The fabric of space-time

grav-universe

In GR, there is said to exist a fabric of space-time, and gravity is the warping of the fabric of space-time. Since GR is simply an extension of SR, the fabric of space-time should exist for both, then, both relating to the same universe and all, right? So could the fabric of space-time be considered the mechanism that physically produces length contraction and time dilation in SR? Why or why not?

If not, why do length contraction and time dilation occur, and why isn't the universe Galilean? Also, what is the fabric of space-time?

atyy

Yes, that is that "standard" view of SR which you don't prefer.

I will interpret "fabric of spacetime" = spacetime metric.

In GR, the spacetime metric is the gravitational field.

In standard SR, distance and time are defined by the Minkowski metric.

grav-universe

If the fabric of space-time is said to physically produce length contraction and time dilation, then I prefer it, as it makes conceptual sense to me by introducing a mechanism rather than just unexplained distortions of perceived reality according to each particular frame, but I was incorrectly referring to it by a different name in that case.

atyy

Oh you LET traitor!

Actually, in GR matter and spacetime codetermine each other - spacetime is a sort of matter since it is the gravitational field, which is just another field like the electromagnetic field or the electron field. The main difference between the gravitational field and all other fields is that the gravitational field does not have localized energy. A second important property of the gravitational field is that it interacts with all other forms of matter, and so all forms of matter interact with each other via the gravitational field.

grav-universe

Right, okay, that would be the mathematics involved which describes the observations involved, but is the fabric of space-time considered to be physically real which acts as the true mechanism of space-time or is it only conceptual?

atyy

Spacetime=gravitational field

The gravitational field is "real", if you consider the electromagnetic field "real".

The gravitational field and matter (including your measuring rod and clock) codetermine each other.

Most often, you will see approximations in which your measuring rod and clock don't contribute to the curvature of spacetime, since their mass is small compared to the stars and planets. But in principle, according to GR, they do.

grav-universe

So it appears that you are saying that the fabric of space-time is physically real and is the cause of the space-time metric, determining how mass moves and behaves, as well as how fields interact. Okay, very cool, thanks.

TheAlkemist

Why?
The EM field has localized energy because it's associated with an object, right? If an object = matter and matter = energy, then why isn't gravity localized? Or is this what the LIGO and VIRGO are looking for?

And what do you mean by "spacetime is a sort of matter"?

Please forgive my ignorance, i'm not a trained physicist. Thanks

TheAlkemist

I don't consider the EM field to be real. A field is a concept.

atyy

That's fine, but I actually think of it a bit differently - since matter determines the gravitational field, it can be said that matter determines metric relations via the gravitational field.

atyy

If you define matter as that which has localized energy, then the gravitational field is not matter.

On the other hand, the gravitational field obeys differential equations just like the electromagnetic field, so it is just a field and is matter in that sense.