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General Relativity, is gravity a force?

  1. Feb 27, 2010 #1
    In general relativity, gravity is modeled as a curvature in spacetime. So the earth moves in a 'straight' path in a curved space. At least, this is how it has been explained to me in the past. The sun isn't actually 'pulling' on the earth, the earth is just moving around in the 'gravitational well' of the sun. So in this sense, there is no 'force' of gravity is there? It's just a dynamic of spacetime.

    I don't understand how gravity can be one of the four forces of nature if it's just curved spacetime. How is gravity still a force in general relativity?
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  3. Feb 27, 2010 #2
    gravitation is a force. space time curvature in general relativity is just a tools to explain in another way
  4. Feb 27, 2010 #3
    in every era, human beings have different understanding of the nature.
    may be we can treat gravitational force as the MOTHER of concept of curved space-time
    or in literal way, curved spacetime is the "improvement" of the concept of gravitational force

    at least curve spacetime concept can describe the happen of the invariance of the speed of light.but not in the concept of gravitational force,
    of course curve spacetime concept requires more complex formulation
  5. Feb 27, 2010 #4
    As you guessed, gravity is not a force in general relativity.

    This is a change from Newtonian physics. An object that falls toward a gravitating body in Newtonian physics is subjected to the force of gravity. In general relativity no force acts upon the object. It is said to be 'freely falling'.
    Beware, there is more than one way the word 'force' is used in physics. The four fundamental forces include the strong force, the weak force, the electromagnetic force and gravitational force.
    Last edited: Feb 27, 2010
  6. Feb 27, 2010 #5


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    How would you then define "acceleration due to a gravitational field" if the equivalence principle holds?
  7. Feb 27, 2010 #6
    Well, I think that depends on how you define concept of force. I would say gravity is force. First mass can change momentum of another one by an act of gravity? Therefor gravity is force! I don't know why people disqualify gravity as a force. Maybe because we don't have field theory of gravity, but IMHO that argumentation is void until someone shows gravity can not be quantized. Until then, statements like "gravity isn't a force" is an ideological extrapolation.
  8. Feb 27, 2010 #7
    The acceleration of a mass towards another body is a byproduct of the curvature of spacetime.
    If people argue this, then they don't understand it. Which will be common since four dimensions is one dimension bigger than our brain evolved to naturally conceptualise.

    the concept of a force is a simplification we use of a physical process so our meagre intellects can interpret it e.g. Newtonian physics is a simplification of Einsteinian mechanics

    For simplicity of calculations, we conform to the standardized F=mg


    What you are saying it that you think gravity should be changed to units of kg.m/s/s and not the m/s/s that everyone else uses. In which case we would call it a force, and not gravity.
  9. Feb 27, 2010 #8


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    Gravity, experimentally, is neither a force nor curvature. Experimentally it is simply a phenomena. Now, when you ask a question like "is gravity a force", you must always pose that question within a conceptual framework ('theory') that describes this phenomena. Newton's original theory of gravity is one such framework, and in that theory gravity is a force. Einstein's general relativity is another theory that describes the phenomenon, and in that theory gravity is represented in the formalism as curvature of spacetime.

    Theoretical notions like 'force' are not properties that exist in nature, but ideas in a conceptual framework that is used to describe nature. For example, Newtonian mechanics can be reformulated in terms of the so called 'principle of least action', and the description of motion in that theory does not involve the idea of 'force', even though the two descriptions are completely equivalent.
  10. Feb 27, 2010 #9


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    GR did not remove the "force status" from the "force of gravity". It just moved it to the "inertial forces", saying that if you are observing a "force of gravity" then you are not in an inertial frame.
  11. Feb 27, 2010 #10


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    The above two posts do a good job uncovering some of the ambiguity of the original question, so I won't talk about that. What I do want to do is go into the GR description of the situation a little further. Like dx says, this is merely the interpretation within one framework.

    In GR, the equation of motion for a free particle (i.e. no forces. Note: Gravity does not even exist in GR. So it makes no sense to speak of it as a force.) is the following:
    [tex]\frac{d^2 x^\alpha}{d \tau ^2} = - \Gamma^\alpha_{\beta \gamma} \frac{d x^\beta}{d \tau} \frac{ d x^\gamma}{d \tau} [/tex]

    In the case of a flat spacetime, this reduces to:
    [tex]\frac{d^2 x^\alpha}{d \tau ^2} =0 [/tex]
    Which is precisely Newton's 2nd law for a free particle.

    However, if we imagine our particle to be confined to the surface of a sphere, say, then it does NOT reduce to Newton's 2nd law. In this case, there are no identifiable forces (if we look at this classically, we do not even observe gravity!), and yet there is a deviation from the newtonian motion.

    All that changes when we introduce mass into the picture is that the [tex]\Gamma^\alpha_{\beta \gamma}[/tex] change in a predictable way.

    No mention of the word gravity is ever needed.

    This is the way I see it from GR, at least.
  12. Feb 28, 2010 #11

    Good vid. 33:30 onwards talks a bit about this, and up to around 40:00, specifically the point regarding gravity and it's affect on light. (i.e if gravity were a force, it would not cause light to bend since light has zero mass)
    Last edited by a moderator: Sep 25, 2014
  13. Feb 28, 2010 #12
    I'm sorry, but what happens to the spacetime to be flat? The gravitational field exerts a force on both particles and the fabric of spacetime and if it is not present, the spacetime reduces to a flat spacetime so all particles move along straight lines! If it is present, then the particles would have proper accelerations due to the force acting on them!

    The gravity does not affect photons directly and this is right! The gravitational force affects spacetime that the photons are travelling in so their trajectories will be bent!

  14. Feb 28, 2010 #13
    I am sorry, but I do have trouble understanding what you just said, since my native language is not English. However, I think you are implying that it's geometric nature is the reason why gravity is not force, but rather a background context. If this is the case, I am not convinced that gravity will retain it's geometric nature at physical regimes where quantum effects are relevant too; that is why I don't want to disqualify gravity as a force just yet. There are gravitational phenomena which can not be reduced to pure geometry - for an example, quantum effect of gravity-induced phase change which are theoretically predicted and experimentally demonstrated by neutron interferometry.

    Would you, please, comment on how you see this phenomena.
  15. Feb 28, 2010 #14


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    What causes spacetime to be flat is the absence of mass. The Einstein equations read:
    [tex]G_{\mu \nu} = 8 \pi T_{\mu \nu}[/tex]
    Where [tex]T_{\mu \nu}[/tex] is the stress-energy-momentum tensor. When this is zero, the EE reduce to the vacuum Einstein equations, one solution to which is flat (minkowski) spacetime (Other solutions exist, which involve dirac delta functions. For example, a schwarzschild black hole). This is what I mean by spacetime being flat: the absense of any contribution from the stress-energy-momentum tensor. In this scenario, Newton's 2nd law is followed for free particles. The introduction of anything that makes the stress-energy-momentum tensor non-vanishing necessarily curves space-time, changing the christoffel symbols, and thus the EOM for the particle.

    Please notice, I have not mentioned the word gravity even once. The word is not necessary in GR. Do not attempt to introduce it, and refer to the preface in my previous post.
  16. Feb 28, 2010 #15
    Please stop here! What comes to mind when hitting the stress-energy-momentum tensor in general relativity? You're saying that if [tex] T_{\mu\nu}[/tex] is zero, the spacetime is flat. Okay, but the story has not reached its end yet as you are missing two points:

    1- In GR, every mass that curves spacetime has a gravitational nature but in general the tricky word "mass" can replace the widely- used 'stuff' from a physical point of view which has nothing to do with the curvature of spacetime unless we spacify whatever happens between these masses and the fabric of spacetime. You're just putting a cap on the name "gravity"!

    2- The stress-energy-momentum tensor describes matter (density, pressure and stress), radiation and non-gravitational "force fields"! All these attributes belong to "gravitational field" (which exerts a gravitational force on the things around) in the Einstein's field equations and this field in turn may be inspired by the existence of "mass" as in the theory of Newtonian gravity.

    That is just because you're indirectly referring to it! I can also say something about a guy named "Baron Schilling Von Canstatt" but never quote his name clearly and rather use "he was a great guy who invented the telegram in 1832"!

  17. Feb 28, 2010 #16


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    I get the feeling we're arguing over semantics, or else I'm not understanding you clearly. My point is as follows: within the theory of GR (independent from newtonian mechanics!) one never need mention a mysterious "gravity". All you need to mention is the stress-energy-momentum tensor.

    I've re-read your post a dozen or so times and I really have a hard time understanding, I'm sorry. Could you, or perhaps someone else who understands, try and phrase it differently?
  18. Mar 1, 2010 #17
    The phrase 'the force of gravity' is a misnomer. It is not a force. (gravity is acceleration, Newton defined "force" as being equivalent to acceleration multiplied by mass)

    As others have stated, gravity does not exist in an Einsteinian world. If you are going to using gravity to explain things, and treat it as a force, then shows us some equations on how gravity affects zero-mass objects. (it doesn't work)

    THe video I quoted shows at low speed, Newtonian mechanics is the same as Einstein Mechanics. The effect of gravity on an object with mass can be used to explain low-speed phenomena. It also shows at the beginning (if you watch the whole video) how the Newton equations are derived from the (1+[tex]\epsilon[/tex])n example
  19. Mar 1, 2010 #18
    Again the gravitational field affects the fabric of spacetime through exerting a force on it and all particles such as photons moving in the curved spacetime will have their trajectories curved. This can also be seen for example from Rindler metric where spacetime is flat, but yet a uniform gravitational field exists locally to make the particles fall free by applying a uniform gravitational force on them.

  20. Mar 1, 2010 #19


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    Newtonian physics can predict the deviation of light paths around massive bodies. The eclipse observations early in the last century determined that the value was closer to that predicted by GR than by the Newtonian method. The GR prediction is just double the Newtonian prediction.

    See http://en.wikipedia.org/wiki/Tests_of_general_relativity for a discussion.

    Last edited: Mar 1, 2010
  21. Mar 1, 2010 #20
    This is in agreement with some part of one of my posts here:

    The point is that nothing can be accelerated by itself. There must be a force acting on particles which in GR it is considered to be gravitational field! I don't know why that is such a big challenge for people to simply see why gravity is a force though I'm aware of the differences physicists have in the literature. Some believe it's no longer a universal force but curvature and distorsion in GR such as

    The grip of gravity: the quest to understand the laws of motion and gravitation By Prabhakar Gondhalekar, page 161.

    Define Universe and Give Two Examples By Barton E. Dahneke, page 167.

    The search for gravity waves By P. C. W. Davies, chapter 2, section 1.

    But all say that this is just because in GR one can't make use of a universal (Newtonian) force and can only retrieve such "force of gravity" locally. I agree with this but this does not imply the word "gravity" isn't a force in GR at all! Let's say it's not a universal force that we are used to encountering it in the classical physics.

  22. Mar 1, 2010 #21


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    It is possible to think of gravity in GR as a 'pseudo-force'. The equations of geodesic motion state that

    \frac{d \dot{x}^\alpha}{d \tau} = - \Gamma^\alpha_{\beta \gamma} \dot{x}^{\beta} \dot{x}^{\gamma}

    from which

    \delta \dot{x}^\alpha = - \left( \Gamma^\alpha_{\beta \gamma} \dot{x}^{\beta} \dot{x}^{\gamma}\right) \delta \tau

    For suitable starting conditions for the velocities and positions of a test particle one can use this as the basis of a numeric solution.

    The point being that here the Christoffel symbols act like a velocity dependent potential.
  23. Mar 1, 2010 #22
    An argument I posted for xlines is that dimensions need to be conserved.

    i.e. Force=kg.m.s[tex]^{-2}[/tex] (joules/distance)
    gravity =m.s[tex]^{-2}[/tex] (joules/distance/mass)

    i.e. it doesn't fit the what we currently define as force, just by it's unit nature.

    I think one of the consequences of using this approach means black holes evaporate, but that doesn't mean you can't use this wrong concept to solve day to day problems (it got used for 250 years just fine :).
  24. Mar 1, 2010 #23
    Do objects still accelerate due to gravity in GR?
  25. Mar 1, 2010 #24

    See Nebeshin's answer on page 1
  26. Mar 1, 2010 #25


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    For the benefit of readers who can't follow the technical jargon of this thread, in relativity acceleration and force are relative like lots of other things. Two observers can disagree over whether something is accelerating or not. As another contributor to this forum once said, to decide if something is accelerating, you first have to decide what is not accelerating, and measure things relative to that.

    Relative to someone stood on planet Earth, falling objects accelerate and there is a force causing the acceleration. Relative to someone who is falling under gravity, another local falling object moves with constant (or zero) velocity and there is no force acting on it. This second point of view is particularly relevant: acceleration relative to a local, free-falling observer (momentarily travelling at the same speed) is called "proper acceleration" and it's what an accelerometer measures. Someone falling under gravity experiences zero proper acceleration. Someone stood on the Earth's surface experiences 1 g proper acceleration upwards.

    I was careful to use the word "local" in certain places above, because "tidal forces" (a.k.a. spacetime curvature) can cause two free-falling particles which are a distance apart to accelerate from each other even though both have zero proper acceleration.

    In GR, when people talk of acceleration they often mean proper acceleration; any other sort of acceleration is called "coordinate acceleration".
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