# Do the Doppler Effect and EM Stress-Energy Tensor Imply An Object's Emitted Light Exerts More Gravity Upon You When You Are Moving Towards It?

(Please message me or comment if this is not concise enough as a question)

GIVEN:

1. Energy in the form of electromagnetic waves (aka photons) exerts a gravitational force proportional to said energy:

Does a photon exert a gravitational pull?

1. Moving towards any direction increases the frequency (decreases wavelength) of electromagnetic waves from that direction ("blueshift") and decreases the frequency ("redshift") of electromagnetic waves from the opposing vector:

https://en.wikipedia.org/wiki/Relativistic_Doppler_effect

1. The energy of a photon is directly proportional to its frequency: (Also see mass-energy equivalence)

https://en.wikipedia.org/wiki/Photon_energy

Any velocity you have relative to a light-emitting object creates an energy gradient in your frame of reference, biased towards said object [2 & 3]

You are gravitationally attracted to higher energy areas in your frame of reference [1]

This would thus imply that any velocity 'towards' any object would cause a small but constant acceleration further towards it.

It would similarly imply that an object's apparent mass changes based on your velocity relative to it.

Original Post:

"At Relativistic Speeds, Would the Blue-Shifted Light at the "Front" of the Spacecraft cause Gravitation?" I was doing a thought experiment about how mass is lost from gravitational waves, which led me to thinking about how a "bow shock" or gravitational shock wave might appear in front of any object moving near the speed of light. Obviously from the reference frame of the spacecraft there would be no such shockwave.

However, when you are travelling at such speeds, the light from stars and the CMB in front of you is blue-shifted and the light behind you is red-shifted. This eventually creates a massive energy gradient. As we all know, energy itself generates gravity like mass does.

So my question is: does this energy gradient cause the spacecraft to experience gravitational attraction towards the direction it's already moving? (Let's ignore photon pressure for this thought experiment)

EDIT: If you are travelling near the speed of light, would the difference in energy between blueshifted/highly energetic light "in front of you" and the much lower energy/redshifted light behind you cause a gravitational attraction in one direction - namely - the direction that has 'higher energy'?

Remember that relativity applies, so the universe doesn't care if you're moving or everything else is moving; yet there is a difference in energy received between one side of your spacecraft and the other in your frame of reference.

Related: When travelling at relativistic speeds, gravitational waves would also be "blue-shifted", given a higher frequency. This would obviously have an effect on the spacecraft. I'm curious as to what that might be.

However, when you are travelling at such speeds, the light from stars and the CMB in front of you is blue-shifted and the light behind you is red-shifted.

This is mis-stated in a small but important way. It is not the light that is in front of you which is blue-shifted, it is light going in the opposite direction as you that is blue shifted. If it is behind you but going in the opposite direction then it is still blue shifted.

This eventually creates a massive energy gradient.

There is no such gradient. In the frame of the ship the CMBR is anisotropic, but it is still homogenous. There is an increased energy flux in one direction, but not an increased energy density.

• So if you were being followed (but not caught!) by something with powerful headlights traveling at nearly c wrt you this might be an issue ;) That took some thinking about! Commented Mar 28, 2023 at 8:49
• If one-half of the photons you receive are X-Rays coming from one direction, and the other half are (less energetic than) radio waves, does that not imply that one half of your degrees of freedom contain more energy than the others, from your reference frame? And shouldn't fluxes cause force differentials anyways? Commented Apr 12, 2023 at 0:51
• @Severan indeed. If we do not “ignore photon pressure” then there will be a decelerating force.
– Dale
Commented Apr 12, 2023 at 1:49
• @Dale It should also be noted that due to relativistic doppler effect, the direction of travel would appear not only blue shifted but more concentrated due to spacetime distortions: en.wikipedia.org/wiki/Relativistic_Doppler_effect (fig. 8) So even with blueshifted photons 'behind' you (from passing you), the density of energy is more concentrated towards your "direction of travel" in your reference frame. I do agree though that if a light source emitted parallel light in your direction in classical physics, the densities would cancel. As always, relativity complicates things! lol Commented Nov 27, 2023 at 4:31
• @Severan indeed, this is all correct, but not relevant to this question. The question specified “Let's ignore photon pressure for this thought experiment”. The question is only asking about gravitational effects, not EM interactions. There is anisotropy in the EM energy flux, but the EM energy density remains homogenous. So there is an EM force but not an EM energy gradient producing a gravitational acceleration.
– Dale
Commented Nov 27, 2023 at 10:08