(a cut out from a discussion, with later-edit done in the double-parentheses only)
There is no mass here that is moving. Isn’t it gravitational mass-energy? (and not gravitational mass) simply saying mass is misleading especially in a context where we are saying photons don’t have mass, since any mass photons are associated with is from the kinetic energy. (and as you said in a gravitational formulation from energy-momentum)
All the gravitational principle of mass-equivalence does is it equates inertial mass with gravitational mass. The mass-energy equivalence comes simply from E=mc^2 which is not just for gravitational mass but all forms of mass.
((meaning the energy-mass or mass-energy is an idea also in QED/QCD process, every-where there are particles that convert into energy and energy packets that convert into mass))
SO mass-energy equivalence is a special theory of realtivity effect and gravitational tensor-coupling has got nothing to do with it. A photon gets it’s energy-momentum (( energy/momentum)) from QED energy-mass (so a photon’s parent has a mass but not photon)
Which also means gravitational formulation in general theory has got nothing to do except to accept the special theory effect.
((and strictly it’s not a special theory effect but a particle-physics effect, but a tribute to Einstein, how he envisaged something that has wide implication for particle processes. In particle processes from good old energy-conservation, also using the fact that if mass has been used up and is not produced in/to conservation, it is energy that has to compensate for that, the reverse reasoning is also applicable in particle processes, how much of particle processes were understood in his days?))
A photon has gravitaional mass-energy but no gravitational mass, in a strict understanding. Albert Einstein is a great mind because despite of the fact that particle physics processes and QED were yet to be discovered/invented he understood the mass-energy equivalence which is nothing but a manifestation of conservation of energy theorem.
(energy is taken for mass formation, understood from the reverse: mass is needed for energy, isn’t that a central point about particle physics process)
SO Einstein understood only conservation theorm and derived many results based on many problems of his time. Photons are a part of a gravitational mass-energy movement but not just mass movement.
In a discussion where we say photon has zero mass it’s necessary to point out that what you are saying is really mass-energy and not simply mass. The energy-momentum tensor term you are refering to comes from the fact that energy is conserved and in a particle physics process such as the one involving a photon creation since mass-energy has been spent in some form it must show either as energy of final states or mass of final state.
A photon’s parent such as an electron has a mass and energy and after the photon is created energy conservation is satisfied only if photon has got some kinetic energy. It can be created with kinetic energy but all it’s potential energy are zero, it has zero charge so zero electromagetic potential ((energy)), zero gravi-mass so zero gravitational potential ((energy)).
But kinetic energy comes from the amount of energy that is necessary to conserve ((satisfy)) mass-energy conservation principle, the mass must be zero since it has to travel at a speed it has, known from experiments such as radio-broad casting which is the highest speed therefore lowest mass which is zero.
The energy-momentum tensor coupling term has got nothing to do with a photon as such, it merely recognizes a photon from it’s energy not from it’s zero mass. The photon is governed by principles of QED and not gravitational laws. Photon is more special but for many special reasons other than gravitational facts.
Nothing in the world ever, gives photon any mass. It’s still energy that you are talking about, which is summed up in general theory as a mass-energy term because gravity is not sensitive to mass and energy differently. The len…sing of photon in a strong Gravity-field is because of the kinetic-energy of the photon and not it’s mass which anyway it does not have.
In case of photon we must say it is mass-energy and not mass (otherwise it may be misleading given we also say it has no mass) In all other cases we can say it’s mass or energy depending on the situation.
e.g. a particle may not have enough mass which we may be ascribing it to, in that case mass and energy must be differentiated quantitatively but mass-energy can be used qualitatively.
But in case of photon it’s clear that it’s all energy no matter what, so either mass-energy or energy is a good term. simply mass does not make any sense in case of photons.
The other special attribute of photon I wanted to mention (which I hit recently: 6 months or so ago) is a photon does not obey energy-time uncertainty principle… ((corrected this statement at the bottom))
very special, no one can attain it’s speed so no one interacts with it enough to know it has zero mass, it’s running away from us at the highest speed to hide the fact it has slimmed the most by not eating enough for a long long time. ((
so no one ever reaches the rest-frame of photon except another massless particle 1). READ here why I struck that off, other related articles will be pasted if-and-when I find them and can get back here and 2). here Many other related articles of photon characteristics I am appending the links on the quite bottom, okay? The links at the bottom INCLUDES the two article that are linked just here; 1 and 2. ))
but I propose one experiment where we measure it’s energy from a photon-detector (like at belle) and it’s energy again from a gravitational lensing so any additional energy may point to any non-zero rest-mass ((of the photon itself) in case we want to prove/disprove it has a zero mass or not.
I would actually like to correct myself for saying above that photons violate time-energy uncertainty. The correct thing to say is: Photons being relativistic it is absurd to say they have a specific position, this comes from an additional form of uncertainty which is a result of the time-energy relation in relativistic case,
so, valid for not only photon but all fast moving particles, for the latter case we can not measure the momentum as precisely as we want it in as small time as we want, but for photons, they being massless their position can not be arbitrarily precise in a((n)) arbitrarily small time.
The criteria is the position ((space distance)) should be larger than the wavelength in question ((in the least error making epoche)), therefore photon position is not talked about in quantum mechanics, in classical mechanics this results in ray-optics because: we can talk about it’s position”.
the additionl form of uncertainty equation is momentum-time uncertainty for mass-have particles and position-time uncertainty for mass-havenots (a photon is a mass-havenot but it does not believe in rioting in Birmingham)