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Gravity: force or space-time curvature?

  1. Feb 14, 2009 #1


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    Please note that I do NOT want to discuss whether gravity is a force or the effect of space-time curvature here. If you want to discuss this, please post a separate topic about it.

    What I wanted to ask is what Einstein's own beliefs on this were. Up till now I had always believed he had postulated gravity to be the effect of space-time curvature rather than a natural force akin to electromagnetism.

    However, I just read:

    Which was written in the following article: http://www.indopedia.org/Tom_Van_Flandern.html (the subject matter of which I wish NOT to discuss here).

    They give the following source:

    [5] A. Einstein (1920), Ether and the theory of relativity, Springer, Berlin, reprinted Dover (1983), 23.

    However, everywhere else I have always read otherwise. Is this but a widespread myth?

    If you reply, please adduce external sources.
  2. jcsd
  3. Feb 14, 2009 #2
    I'd like to know why you're so interested in what personally his current view was a whole century ago? But since you're insisting, you should read for yourself (translations of) his major publications from that early time (some are online, others at the university library). That way you will less be interpreting quotes stripped of context.
  4. Feb 14, 2009 #3


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    I've tried a couple of combinations of keywords on Google, and sought for a link for Einstein's journal on general relativity, but I've only found his papers on electrodynamics and second-hand articles about general relativity.

    In his paper on special relativity, as well as in quotes in articles on general relativity he often uses the terms "curvature," (such as in the phrases "curved time," or "the curves path of the electron) but I've never read any statement in which he explicitly states that space itself is inherently characterized by a four-dimensional curvature.

    If you can link me to his paper on general relativity if you'd know where it is, I'd very much appreciate it.

    I'm interested purely for historical reasons, not for arguments for or against space-time curvature. The article I mentioned made a statement that raised both questions and eyebrows.
  5. Feb 15, 2009 #4
    Here's a decent version of SR and GR by Einstein. http://www.bartleby.com/173/.
    Another link: http://einstein.relativitybook.com/Einstein_gravity.html.

    Einstein's own writings are interesting historically, and in some ways more insightful than current writings. His way of looking at things was definitely very different than a lot of modern authors.

  6. Feb 15, 2009 #5


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    A good university library should have his collected papers which are being published by Princeton University Press.

    http://press.princeton.edu/catalogs/series/cpe.html [Broken]

    It looks like they've gotten up to 1921 which at least covers the birth of GR.
    Last edited by a moderator: May 4, 2017
  7. Feb 15, 2009 #6
    I've been puzzled by that as well and do not have a definite answer but a thought: I think his views likely changed over time, due to his own explorations and as advances in science by others shed new insights on his work.

    I just reread the first few pages of Chptr XIX my paper copy of RELATIVITY, the special and general theory....you can find it as noted above at
    Since this is a book by Einstein for laymen, maybe it's a poor choice for a subtle topic.

    Einstein says in XIX:
    referencing "the more careful study of electromagnetic phenomena" and he proceeds to discuss a field interpretation of the earths gravitational attraction to a stone....
    so here it sounds like he IS discussing a "force like" interpretation. But I could also argue the opposite for he points out some significant differences between electromagnetic and gravitational influences and he never claims them "nearly identical"....and on page 113 he notes "the behavior if measuring rods and clocks is influenced by gravitational fields.."

    When he first published GR, I don't think there were any exact solutions to his formulations..did he not use perturbations (approximations)....was the first exact solution from the Russian artillery officer?? anyway they must have added insight...Also Brian Greene notes (THE ELEGANT UNIVERSE) "historically Einstein focused on the warping of time and subsequently realized the importance of the warping of space.." One thing is clear: he was learning as he was going, feeling his way along...
  8. Dec 15, 2011 #7
    First of all, if a physicist casually uses the word « force » when really concentrating on something else, this is not strong evidence that they thought gravity was a force *as opposed to* a pseudo-force. So Einstein and others may sometimes talk as if they thought gravity was a force, but this does not answer your question. But what does begin to answer it is that even in Newtonian Physics, force is a co-variant vector, displacement is a contra-variant vector, and it is only their inner product, which is the contraction of their outer product, that is an invariant quantity in a sense in which neither of them were. (One must distinguish betweeen « covariant » and « co-variant » sometimes....in larger contexts, «covariant» really means «invariant»). That quantity is work. Therefore force is given by a tensor, but by itself it is not an invariant notion: changing to a rotating system of coordinates introduces what for Newton were pseudo-forces, in particular, centrifugal force. So in Einstein's theory it is not « physical » : all physical laws and concepts must be invariant (or, as often expressed, «covariant»). It is crystal clear from this that gravity is not a force. The metric is also a tensor. Einstein's equations which relate the energy-density to the Christoffel symbols, another tensor with the same transformation laws under changes of coordinates, is a covariant relation: (which means invariant relation): if it holds in one system of coordinates, it holds in every system of cooridinates. Weyl speaks in exactly the same way. So the Newtonian concept of gravity is not relativistically invariant, and neither is the Newtonian concept of force. The metric and curvature of space-time are invariant («covariant») and are physical, and Weyl speaks of the metric as expressing gravity.
    So Weyl says explicitly gravity is a pseudo-force....and goes further in explaining why, but this question is about Einstein. (I brought up Weyl since he is a contemporary, and if his parallel account had been disagreeable to Einstein, there would have been some record of this.)
    This is distinct from philosophising about whether gravity acts on matter by acting on space-time which then shapes the environment within which the inertial lines of a free particle travel, or whether you want to collapse this causal chain and say gravity acts on the matter so after all it is a kind of force. That whole line of philosophising is sloppy and uses undefined concepts like «cause» and «acts» and uses «force» in a non-technical sense of the word.
    But Einstein was willing to philosophise about it and he definitely avoided using the word «force» in this context. The reason for him is clear: in mechanics, it is free particles which follow geodesics, and it is deviations from this motion which lead one to postulate forces. In Einstein's system, every particle is free in this sense, but free particle always meant not acted on by forces....
    Now as for a smoking gun, Einstein saying in so many words « gravity is not a force », I will look around and see. ¿Would you consider a pseudo-force to be a force? The best place to find this kind of meta-statement would be in a popular or survey article.
    Last edited: Dec 15, 2011
  9. Dec 15, 2011 #8


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    These are not two different issues. The only thing that can answer a question like "Is gravity a force or just geometry?" is a theory. The two main theories of gravity are Newton's and Einstein's (general relativity). The former says that gravity is a force, and the latter says that gravity is geometry. Einstein obviously thought GR was a better theory of gravity than Newton's, so he would certainly have preferred the answer given by GR, which is that gravity is geometry.

    It wouldn't make sense for a physicist to think "This is what my theory says, but this is what I really believe".
  10. Dec 15, 2011 #9


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    I would suggest looking at Einstein's "The Meaning of Relativity", which is a technical (rather than lay) introduction to relativity (special and general), with additions and corrections through the end of Einstein's life (including his final attempt at a unified field theory). I would say this is the single best, periodically updated, statement of Einstein's understanding of relativity aimed at a technical audience. It is readily available at a reasonable price. (First published 1921; last update 1950s, shortly before his death).
  11. Dec 15, 2011 #10


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    Necropost alert! This thread is nearly three years old.
  12. Dec 15, 2011 #11
    Collected Papers of Albert Einstein suppl. (translations) volume 6,
    Not directly on point, but here is Einstein being very categorical about a relatied point: « which makes space-time coordinates into physically meaningless parameters ».

    p. 156
    « Thus, according to the general theory of relativity, gravitation occupies an exceptional position with regard to other forces, particularly the electromagnetic forces, since the ten functions rpresenting the gravitational field at the same time define the metrical properties of the space measured. »

    This is hardly a smoking gun, but expresses his real thoughts very clearly, and has been often restated in secondary sources. Many scientists have taken note of this distinction, even the webpage of the Perimeter Institute...

    p. 178f.
    « A freely movable body not subjected to external forces moves, according to the special theory of relativity, in a straight line and uniformly. \dots »
    This is exactly what I said about Classical Mechanics: when the metric is flat and can be made to vanish identically in some coordinate system, the geodesics are straight lines too, as he analyses next, but I omit it.
    He then writes down the corresponding covariant equations which express this.
    « We now make the assumption, which readily suggests itself, that this covariant system of equations also defines the motion of a point in the gravitational field in the case when there is no system of reference \dots
    If the $\Gamma^\tau_{\mu\nu}$ vanish, then the point moves uniformly in a straight line. These quantities therefore condition the deviation of the motion from uniformity. They are the components of the gravitational field »'
    Note here that the deviation of the motion from a straight line would be the Newtonian concept of force, and here he identifies it as due to the Christoffel symbols. It is the difference between a straight line (in the particular coordinate system), and a geodesic. But, N.B., the Christoffel symbols by themselves are not covariant, not even a tensor, so by themselves you could say they were not physical. The geodesics are physical.

    Now this pretty much proves that he did indeed think this way, but it is still not a smoking gun.

    p. 238f.
    « Are the Forces of a Field of Gravitation "Real" Forces? »
    Here he defends himself against an attack that by the above remarks on the Christoffel symbols he had introduced «real forces of the gravitational field».
    «My answer to this is that \dots the naming of the parts, which I have introduced, is in principle meaningless and only meant to appeal to our physical habit of thinking. This is especially true of the concepts \dots [The Christoffel symbols] (components of the gravitational field) and $t^\nu_\sigma$ (energy components of the gravitational field). The introduction of these names is in principle unnecessary, but at least for the time being and in order to maintain the continuity of ideas, I do not think they are worthless---and that is why I introduced these quantities even though they do not have tensorial character.»
    From this one sees he didn't even think that the gravity field was really real.
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