Matter tells matter how to move

[jonmtkisco]

Please excuse me for what is possibly a meaningless or misinformed question about the motivations behind GR.

John Wheeler famously said: "matter tells Spacetime how to curve, and Spacetime tells matter how to move." I interpret this school of thought to reflect a conjecture that Spacetime is not simply a mathematically convenient tool for calculating and graphing the effects of relativity; it also is the actual physical mechanism by which gravity operates. That is, gravity actually changes the physical geometry of local space and time.

I understand that this school of thought originally was motivated to provide an explanation for aspects of the Equivalence Principle which in the absence of that definition were considered to be coincidental or mysterious. For example this definition of the Strong Equivalence Principle: "The gravitational motion of a small test body depends only on its initial position in spacetime and velocity, and not on its constitution." My question is, why should we be at all puzzled that gravitational motion is independent of the constitution of the test body?

If gravity is thought of as a plain-vanilla force, rather than as a creator of "spacetime curvature", the SEP is not only intuitively obvious, but any behavior other than the SEP would be inexplicable.

Any massive test body is comprised of atoms, and the vast majority of the mass of atoms is comprised of hadrons (protons and neutrons). So to simplify this discussion I'll just ignore the mass of electrons and assume that all hadrons have the same mass. When a "force" such as gravity acts on a hadron, Newton tells us that F=Ma, so any given force potential causes a single hadron of mass=1 (in a hadron-based mass scale) to accelerate toward the source at a specified acceleration rate (let's say a=1 in our scale). The hadron's inertia is what resists the force of gravity and it is what that force must overcome in order to accelerate an M=1 hadron at a=1. If our test mast contains 1M hadrons, then the same force of gravity as before will separately and equally pull on each hadron, causing each hadron to accelerate at a=1 and, indirectly, causing the test particle as a whole to accelerate at a=1. Gravity is an inexhaustible source of force, in the sense that it can pull on an unlimited number of hadrons at once (subject to physical space limitations) without diminishing the force it applies to each individual hadron.

By this elementary reasoning it would defy common sense to expect a more massive object to accelerate faster than a less massive object. Linking individual hadrons together (chemically) does not cause any (significant) change in their individual inertias. It would be bizarre indeed if linking hadrons together caused them to each become more (or less) susceptible to gravitational force than the same number of hadrons that are unlinked.

As I said, all of this seems entirely obvious and elementary. So I don't understand why so many great minds have spent so much time marveling about it. I am missing something.

Of course GR makes slightly different predictions about the effects of gravitational force than Newton does. Plotting gravity on a 4-axis spacetime diagram makes these differences seem easily explainable as geodesics through a physically curved local spacetime. But why can't an old-fashioned "force" have complexities in its effects, without mandating that we adopt spacetime curvature as the physical mechanism?

Jon

 

[Mentz114]

I don't think many people are amazed that all matter appears to fall with the same acceleration. It has been experimentally established for a long time.

Given that this is the case, it seems that gravity is not a force field but an acceleration field. And this acceleration acts equally on all bodies, and so may be thought of not as a property of the body but the space-time.

Space-time was first geometrised some years before GR in order to formalise the rules of special relativity as Minkowski space-time, and this leads naturally to GR when the field is coded into the curvature of the space-time.

Metric theories automatically include the SEP, other types of gravity theories have to state the relationship between inertial and gravitational mass.

I think you've said this in your long question.

But why can't an old-fashioned "force" have complexities in its effects, without mandating that we adopt spacetime curvature as the physical mechanism?

Not everyone believes that space-time curvature is a physical effect. Old-fashioned "force" has failed the experimental tests, so who needs it ?

M

 

[RandallB]

GR vs. SM

Please excuse me for what is possibly a meaningless or misinformed question about the motivations behind GR. ...

... GR makes slightly different predictions about the effects of gravitational force than Newton does. Plotting gravity on a 4-axis spacetime diagram makes these differences seem easily explainable as geodesics through a physically curved local spacetime. But why can't an old-fashioned "force" have complexities in its effects, without mandating that we adopt spacetime curvature as the physical mechanism?

IMO your comments less about the “motivations behind GR” and better describe the differences in the GR vs QM-Standard Model solution to the Classical Newton instantaneous gravity which both take as wrong.

Your description of GR as accounting for gravity using no force or “gravitons” by using warping across an extra dimension we cannot see directly is reasonable. Consider it as requiring at least 4 or 5 dimensions to effect the warping with no force action reactions required.
Contrast that with the QM – Standard Model expectation; gravitons emitted from all elements of mass cause mass to react in attraction to account for gravity.

And yes I expect that for force based on gravitons to be built into a successful explanation of gravity (Let alone being detected some day) will require some “complexities in its effects”. Not sure if calling that “old fashioned” would fit; if someone were to crack that nut and show GR wrong I’m sure it would be a new big deal.

 

[jonmtkisco]

Hi M, thanks for answering.

Given that this is the case, it seems that gravity is not a force field but an acceleration field.

I don't understand the semantic distinction you draw between a "force field" and an "acceleration field." Don't the words have exactly the same meaning?

Is the concept of a "force field" you are referring to one in which there is a total amount of force available, which divides itself among the hadrons located in the field, such that a test particle of 1M hadrons in a "force field" will accelerate less than an individual hadron? That strikes me as a nonconventional definition of a "force field." Are you aware of any "force" which acts in that manner?

Or conversely, is there any example of a force field which accelerates a structure made of multiple identical particles at a higher acceleration rate than an individual such particle?

And this acceleration acts equally on all bodies, and so may be thought of not as a property of the body but the space-time.

The fact that something "may" be thought of as a property of spacetime doesn't mean that it "must" be thought of that way. I really don't mean to be argumentative here, but I don't understand why we aren't (at least) equally justified to think of gravity as something that acts directly on an inertial mass, rather than on spacetime.

Not everyone believes that space-time curvature is a physical effect.

Maybe that includes me, but I'm quite open to being convinced otherwise.

Old-fashioned "force" has failed the experimental tests, so who needs it ?

Isn't it more correct to say that Newton's simple formulation of gravitational force has proved to be inaccurate or perhaps incomplete? I don't understand why it would be considered impossible to adopt a modified Newtonian formulation which describes gravity accurately as a force. What if we discover someday that the concept of spacetime curvature has no actual physical meaning? Unless and until its physical reality can be demonstrated, I think we need more than one way to think about these phenomena.

Jon

 

[jonmtkisco]

Hi Randall,

Consider [GR]as requiring at least 4 or 5 dimensions to effect the warping with no force action reactions required.

If I understand you, I'm with you 100% here. In general, it appears to me that in order for the spacetime curvature model to be physically possible, there must be at least a 4th spatial dimension (beyond treating time as if it were a "4th dimension"). I am not aware of any scientific demonstration that a 4th spatial dimension is a physical reality.

Not sure if calling that “old fashioned” would fit, if someone were to crack that nut and show GR wrong I’m sure it would be a new big deal.

Please don't interpret me as suggesting that GR is "wrong," or that its predictions are inconsistent with what a QM theory might predict. I have no reason to suspect that GR's mathematical predictions are at all inaccurate above the Planck scale. I'm probing only whether a strong case has been made that spacetime curvature is a physically real effect, as opposed to a more limited view that it is just a superb mathematical analogy for modeling the force of a gravitational field.

Jon

 

[MeJennifer]

John Wheeler famously said: "matter tells Spacetime how to curve, and Spacetime tells matter how to move."

Just for clarity's (and I suppose nitpick's) sake Wheeler never said that as that would not have made any sense.

He actually said: "Matter tells space how to warp. And warped space tells matter how to move".

 

[jonmtkisco]

Hi Jennifer,

Just for clarity's (and I suppose nitpick's) sake Wheeler never said that as that would not have made any sense.

He actually said: "Matter tells space how to warp. And warped space tells matter how to move".

OK thanks, that's a result of my laziness. Although I've seen the phrase many times, in this case I picked the quote up secondhand from the paper "Expanding Space: the root of all evil?" by Francis, Barnes, James & Lewis (7/07). They do refer to it as an "adage", perhaps that justifies their unattributed rearrangement of the wording.

In any case, the words "warp" and "curve" seem to me to have essentially the same meaning in this context. So do you mean that it makes more sense for "space" to tell matter what to do than for "spacetime" to do so?

Jon

 

[pmb_phy]

Please excuse me for what is possibly a meaningless or misinformed question about the motivations behind GR.

The only kind of question that I know that is like that is Why should I bother learning anything?

John Wheeler famously said: "matter tells Spacetime how to curve, and Spacetime tells matter how to move." I interpret this school of thought to reflect a conjecture that Spacetime is not simply a mathematically convenient tool for calculating and graphing the effects of relativity; it also is the actual physical mechanism by which gravity operates. That is, gravity actually changes the physical geometry of local space and time.

That is a misinterpretation of what Wheeler said. Nobody knows the actual mechanism behind gravity. General relativity was never intended to provide such a mechanism.

I understand that this school of thought originally was motivated to provide an explanation for aspects of the Equivalence Principle which in the absence of that definition were considered to be coincidental or mysterious.

One can only speculate as to what Wheeler's motivation was. But the equivalence principle is one of the postulates that is utilized when deriving Einstein's field equations.

For example this definition of the Strong Equivalence Principle: "The gravitational motion of a small test body depends only on its initial position in spacetime and velocity, and not on its constitution."

I never heard of this phrasing of the strong equivalence principle. There are two equivalence principles and are defined as follows

Weak Equivalence Principle: A uniformly accelerating frame of reference is equivalent to a uniformly accelerating frame of reference.

Strong Equivalence Principle: Any physical law which can be expressed in tensor notation in SR has exactly the same form in a locally inertial frame of a curved spacetime (also known as the 'comma-goes-to-colon' rule). I.e. One can discover how all the forces of nature behave in a gravitational field by postulating that their laws in a freely falling frame are identical to their laws in SR, i.e. when there are no gravitational fields.

My question is, why should we be at all puzzled that gravitational motion is independent of the constitution of the test body?

This is different than one might expect in other kinds of fields. E.g. if you have a changed object in an electric field then its motion will depend on its shape and charge distribution. When tidal forces are neglected then this is not the case for a body in a gravitational field.

If gravity is thought of as a plain-vanilla force, rather than as a creator of "spacetime curvature", the SEP is not only intuitively obvious, but any behavior other than the SEP would be inexplicable.

What is a plain-vanilla force? What does SEP stand for?

Any massive test body is comprised of atoms, and the vast majority of the mass of atoms is comprised of hadrons (protons and neutrons). So to simplify this discussion I'll just ignore the mass of electrons and assume that all hadrons have the same mass. When a "force" such as gravity acts on a hadron, Newton tells us that F=Ma, so any given force potential causes a single hadron of mass=1 (in a hadron-based mass scale) to accelerate toward the source at a specified acceleration rate (let's say a=1 in our scale). The hadron's inertia is what resists the force of gravity and it is what that force must overcome in order to accelerate an M=1 hadron at a=1. If our test mast contains 1M hadrons, then the same force of gravity as before will separately and equally pull on each hadron, causing each hadron to accelerate at a=1 and, indirectly, causing the test particle as a whole to accelerate at a=1.

Pretty simple, huh?

Gravity is an inexhaustible source of force, in the sense that it can pull on an unlimited number of hadrons at once (subject to physical space limitations) without diminishing the force it applies to each individual hadron.

That is incorrect. If the body moving in the field has a mass which is not neglegible with respect to the source of the field then the acceleration of the bodies in the field will start to depend on the mass of those bodies. When it is said that the motion of a body is indepdanant of the mass it refers to bodies whose mass is small compared to the source.

As I said, all of this seems entirely obvious and elementary. So I don't understand why so many great minds have spent so much time marveling about it. I am missing something.

You haven't said anything different that Newton has said. What Einstein came up with is much more than this. For example, there is no concept of wormholes in Newton's theory and a closed universe was beyond Newton's imagination.

Pete

 

[pmb_phy]

Just for clarity's (and I suppose nitpick's) sake Wheeler never said that as that would not have made any sense.

He actually said: "Matter tells space how to warp. And warped space tells matter how to move".

Wheeler phrased it differently in different places.

Pete

 

[jonmtkisco]

Hi Pete,

Nobody knows the actual mechanism behind gravity. General relativity was never intended to provide such a mechanism.

I should probably stop while I'm ahead. This was precisely my point. "Mainstream" GR was never intended to claim, and does NOT claim, that the warp or curve of space or spacetime is the actual physical cause for the motion of a test particle near a massive object. Does anyone disagree with that statement?

I never heard of this phrasing of the strong equivalence principle.

I quoted this one from Wikipedia, although it also includes alternative phrasing similar to yours. Since you asked, by "SEP" I mean Strong Equivalence Principle.

This is different than one might expect in other kinds of fields. E.g. if you have a changed object in an electric field then its motion will depend on its shape and charge distribution.
When tidal forces are neglected then this is not the case for a body in a gravitational field.

Hmmm, well of course a massive body is capable having a charge distribution that differs from its mass distribution, but it is incapable of having a distribution of inertia that differs from its mass distribution. So which is different, an attribute of matter, or an attribute of the force itself? (That's probably a rhetorical question.)

That is incorrect. If the body moving in the field has a mass which is not neglegible with respect to the source of the field then the acceleration of the bodies in the field will start to depend on the mass of those bodies. When it is said that the motion of a body is indepdanant of the mass it refers to bodies whose mass is small compared to the source.

If you are referring to the fact for example that two bodies (e.g. Earth and moon) revolve around their combined center of mass, that phonemon is defined in Newtonian physics, and it is a complexity which doesn't change my point. Each object exerts the same gravitational pull on the other's individual hadrons as it would on a lone hadron. If you are referring to something specifically non-Newtonion like GR frame dragging, then I was asking why it's not possible to consider it as a more complex manifestation of a spinning force field, rather than as a physical warping of space or spacetime per se.

What Einstein came up with is much more than this. For example, there is no concept of wormholes in Newton's theory and a closed universe was beyond Newton's imagination.

Well, I think it's fair to say, the fact that so many exotic concepts which have not been physically observed were derived by Einstein and many later cosmologists using the math of GR doesn't demonstrate that the physicality of spacetime warp is real, on the contrary it throws up a red flag indicating that we should be cautious in attributing physicality to these concepts. Lately I've seen the technical literature leaning away from the practical viability of wormholes. And as I said, a closed universe cannot physically exist unless a 4th spatial dimension is a physical reality. Surely we aren't entitled by the scientific method to assume the existence of a 4th spatial dimension just because it neatly rounds out a set of mathematical predictions that are still accurate (but more limited) absent that assumption.

Jon

 

[jonmtkisco]

Hi Pete, one more thought:

I.e. One can discover how all the forces of nature behave in a gravitational field by postulating that their laws in a freely falling frame are identical to their laws in SR, i.e. when there are no gravitational fields.

I think that if anything, this version of the SEP supports the notion that space/spacetime curvature is not the physical mechanism of gravity. Gravity and acceleration are indeed indistinguishable in some (but not all) ways; yet no one claims that non-gravitational acceleration (such as by a rocket in an otherwise empty universe) is caused by the rocket motor inducing a local physical space/spacetime curvature. I don't want to attribute too much significance to the equivalence principle, but arguably if it says anything about this subject, it suggests that the spacetime geometry local to a self-accelerating spaceship might be the same as that local to a source of gravitational acceleration.

Jon

 

[Mentz114]

This was precisely my point. "Mainstream" GR was never intended to claim, and does NOT claim, that the warp or curve of space or spacetime is the actual physical cause for the motion of a test particle near a massive object. Does anyone disagree with that statement?

This is what I was trying to say in my earlier post. There is no observable thing that corresponds to 'space-time curvature' ( in my opinion).

I doubt if anyone knows what 'actually' causes motion of any kind.

M

 

[pmb_phy]

This is what I was trying to say in my earlier post. There is no observable thing that corresponds to 'space-time curvature' ( in my opinion).

The effects are certainly observable. Spacetime curvature is the exact same thing as tidal gradients. The former is in the language of differential geometry, the later in the language of Newton. Saying that there is nothing observable that corresponds to this is like saying that nobody has ever observed the effects of tidal gradients, which certainly isn't true. While we can't observe tidal gradients we can definitely observe their effects. I'd even go so far as to say that they are one in the same. E.g. when you observe the ocean tides you are observing the effects of spacetime curvature.

Have you ever wondered what Kip Thorne meant in Black Holes & Time Warps on page 111 where he wrote

Therefore, spacetime curvature and tidal gravity must be precisely the same thing, expressed in different languages.

Think about what this means observationally; when two geodesics deviate (aka spacetime curvature) it means that when two particles start near each other there will be a relative acceleration between them, i.e. they will start to accelerate relative to each other (aka tidal gravity). Simple!

Pete

 

[jonmtkisco]

Hi Pete,

The effects are certainly observable. ... While we can't observe tidal gradients we can definitely observe their effects.

I can't speak for M, but...

Obviously saying that you can "observe the effect of X" is different from saying you can "observe X itself." We can all agree that certain gravitational effects we observe are physically real and are the result of ... uh, some particular mechanism which is physical ... but that realization in itself provides nothing to help us decide whether any particular postulated physical mechanism is physically real or is the correct choice.

Unfortunately this kind of justification is circular.

Edit: Tidal gradients depend on certain configuration features of the gravitational source: finite size, specific shape (e.g. spherical), inverse-square distance law. None of those features helps us distinguish whether gravity is a force field or a curvature of spacetime.

Jon

 

[jtbell]

We can all agree that certain gravitational effects we observe are physically real and are the result of ... uh, some particular mechanism which is physical ... but that realization in itself provides nothing to help us decide whether any particular postulated physical mechanism is physically real or is the correct choice.

How will we recognize that a particular mechanism is "physically real," when we find it?

 

[pmb_phy]

Hi Pete,

I can't speak for M, but...

Obviously saying that you can "observe the effect of X" is different from saying you can "observe X itself." We can all agree that certain gravitational effects we observe are physically real and are the result of ... uh, some particular mechanism which is physical ... but that realization in itself provides nothing to help us decide whether any particular postulated physical mechanism is physically real or is the correct choice.

Unfortunately this kind of justification is circular.

Edit: Tidal gradients depend on certain configuration features of the gravitational source: finite size, specific shape (e.g. spherical), inverse-square distance law. None of those features helps us distinguish whether gravity is a force field or a curvature of spacetime.

Jon

Why would you associate gravitational force with spacetime curvature in the first place?

Pete

 

[MeJennifer]

Why would you associate gravitational force with spacetime curvature in the first place?

Pete

Tidal gradients is spacetime curvature or alternatively you can think of it a spacetime deformation.

 

[Mentz114]

Pete,

I stick to my assertion that space-time curvature may not have a physical correlate. Observing something and then stating it is caused by this or that is not the same as a direct measurement.
I see that jonmtkisco makes this point.

It's not important, surely, whether curvature is real or not, is it ? So long as we can use it to calculate effects properly.

M

 

[RandallB]

GR vs. SM cont.

In general, it appears to me that in order for the spacetime curvature model to be physically possible, there must be at least a 4th spatial dimension (beyond treating time as if it were a "4th dimension"). I am not aware of any scientific demonstration that a 4th spatial dimension is a physical reality.

I agree with the other comments that warping of space says it more clearly than “spacetime curvature”. IMO spacetime is an unnecessary technique applied to SR that some still find convent to use.

And of course if real evidence had been found to support and resolve that gravity was caused extra dimensional warping of space by proving that it existed we would already know QM-SM was wrong. Just like if gravitons were convincingly detected we would know something was wrong with GR.

Please don't interpret me as suggesting that GR is "wrong," or that its predictions are inconsistent with what a QM theory might predict. I have no reason to suspect that GR's mathematical predictions are at all inaccurate above the Planck scale. I'm probing only whether a strong case has been made that spacetime curvature is a physically real effect, as opposed to a more limited view that it is just a superb mathematical analogy for modeling the force of a gravitational field.

You don’t even get the chance to suggest GR is wrong. By their own definitions the two GR vs. QM-SM are fundamentally incompatible as in they cannot both be right, therefore at least one one of them must be “wrong”. Many have and still are trying to reconcile the two into a unified “Quantum Gravity” so far without success, and to be successful will require at least the reinterpretation of one of the two as defining some fundamental part of the original as wrong.

Sure someone can just not care if gravity is caused by force particles interacting with mass over time, OR by mass interacting with unseen extra dimensional warping of space; as long as the math of either approach give correct predictions when and where they need them. That is just a practical application of conflicting ideas and does nothing to resolve which fundamental concept is correct.

My guess is the approach where someone will find a solution will not be based on confirming something already believed true, but by demonstrating something we believe we know is in fact wrong.

 

[jonmtkisco]

Hi JT,

How will we recognize that a particular mechanism is "physically real," when we find it?

That's a really tough question, especially since it apparently is well beyond our means to physically distinguish a force field from spacetime curvature using current "macrophysical" observation techniques. Presumably in due course many questions can be answered definitively through better understanding and measurement of QM particle physics.

When two quite different theories both are observationally and logically viable, sometimes the most practical course is to try to determine whether one of the theories can be excluded or at least determined to be relatively unlikely. So far we can't exclude either concept of gravity's physical mechanism. So we are reduced to making somewhat subjective value judgements about which is most unlikely, which in turn demands that we keep a very open mind about the whole subject.

I think the strongest qualitative argument against the force field concept is that the coupling action of the force on a test particle is quite complex, as already mentioned. But since the same, highly complex Einstein Field Equations (EFE) supply the math underlying either physical mechanism, perhaps the complexity could be resolved if more effort were made by physicists to define a standard formal methodology for the coupling of a force field stated in terms of the EFE. I don't understand why such an effort must wait until a working QM theory of gravity comes around, although obviously the latter would be an enormous help.

The strongest qualitative argument against the concept of spatial curvature is that it requires 4 spatial dimensions. The physical existence of a 4th spatial dimension is entirely undemonstrated, and is literally orthogonal to everything we experience and sense about our nearby physical world. But for its neat mathematical linkage to GR, taking a physical 4th spatial dimension for granted would sound as outlandish to us as embracing the concept of the physical Aether does now. There is sound support throughout the history of physics for exercising strong caution against accepting the reality of proposed mechanisms which require the invention of a whole new underlying physics regime. Occam's Razor also applies here. Again I'm not saying this theory should be considered to be wrong, rather that it is unsupported by a physical demonstration of the indispensable concept of a 4th spatial dimension, which in my subjective opinion is unlikely to be physically real.

An additional qualitative argument against spacetime curvature being the physical mechanism for gravity is that this geometrical mixture of time with length doesn't seem like a unified physical entity at all. It seems just like a mathematical model for charting spatial length and motion on 3 axes and time separately on another axis. Which of course is what it was originally built to be. Subsequently it has become encrusted with terminology and modes of common usage which imply physicality. I am still unsure about whether the mainstream physics community has a consensus on whether spacetime curvature (as distinguished from spatial curvature) is a real physical phenomenon.

M asks:

It's not important, surely, whether curvature is real or not, is it ? So long as we can use it to calculate effects properly.

I suppose it's not important if all we want to do is perform calculations using our existing level of knowledge. I don't know about you, but I'm curious to learn a whole lot more about how this astounding universe of ours works. So yes, it is relatively important that someday we able to distinguish mundane physically tangible phenomena from those which exist only as brilliant mathematical equations in our minds.

Jon

 

[jonmtkisco]

Hi Jennifer,

Tidal gradients is spacetime curvature or alternatively you can think of it a spacetime deformation.

I enjoy your cryptic little sound bites.

As far as I can figure it out, saying that Tidal Gradients = Spacetime Curvature is saying nothing more than that Gravity = Spacetime Curvature. Which, if we're talking about a physical mechanism for gravity, strikes me as an assertion, not an established fact.

Also, I thought you preferred the terminology "warping of space" over "spactime curvature" (?)

Jon

 

[Mentz114]

jon,

I suppose it's not important if all we want to do is perform calculations using our existing level of knowledge. I don't know about you, but I'm curious to learn a whole lot more about how this astounding universe of ours works. So yes, it is relatively important that someday we able to distinguish mundane physically tangible phenomena from those which exist only as brilliant mathematical equations in our minds.

Jon

Yes, don't we all. I found the best way with gravity is to study other theories also. GR tends to hog the limelight, but there are at least two other theories which make identical predictions to GR in the low/medium energy ranges. One is an elegant metric theory without curvature, where the field is encoded in the torsion ( twist ?) of space-time. It has forces, but it is not 'old-fashioned'. The other is a tensor field theory that has a classical Lagrangian with an interaction term between the field and the rank-2 stress-energy tensor of the source. This is probably not the place to go further.

So, I have good reason to doubt the physical existence of curvature, because these phenomena can be described without it.

M

 

[jtbell]

it apparently is well beyond our means to physically distinguish a force field from spacetime curvature using current "macrophysical" observation techniques. Presumably in due course many questions can be answered definitively through better understanding and measurement of QM particle physics.

As you're probably aware, QM is just as bad as (or even worse than) GR in terms of "underlying physical reality," with several competing interpretations that all reduce to the same mathematics for predicting results of experiments.

I'm not saying we shouldn't look for other approaches, but they do have a lot of experimental data to satisfy, and so far GR and QM have met those data pretty well. "Don't shoot the piano player, he's the only one we've got!" (who can actually play the piano, that is)

 

[pmb_phy]

As you're probably aware, QM is just as bad as (or even worse then) GR in terms of "underlying physical reality," with several competing interpretations that all reduce to the same mathematics for predicting results of experiments.

Did you ever read the article Quantum Theory Needs No 'Intepretation' by Chrisopher A. Fuchs and Asher Peres in the March 2000 edition of Physics Today? If you'd like to I can send it to you, or anyone else for that matter.

Pete

 

[pmb_phy]

Tidal gradients is spacetime curvature or alternatively you can think of it a spacetime deformation.

Yes. I've stated that myself numerous times. :)

But there is a major difference between gravitational force and gravitational tidal force. I assumed that you knew that? The former does not require the presence of spacetime curvature while the later does. Hence my question to you.

Pete

 

[pmb_phy]

Hi Jennifer,

I enjoy your cryptic little sound bites.

That's the furthest thing from cryptic that you're going to find. MJ hit the nail square on the head with that comment.

As far as I can figure it out, saying that Tidal Gradients = Spacetime Curvature is saying nothing more than that Gravity = Spacetime Curvature.

Tidal gradients and gravity are different phenomena.

Pete

 

[MeJennifer]

But there is a major difference between gravitational force and gravitational tidal force. I assumed that you knew that?

Yes I understand, but respectfully disagree with, your position on this matter. :)

Without a tidal force there will be no gravitation in general relativity at least not in any valid solutions of Einstein's equations.

 

[MeJennifer]

But there is a major difference between gravitational force and gravitational tidal force. I assumed that you knew that?

Yes I understand, but respectfully disagree with, your position on this matter. :)

Observers in a spacetime without any tidal forces that is a valid solution to Einstein's equations will not observe any gravity.

 

[jonmtkisco]

Hi Pete,

Tidal gradients and gravity are different phenomena.

Well I tend to be dense but I don't quite get your point.

The gravitational field of spherical massive bodies is of course not "uniform", in the sense that it has two components of tidal gradient. First, the gravitational potential weakens per the inverse-square law as one moves radially outward from the surface, causing a radial "elongation" of a batch of test particles. Second, Gauss' Law says the gravity of the body will act as if it were a point source, which causes an angular directional "squeezing" force on a batch of test particles (assuming in both cases that the batch of test particles has more than de minimus length parallel to the surface.)

Consider an infintesimal "point" test particle in circular orbit around a stationary spherical massive object with no atmosphere. It certainly feels the mathematical consequences of "spacetime curvature", despite experiencing no tidal gradients. So clearly "Gravity = Spacetime Curvature" is an accurate description here. If you change the scenario to add tidal gradients, that's just an additional directional aspect of plain old gravity, nothing fundamentally different.

Consider an infintesimal "point" test particle in freefall in a flat, homogeneous, expanding, decelerating, matter-only dust cloud universe. Again it will feel the mathematical effects of "spacetime curvature," (Gauss' Law) but will experience no tidal gradients because the homogeneity rules out the possibility of any directional gradient.

Jon

 

[jonmtkisco]

"Don't shoot the piano player, he's the only one we've got!" (who can actually play the piano, that is)

Good advice JT. I definitely do not want to throw out the mathematical predictions of GR, which I have no reason to critisize. If we someday discover a definitive QM solution, I'm confident it will substantially comply with Einstein's equations at the macro scale, regardless of what weird things might happen below the Planck scale.

I'm focused on one very narrow point here: Whether spatial curvature and spacetime curvature are the actual physical mechanisms by which gravity exercises its effects.

Jon

 

[Mentz114]

jon,

I'm focused on one very narrow point here: Whether spatial curvature and spacetime curvature are the actual physical mechanisms by which gravity exercises its effects.

It will be a unicorn hunt. I don't think there's anything in the literature about this.

M

 

[pmb_phy]

Yes I understand, but respectfully disagree with, your position on this matter. :)

I don't follow. Please state what it is you disagree with. Thanks.

Observers in a spacetime without any tidal forces that is a valid solution to Einstein's equations will not observe any gravity.

Seems circular to me since the validity of that statement depends on what is meant by "gravity."

Without a tidal force there will be no gravitation in general relativity at least not in any valid solutions of Einstein's equations.

Huh? Since when? Then again we're back to the definition of "gravity." What is it you're referring to when you speak of "valid solutions of Einstein's equations."?? What does that have to do with the definition of "gravity."

 

[pmb_phy]

Hi Pete,

Well I tend to be dense but I don't quite get your point.

A tidal force relates two particles which are accelerating with respect to each other when each are in free-fall. The gravitational force refers only to the force on one particle relative to the frame of reference. The presence of a gravitational field can be detected with one test particle. The presence of tidal forces requires the use of two test particles.

The gravitational field of spherical massive bodies is of course not "uniform", in the sense that it has two components of tidal gradient.

Two components of tidal gravity? What does that mean?

First, the gravitational potential weakens per the inverse-square law ..

Poential decreases as 1/r. Gravitational force decreases as 1/r^2. And this is the Newtonian approximation. GR is a bit different.

Consider an infintesimal "point" test particle in circular orbit around a stationary spherical massive object with no atmosphere. It certainly feels the mathematical consequences of "spacetime curvature", despite experiencing no tidal gradients.

This is an example of when there is a gravitational force acting on the particle. This force can be transformed away.

So clearly "Gravity = Spacetime Curvature" is an accurate description here.

I don't see how from what you said.

If you change the scenario to add tidal gradients, that's just an additional directional aspect of plain old gravity, nothing fundamentally different.

There is no change in scenario. The tidal gradients didn't go away because you were only looking at one particle.

Pete

 

[MeJennifer]

What is it you're referring to when you speak of "valid solutions of Einstein's equations."?? What does that have to do with the definition of "gravity."

Unless you claim that GR is incomplete only spacetimes that are a solution to Einstein's GR equations are valid, that implies that only matter-free spacetimes are Riemann flat, all other spacetimes must have at least some curvature. Note, in this context, that conformally flat is not equal to Riemann flat.

Einstein's field equations: http://en.wikipedia.org/wiki/Einstein_field_equations

The presence of a gravitational field can be detected with one test particle.

How?

 

[pmb_phy]

Unless you claim that GR is incomplete ...

I've never posted anything on the internet or elsewhere which would indicate, or even hint at me thinking that. Why would you coime to that conclusion?

..only spacetimes that are a solution to Einstein's GR equations are valid, that implies that only matter-free spacetimes are Riemann flat, all other spacetimes must have at least some curvature.

That is not the case. Einstein's field equations imply that, if there is matter at an event P in spacetime then the spacetime curvature at that event is non-zero. That does not imply that the region of spacetime outside the source has a non-zero spacetime curvature.

How?

MJ - There is no use in going into that until you understand what I'm referring to when I use the term "gravity."

Do you have the text Gravitation, by Misner, Thorne and Wheeler? If so then turn to page 467. The authors explain

One can always find in any given locality a frame of reference in which all local "gravitational fields" (all Christoffel symbols; all $\Gamma^\alpha_{\mu\nu}$) disappear. No $\Gamma$'s means no "gravitational field" ...

Recall the geodesic equation which relates the inertial accleration of a test particle to the Christoffel symbols and the velocity of the particle. That equatioin implies that if you place a free test particle at a point P in a region of space in the spacetime and the particle accelerates when placed there then there is a gravitational field at that point. This doesn't come as a surprise to you does it?

In Einstein's words

what characterizes the existence of a gravitational field from the empirical standpoint is the non-vanishing of the components of the affine connection], not the vanishing of the [components of the Riemann tensor]. If one does not think in such intuitive (anschaulich) ways, one cannot grasp why something like curvature should have anything at all to do with gravitation. In any case, no rational person would have hit upon anything otherwise. The key to the understanding of the equality of gravitational mass and inertial mass would have been missing.

This quote is from General Relativity and Gravitation, Proceedings of the 11th International Conference on General Relativity and Gravitation, (Stockholm,Cambridge University Press, Jul 6-12, 1986), How Einstein Discovered General Relativity: A Historical Tale With Some Contemporary Morals, J.J. Stachel

I have a question for the good folks here: How do you believe that Einstein defined the gravitational field in his published papers on the general theory of relativity. I.e. what mathematical quantities defined the presence of a gravitational field in Einstein's GR papers and his GR book?

Pete

Ps - I'm sending you additional information in PM.