Gravitation is not force?

12,651

Solution 1

Websters specifically defines force as the gravitational interaction (definition 4b). We all were taught in high school that gravity was a force.

Given the lack of consensus among the authorities, a more edifying, less controversial, and equally true statement might be:

In general relativity, gravity is a fictitious force.

In classical mechanics, fictitious forces are not considered "real" forces. However, nobody, not even relativists, goes around claiming "the Coriolis force is not a force".

The issue of gravity being a force or not has nothing to do with general relativity. If you believe that inertial forces are forces, then gravity is a force. If you believe that inertial forces are not forces, then gravity is not a force.

Solution 2

In GR, there are always two points of view--- local and global. In the local point of view, you look in a neighborhood of a point, and make a free-falling frame, and then motion is entirely in straight lines at constant velocity so that you don't see gravity. In this way of looking at it, gravity is not a "force", meaning it doesn't make a generally covariant contribution to the local curvature of the particle space-time paths.

In the global point of view, you see an incoming particle from infinity deflected by a field, and you say a force has been acting if the particle is deflected. In this point of view, every deflection is a force by definition.

The global point of view is the way in which gravity is treated in quantum field theory or string theory. The local point of view is the insight due to Einstein, and it is no surprise he would emphasize it in his public remarks.

The answer is "it depends on your philosophical definition of force, whether you take a local view or a global view." I prefer the global view, since it is more quantum, so I say gravity is a force, but I don't disagree with people who take the other view, since it is also valuable.

Solution 3

Well, if we're talking about what Einstein said, then the way Einstein defined gravitational field and gravitational force in GTR is that it is given by the connection, with its components by the Christoffel symbols: $$\Gamma^{\alpha}_{\mu\nu} = \frac{1}{2}g^{\alpha\beta}\left[g_{\mu\beta,\alpha}+g_{\nu\alpha,\beta}-g_{\mu\nu,\beta}\right]$$ where commas denote partial derivatives and the metric $g_{\mu\nu}$ plays the role of gravitational potential.

But this is quite different from Newtonian gravitational force.

In Newtonian mechanics, you have 'real' forces and 'inertial' (aka "fictitious") forces, the difference being that you can make inertial forces disappear by adopting an inertial frame. For example, Newton's laws in a uniformly rotating reference frames introduce centrifugal and Coriolis forces that are proportional to the mass of the object acted upon and can be removed changing to an inertial, and hence non-rotating, frame.

In other words, inertial forces are the "fault" of choosing a non-inertial frame of reference.

By the above definition, gravity is an inertial force. Similarly to the Newtonian case, it can be made to disappear by changing the reference frame--but there is also a big difference: in the Newtonian framework, inertial frames are global, and so inertial forces disappear everywhere. In GTR, that's no longer the case: there are only local inertial frames in general, and so you can only make it disappear locally.

Caution: modern treatments of general relativity do not adopt this definition. Many of them (e.g., Misner, Thorne, and Wheeler) intentionally do not identify either 'gravity' or 'gravitational field' with any particular mathematical object, not the connection, not the curvature, nor anything else. But then (for MTW) it is not technically correct to say that gravity is spacetime curvature either, but rather refers "in a vague, collective sort of way" to all of these geometrical constructs.

Solution 4

Gravity is not a force. It looks like a force because objects with non-zero rest mass have always a non-zero time-like component to their 4-velocity tangent vector to their worldline in the spacetime manifold. In other words, no mater how fast or slow you move relative to anything through space, your time coordinate may look smaller or bigger with respect to those things, but never zero. As long as you have mass, you cannot stop the flow of time for you, not even by accelerating, in flat or even curved spacetime.

Since you cannot stop in time, if spacetime is curved by a massive object like Earth, your motion through curved time will keep bumping you against it. The real force is the electromagnetic attraction between the Earth's crust particles (and the seat of your chair, ground of your house, etc!) preventing you from going all the way to the center of the Earth.

Good books that helped me really understand this (and the wonderful diagram in answer Jul 18 '13 at 12:31 by user Calmarius) are The Large Scale Structure of Spacetime by Stephen Hawking, Gravitation by Misner, Thorne and Wheeler, Spacetime and Geometry by Carrol, Introduction to Smooth Manifolds by Lee, among several others, plus sitting in topology and differential manifolds courses at my local university.

Heck, just look at the cover of Gravitation: it shows ants crawling on an apple starting at its equator with their initial tangent vectors totally parallel to each other at the apple's equator. As they crawl forward, never changing direction in their own frame of reference, what happens if they cannot stop their own crawling, just as you cannot stop your own time from passing? They meet at the top of the apple! No force attracted them, they just followed their path through the apple's curved surface and bumped into each other, just as if some so-called "gravity" had attracted them.

I believe this view of gravity is much more accurate than the "force" view of it because all experiments to date confirm this much better accuracy. Namely, they have debunked Newtonian "gravitational force". No such thing exists. Moreover, increasing the precision of our measurements will not restore the understanding of gravity as a force like the true forces, but push even further away from it. That's why the idea of "unifying the 'four' 'forces'" is mathematically nonsense, and is either a lame attempt at popularizing science, or most physicists really need to learn some math. I don't know string theory and all the other "quantum gravity" fads, but if they really result from "unifying the four forces", they need to be thrown in the trash, and somebody really needs to start hitting the math books.

Solution 5

In the framework of GR, gravity is indeed not a force as it's a consequence of Newton's first law instead of the second one.

Each point in space-time comes with its own velocity space attached, and you need the parallel transport (and thus a connection aka gravity field) to be able to even define what you mean when you say a body moves without acceleration.

In the more general setting of arbitrary second-order systems (ie if we forget about Newton's laws), the space of acceleration fields carries an affine structure. A connection is one way to choose a zero point and make it into a vector space so you can have the notion of addition of forces (or rather acceleration fields). From this point of view, gravity would indeed be a force like any other, but special insofar as it gets chosen as the one that is called zero.

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Updated on September 12, 2020

Comments

  • german
    german about 3 years

    Einstein said that gravity can be looked at as curvature in space- time and not as a force that is acting between bodies. (Actually what Einstein said was that gravity was curvature in space-time and not a force, but the question what gravity really is, is a philosophic question, not a physical one)

    • Luboš Motl
      Luboš Motl over 11 years
      The spacetime curvature is the modern explanation for the force. But the force is still there. The force, as defined by Newton, is what one may read out of the acceleration of massive bodies via $F=ma$. Because the apples still accelerate, there's still a force even though we know that the reason is a curved spacetime.
    • german
      german over 11 years
      @Luboš Motl how about unit of force how can you show unit of force N is spacetime curvature
    • Asphir Dom
      Asphir Dom over 11 years
      You can look like that (in terms of space distortion) at other fundamental forces too. What is unique to gravity is that it acts on all bodies so you can say that the geometry of the gravity force is actually the geometry of the REAL physical space. Further insights are in the field of solid state physics.
    • Bowler
      Bowler over 11 years
      True story, my girlfriend was in a bus which went into the back of another car and she hit her arm on the seat in front. She wasn't best pleased when I told her that she couldn't have really hurt her arm as the force was only fictitious (intertial). Gravity may not be a quantum field (or it may be, I should say probably is, I got in trouble before for not accepting that the graviton is all but discovered) I'm not sure that makes it any less of a force especially using the classical definition as pointed out by @Lubos Motl.
    • Nick
      Nick almost 11 years
      @german, Curvature corresponds to "tidal force" (tidal acceleration), not force. The unit of curvature isn't the Newton, it is acceleration per meter ($s^{-2}$).
    • Admin
      Admin over 10 years
      @Nick: Curvature corresponds to "tidal force" (tidal acceleration), not force. The Riemann tensor can be broken up into two parts, one of which is tidal and one of which (the Einstein tensor) is not tidal.
  • Ron Maimon
    Ron Maimon over 11 years
    This is a question of local vs. global again.
  • Admin
    Admin over 10 years
    I don't follow your logic here. If you believe in the equivalence principle, then you get gravitational time dilation. But I don't see how that connects logically to the question of whether gravity is a force.
  • Calmarius
    Calmarius over 10 years
    @BenCrowell my logic is about the force-field vs. curvature thing. Both of them satisfy the equivalence principle. You cannot feel if a mysterious force move all particles in your body. Just as you cannot feel it when you are in free fall. If gravity is a force field and you stand on the ground, you are not accelerating, as the forces cancel each other. The same happens with the observer at top of the tower. No relative motion, clocks are in sync. But in reality clocks are not in sync. So you must be in an accelerating frame and gravity can only be a fictitious force.
  • Auden Young
    Auden Young over 7 years
    Welcome to Physics.SE! I suggest the following: 1) Take the tour (mathematica.stackexchange.com/tour)! 2) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. 3) If you have a good question, ask it! Just remember if you do so and get a satisfactory answer to accept it by clicking on the green checkmark.
  • Selene Routley
    Selene Routley over 7 years
    I suggest you change the first sentence to "gravity is not a force in the classical Einsteinian picture" or something like that. This is a good answer (+1 BTW), and I find gravity in terms of geometry extremely satisfying intellectually, but increasingly I find that my view seems to be kind of an "old person's viewpoint". Whatever we geometers think, one can't ignore the fact that a significant proportion of this generation's physicists think of a real force, mediated by a boson in a flat, empty background. I personally struggle philosphically with "empty background", but I don't believe ....
  • Selene Routley
    Selene Routley over 7 years
    .... one can give an accurate picture of what the physical community thinks without mentioning the force viewpoint as a possible alternative. Until a workable quantum gravity theory is accepted, we simply don't know whether it is or it isn't. BTW I really like your sentence about the ants just bumping into one another - I'll have to remember that one.
  • Admin
    Admin over 7 years
    According to GR, gravity is not a force, but then massive objects will collapse into themselves. Then you have to invent new mathematical remedy and hack such as weakly strong force which acts at atomic scale that pushes particles with mass from pulling and collapsing together. It gets hackier and uglier. Terrible convolution and obfuscation.
  • gdahlm
    gdahlm almost 5 years
    The concept is conveyed better if you replace "fictitious" with "inertial", "apparent", or "pseudo". Under GR gravity as a force is an apparent force that arises in an accelerated frame of reference. Centrifugal force is a "fictitious force" but would be a useful construct if your frame of reference is the inside of the rim of a rotating bicycle tire. Labeling a force as fictitious does not mean it is forbidden or a useless concept, just that it is an artifact of your chosen frame of reference.