Light and Gravitational Fields

[SsDd]

Hello everyone,

A question on Light and gravitational fields,

I was engaging in friendly banter with an engineer friend of mine, and he proceeded to ask me, quite out of the blue, if light has its own gravitational field.

Initially, the question appeared to be rather strange, and I had not quite considered that question before (being an engineer myself). My initial reaction was, probably not, since photons are regarded as having no mass, hence they do not affect spacetime curvature the same way that mass does, but then again, mass is nothing by energy that occupies some space, and photos do have energy, so do they have their own gravitational field?

I dug in further, and came up with this link :- http://www.lightandmatter.com/html_book ... /ch08.html, Apparently, since photons contribute to the stress-energy tensor, they exert a gravitational attraction on other objects, according to the theory of general relativity.

Anyhooooooo, my question is now in the form of a thought experiment. if you were to shoot two theoretically perfect laser beams in vacuum, would they end up converging due to their own gravitational fields?

Thanks
Abhi

[Chris Peterson]

I was engaging in friendly banter with an engineer friend of mine, and he proceeded to ask me, quite out of the blue, if light has its own gravitational field.

Yes, it does. Spacetime is bent the same way by either mass or energy (the two are equivalent, of course).

Initially, the question appeared to be rather strange, and I had not quite considered that question before (being an engineer myself). My initial reaction was, probably not, since photons are regarded as having no mass, hence they do not affect spacetime curvature the same way that mass does, but then again, mass is nothing by energy that occupies some space, and photos do have energy, so do they have their own gravitational field?

Photons are not massless. They have a rest mass of zero, which is why they are always found traveling at c. But since they have an energy, they have a mass equivalence. E = mc^2 = hv. Whether you look at energy or mass, photons warp spacetime.

Anyhooooooo, my question is now in the form of a thought experiment. if you were to shoot two theoretically perfect laser beams in vacuum, would they end up converging due to their own gravitational fields?

If we consider a pair of photons racing together, then no, because the gravitational field of each photon itself only propagates at c, so the photons are causally disconnected from each other. It's kind of like a couple of speedboats racing along, leaving wakes. The wakes interact behind the boats, but neither boat affects the other. It's more interesting to consider a "beam", which means a continuous linear region of photons. In that case, you might have photons interacting. But I'm pretty sure that the gravitational field of a photon is a gravitational wave, so again we should see the gravitational distortion as a wake, not a continuous distortion about some region of space. I suspect this means that two beams won't converge due to mutual gravitational effects, but I'll have to think about it some more.

[Magnum LL]

Now that is a very good question. though i am 14, maybe i can help you. Now, to have gravity, you first need a mass. Now photons, light particles, have a still mass of 0, then that does mean it would have a gravitational pull. hope it helps

[neufer]

my question is now in the form of a thought experiment.
if you were to shoot two theoretically perfect laser beams in vacuum,
would they end up converging due to their own gravitational fields?

Classical (non-quantum) field theory would probably say that they do converge.

Click to play embedded YouTube video.

Click to play embedded YouTube video.

[Ann]

Neufer wrote:

Classical (non-quantum) field theory would probably say that they do converge.

Isn't that like noting that classical (Ptolemaic) cosmology would say that the Earth is at the center of the universe?

Click to view full size image

(Sorry about the large picture - I don't usually, but I couldn't resist...)

And, eh - don't cross the stream? Don't think about pink elephants, hmm?



Ann

[SsDd]

If we consider a pair of photons racing together, then no, because the gravitational field of each photon itself only propagates at c, so the photons are causally disconnected from each other. It's kind of like a couple of speedboats racing along, leaving wakes. The wakes interact behind the boats, but neither boat affects the other. It's more interesting to consider a "beam", which means a continuous linear region of photons. In that case, you might have photons interacting. But I'm pretty sure that the gravitational field of a photon is a gravitational wave, so again we should see the gravitational distortion as a wake, not a continuous distortion about some region of space. I suspect this means that two beams won't converge due to mutual gravitational effects, but I'll have to think about it some more.

Thank you, that explains everything a lot more clearly than any textbook I looked into.

[neufer]

If we consider a pair of photons racing together, then no, because the gravitational field of each photon itself only propagates at c, so the photons are causally disconnected from each other. It's kind of like a couple of speedboats racing along, leaving wakes. The wakes interact behind the boats, but neither boat affects the other.

Photons are not speedboats with well defined positions

There is a finite probability that even distinct photons (e.g., ones with different polarizations) will converge together after some distance (and the longer the distance the higher will be the probability). This converged position has a lower gravitational potential than that of the separated photons. The two photons still traverse the diagonal distance to their mutual merger point with the speed of light.

[Chris Peterson]

Photons are not speedboats with well defined positions :!:

Obviously not. It was an analogy to help visualize the physical reality. And for practical purposes, a photon actually does have what amounts to a well, if not perfectly, defined position.

There is a finite probability that even distinct photons (e.g., ones with different polarizations) will converge together after some distance (and the longer the distance the higher will be the probability). This converged position has a lower gravitational potential than that of the separated photons. The two photons still traverse the diagonal distance to their mutual merger point with the speed of light.

An interesting point, but not one that I am convinced is accurate. I still need to think about this some more. <g>

I think the complicating factor is that a photon produces a gravitational wave, and a gravitational wave actually expands and compresses space as it passes, which is quite different than what occurs with a sub-c mass.

[Beyond]

I think the complicating factor is that a photon produces a gravitational wave, and a gravitational wave actually expands and compresses space as it passes, which is quite different than what occurs with a sub-c mass.

Similar to a jet breaking the sound barrier??