# Gravitational Mass of Photons: Passive & Active

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• SteveDC
In summary, photons have zero rest mass but do have a passive gravitational mass, allowing them to respond to gravity. However, in order to properly understand the gravitational effects of light, one must apply the principles of general relativity rather than Newtonian gravity. This means that light, despite being massless, can still have its own gravitational field due to its energy and momentum. While parallel light beams do not interact gravitationally, antiparallel beams will attract each other due to the stress-energy tensor.

#### SteveDC

As I understand a photon has zero rest mass (as far as we can tell) but it does have a passive gravitational mass in order for it to be able to respond to gravity.

But I've been shown that passive gravitational mass should be equal to active gravitational mass, and if this is true and photons have active gravitational mass then is it the case that a beam of light will have its own gravitational field? So would two beams of parallel light in an empty Universe (i.e. no gravity from other objects) be drawn to each other?

You have a too classical view of how gravity works. It isunclear what you think gravitational mass means for objects traveling at or close to the speed of light. You cannot apply Newtonian gravity, you need to apply general relativity.

Yes. An EM wave has a non-zero stress-energy tensor, so it will distort spacetime and have its own gravitational field. Note that the effect would be extraordinarily weak.

Applying GR should give the same conclusion though shouldn't it? If photons have passive mass and therefore have active mass they are able to curve space.

To further what @Orodruin and @phyzguy said, in GR mass is not the source of the gravitational field, the stress energy tensor is. Light has energy and momentum so it gravitates, regardless of the fact that it is massless.

The gravitational field of light is called a pp wave spacetime.

I've heard that parallel light beams do not interact with one another gravitationally, but antiparallel beams would attract each other. I think it's possible to guess that anyway from the fact that the mutual acceleration between massive particles traveling at the same speed at very nearly the speed of light in the same direction is time dilated to near zero.

SteveDC said:
As I understand a photon has zero rest mass (as far as we can tell) but it does have a passive gravitational mass in order for it to be able to respond to gravity.

But I've been shown that passive gravitational mass should be equal to active gravitational mass, and if this is true and photons have active gravitational mass then is it the case that a beam of light will have its own gravitational field? So would two beams of parallel light in an empty Universe (i.e. no gravity from other objects) be drawn to each other?

I'd be curious to see where you were shown that passive gravitational mass was equal to active gravitational mass. Do you have a reference? Can it be tracked down to a peer-reviewed paper?

To answer your question, as others have pointed out, parallel beams of light won't attract each other, while anti-parallel beams will attract.

Jonathan Scott said:
I've heard that parallel light beams do not interact with one another gravitationally, but antiparallel beams would attract each other.

Yes, and this result can be derived from the stress-energy tensor of the light beams. MTW has a brief discussion of this, and (IIRC) refers to a paper by Tolman that was the first publication of the result.