General Relativity General: Space-time "Curvature"

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Heard this long time ago, but really how? We already have deformation of space-time in special relativity and there's no way around that.

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>>9107242

So far as I can tell, it was Weyl and not Einstein who pushed this interpretation.

"But one must not legalize the mentioned sin so far as to imagine that intervals are physical entities of a special type, essentially different from other physical variables (“reducing physics to geometry”, etc.)."

It just looks like a crutch that intuitively separates the form of gravitation from any other field theory.

>>9107248

Relativity is based on measurements of time and distance. Local measurements are affected by the finite and (locally) constant speed of light. This is mathematically modeled on a psuedoreimannian manifold, but it's lazy to interpret that as space itself being a psuedoreimannian manifold. Physical momentum is not literally a differential operator.

There is no reason to say space is anything more than the aggregate of our possible measurements/coordinate systems, because there is no other physical measurement that can define space. At least that's how my book puts it

>>9107242
curved from an outside perspective. to the object passing through any region of of space, it's a straight path.

>>9107242
Why would the interpretation of spacetime as a geometric manifold be unintuitive? The metric and the other tensors derived from it are mathematical objects that perfectly correspond to intuitive notions of curvature (at least in lower dimensions).

spacetime is a shitty math construct that doesn't actually exist like virtual particles but confuses and tricks people all the same.

>>9107294

It's intuitive, I just think it's an excessive logical jump to say gravitation is purely geometric just because we have a useful geometric model for it. You could make similar arguments for any field theory but nobody hypes those up in documentaries

>>9107262
If there's no other way to define space, then you can't define it any way other than through measurement or you would need to introduce unobservable space.

>>9107320
>I just think it's an excessive logical jump to say gravitation is purely geometric just because we have a useful geometric model for it
Well models are rarely unique, and indeed for gravity there are a few different models for it. But for the commonly accepted one (General Relativity) that's the physical interpretation of the mathematics.

>You could make similar arguments for any field theory but nobody hypes those up in documentaries
The geometry of field theories is much hard to understand than a bowling ball on an elastic sheet. The idea of pop-sci documentaries is to make an incomprehensible subject accessible to the layman, introducing GR as "like an elastic sheet" is a lot better than an equivalent geometric description of some gauge theory, especially considering that for a gauge theory you could just draw a hand full of Feynman diagrams and then say "the electron and positron exchange a photon" or whatever.

>>9107320
I don't know the details but in my recollection the connection between differential geometry and, for example, classical electrodynamics (expressing Maxwell's equations through differential forms) didn't really lend itself to a nice physical picture. Gravity on the other hand is perfectly suited for a geometric interpretation because of the equivalence principle.
My personal problem with the rubber sheet is that it seems to miss pretty much the whole point of the pseudo-Riemannian manifold by giving a picture of just the curved space - whereas all the actual dynamics of the theory necessarily only make sense when including the time dimension.

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>>9107262
And how to interpret Friedman's solution with positive curvature if it's not space?

>>9107242
>Any thoughts?
agreed

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>>9107354

How do we respond to the assertion that "gravity isn't really a force, just intrinsic curvature in space-time that appears to be a force"? It just feels fundamentally wrong, but maybe that's my autistic reductionism talking.

>>9107367
Not OP but in the classical theory there is no problem in considering gravity as a gauge theory in Minkowski spacetime. The closed orbits in the FRW metric turn into sorts of great circles by appropriate gauge transformation of the metric (normally called a coordinate transform).
Whether the approaches are equivalent in a quantum theory is unknown as far as I know.

>>9107411
You mean the space-time metric? What gravity has to do with it?

>>9107242
>The notion that the gravitational field can be reduced to curvature just doesn't seem any more valid than attributing electromagnetic or fluid flow fields to curvature.

What's funny is people think they are different things, gravity and electromagnetism. They are in fact one in the same thing, people just assume that since a magnet mainly attracts mainly ferrous metals that that it is a separate force. The only difference is how "cohesive" the force is, What makes earth a cohesive force is the fact that its mass is spinning on an axis.

But what is "mass". From a scientific standpoint if it's mostly empty space then where does the gravity come from? Perhaps that special force that surrounds an atom? Maybe?

>The field has an effect on the results of local measurements, and the equations describe that.

Descriptions do not describe things especially when your descriptors are mere expressions. There is unfortunately no equation that tells you what a magnet or gravity "particle" does when it isn't moving, because they are ALWAYS moving.

All 4 forces are some form of curvature in their classical descriptions.

A gauge field (electromagnetic, gluon, etc.) corresponds to a connection on some principal bundle over spacetime. The strength of this field is the curvature of this connection. However these bundles are not actual physical spaces.


The gravitational field is the actual spacetime metric. So the gravitational field strength is the curvature of the natural metric connection, this is equivalent to actual physical spacetime being curved.

>it's lazy to interpret that as space itself being a psuedoreimannian manifold.
>“reducing physics to geometry”
these things

>gravitational field strength is the curvature of the natural metric connection, this is equivalent to actual physical spacetime being curved.
not these things

>>9107959
>it's lazy to interpret that as space itself being a psuedoreimannian manifold

Its a mathematical model that makes predictions aligning with experiment. Thats what all of physics is.

And like all models in physics, it is only used within its appropriate limits.