That's described by studying the electromagnetic field on a curved background. One known consequence is that, in a curved background, the vacuum of quantum fields isn't globally defined, which means that the statement about a single photon is observer dependent. This isn't anything new: http://www.scholarpedia.org/article/Unruh_effect and is known as the Unruh effect.

In practice it's the shot noise that's the useful observable, which, in a curved background, is observer-dependent.

Gravitation inside electromagnetic wave

General relativity (GR) derivation of gravitational frequency shift of light does not provide the quantum mechanism of the frequency shift. However with periodic time in Periodic Relativity (PR), it is possible to explain this quantum mechanism as follows.

In an electromagnetic wave there is a stream of successive wavelets traveling at constant velocity of light. Each wavelet having energy equal to a quanta called photon. The mass equivalent of this energy is given by E/c^2. If we consider the gravitational attraction between two successive photons within the electromagnetic wave then we can write the expression for gravitational force between them as described in sec. 9A of following article.

Periodic relativity: the theory of gravity in flat space time

https://www.academia.edu/48914611/Periodic_relativity_the_theory_of_gravity_in_flat_space_time

So here we have the robust relativistic derivation of the variable gravitational redshift as the Hubble parameter rolls down from Planck epoch to the present epoch. This is done using de Broglie force, periodic time and gravitational attraction between two successive photons within the electromagnetic wave which merge with each other at about 10^{-26} sec. before the big crunch in PQG terminating the motion of the wave meaning that the wave will collapse. In PQG it is not possible to generate photon parameters before this time. This is where gravity unites with the electromagnetic force. So what we have here is the first theoretical evidence of existence of gravitational forces within the electromagnetic wave.

From these calculations we can conclude that the electromagnetic wave is held together by gravitational forces. Not only so, but even the seven monochromatic wave frequencies are held together by gravitational forces as a packet of white light. When these gravitational forces are overcome by processes like refraction, diffraction or polarization, then the electromagnetic wave decomposes into components like photon particles or seven colors of the rainbow etc. Mechanism of gravitational frequency shift of light can thus be explained as due to absorption or ejection of quanta of energy from or to the gravitational field of a gravitating body by photons. When photons absorb gravitational energy, two successive photons come closer due to greater gravitational attraction as per Newton's inverse square law and thus light gets blue shifted. When photon loses energy to the gravitational field, the gravitational attraction between two successive photons is reduced which stretches the wavelength and the light get red shifted. All this happens at a constant velocity of light.

Whenever GR physicists use Lorentz force as the rate of change of momentum, they are ignoring the de Broglie force and the periodic time. This is because GR has abandoned the relativistic mass and thus further differentiation of momentum is not possible. This eliminates the de Broglie force and saves the principle of equivalence. As a consequence, both the principle of equivalence and the gravitational red shift are not invariant in GR. But in PR, relativistic mass is part of the theory and the gravitational mass is equal to relativistic mass. This makes both, the principle of equivalence as well as the gravitational red shift invariant.

If we plug in gamma ray photon data in equation, we get gravitational redshift of about 1.13 x 10^{-22} at 10^{-26} sec. after big bang which is very small. If we plug in Saviton data which is a massless boson having Planck energy then we get gravitational redshift of 0.4 at Planck time which is significant. This is the kind of gravitational radiation coming out from about 10^{62} Savitons at Planck time which created the entire universe. Hence all the known fundamental particles of physics are products of this gravitational radiation.

Whether it is a single photon or a steam of photons the influence of gravitation would be the same

In my view entanglement is a different issue

In my book Born:A universe (can be downloaded from my profile) from 2015 I derived a relativistic formulation of the Newton law. It is based upon particles self energy and not just the normal mass. As a consequence, photons interact vith gravity through their energy content. Another consequence is that a pair of photons can interact through the gravitational force. Quite simple in fact.

Calculate the equivallent mass of photon energy , use Newton s Gravity law, and find ouț that the searched value is such as small that no one could measure it

It is taught that gravity is an effect of the undefined, unexplained property of mass. It is taught that the effect we call gravity increases the energy of photons as they approach the Earth. What is not taught is that the equation describing the change in photon energy equated to gravity-caused acceleration can be read both forward and backward. In other words, the increase in photon energy causes the effect we call gravity.

What would cause the photon to increase its energy in the absence of a gravitational field? The answer is that the speed of light varies. This possibility is far less difficult to substantiate than is the idea that space and time are objects interacting with photons.

Physicists have no direct empirical support for telling us anything about either space or time affecting objects or for objects affecting them. If physicists would cease to argue theoretically that time accelerates but light does not, we could return to learning the nature of the Universe from the science of measurements.

No one has measured either space or time. No one has written a physics equation that contained the direct representation of either space or time. Both have always been substituted for by object-related measurements. Follow the units. The units tell us what it is that physicists are measuring and are, thereby, learning about.

James A Putnam

James A Putnam

The effect we call gravity is caused by a time-gradient, so it's true that time doesn't accelerate... but a time-gradient does ! However, a "photon" {they don't exist} can't be accelerated by gravity... the effect is in any case that the frequency of the radiation {a photon as a particle can't have a frequency} is decreasing {red-shifted}. The speed of light may be different in different transparent media, but is never variable. The speed of light is a constant that only depends on the properties of the transparent medium. But that is MY humble opinion which is based on my work which is not supporting Einsteinian physics !

Dear Bikash Kumar Das,

You have gotten an excellent answers from Preston Guynn, James A Putnam...

The photon energy well increase, which will appear in changing of the associated length of wave... With help of the concept of gravity: 'Article Gravity a paradym shift in reasoning

https://www.researchgate.net/post/Exists-the-next-situation-when-an-outsider-researcher-who-has-achieved-a-very-encouraging-result-in-earthquake-forecasting-is-not-supported

Regards,

Laszlo

Thank you.

Hi my name is shahid shaikh i discovered the new law of physics that explained how gravity work for subatomic particle like photon. And my discovery is published in ijser known as international journel of scientific and engineering research.

And you can find my paper in research gate

.https://www.researchgate.net/publication/354189918_SHAHID_theory_of_Quantum_Gravity/stats

Form here

If you want the answer of this question read my paper i explained mathematically how gravity work between two photons.