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Matter tells matter how to move

  1. Jun 25, 2008 #1
    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?

    Last edited: Jun 25, 2008
  2. jcsd
  3. Jun 25, 2008 #2


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    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.

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

  4. Jun 25, 2008 #3
    GR vs. SM

    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.
    Last edited: Jun 25, 2008
  5. Jun 25, 2008 #4
    Hi M, thanks for answering.
    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?

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

    Last edited: Jun 25, 2008
  6. Jun 25, 2008 #5
    Re: GR vs. SM

    Hi Randall,
    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.
    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.

    Last edited: Jun 25, 2008
  7. Jun 25, 2008 #6
    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".
  8. Jun 25, 2008 #7
    Hi Jennifer,
    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?

    Last edited: Jun 25, 2008
  9. Jun 25, 2008 #8
    The only kind of question that I know that is like that is Why should I bother learning anything? :tongue:
    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.
    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.
    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.
    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.
    What is a plain-vanilla force? What does SEP stand for?
    Pretty simple, huh?
    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.
    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.

  10. Jun 25, 2008 #9
    Wheeler phrased it differently in different places.

  11. Jun 25, 2008 #10
    Hi Pete,
    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 quoted this one from Wikipedia, although it also includes alternative phrasing similar to yours. Since you asked, by "SEP" I mean Strong Equivalence Principle.
    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.)
    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.
    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.

    Last edited: Jun 25, 2008
  12. Jun 25, 2008 #11
    Hi Pete, one more thought:
    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.

  13. Jun 25, 2008 #12


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    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.

  14. Jun 25, 2008 #13
    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
    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!

    Last edited: Jun 25, 2008
  15. Jun 25, 2008 #14
    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.

    Last edited: Jun 25, 2008
  16. Jun 25, 2008 #15


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    How will we recognize that a particular mechanism is "physically real," when we find it?
  17. Jun 26, 2008 #16
    Why would you associate gravitational force with spacetime curvature in the first place?

  18. Jun 26, 2008 #17
    Tidal gradients is spacetime curvature or alternatively you can think of it a spacetime deformation.
  19. Jun 26, 2008 #18


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    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.

  20. Jun 26, 2008 #19
    GR vs. SM cont.

    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.

    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.
  21. Jun 26, 2008 #20
    Hi JT,
    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 indispensible 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:
    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.

    Last edited: Jun 26, 2008
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