation but the curvature of the Vaidya spacetime is not zero. In fact, the metric is similar to the Schwarzschild metric, the only difference is that the "mass parameter" is function of (retarded) time.

Another simple example is the Reissner-Nordstrom metric, which describes black hole with spherically symmetric electric field filling the universe. Moreover, this solution is static.

To conclude, there are many examples in which only the free electromagnetic field is the source of the curvature. 

Here is the article

The answer to the question, as posed,  is given by solving Einstein's equations, where the right hand side is given by the appropriate energy-momentum tensor and the corresponding boundary conditions. That's all. There's no need for guessing.

Stefano ~

I realize now that I had in fact already seen the article by Okun et al. But I don't agree that it supports your conclusion. The only viable gravitational theory we have is a purely classical theory, in which energy-momentum, including that of Maxwell's EM, is the source of the gravitational field. Choosing parts of total energy-momentum to include, and parts to leave out, is neither permitted nor required. The idea of a photon, and its property E = hν, are purely quantum-mechanical concepts. This kind of mixed theorizing is dangerous. (It obviously doesn't make sense, for example, to combine E = hν with E = mc2 and then treat a photon as a massive particle with m = hν/c2!) It may be true that the gravitational red shift doesn't imply any energy exchange  between the Maxwell field and the gravitational field, but that doesn't imply that electromagnetic energy-momentum (carried by photons) doesn't contribute to the source of gravity. In any case, exchange of energy-momentum between gravity and other fields presents an intractable puzzle, insoluble even in principle in a coordinate-independent way.

When talking about photons, one is talking about the electromagnetic field. Matter charged under this field-scalar or spinor, depends on the problem, can, also be included in a straightforward way.  One specifies boundary conditions and computes the energy-momentum tensor. This is the right hand side of Einstein's equations. One solves these equations and finds the metric. Of course it might prove useful to impose some symmetry conditions to simplify the equations. But there isn't any sort of ambiguity here: all equations can be explicitly defined. There may be *practical* difficulties in solving the equations, imposing the constraints, taking care of numerical instabilities, watching out for black hole formation and so on. But there isn't any issue of *principle*: all sources of energy and momentum gravitate, which means they are right hand sides of the Einstein equations in the form of the energy-momentum tensor  and modify the metric accordingly-a standard result of general relativity. One doesn't talk about ``the gravity field'' of some source, but of the metric, solution of Einstein's equations, given the corresponding energy-momentum tensor.

This is standard material of a general relativity course. There isn't any such distinction between a stress-energy tensor that ``creates'' curvature and one that doesn't. That's a meanigless  distinction. The Einstein equations are clear. I don't understand why people are still making metaphysical statements about them, instead of simply setting them up and solving them.

The approximations that are involved in general relativity have nothing to do with the subject at hand. For the moment all that's been presented here are assertions-which is strange, since Einstein's equations are available. So what should be done-by the people claiming there's a problem-is  solve them and then show that the solutions can't account for the experimental data, within experimental error.  Of course, given what is known about general relativity, it's rather doubtful that any  disgreement will be found. What is much more likely is that the electric effects involved in the Biefeld-Brown effect (assuming, of course, it can be confirmed; a patent isn't sufficient) are so much stronger than the general relativistic corrections that they dominate and, furthermore, a Newtonian approximation for the gravitational effects is adequate. Such an approximation *is* consistent with general relativity, since the effect involves non-relativistic motion. Incidentally, this doesn't have anything to do with the question discussed here.

For a nice presentation of the physics involved in the Biefeld-Brown effect, cf. http://dspace.mit.edu/bitstream/handle/1721.1/77114/825070978.pdf?sequence=1

As expected, gravitational effects are not relevant.

@ Martin Scholtz and Antonio Alfonso-Faus

It is posible to insert relativistic expressions into Newton's law (with some modifications). Newton's inverse square law can be rewritten in terms of attracting energies instead of classical description of attracting masses. This is the basis of Periodic quantum gravity and cosmology theory.

@Algis Džiugys The gravity field will not change. as explained by V. T. Toth.

Article Periodic quantum gravity and cosmology

Eric,

I can agree with your point of view that it is not demonstrated that the energy-momentum tensor does not contribute to curvature and then to gravitation. Though reading the EINSTEIN'S GR,I found that he neglected such contribution of radiant energy. Since the integration of Maxwell and Einstein equations was attempted but failed, otherwise we would have a unified theory, I would suggest that It can't be affrimed  that the stress tensor is not influenced by radiant energy, but I can't see either how the opposite can be affirmed.

If the boundary conditions in the domain are reflecting, then the conversion to radiation will not be the stationary state of the process. Therefore the statements in the question aren't compatible. If one *does* want to describe the transition from a certain density of matter+antimatter, in equilibrium with radiation, to a state with only radiation, other boundary conditions are needed. For the reaction Q + Q' -> 2 gamma will be balanced by the reaction 2gamma->Q + Q', under reflecting boundary conditions. Open boundary conditions would do the job-only a mechanism would be required then to replenish the radiation. 

Of course it's ``demonstrated'' that the energy-momentum tensor ``contributes'' to curvature and gravitation-that's what the Einstein equations *mean*.

Stefano ~

There’s an obvious reason why the energy-momentum tensor for radiant energy can’t be absent from the right-hand side of Einstein’s equations. The right-hand side must satisfy Tij;i = 0 because of the Bianchi identity. Undeniably, radiant energy and “matter” interact with each other. There is energy (and momentum) exchange there, so that the Tij of “matter” doesn’t, in general, satisfy Tij;i = 0.  Total energy-momentum is required.

The *total* energy-momentum tensor is (covariantly)  conserved, of course. But it's this quantity that we're talking about, since it's the combined system that matters.This doesn't have *anything* to do with unifying gravity with electromagnetism and everything to do with the definition of the energy-momentum tensor.

Dear Vikram Zaveri,

can you, please, tell me, which my argument is wrong? Of course, you can formally replace m by E/c^2 in the Newton law. However, this is not what general relativity gives. I mentioned retardation effects, for example. These effects cannot be neglected because photon is an ultrarelativistic object.

Dear Mr. Scholtz:

There is nothing wrong with your argument that "it is inconsistent to insert relativistic expressions into Newton's law." My theory requires a revised principle of equivalence which states that the gravitational mass is equal to relativistic mass." I have used this principle throughout all my work and obtained reasonably acceptable results. Secondly gravitational waves and associated particle "Graviton" can exist in my theory much later in the evolution of the universe after the formation of stars and galaxies. However, the gravity existed right from the beginning of the universe. This would mean that gravitational attraction has nothing to do with gravitational waves and graviton. So my conclusion is that the gravitational waves arise due to loss of kinetic energy of the orbiting star. It is the kinetic energy that gets converted into gravitational waves if at all they exist. Therefore speed of gravitational waves and retardation effect does not come into picture when discussing the gravitational attraction between photons or between photon and other objects.

@ Stam Nicolis

Regarding to Biefeld-Brown effect (BBE), some years ago I made simple experiment. I constructed flying apparatus based on BBE. It worked. However, if apparatus was isolated from surrounding air (e.g. simply pushed into light plastic bag) it did not work. So, most probable conclusion is that BBE is based on ionic wind.

Dear Algirdas Antano Maknickas,

I am sorry, I did not presented more details about my Biefeld-Brown effect (BBE) experiment. The flyer was hanged vertically on a fillament in such way that could generate lift force perpendicular to the gravity vector. So, any generated lift force resulted to deviation of filament and flyer from initial vertical position. As I wrote before, the flyer pushed into plastic bag did not generated any force in contrary to the case of the flyer without plastic bag. So, the most probable reason for BBE could be ionic wind.

It is reason, why I would not like to start and continue discussions about BBE in this branch. It could be done in another branch.

Actually in this experiment you mix two different fields : the gravitational field, and the electromgnetic field (because of the mirrors). What ever your experimen the sphere is transparent for the gravitatioanl field, so at the initial conditions you have an equilibrium which includes the gravitational field out of the sphere. Next you envision a sudden change in the state of the system, at this point the equilibrium is broken, and the usual equations (whatever they are) do not apply any longer. Eventually another equilibrium is established. Clearly there is something that has propagated out of the sphere to establish the equilibrium of the gravitational field, they are either gravitational waves, or gravitons.

More generlly bosons, particles associated to force fields, should be seen as the manifestation of discontinuities in the propagation of the field. So whenever youhave some rupture of a previous equilibrium (such as the anhliation of two charged particles) a boson is emitted. Boson are like shoch waves.

Here (https://www.researchgate.net/post/Do_photons_have_mass#541f3fe0d685cc866c8b4649 ,

the thread “Do photons have mass” ) is some discussion now, which relates to this thread.

Cheers

Photon Energy:

E= hf =mc2=Pc

Photon mass:

m=hf/c2

Newotonian gravity force:

F=Gm1m2/r2

Force exerted on two photons:

F=G(hf1)(hf2)/r2

The photon is a quantum item. So at the best we should take in the r,h,s of the Hilbert-Einst.Eq. the energy-momentum tensor averaged over the one-photon state. And then to try to resolve the equation to find the metric. It is clear that the scalar curvature R=0.

“…The photon is a quantum item.….”

Every other particle in Matter, including particles, which compose the “masses that cause the GR’s non-zero curvature of the spacetime”, is a quantum item…

That is another case, that for anybody, who, in contrast to the authors of the SR/GR, who didn’t understand what are the phenomena/notions “Space” and “Time” and so assigned to these uncertain phenomena rather strange properties, understands what these phenomena/notions are, it is quite clear that there cannot be fundamentally of the “fundamental relativistic effects”, i.e. the “space contraction”, the “time dilation”, the “spacetime curvature”.

And that in the reality Matter’s utmost universal [someone can include in the spacetime a lot of other dimensions that relate to concrete parameters of material objects] spacetime is the absolute [5]4D Euclidian empty container, where material objects and Matter as a whole, exist and evolve. Which, of course, isn’t Minkowski/Pseudo Riemannian spaces with evidently strange imaginary either space or time; and the emptiness cannot be contrcted/dilated/curved/etc.

More see https://www.researchgate.net/publication/260930711_the_Information_as_Absolute

DOI 10.5281/zenodo.268904 - to understand what are the phenomena/notions “Space” and “Time”, and https://www.researchgate.net/publication/273777630_The_Informational_Conception_and_Basic_Physics DOI 10.5281/zenodo.16494 - to understand what is the Matter’s spacetime and why it is as that is pointed above.

The SS post above and link in the post are useful also.

Cheers

Gravity is produced not by mass but rather by energy.

“…Gravity is produced not by mass but rather by energy.….”

Everything in Matter is produced by energy, that follows from the absolutely fundamental law that to change some information, including, of course, to create a new information [when there is/are nothing else then some informational patterns/systems that are element of the absolutely fundamental and absolutely infinite “Information” Set; that is absolutely fundamental rigorously proven fact; including all material objects and Matter as a whole are some informational patterns/systems/sub-Set also, see the first link in the SS post above] it is absolutely obligatorily to spend some, indeed seems utmost weird absolutely fundamental Quantity “Energy”.

But energy only makes changes, including, in this case make concrete patterns, first of all the particles, however at that it acts completely “dully” and by any means doesn’t determinate the content of changing/created particles/systems of the particles. That other, including specific for concrete patterns/systems laws/links/constants, make.

Matter is rather simple logical system that is built and changes in accordance with a rather small set of basic laws/links/constants, including in Matter at least 4 fundamental “Nature forces” act [Strong, Weak, EM and Gravity]. And, though all interactions on fundamental depth in Matter happen with fundamentally universal exchange by energy, however the results of the interactions are quite different depending on what the forces act in concrete interacting systems.

Returning to Gravity, it is, again, nothing else then some Nature force, which is in many traits like the EM force, including, at that, the corresponding the forces’ fields are formed by corresponding charges – by the electrical charges in EM and by the gravitational charges, i.e., the gravitational masses [which is equivalent to the inertial mass, however is principally different – why? - see the second link in the SS post above]; the fields indeed can be characterized by some tensors – by the electromagnetic field tensor in EM, and by some analogous tensor in Gravity.

However these tensors are characteristics of the quite material fields [that very possibly, as everything in Matter, are some disturbances in the dense 4D “ether” that fills Matter’s 4D Euclidian sub-spacetime] and by no means they are some characteristics of “contracted/dilated/curved” spacetime.

Happy 2019!

Cheers

Note, that in the above, as in any other SS post/paper, etc. the term “absolutely fundamental” relates to facts, phenomena, etc. that are/act, etc. in whole “Information” Set, when the term “fundamental” relates to facts, phenomena, etc. that are/act, etc. in whole Matter

Preprint THE PHILOSOPHICAL SKETCH OF GRAVITATION ORIGIN