Light & Gravity: Impact on Spacetime?

[mgkii]

TL;DR Summary

Does light have any influence on gravity?

This is probably going to sound like a ridiculous question... but here goes.

I (think) I understand that matter tells spacetime how to curve and spacetime tells matter how to move. I also know that light obeys the same laws of general relatively as matter. What I can't get my head around is whether light has any impact on spacetime? Is spacetime curved more by the presence of more energetic/intensive light?

Sorry if this is a daft question!

 

[Ibix]

It does in principle, but the effect is incredibly small. It also has some odd effects - parallel light beams do not attract each other but anti-parallel ones do, as I recall.

Note that $E=mc^2$. To have a gravitational effect comparable to a 1kg mass you'd need around 10¹⁷J worth of light energy. As far as I'm aware, then, all our knowledge on the topic is theoretical.

 

[mgkii]

Thanks! That's really reassuring

 

[pervect]

Summary: Does light have any influence on gravity?

This is probably going to sound like a ridiculous question... but here goes.

I (think) I understand that matter tells spacetime how to curve and spacetime tells matter how to move. I also know that light obeys the same laws of general relatively as matter. What I can't get my head around is whether light has any impact on spacetime? Is spacetime curved more by the presence of more energetic/intensive light?

Sorry if this is a daft question!

To get a mathematically accurate description of how light curves space-time, you need the stress-energy tensor.

The mathematically accurate approach comes straight from Einstein's field equations

$$G_{\mu\nu} \propto T_{\mu \nu}$$

i.e. the Einstein tensor, $G_{\mu\nu}$ is some constant multipled by the Stress-energy tensor $T_{\mu\nu}$. Equivalently, we can say that the Einstein tensor is proportional to (the symbol for this is $\propto$) the stress energy tensor.

Unfortunately, the concept of tensors in general is a graduate level topic, so it's likely that neither the Einstein tensor, nor the stress-energy tensor, is a familiar topic.

I should qualify when I say you "need" the stress-energy tensor. It's always risky to say you "need" something, as there are often multiple approaches, and sometimes one of them avoids the "need". However, I'm not aware of any treatment of the topic that doesn't use the concept of the stress-energy tensor.

A casual treatment that usually gets you within a factor of 2 is to say that it's that it's the energy in light that curves the space-time.

The casual treatment ignores the other components of the stress-energy tensor other than energy. These other components are given the names momentum, and pressure. They're both probably somewhat familiar, though it may well seem puzzling as to why we need them at all.

So, the inaccurate treatment glosses over the difficult point of what momentum and pressure are, and why they are relevant.

Unfortunately, as a consequence of ignoring these extra terms, one gets only half of the correct answer.

While being off by a factor of 2:1 is rather annoying, it avoids having to learn about a number of graduate level topics such as tensors in general, and the stress-energy tensor in particular. All things considered, unless one is going to do a serious mathematical study of the topic, taking the simple view and knowing that it's typically off by a factor of two or so isn't a bad approach.

Alas, in some common situations, one may be off by a factor of more than two. For instance, parallel light beams don't attract each other at all, and anti-parallel light beams attract each other four times as much. The full treatment explains this nicely, though it may seem mysterious.