Stress-energy Tensors for Dummies

[immijimmi]

I'd like to learn about this, but the wiki page is incomprehensible to me. From my understanding, this explains how energy can exert a gravitational pull (along with a lot of other factors). Can someone explain how that works to me? I'm currently learning AS physics so I don't have much of an understanding of any complex ideas... keeping that in mind please don't overcomplicate it, or introduce any theories I won't understand without explanation.

Thanks in advance!

[Schrödinger's hat]

Can someone explain how that works to me? I'm currently learning AS physics so I don't have much of an understanding of any complex ideas... keeping that in mind please don't overcomplicate it, or introduce any theories I won't understand without explanation.

 

I'm not sure there is a simple version. Also AS physics doesn't tell me much, not everyone has the same education system. Mentioning how many years of education or the average age of people learning something is more informative.

 

Here goes an attempt at explanation.

Relativity treats energy, momentum, and mass in much the same way. As well as treating time and space the same way. Call it energy-momentum and treat it as a vector. It has a magnitude -- how much stuff -- and a direction -- although this direction also includes information about its motion.

Energy (which includes mass) is energy-momentum that is pointed in the time direction. Momentum is energy-momentum that is pointed in one of the other three.

 

So four elements is enough to describe the...stuff-ness of a particle, but this is not enough if you have a big bunch of particles that you want to treat together, or a continuous field.

 

Coming back to classical physics for a moment.

If you consider a solid block of something stretchy and compressable, like foam rubber. There are different ways you can store energy in it.

If you compress some section of it, it'll want to spring back. This stores energy.

So would twisting a section.

Energy can also be stored in the motion. A ripple will move through it if you hit it hard enough.

 

The stress energy (or stress-energy-momentum) tensor is a bit like that.

You count the energy-momentum in a region of space, the amount of energy-momentum moving through it, and the interactions between adjacent regions of your field.

 

 

I'm afraid that's about the best I can do in terms of simplifying the concept. Someone better versed in GR may be able to help further.

[ajb]

In essence you are asking about the basic idea of general relativity. The Einstein field equations are

 

"Local Geometry = Matter Content"

 

The left hand side describes the shape of space-time. It is the curvature of space-time that is responsible for gravity. Basically test particles will always follow the "straightest possible path" in space-time under the assumption of no forces other than gravity are acting on the particle. Look up great circles on the sphere, it will help you here.

 

The right hand side is matter content, which is described by the Energy-Momentum tensor. This contains all the information about the "non-gravitational stuff" in the Universe.