Is mass or the stress-energy tensor the source of gravity? If it’s the latter could someone explain what the difference between it and mass is?
One more time and then I’ll let it slip off into oblivion.
Mass is one thing that contributes to the curvature of spacetime, but it is not the only thing. The stress-energy tensor puts into a convenient mathematical package all of the things that matter: energy and momentum densities and flows.
Stress-energy tensors show up throughout physics since it is not uncommon to deal with energy and momentum and space and time all mixed together this way.
Depends upon what you mean by “source”. A tensor is a mathematical object, of course. It quantifies the effect of mass and energy, not just mass.
Thanks, my problem is that I can’t think of any energy or momentum that isn’t included in mass, and internal pressure is the result of gravitation, isn’t it? Is it the flows of these quantities that render mass not up to the task? Aren’t stress and strain also reflected in the mass of an object? Did Einstein invent the SET or did it already exist and he just made use of it?
What would be missed if you just used mass? The gravitomagnetic effect?
But mass includes the internal energy doesn’t it?
How are you using the term “mass”? A photon has no mass, but does have energy.
Yeah, I forgot about that. But that can’t be whole reason to use something as incomprehensible as the stress energy tensor, can it? Prior to general relativity was Newton’s theory happy with just using mass?
Easy to forget, I suppose. Einstein also liked that the stress energy tensor was generally covariant–hence the name general relativity. So, it works, Newton’s don’t. It’s not as incomprehensible as all that, either.
Doesn’t that just mean that it transforms as a tensor should transform? You could also say that it’s generally contravariant I believe.
Easy for you to say. Having a masters in math probably helps a little, huh? On second thought I thought you didn’t have any background in tensors? Have you picked this stuff up? How about explaining it…you know just a few general comments.
So? The point is, that Newton’s laws don’t.
As to the other thing, I would accept “incomprehensible to me,” as that would be a relative thing, not an absolute.
You are exactly right: if you only used mass, you would miss the energy and momentum flows.
For instance, a rotating sphere produces a different gravitational field than a stationary sphere.
A good intro text is the one by Hans Ohanian.
It’s not just the pressure due to gravitation which is significant. All stresses, from any source, have a contribution. So, for instance, if you have two like charges connected by a rubber band, and the repulsion of the charges is stretching the band, the rubber band’s gravitational field will be different due to being stretched.
Mmmm… sort of. You’ve stumbled onto one of the many unfortunate uses of terminology in physics. It could have been called contravariant, but it’s not. The best thing to do is understand it’s silly and get used to it anyway.
Photons do have mass, they have relativistic mass, but zero rest mass.
Thanks FriendRob, I have Schutz but I’m trying to learn a little tensor stuff first. Would you have any idea what it was that made Einstein realize that mass by itself wasn’t up to the task?
I didn’t know that "a rotating sphere produces a different gravitational field than a stationary sphere," would that be due to frame dragging? Where does pressure fit into this thing? Is the pressure due to gravity?
Jeez Chronos when I made my last post yours wasn’t there. That little example really helped me out. Usually if I can get one simple visualization of a concept I can handle the more abstract stuff, so again, thanks. Now I kind of get it.
Was it Feynman that said if you really understand something you should be able to explain it to a waitress?
The Stress-Energy Tensor that Einstein used was developed for use in electromagnetism, curiously enough. That’s one of the reasons it’s called relativity since the “relativistic” nature of electromagnetism is incorporated into the SET.