Is Spacetime Curvature Real? - Take 2

[PeterDonis]

Asking if spacetime really curves, is asking the same thing as does spacetime really expand. It's just asking about the "dynamical" qualities of space - does it really have some? But, I guess I'm not supposed to ask how/why? Legs within LIGO's observatory will shorten and lengthen, and yet somehow, we're not supposed to ask how/why?

It's perfectly OK to ask how/why. But the answers you get may not fit with the intuitions you had before you asked the question. (I realize that that remark probably wasn't aimed at me, since you did say some people in this thread have been giving you useful information. But I wanted to make clear my position.)

In my previous post I gave a definition of what it means for spacetime to "physically curve". Here's a similar definition for what it means for spacetime to "physically expand". Take two observers, both freely falling, and who both see the entire universe as isotropic (i.e., it looks the same in all directions) at all times. If these observers see the proper distance between them (i.e. the distance they would actually measure by, for example, exchanging radar ranging signals) increasing with time, spacetime is expanding. If the distance is decreasing with time, spacetime is contracting. If the distance stays the same, spacetime is neither expanding nor contracting.

Note the similarity with the test for tidal gravity. In fact, the expansion of the universe can be thought of as "tidal gravity in the time dimension".

Note also that both of my definitions, for spacetime curvature and for spacetime expanding, involve purely "mundane" observations, so to speak. You don't have to wonder about whether spacetime has "dynamical qualities" and so forth; you just make the measurements I describe and see what they tell you, the same as with LIGO's legs. Whether or not you like using the term "curvature" or "expansion" or "gravitational wave" to describe the experimental results is, as I said before, a matter of words, not physics.

 

[PeterDonis]

It's good that you're not sure, because this line of thinking appears to be leading you astray.

I should add one clarification: I'm not saying that the difference you are talking about between gravity and the other forces is not there. It is: I would describe it as the fact that only gravity obeys the equivalence principle (all bodies "fall with the same acceleration" in a gravitational field--that's not necessarily the best way to describe it, but it will do for now as a hand-waving sort of definition). I was only commenting on how all this relates to whether spacetime "physically curves" or not.

 

[Mentz114]

You may object to the fact that we use the term "spacetime curvature" as equivalent to the term "tidal gravity", when they seem to be describing very different things. However, as DaleSpam hinted earlier, the test I just described for how to detect tidal gravity is the same kind of test we use for detecting a curved surface.

The presence of tidal gravity is not a test for relativistic effects because the same thing is predicted by Newtonian gravity.

The deflection of light by the sun is a much better test because Newtonian theory and GR make different predictions. The difference can be ascribed to spatial curvature.

 

[PeterDonis]

The presence of tidal gravity is not a test for relativistic effects because the same thing is predicted by Newtonian gravity.

The deflection of light by the sun is a much better test because Newtonian theory and GR make different predictions. The difference can be ascribed to spatial curvature.

I wasn't saying that tidal gravity is a good test for relativistic effects; I agree it isn't. I was saying that, as a matter of definition, GR defines "spacetime curvature" as equivalent to the presence of tidal gravity. The definition is justified by the correspondence I described between the test for the presence of tidal gravity and the test for curvature of a surface.

 

[A.T.]

Have fun weeping and gnashing your teeth as you nitpick apart my post.

Sorry, too long, didn't read.

 

[Dale]

But, I guess I'm not supposed to ask how/why? Legs within LIGO's observatory will shorten and lengthen, and yet somehow, we're not supposed to ask how/why? (Really the lack of curiosity along these lines is amazing)

So anyhow, it reminds me of the Christian fundamentalists who took my question as a big no, no.

This is a completely disingenuous assertion. Nobody has dissuaded you from asking your question, in fact, quite the opposite; we have universally and repeatedly encouraged you to clarify your question. It has nothing to do with a lack of curiosity on our part, but a lack of clarity on your part.

Until you can clarify your meaning you have not even asked a question, but simply strung together meaningless syllables. We encourage your question and have repeatedly invited you to ask it clearly.

 

[Dale]

The presence of tidal gravity is not a test for relativistic effects because the same thing is predicted by Newtonian gravity.

It is not a test for relativistic effects, but it is a test for curvature. Remember that Newtonian gravity can be geometrized and expressed in terms of curvature also.

 

[Mentz114]

It is not a test for relativistic effects, but it is a test for curvature. Remember that Newtonian gravity can be geometrized and expressed in terms of curvature also.

Well naturally, if you use any theory that geometrizes gravity then tidal effects are explained in terms of curvature. That is irrelevant. My point is that tidal effects are also predicted by plain-vanilla old fashioned Newtonian gravity in terms of second derivatives of the potential. No curvature required.

So the presence of tidal effects cannot be used to support your case.

 

[Dale]

My point is that tidal effects are also predicted by plain-vanilla old fashioned Newtonian gravity in terms of second derivatives of the potential. No curvature required.

Certainly curvature is not required to explain tidal gravity, I don't think I ever made that assertion.

Similarly forces are not required to explain classical mechanics; you can predict everything in classical mechanics in terms of Lagrangians instead. Any mathematical formula may be expressed in an infinite number of equivalent and equally valid forms. The mere fact of the existence of an alternative form does not in any way negate the existence of the first form, particularly since their mathematical equivalence implies that they are just different ways of saying the same thing.

Spacetime curvature is tidal gravity, regardless of the fact that there are ways to express tidal gravity that are not obviously equivalent to curvature at first glance.

 

[Mentz114]

Certainly curvature is not required to explain tidal gravity, I don't think I ever made that assertion.

Then you can't use the existence of tidal forces to argue for the existence of curvature. You can only do that if the existence of curvature is a necessary condition. If you're not doing that, 'nuff said.

Spacetime curvature is tidal gravity, regardless of the fact that there are ways to express tidal gravity that are not obviously equivalent to curvature at first glance.

Spacetime curvature is sufficient to explain tidal forces, but not necessary.

 

[Dale]

Spacetime curvature is sufficient to explain tidal forces, but not necessary.

OK, but don't forget that every other explanation of tidal forces is necessarily mathematically equivalent to curvature. If A=B then evidence for B is also evidence for A, so I don't really see the distinction you are trying to assert here.

 

[Mentz114]

... don't forget that every other explanation of tidal forces is necessarily mathematically equivalent to curvature.

No it is not. The Newtonian description of tides does not use relativity or spacetime and explains and predicts tidal forces in agreement with experiment. So does teleparallel gravity through the field tensor.

Tidal forces are the spatial derivatives of the field strength and do not require curvature - as you said.

 

[DaveC426913]

Not only is this reminding me of something religious, but even as religious fundamentalism.
...
Have fun weeping and gnashing your teeth as you nitpick apart my post. Laters ;-)

Ah there it is.

The old 'I asked a question and you asked me for clarity that I can't give so it must be your shortcoming and not mine and now I will insult you as much as possible before running away before I get banned' post.

Anyone else been waiting for that penny to drop for about 50 posts?

 

[A.T.]

Ah there it is.

The old 'I asked a question and you asked me for clarity that I can't give so it must be your shortcoming and not mine and now I will insult you as much as possible before running away before I get banned' post.

Anyone else been waiting for that penny to drop for about 50 posts?

I just needed two posts to make the troll loose temper and make the usual frustrated rant. Not like it wasn't obvious before that.

 

[PeterDonis]

Spacetime curvature is sufficient to explain tidal forces, but not necessary.

As I said a few posts ago in response to your original statement along these lines (which was in response to an earlier post of mine), GR does not say that tidal gravity is evidence for spacetime curvature, or that it "explains" spacetime curvature, or that spacetime curvature explains tidal gravity; it says that tidal gravity *is* spacetime curvature. It's more like a definition than a conclusion. As I said in my earlier post, the definition is justified by the fact that the test for tidal gravity works exactly the same as the test for curvature of a surface (initially parallel geodesics do not stay parallel).

 

[Dale]

Tidal forces are the spatial derivatives of the field strength

Yes, tidal force is the derivative of the field strength, and spacetime curvature is also the derivative of the field strength. They are equivalent, as I have said. You can call it a tidal force or you can call it curvature, they are mathematically and experimentally equivalent.

I don't understand the point you are trying to make. If I took a conservative system and wrote a Lagrangian I could determine the equations of motion without ever writing down the forces. Would you therefore say something like "then you can't use the equations of motion to argue for the existence of forces"? If you would say that then I think you are at least being consistent in your approach, but your approach neglects the equivalence of the two.