Is Spacetime Curvature Real? - Take 2

[Mentz114]

Physics is about modelling reality. It is conceivable, as mentioned many posts earlier, that a phenomenon could have many interpretations. For example, there is a teleparallel equivalent of general relativity in which spacetime is *flat* [Riemannian curvature vanishes] but torsion is non-vanishing. They have very different mathematical formulation/description, but the *phenomena* they seek to describe are the same - apples still fall the same away, though I am not sure how TEGR would model gravitational wave [See however, last paragraph of "http://arxiv.org/PS_cache/gr-qc/pdf/0612/0612062v1.pdf"]. The latter is what we may call physical reality, but curvature of spacetime is "reality as far as if we agree on the mathematical model".

There's little doubt that TEGR makes the same predictions as GR. Gravity can be modeled as a spacetime defect - in GR curvature causes a rotation of a transported vector, in TEGR there is an added translation due to non-zero torsion. Both these theories are special cases of Cartan's theory.

Curvature, torsion, vectors, numbers are mathematical abstractions. Gravity is real.

 

[bcrowell]

At this point, I would suggest we maybe just leave math out of it for now.

No math and no definitions of terms? Not a very promising way to have a discussion.

 

[PeterDonis]

Does one leg of LIGO really shorten compared to the other? If not, what really does happen.

Are you asking if there is any other possible cause for the interference patterns that are seen, besides one leg actually shortening compared with the other? What else could possibly cause those patterns?

 

[bcrowell]

Interesting post, Lut! I'm going to follow up in a separate thread about an aspect of this that I don't understand.

 

[bcrowell]

Are you asking if there is any other possible cause for the interference patterns that are seen, besides one leg actually shortening compared with the other? What else could possibly cause those patterns?

See Lut's #31. The teleparallel formulation of GR wouldn't describe the effect in geometrical terms like that, but it's equivalent to GR, so it would predict the same experimental results.

 

[dm4b]

I agree. I supposed what I meant was that *if* there is an alternate theory of gravity that reproduces all physics as GR does despite using different mathematical structures, and *when* there is no experiments that can distinguish between the two so that the two are completely equivalent [TEGR might or might not do this, I am not an expert, but hypothetically speaking we can suppose such thing to be possible], then we will quite lost to distinguish whether spacetime curvature is real or not. We can only distinguish something based on reality if we have observation or experiments to do so. In the absence of that, I don't know how.

Hi yenchin,

That is my pretty much my line of thinking on this too. We'd end up in the same boat that QM is in, which has an almost ridiculous amount of interpretations.

I guess I have the Casimir Force in mind too. Lots of folks used to like to think it showed the vacuum energy was real, that is, until it was explained also in terms of the Van Der Walls forces.

The question is would LIGO results have another interpretation, as well. In addition, if LIGO is only able to produce results based on one leg physically contracting/stretching and GWs aren't truly "ripples" in spacetime, will LIGO even succeed in detecting GWs. I'm sure all of this has already been thought of. It would just be interesting to hear more, because I think it could be enlightening on whether or not spacetime curvature has any reality to it.

 

[dm4b]

Are you asking if there is any other possible cause for the interference patterns that are seen, besides one leg actually shortening compared with the other? What else could possibly cause those patterns?

I've got no clue. That's why it seems to me LIGO might indicate that spacetime curvature would have to physically happen for LIGO to operate. However, that's a completely uninformed opinion on my part.

 

[dm4b]

See Lut's #31. The teleparallel formulation of GR wouldn't describe the effect in geometrical terms like that, but it's equivalent to GR, so it would predict the same experimental results.

Check that out browell. No math or definition of terms and I think you guys may have clinched it anyhow ;-)

I'll have to look into the teleparallel formulation a bit more, but it sounds like it may offer a reason to suspect that spacetime curvature may not be physically real.

 

[PeterDonis]

See Lut's #31. The teleparallel formulation of GR wouldn't describe the effect in geometrical terms like that, but it's equivalent to GR, so it would predict the same experimental results.

In other words, the teleparallel formulation agrees that one leg of LIGO actually shortens.

I've got no clue. That's why it seems to me LIGO might indicate that spacetime curvature would have to physically happen for LIGO to operate. However, that's a completely uninformed opinion on my part.

If everybody agrees that one leg of LIGO actually shortens, thus causing interference patterns to appear, then it seems to me that whether we label that as "spacetime curvature" or "teleparallel gravity" or something else is a matter of how we define words, not physics. The only "real, physical" question, it seems to me, is whether one leg of LIGO actually shortens, thus causing the interference patterns, or whether there is no actual shortening, the patterns are caused by something else--maybe the detectors are miscalibrated or something. As far as I know, nobody disputes that the patterns are caused by actual shortening of one leg, and both theories (standard GR with spacetime curvature, vs. teleparallel gravity) predict the same thing.

I'll have to look into the teleparallel formulation a bit more, but it sounds like it may offer a reason to suspect that spacetime curvature may not be physically real.

But it wouldn't change the experimental facts, just the label you choose to put on them. Of course, if using a different label leads you to make different predictions about other experimental results, then you have a way of determining which label is more "real"--look at the actual experiments to see which way they vote. But as far as I can tell, teleparallel gravity makes exactly the same predictions for all experiments as standard GR does. So there's no way of resolving the question of which theory is "real". Either neither one is, or they both are, to the same extent, because they both make all the same predictions.

 

[dm4b]

See Lut's #31. The teleparallel formulation of GR wouldn't describe the effect in geometrical terms like that, but it's equivalent to GR, so it would predict the same experimental results.

In other words, the teleparallel formulation agrees that one leg of LIGO actually shortens.

Well, maybe I read too much into this. I was assuming since it was describing it in non-geometrical terms, it would offer an interpretation that did not involve one leg of LIGO shortening, etc, (i.e. did not involve any change in the geometry of spacetime)

Would this not necessarily be true?

 

[yenchin]

Well, maybe I read too much into this. I was assuming since it was describing it in non-geometrical terms, it would offer an interpretation that did not involve one leg of LIGO shortening, etc, (i.e. did not involve any change in the geometry of spacetime)

Would this not necessarily be true?

Teleparallel is certainly geometric, just that the metric does not have curvature.

 

[PeterDonis]

Well, maybe I read too much into this. I was assuming since it was describing it in non-geometrical terms, it would offer an interpretation that did not involve one leg of LIGO shortening, etc, (i.e. did not involve any change in the geometry of spacetime)

You're confusing two different things. Whether or not one leg of LIGO actually shortens is an experimental question. Unless someone proposes another way for interference patterns to appear in LIGO's detector (which AFAIK no one has), I view the interference patterns as sufficient experimental evidence for one leg actually shortening.

Whether you call the cause of one leg shortening a change in "spacetime geometry" or the effect of a "force" is, in my view, a matter of words, as I said before, as long as both models make exactly the same predictions for the experimental results.

 

[dm4b]

You're confusing two different things. Whether or not one leg of LIGO actually shortens is an experimental question. Unless someone proposes another way for interference patterns to appear in LIGO's detector (which AFAIK no one has), I view the interference patterns as sufficient experimental evidence for one leg actually shortening.

Whether you call the cause of one leg shortening a change in "spacetime geometry" or the effect of a "force" is, in my view, a matter of words, as I said before, as long as both models make exactly the same predictions for the experimental results.

Actually, I'm pretty much in agreement with you Peter. You just stated it much more clearly than I did above.

What it still unclear to me is how TEGR mentioned above would actually cause the leg shortening?

I plan to read that arxiv paper later today, so hopefully that will clear things up

 

[pervect]

I think a lot of this goes back to Einstein's "heated disk" thought experiment. One might be able to come up with a theory where there is some underlying space-time-equivalent that's not curved, and our rulers are distorted, as is the case in the "heated disk".

And such theories might be useful for a number of reasons. (Rather than teleparallel gravity,which I'm not familiar with, I'd suggest something along the lines of http://arxiv.org/abs/astro-ph/0006423 non-geometrical approach.)

However, I think an important point is that if we use SI rulers and SI clocks, GR predicts that space-time is curved, and that there is nothing "philosophical" about this prediction, i.e given a way of measuring distances (or more generally, intervals), there is a standard definition of what it means to be curved, and GR unequivocally predicts that space-time is curved.

 

[pervect]

Let me add a bit on experimental testing of curvature. *IF* one assumes that gravity can be modeled by the PPN (Parameterized Post-Newtonian formalism, see http://en.wikipedia.org/w/index.php?title=Parameterized_post-Newtonian_formalism&oldid=418477605), the deflection of light is a direct measurement of one component of space-time curvature (a purely spatial component in the usual frame of reference).

This is because non-Newtonian deflection of light is only sensitive to the PPN parameter gamma, and gamma measures a component of curvature. So, in some sense, we've already measured curvature.

I'm not sure if there is any more direct measurement of curvature, one that does not require the seemingly rather modest assumption that gravity can be modeled by the PPN formalism.

 

[PAllen]

Let me add a bit on experimental testing of curvature. *IF* one assumes that gravity can be modeled by the PPN (Parameterized Post-Newtonian formalism, see http://en.wikipedia.org/w/index.php?title=Parameterized_post-Newtonian_formalism&oldid=418477605), the deflection of light is a direct measurement of one component of space-time curvature (a purely spatial component in the usual frame of reference).

This is because non-Newtonian deflection of light is only sensitive to the PPN parameter gamma, and gamma measures a component of curvature. So, in some sense, we've already measured curvature.

I'm not sure if there is any more direct measurement of curvature, one that does not require the seemingly rather modest assumption that gravity can be modeled by the PPN formalism.

J. L. Synge, in his 1960 book, derives a 5 point curvature detector wherein 10 opticial distances are measured between different pairs 5 world lines. His derivation is coordinate free and and exact. The assumption here is that the mis-match in the result versus what could be possible in flat spacetime is evidence of curvature. Five is the minimum number of world lines for which this can be done in such a general way.

He also shows that the device is not practical for the foreseeable future as a way to measure curvature of spacetime near the Earth - the effects are way too small.

 

[dm4b]

Whether you call the cause of one leg shortening a change in "spacetime geometry" or the effect of a "force" is, in my view, a matter of words, as I said before, as long as both models make exactly the same predictions for the experimental results.

However, I think an important point is that if we use SI rulers and SI clocks, GR predicts that space-time is curved, and that there is nothing "philosophical" about this prediction, i.e given a way of measuring distances (or more generally, intervals), there is a standard definition of what it means to be curved, and GR unequivocally predicts that space-time is curved.

Above we were talking about the leg shortening within LIGO to be equivalent under a shortening due to a "force" or a shortening due to "spacetime curvature"

I'm wondering if we were thinking about that correctly now. I can see a shortening of the leg from a "force" being equivalent to a curvature of "space", but maybe not in "spacetime"

In addition, spacetime curvature can be said to effect not just the objects in spacetime (LIGO's legs), but spacetime itself, as the name implies. The same cannot be said of a force, as we typically think about it under the other three forces. Gravity is distinct in that regard. Perhaps, part of the reason GR purists don't like to call gravity a "force"?

 

[PeterDonis]

Above we were talking about the leg shortening within LIGO to be equivalent under a shortening due to a "force" or a shortening due to "spacetime curvature"

I'm wondering if we were thinking about that correctly now. I can see a shortening of the leg from a "force" being equivalent to a curvature of "space", but maybe not in "spacetime"

No, it has to be spacetime, because the shortening is not static; it varies with time. The exact variation depends on the orientation of LIGO's arms relative to the incoming wave; in the simplest case, where the arms are perpendicular to the wave's direction of travel, the arms alternately shorten and lengthen (one arm is shorter when the other is longer, and then vice versa) at a frequency which is twice the frequency of the wave (because the wave is quadrupole--spin 2). So the force has to be periodically varying in time; it's not just a static force in space.

In addition, spacetime curvature can be said to effect not just the objects in spacetime (LIGO's legs), but spacetime itself, as the name implies. The same cannot be said of a force, as we typically think about it under the other three forces. Gravity is distinct in that regard. Perhaps, part of the reason GR purists don't like to call gravity a "force"?

Yes, gravity is distinct, because an object moving solely under the influence of the "force" of gravity is weightless--it feels no force at all. For all the other forces, objects moving under the influence of them feel a force.

I'm not sure I agree with the distinction you draw between curvature affecting "spacetime itself" vs. it affecting "objects in spacetime". The model we use to treat gravitational waves does draw a distinction between the curvature of the "background" spacetime through which the wave travels, and the fluctuations in curvature caused by the wave itself. We then separate, in our minds, the underlying motion of objects due to the "background" spacetime (for example, the Earth orbiting the Sun and carrying LIGO along with it) from the motion of particular objects in response to a wave (such as LIGO's arms). This distinction is not "really" there, it's just a convenience to help us construct a model we can actually use; in "reality" (I'm using the scare quotes because I'm still talking about a model of reality, not reality itself, but it's the underlying GR model rather than the approximation we use to treat gravitational waves), there is just spacetime curvature, and it affects the observed motion of objects. Even in the approximate model we use for the waves, though, both types of curvature affect the motion of objects; we just separate out different types of motions for ease of calculation.

 

[dm4b]

No, it has to be spacetime, because the shortening is not static; it varies with time. The exact variation depends on the orientation of LIGO's arms relative to the incoming wave; in the simplest case, where the arms are perpendicular to the wave's direction of travel, the arms alternately shorten and lengthen (one arm is shorter when the other is longer, and then vice versa) at a frequency which is twice the frequency of the wave (because the wave is quadrupole--spin 2). So the force has to be periodically varying in time; it's not just a static force in space.

Yes, all that, I am familar with. But, you mention force in the above ... hold that thought ...

I'm not sure I agree with the distinction you draw between curvature affecting "spacetime itself" vs. it affecting "objects in spacetime".

That's not the distinction I was trying to draw. I don't think gravity really cares about that.

I was trying point the distinction between how gravity works and how we normally think of the other three forces working, which do not effect spacetime itself, but rather just the objects within spacetime.

From that perspective, perhaps one could say the LIGO results produced by spacetime curvature would NOT be equivalent to the results being produced by a "force".

So, you can still call gravity a "force" and say a "force" caused the differences in the LIGO leg lenghts. As you said above, it is a matter of a choice of words. BUT, the fact that this "force" acts distinctly different than the other three forces, maybe indicates it is NOT equivalent, in that sense. Does the fact that it is different than the other three forces indicate something else is going on? Is that something else a physical curvature of spacetime? Or, something else, all together?

I'm not sure I agree with this line of thinking myself ... I'm just, more or less, thinking out loud

 

[Dale]

Again, it is impossible to answer this question until you can tell us what you mean when you say "a physical curvature of spacetime". It seems to me that you don't know what you are asking either or you could could be specific about the alternative instead of just "something else".

 

[dm4b]

Again, it is impossible to answer this question until you can tell us what you mean when you say "a physical curvature of spacetime". It seems to me that you don't know what you are asking either or you could could be specific about the alternative instead of just "something else".

Dale,

Part of the problem is, nobody knows what it means for spacetime to physically curve.

In fact, one of the more common reasons I've heard for people not buying into it being real is "I can't wrap my brain around it", or "I can't visualize it, or imagine it".

I just think it would pretty neat if we could actually find a way to test it. It's not an easy question, but then again, the situation doesn't appear quite as hopeless as sorting out the quadrillion QM interpretations out there.

I personally find it interesting to think about. If other's don't .. that's cool too.

 

[DrGreg]

Part of the problem is, nobody knows what it means for spacetime to physically curve.

So, if nobody knows what your question means, nobody can answer it. Thread solved.

 

[dm4b]

So, if nobody knows what your question means, nobody can answer it. Thread solved.

Well some folks don't seem to be having a problem discussing it.

If you don't want to contribute .. feel free to ingore it .. that's what I will be doing to the rest of the posts like this one.

 

[romsofia]

That's what gravity IS. Spacetime curvature!

That's not what you were asking, you were asking if spacetime curvature is real and physical and proceeded to insult everyone.

Something existing and something being physical can be interpreted in many different ways. Talk about mathematics. Is mathematics physical? Can I touch math? No. Does it exist? If by exist you mean it's something we use abstractly to provide insight into our physical word, then yes.

I can't go out and TOUCH spacetime. LIGO has nothing to do with changing that idea.

I would say this answers you question.

 

[Dale]

Part of the problem is, nobody knows what it means for spacetime to physically curve.

B.S. Nobody knows what YOU mean when you ask the question, but I gave a reasonable definition for "physical" under which the answer is clearly "yes, spacetime physically curves".

The only mystery is your meaning, and that is only a mystery because you continue to be evasive despite repeated requests for clarification from multiple people.

 

[A.T.]

Part of the problem is, nobody knows what it means for spacetime to physically curve.

That "problem" of yours is not physical, but purely philosophical. There is no quantity in physics called "realness" or "physicality".

Try it here:
https://www.physicsforums.com/forumdisplay.php?f=112

 

[dm4b]

That "problem" of yours is not physical, but purely philosophical. There is no quantity in physics called "realness" or "physicality".

Try it here:
https://www.physicsforums.com/forumdisplay.php?f=112

Seems to me, if physics cannot distinguish between what is real and what is not real ... it's operating on the exact same level as philosophy and religion.

Anyhow, I don't know how to explain any better what I was asking.

Even the silly science channel shows know what is meant by a "physical interpretation of spacetime curvature", when they use their simplistic rubber sheet, bowling ball analogy.

But it doesn't really matter, seems like several got what I was asking and gave me some good information. Thanks to them for the help.

I don't see this thread going anywhere else positive at this point, so I'm done, unless that changes.

 

[A.T.]

Seems to me, if physics cannot distinguish between what is real and what is not real ... it's operating on the exact same level as philosophy and religion.

No, that is exactly what sets physics apart from philosophy and religion, which are both happy to offer a lot of blather about what is "real" or "the holly truth".

The job of physics is to make quantitative predictions about observations. In other words: Use mathematical models to produce numbers that match measurements. If something doesn't affect the numbers (like musings about "realness" of some model-elements) then it is not part of physics.

Anyhow, I don't know how to explain any better what I was asking.

If you can't say it with math then it is a good hint, that your question is a philosophical and not physical.

Even the silly science channel shows know what is meant by a "physical interpretation of spacetime curvature", when they use their simplistic rubber sheet, bowling ball analogy.

The rubber sheet bowling ball analogy is neither an analogy for gravitation in GR nor does it say something about the "realness of space-time". It is just a bad analogy shown on silly channels.

I don't see this thread going anywhere else positive at this point, so I'm done, unless that changes.

I hope I helped to clarify what physics is about. You misconception here has nothing to do with curvature of space-time, but is a much more general one. You could ask the same questions about classical Newtonian forces: Are they "real", or just a mathematical model? Whatever you answer to that, the same applies to curved space-time.

 

[dm4b]

No, that is exactly what sets physics apart from philosophy and religion, which are both happy to offer a lot of blather about what is "real" or "the holly truth".

The job of physics is to make quantitative predictions about observations. In other words: Use mathematical models to produce numbers that match measurements. If something doesn't affect the numbers (like musings about "realness" of some model-elements) then it is not part of physics.

If you can't say it with math then it is a good hint, that your question is a philosophical and not physical.

I was about to ignore your post until it reminded me of something rather humurous.

Not only is this reminding me of something religious, but even as religious fundamentalism.

A ways back I was speaking with some christian fundemantalists and asked them where Cain and Abel's wives came from, and it reminded me much of this conservation.

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? (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. Just stick to what is within the book, stick to our rigid worldview and don't ask questons. Do not look outside it at all. From you and others I'm hearing, stick to what's in the physical review letters and our empirical worldview, and ask no questions outside of that. So, the first two similarities to religious fundamentalism:

(1) Dogmatic, (2) Adherence to a rigid worldview

Next, I've seen several times dismissal of ALL religion and philosophy, as you put it, as "blather". Apparently you feel they leave nothing to offer humanity. So, here comes the next comparisons to religious fundamentalism:

(3) Intolerance of others views, (4) Claim to be Sole Owners Of The Truth.

Sorry if you don't like to hear that, but that is the impression quite a few people on this forum give me.

I'm sure I risk the next similarity I could make - (5) being excommunicated - ahem, banned from the forum. Go ahead, I don't see myself posting here too often anyhow at this point. Besides, if I want an open-minded, friendly, and intelligent conversation at this level, I'll just invite in the Jehovah's Witness for dinner next time they stop at my door, and I'll ask them why the genealogies between Matthew and Luke are different.

Have fun weeping and gnashing your teeth as you nitpick apart my post. Laters ;-)

 

[PeterDonis]

BUT, the fact that this "force" acts distinctly different than the other three forces, maybe indicates it is NOT equivalent, in that sense. Does the fact that it is different than the other three forces indicate something else is going on? Is that something else a physical curvature of spacetime? Or, something else, all together?

I'm not sure I agree with this line of thinking myself ... I'm just, more or less, thinking out loud

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

Dale,

Part of the problem is, nobody knows what it means for spacetime to physically curve.

In fact, one of the more common reasons I've heard for people not buying into it being real is "I can't wrap my brain around it", or "I can't visualize it, or imagine it".

That's hardly the same as "nobody knows". Nor is it a good reason for not considering something "real". But in any case, you're wrong that nobody knows what it means for spacetime to physically curve. In GR, the definition of what it means for spacetime to physically curve is simple: spacetime is physically curved if tidal gravity is present. You test for tidal gravity as follows: take two freely falling objects (i.e., objects that feel no force, no weight) that are close together and mutually at rest at some instant. If they remain mutually at rest, there is no tidal gravity (spacetime is flat); if they do not remain mutually at rest, there is tidal gravity (spacetime is curved).

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--for example, to detect that the surface of the Earth is curved. We take two initially parallel lines, such as two different meridians at the equator, and see whether they stay parallel as we move over the surface. On a flat sheet of paper, they do; on the surface of the Earth, they don't--the meridians converge, ultimately meeting at the North or South poles. The test for tidal gravity I described above is the same, except that now time is one of the dimensions, so lines that are "parallel" correspond to worldlines of objects that are mutually at rest, and "staying parallel" means staying mutually at rest. Everything then carries over.

So anyone who "buys into" the concept of spacetime at all, should just as easily "buy into" the concept of spacetime being curved. And someone who doesn't "buy into" the concept of spacetime in the first place, shouldn't even be trying to think about GR and relativistic gravity; they need to first come to terms with special relativity.