Is Spacetime Curvature Real? - Take 2

[dm4b]

Alright, my first thread with this title got locked down. Let's see how long this one lasts ;-)

Actually, this time I have a specific queston.

It is often stated there is no test that can determine if space time curvature is truly real.

What about LIGO?

As I understand it, with the L shape of the observatory, one leg will be "contracted" in size with respect to the other, thereby changing the interference pattern. This will indicate that a gravitational wave propagated through the area.

Wouldn't this prove that spacetime curvature is indeed physical, or physically real?

Or, is there another way to interpret the results, which explains spacetime curvature completely out of the picture?

 

[bcrowell]

It is often stated there is no test that can determine if space time curvature is truly real.

Often stated by whom...?

Unless you define "real," there is no way to discuss this.

I can't imagine a definition of "real" for which a positive LIGO result would be more proof of "reality" than all the currently available tests of GR.

Nobody has a viable theory of gravity in which gravitational waves don't exist, and we also have very strong indirect empirical evidence that gravitational waves do exist (the energy loss rate of the Hulse-Taylor pulsar). Therefore a positive result from LIGO has no real implications for preferring one theory of gravity and another. LIGO is really an astronomical instrument, not a physics instrument.

 

[dm4b]

Often stated by whom...?

Unless you define "real," there is no way to discuss this.

Don't get hung up on some philosophical definition of real.

Let's just rephrase it as "is spacetime curvature physical", in contrast to being just a mathematical artifact, or an analogy

More specifically, explain how LIGO works, if spacetime curvature (in this case, just contraction) does not physically happen.

 

[bcrowell]

Let's just rephrase it as "is spacetime curvature physical", in contrast to being just a mathematical artifact, or an analogy

How do you define "physical," "mathematical artifact," and "analogy?"

More specifically, explain how LIGO works, if spacetime curvature (in this case, just contraction) does not physically happen.

The answer to this depends on what you mean by "physically." (BTW, a gravitational wave is not just a contraction.)

I don't understand how your question would differ from the following question:
"Explain how the Hulse-Taylor system loses energy if spacetime curvature does not physically happen."

To me, a more empirically definable question is how Machian the universe is. Einstein wanted GR to be a lot more Machian than it really is. That's why he didn't want to believe in gravitational waves. But it's been established for many decades now that Einstein was wrong about that. I don't see how a positive result from LIGO would change that. The fact that the Brans-Dicke \omega parameter is constrained to be very large is also a good indication that the universe is not very Machian.

 

[dm4b]

How do you define "physical," "mathematical artifact," and "analogy?"

...

You could have just not beat around the bush and said the following right away

I don't see how a positive result from LIGO would change that.

Can anybody offer any useful insight into whether or not LIGO would imply spacetime curvature is physical, or not?

 

[bcrowell]

Can anybody offer any useful insight into whether or not LIGO would imply spacetime curvature is physical, or not?

Probably not, because you haven't defined "physical."

Asking you to define your terms isn't just an irrelevant distraction. Until you define your terms, there can't be any meaningful discussion.

 

[dm4b]

You study physics, and can't surmise what is meant by physical?

I do love how these "irrelevant distractions" come up on this question, but not easier ones. If I asked is the Earth physical or real, nobody would have hesitated.

Gee, it's almost like people are trying to avoid saying "We don't know"

Anyhow a serious answer would be highly appreciated from anybody ... thanks.

 

[HallsofIvy]

Asking you to define your terms- in other words asking you to say exactly what you mean- is NOT an "irrelevant distraction". Until you do that, there can't be a "serious" answer.

Yes, people are saying "we don't know"- we don't know what you are asking and you have repeatedly refused to clarify.

 

[Dale]

I love how some people ask a question and then when you ask for them to clarify it they avoid defining their key terms at all costs. Just define your terms, if you can't define a key term then the question is meaningless.

Btw, I would define "physical" as "of or pertaining to physics" and that space-time curvature therefore qualifies as "physical". If you don't like that definition, fine, provide yours.

 

[Nabeshin]

We're not just being difficult because we're all out on a personal vendetta against you or because we're a bunch of rigid people who refuse to entertain theories that aren't written in 50 year old textbooks. It's a very legitimate question as to what you mean by physical, actual, truly, etc. If someone asked me if the Earth was physical, I would raise an eyebrow at them and ask what they meant. Perhaps they would proceed to tell me they mean can I touch it, feel it, measure it, interact with it etc. and then I would of course respond in the affirmative. Similarly here, you really need to define what you mean. Physics is a mathematical subject, and as such rests on very precise definitions. When you start using fuzzy words like "true" or "physical", without clear definition, you depart from the realm of our nice quantitative physics and enter more philosophy.

Or, is there another way to interpret the results, which explains spacetime curvature completely out of the picture?

Now, I will say a few words about what appears to be your actual question. One could perhaps offer an alternative theory of gravity which explains gravitational wave phenomenon as something other than ripples in spacetime. Similarly, just as there are multiple interpretations of the equations of quantum mechanics, it is conceivable that such theories of gravity have multiple interpretations, only one of which corresponds to your notion of spacetime curvature.

 

[dm4b]

I repeat: You also study physics, and can't surmise what is meant by physical?

You should realize that asking for definitions just sometimes gives another term to be defined, as bcrowell already made obvious. You got to just grasp the meaning at some point. If folks who study physics, does not know what is physical ... I don't know what more I can say

So, rather than engage in a circular argument, it would be nice to have a meaningful conversation ... maybe that is asking too much here.

I think my question is pretty straighforward ... does spacetime curve, or not? And, specifically, was looking for an answer in reference to LIGO.

If it does not curve, what does happen to bring about the effect on the interference pattern.

Does anybody understand LIGO that can answer what exactly is happening at that experiment?

 

[Kevin_Axion]

Space-time curvature is real, as far as we can tell. That's the way physics works, everything is falsifiable at any moment in time no matter how well supported or how elegant it is. But some things like GR that have good evidence are considered true until proven otherwise. In the future QG may find that our description of gravity is wrong and that space-time curvature is an emergent property of some other law. If you can't trust the physics then I can't help you. If you need a more personal verification then learn some GR or look at the data.

EDIT: LIGO isn't used to test if gravity curves space-time, the experiment is trying to show if gravitational waves exist. GR and space-time curvature was tested in 1919 by Arthur Eddington and thousands of subsequent experiments with astronomical observations. Space-time curvature is real.

 

[dm4b]

Now, I will say a few words about what appears to be your actual question. One could perhaps offer an alternative theory of gravity which explains gravitational wave phenomenon as something other than ripples in spacetime. Similarly, just as there are multiple interpretations of the equations of quantum mechanics, it is conceivable that such theories of gravity have multiple interpretations, only one of which corresponds to your notion of spacetime curvature.

Wow, we might actually be getting somewhere.

What other interpretations can be offered for LIGO, and what precisely are the alternative theories that offer these interpretations?

 

[khemist]

LIGO is attempting to detect gravitational waves from orbiting massive objects, such as binary stars.

This doesn't really prove that space time curvature is real, rather that gravitational waves are in fact real
(if detected. This could be called curved space time, but I think curved space and gravitational waves are quite different). Does the bending of light around massive objects not give rise to curved space?

 

[Dale]

dm4b, why are you being so evasive?

 

[dm4b]

Space-time curvature is real, as far as we can tell. That's the way physics works, everything is falsifiable at any moment in time no matter how well supported or how elegant it is. But some things like GR that have good evidence are considered true until proven otherwise.

Thanks for the clear answer. Agreed. I'm not asking if curvature is the ultimate description ... but, until other interpretations are offered for what happens in experiments like LIGO ... to me, it seems likely to be the "real" explanation of what is going on.

It sure doesn't seem to fit in the same category, as say, virtual particles, that can be explained away as a mathematical artifact of the perturbation series.

If you need a more personal verification then learn some GR or look at the data.

I have taken up to graduate level GR over 10+ years ago ... got an A. Couldn't get this question answered very well then either ;-)

 

[dm4b]

LIGO is attempting to detect gravitational waves from orbiting massive objects, such as binary stars.

This doesn't really prove that space time curvature is real, rather that gravitational waves are in fact real
(if detected. This could be called curved space time, but I think curved space and gravitational waves are quite different)

How do you feel they are different? and again, if you don't mind, in reference to how LIGO experiment works. Thanks.

 

[bcrowell]

I have taken up to graduate level GR over 10+ years ago ... got an A. Couldn't get this question answered very well then either ;-)

Probably because you refused to define your terms then, as now?

 

[Pengwuino]

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.

 

[Nabeshin]

What other interpretations can be offered for LIGO, and what precisely are the alternative theories that offer these interpretations?

I was purposefully vague in my wording. I do not know if such theories exist, and if they do what they have to say about LIGO phenomenon. I merely admit the possibility that such theories exist. I believe (someone correct me if I'm wrong here) that any theory which embodies the Einstein Equivalence Principle is necessarily a metric theory, and (quoting) "Virtually any metric theory of gravity ... predicts gravitational radiation", i.e. waves. So on one level it actually might be difficult to get away from.

On a side note, within the context of GR it is clear the GW are not a coordinate phenomenon, that is, they actually carry energy and momentum away from the system. So I find it difficult to interpret them as anything but waves.

Once you have the waves, I don't know, it's up to you really how "real" or "physical" that is. It pushes things around, carries energy and momentum, which qualifies for the definitions of both those words in my book.

 

[Pengwuino]

I have taken up to graduate level GR over 10+ years ago ... got an A. Couldn't get this question answered very well then either ;-)

That makes it even more confusing as to why you're asking such odd questions.

 

[dm4b]

I was purposefully vague in my wording. I do not know if such theories exist, and if they do what they have to say about LIGO phenomenon. I merely admit the possibility that such theories exist. I believe (someone correct me if I'm wrong here) that any theory which embodies the Einstein Equivalence Principle is necessarily a metric theory, and (quoting) "Virtually any metric theory of gravity ... predicts gravitational radiation", i.e. waves. So on one level it actually might be difficult to get away from.

On a side note, within the context of GR it is clear the GW are not a coordinate phenomenon, that is, they actually carry energy and momentum away from the system. So I find it difficult to interpret them as anything but waves.

Once you have the waves, I don't know, it's up to you really how "real" or "physical" that is. It pushes things around, carries energy and momentum, which qualifies for the definitions of both those words in my book.

Well, this is why I was thinking of LIGO this time around to try and get insight into this.

How we detect gravitational waves seems to be distinctly different than other types of waves.

LIGO seems to operate on the very principle that one leg of that detector is going to experience a length contraction.

Unless, of course, there is another way to explain exactly how that interference pattern gets modified?

 

[WannabeNewton]

It really depends on what you mean by "Real". For example, in the case of a plane wave passing by two nearby freely falling particles separated only in the x plane will diverge from their geodesics as per \frac{\partial^2 }{\partial t^2}\xi ^{x} = \frac{1}{2}\varepsilon \frac{\partial^2 }{\partial t^2}h_{xx} (say in the TT gauge) and various laser interferometers are designed to measure such very small separations (of course the mechanics is much more complicated). Mathematically this is a statement of the tidal effect of gravitational waves on particles. In my opinion, you have to define if by "real" you mean a mathematical statement of curvature that can be taken to describe physical reality. Otherwise all we know from things like LIGO, if such devices are successful, is that GWs are real. Nothing about curvature is implied.

 

[khemist]

Well, this is why I was thinking of LIGO this time around to try and get insight into this.

How we detect gravitational waves seems to be distinctly different than other types of waves.

LIGO seems to operate on the very principle that one leg of that detector is going to experience a length contraction.

Unless, of course, there is another way to explain exactly how that interference pattern gets modified?

A gravity wave is a gravity wave. One cannot detect electromagnetic waves with LIGO, and one cannot detect gravitational waves with a electromagnetic detector (such as my eye, unless, of course, we see something else interacting with that gravitational wave. e.g. something being stretched and contracted).

http://en.wikipedia.org/wiki/Gravitational_wave

 

[bcrowell]

Btw, I would define "physical" as "of or pertaining to physics" and that space-time curvature therefore qualifies as "physical". If you don't like that definition, fine, provide yours.

Just for the sake of illustration, I'll provide an alternative definition of "physical" that results in the opposite conclusion.

When a feature of GR differs from a feature of Newtonian gravity, I hereby deem it to be physically real if there is no reasonable reformulation of Newtonian gravity that gives it that feature as well. "Reasonable" means not significantly more ugly and complicated than the traditional one. Well, there are formulations of Newtonian gravity in which gravity is not a force, test particles follow geodesics, and spacetime is described as curved. Therefore by my definition spacetime curvature is not physically real.

But because tomorrow is a Tuesday, I think tomorrow I'll change my definition of "physical" to agree with DaleSpam's, and my answer will be that spacetime curvature is, after all, physically real.

 

[dm4b]

It really depends on what you mean by "Real". For example, in the case of a plane wave passing by two nearby freely falling particles separated only in the x plane will diverge from their geodesics as per \frac{\partial^2 }{\partial t^2}\xi ^{x} = \frac{1}{2}\varepsilon \frac{\partial^2 }{\partial t^2}h_{xx} (say in the TT gauge) and various laser interferometers are designed to measure such very small separations (of course the mechanics is much more complicated). Mathematically this is a statement of the tidal effect of gravitational waves on particles. In my opinion, you have to define if by "real" you mean a mathematical statement of curvature that can be taken to describe physical reality. Otherwise all we know from things like LIGO, if such devices are successful, is that GWs are real. Nothing about curvature is implied.

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

Physical things happen in the Universe, whether or not we mathematically model them. If you stood next to a supernova, you wouldn't need any convincing it was real.

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

 

[yenchin]

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".

 

[dm4b]

Thanks for the info on the torsional "flavor" of GR, I'll have a look through that arxiv article

but curvature of spacetime is "reality as far as if we agree on the mathematical model".

I tend to disagree with this, though. It might be a subjective reality to some, but it is not an objective reality. Ptolemy's epicycles, as a mathematical model, worked, with the Earth at the center of the solar system. But, it did not represent objective reality. Reality doesn't care what we agree upon. Something either is, or is not, physical reality. The Earth is either at the center of the solar system, or it is not. Spacetime curvature is either real, or it is not.

 

[yenchin]

Thanks for the info on the torsional "flavor" of GR, I'll have a look through that arxiv article



I tend to disagree with this, though. It might be a subjective reality to some, but it is not an objective reality. Ptolemy's epicycles, as a mathematical model, worked, with the Earth at the center of the solar system. But, it did not represent objective reality. Reality doesn't care what we agree upon. Something either is, or is not, physical reality. The Earth is either at the center of the solar system, or it is not. Spacetime curvature is either real, or it is not.

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.

 

[Dale]

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

Math is much more physical than english. You cannot even tell what spacetime curvature is without using math, let alone whether or not it is physical.

 

[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".