Accelerated Frame of Reference, Gravity as Geometry Question

[DyerWolf]

Something I’ve never fully understood is whether these theories are actually just analogies to help describe the effects of gravity, or actual descriptions of what happens in our universe.

I can see the gravity “well” or bowl shape being a good analogy to explain what is happening – but I have a harder time believing that gravity curves space.

I know that some people point to gravitational lensing as an example of curved space – but it could just as easily be an example of the gravitational source attracting the particles of light as they pass.

I get the idea that a man in a closed room would not be able to distinguish whether his room was on planet earth or in a spaceship experiencing a constant 1g acceleration – this is an apt analogy – but does it mean, necessarily that the person on the planet is actually in an accelerated frame?

I’m not asking for a full explanation of relativity (there’s books for this) but rather, I am asking if someone can distinguish for me the analogy (story used to describe or explain what is happening) from the actual effect sought to be described.

*It’s always seemed to me that all the talk of trains and elevators and rockets was merely a tool to describe something to laypeople, and my concern is whether the 'curved space' analogy has supplanted the reality.

TIA.

[AndreasJ]

Curved space is the reality, according to general relativity. There's no analogy involved, no more than when chemist speak of oxygen.

[steve000]

but I have a harder time believing that gravity curves space.

I thought matter curved space not gravity

[Jeff Root]

Assume that general relativity is an entirely correct theory. That's
a very reasonable assumption since all observations so far tend to
confirm it. We can understand "entirely correct" to mean that when
we have learned everything that it is possible to learn about how
the Universe works, general relativity will still not be contradicted
by observations.

Given that assumption, my guess is that there is no discernable
difference between saying that space is actually curved, and saying
that curved space is analogous to the reality. Things move exactly
as if space were curved by the presence of matter/energy.

I think that is probably the bottom line.

-- Jeff, in Minneapolis

[publius]

It is space-time that is curved not space alone, space-time, space-time, space-time, space-time. Write that a thousand times on the blackboard. Space-time, space-time, space-time, space-time. How you split space-time into space and time is arbitrary, it depends on what the oberserver is doing within that space-time. Whether what a given observer calls "space" is curved or not is somewhat arbitrary. It is the curvature of space-time, the two together that is the invariant.

For example, many of the typical "bowl" pictures are based only on the spatial part of Schwarschild, ignoring the time part entirely. In the weak field, that spatial part is so small it doesn't matter, and the time part is what dominates. There a Newtonian potential well picture is as good as anything. But none of those are capturing the whole picture of space-time as a whole.

General Relativity *models* what we call gravity as mass-energy causing curvature of space-time, which in turn affects how mass-energy itself moves within space-time.

And that is indeed just a model, something that explains what is observed and predicts what will be observed. It's a very beautiful and elegant model, but it is just a mathematical model.

And while it gets pretty deep, something I've come to appreciate is that "curvature" itself is not really the fundamental thing -- the model just makes you think it is. What is fundamental is the "connection", which you can think of as the rules for transforming from one local observer "sees" to what another distant observer sees.

In General Relativity, or better the math that is built on, curvature of the space-time manifold is what "makes the connection". You see the connection as being a consequence of curvature (or lack of it).

But it turns out that doesn't have to be the case. You can adopt some very different, very strange geometric notions where the connection comes about from something else, make it agree with GR's connection, and have a complete equivalent of GR, just using language different from "curvature".

It turns out that GR's Riemannian picture is the simplest compared to some other crazy messes you can come up with, of course, so why worry with it. However, the mathematical experience gained by considering other "crazy messes" may turn out to be useful. "Torsion" and the gravitational spin-spin interaction (something that "should" be there in theory, but it is far too weak to observe yet) is something that invokes some of that.

-RIchard