Questions about Spacetime

[EnolaStraight]

Our reality is essentially four dimensional:
left-right
by
back-front
by
up-down
by
before-after.

Gravity is described by General Relativity as mass distorting a four dimensional field “called” spacetime.

Are the four dimensions of GR in fact identical to our own four dimensional reality?
Or, just degrees of freedom which take place within reality…like paint on a canvas?

As I understand it, various fields like electric, magnetic, Higgs, etc. are said to be superimposed upon spacetime.

Furthermore, various branches of physics describe systems with 10, 11, 26, or as many as 248 dimensions (with tiny, curled-up geometries) doing their thing within what appears to us a four dimensional reality.

What if Gravity’s four dimensions are distinct from our reality…one just sitting atop the other, like the higher dimensional forces seem to be?

[Andy_L]

@tilteddriveway

Yes, general relativity (GR) operates in four spatial dimensions and one time dimension

You mean three spatial dimensions and one time dimension, right?

[FlikTheBlue]

@tilteddriveway

In order to do calculations and stuff in GR you basically have to have a working understanding of tensor calculus as well as differential geometry (this is harder than it sounds).

I recall hearing at some point that the actual math for doing relativity is harder than understanding the theoretical concepts, and that for quantum mechanics the math is (relatively ) easier but that the theoretical underpinnings are a lot harder (or impossible) to understand.

[DPRK]

“Why 4 dimensions” is not something that is explained by classical General Relativity; it is assumed.

Note that GR is not a quantum theory of gravity at all, and does not purport to describe what is “really” there when you zoom in.

[Pasta]

@DPRK

Note that GR is not a quantum theory of gravity at all, and does not purport to describe what is “really” there when you zoom in.

Of course, neither does a quantum theory. Debate rages about what “really” is in QM.

@FlikTheBlue

I recall hearing at some point that the actual math for doing relativity is harder than understanding the theoretical concepts, and that for quantum mechanics the math is (relatively ) easier but that the theoretical underpinnings are a lot harder (or impossible) to understand.

Personally I wouldn’t find such a distinction meaningful. Both have rather accessible concepts and accessible math for some parts, and both also have mind-bending concepts and quite niche math for other parts. At the introductory level, GR could be taught with the same background in hand as for QM, and both require picking up new on-the-job mathematical and intuitional concepts. QM is taught earlier and more commonly since it underlies a lot of other “basic” material (e.g., statistical mechanics, chemistry). GR is often saved as a more advanced elective. But it doesn’t have to be.

[Chronos]

If there’s a difficulty in the math for GR, it’s mostly that relativists are, by and large, the only people who do tensor math the easy way. When tensors come up in materials science or structural engineering, they always do them using this huge messy salad of basis tensors, instead of the much more concise Einstein notation. Once you learn Einstein notation, it’s pretty easy; it’s just that, since it’s not taught outside of relativity classes, you’re starting off behind.

[abcdefghij]

@Chronos

When tensors come up in materials science or structural engineering, they always do them using this huge messy salad of basis tensors, instead of the much more concise Einstein notation.

Some materials scientists use Einstein notation, but that’s probably because we spend too much time around physicists