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If we assume that there is a timelike separation between the two photons, so if the two photons are not emitted together (as two entangled from a crystal), then we can assume that there is a certain distance (spatial separation) between the two photons.

In this case there are two possibilities:

  1. In this case, if we assume too that they were emitted from the same source in the same direction, and the spatial separation between them is long enough so that the second photon (Photon A) is outside the gravitational field of the first photon (Photon B), then we can see that both photons will travel at speed c and the first photon's gravitational effects will travel at speed c together with the photon in the same direction.

In this case, the answer to the question is that the second photon (Photon A) is not affected by the gravitational effects of the first photon (photon A).

  1. If we assume that the spatial separation between the two photons is small so that the second photon (Photon A) is in the gravitational field of the first photon (Photon B) at the time of its (the second photon's Photon A's) emission (which is instantaneous as per QM), then the second photon (photon A) will be affected by the first photon's (photon B) gravitational field.

In this case, since the first photon (photon B) will seem to bend spacetime, and so Shapiro effects will be in effect.

In this case, the second photon (photon A) will be inside the first photon's (photon B) gravitational field, and since the gravitational field itself is traveling with speed c, the second photon (photon A) will be traveling inside bent spacetime all along.

As per the Shapiro effect, for a far away observer, the second photon (photon A) will seem to be traveling slower then c.

The reason for that is exactly what the Shapiro effect describes, because of the first photon's (photon B) gravitational field, time will seem to tick slower for a far away observer. And distances will seem to be longer too. So for the second photon (photon A), it will have to travel at a speed=distance/longer time=smaller then speed c.

This will lead to a contradiction, since if the first photon (photon B) travels at speed c, and the second photon (photon A) travels slower then c, they should become more separated. As per SR, for any observer, a photon is traveling at speed c, so the first photon has to travel at speed c.

The solution is, that if the second photon is inside the first photon's gravitational field, then the first photon is inside the gravitational field of the second photon too. Gravitational effects will equalize, and both photon's will pull each other the same way and they will both seem to travel at speed c for a far away observer and there will be no blueshift and no change of frequency.

Where is my reasoning wrong?

Question:

  1. Is the gravitational effect of a photon traveling together with the photon at speed c?

  2. In this case, will the second photon (photon A) be affected by the first photon's (photon B) gravitational field and how will it change the second photon, will it change it's frequency?

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