Is gravity a force in General Relativity?
It is sometimes stated that gravity is not a force in General Relativity: that a particle moves, force-free, along a geodesic in curved spacetime in the presence of gravity—as it moves, force-free, along a geodesic in Minkowskian spacetime in the absence of gravity—an extension of Galileo’s (and of course Newton’s) law of inertia to curved spacetime [1].
But is this going too far? This is all well and good for a particle that moves along a geodesic in curved spacetime in the presence of gravity. But what about a particle that is NOT allowed to move along a geodesic in curved spacetime in the presence of gravity? Hold a book in your hand. You are NOT allowing it to be in free fall; you are NOT allowing it to move along a geodesic in curved spacetime in the presence of gravity. You feel a force: the weight of the book. It is sometimes stated that the force that you feel is not gravity, but the electromagnetic force that you apply to prevent the book from falling freely, from moving along a geodesic. But the electromagnetic force that you apply is the REaction force. The ACTION force is the yearning of the book to fall freely, to move along a geodesic. Thus gravity IS a force in General Relativity: the yearning of the book to fall freely, to move along a geodesic, if it is NOT allowed to. If this ACTION gravitational force did not exist (as in Minkowskian spacetime, or in a free-falling elevator in a gravitational field as opposed to being at rest relative to the gravitator), there would be no need for any REaction electromagnetic force to resist it!
Of course, in General Relativity, this force, and indeed every gravitational effect, is transmitted at the speed of light via the intermediary of the gravitational field. There is no action-at-a distance as in Newton’s gravitational theory. (Even Newton had reservations about action-at-a-distance, which he wrote about in letters to Bently [2].)
Thus gravitational potential energy is a valid concept in General Relativity, but it must be construed more carefully than in Newtonian gravitational theory. If you lift the book (of mass m, where the local acceleration due to gravity is g) against gravity through RULER distance dz, you have increased its gravitational potential energy by mgdz [3]. Note that it is RULER distance that is pertinent, because it is the actual physical distance through which you lift the book. In General Relativity, it is necessary to specify RULER distance (as opposed to radar distance, area distance, distance from apparent size, etc.) [4]. By contrast, in Newtonian theory, all of these distances are one and the same. Moreover — also unlike in Newtonian theory — if you lift the book with a massless string by RULER distance dz not locally, at the elevation of the book itself, but instead far removed from the gravitator, the work that you require to lift the book by dz, and also the work that you can obtain by letting fall by dz, is diminished by the gravitational redshift [5].
[1] Wolfgang Rindler, Essential Relativity: Special, General, and Cosmological, Second Edition (Oxford University Press, Oxford, UK, 2006), Sections 1.14 and 8.4.
[2] Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler, Gravitation, 2017 Kindle Edition (Princeton University Press, Princeton, NJ, 2017), Box 1.10.
[3] Rindler, op. cit., Sections 1.16, 11.2, and 12.2.
[4] Rindler, op. cit., Sections 11.1, 11.2, 11.5, and 17.5.
[5] Rindler, op. cit., Section 12.2.
The short answer is Yes. The framework of general relativity implies that any force, not, just the gravitational force, can be described in terms of a particular curved spacetime, in which the object of interest moves and it is the curvature that describes the force, any force. Gravity is the result of spacetime curvature in the absence of any other causes, that's all.
And gravity can have as source matter-matter can curve spacetime; and curved spacetime, in fact, does lead to the creation of matter (something noticed by Schrödinger, already in 1939).
Im not a GR expert so im going to be cautios.
It seems to me i could just pick up a stone, toss it,
and expect nature to suddenly realize it needs a local curvature to provide a parabola?
Of course the experts say that newtonian theory is some limit of GR.
But it all shows that the topic is long and delicate.
Yes. There's nothing strange abiut it, beyond a lack of familiarity. But the substance of general relativity is that the effrct of any force can be described by spacetime curvature.
What force?
The real centripetal gravitational force or the centrifugal in the frame of a moving object, or both?
Where is the force if its just a question of following the line of shortest length in curved space time?
Or in the second way there is no force?
A theoretical or imaginary space time curvature?
A geodesic in spacetime is the path along which proper time (time measured by a clock moving along the path) is maximized. But force (or at least one of the manifestations of force) is that that which an object feels if it is NOT allowed to move along a geodesic, its yearning to move along a geodesic if it is NOT allowed to. For purely radial motions relative to a nonrotating gravitator (for example free fall or vertical lifting of a weight) complications of centripetal and centrifugal forces are avoided.
Good point
The real path not a geodesic one.
That is a point which often confuses.
Just raises another.
Does GR calculate real paths? Other than for light rays.
GR calculates real paths for any object whose motion is unconstrained. If the only field is the gravitational field, the path is a geodesic (unless the object is rotating, in which case the path deviates slightly from a geodesic).
Yes an initial condition such as throwing a stone is a constraint, but only for as long as it lasts. Afterwards if an object is undisturbed it moves along a geodesic.
The thtread question “Is gravity a force in General Relativity?” really is rather vague, and yet more vague if to look through the preface, which relate to
“…that gravity is not a force in General Relativity: that a particle moves, force-free, along a geodesic in curved spacetime in the presence of gravity—as it moves, force-free, along a geodesic in Minkowskian spacetime in the absence of gravity—an extension of Galileo’s (and of course Newton’s) law of inertia to curved spacetime……”
Really in the GR gravity is, of course, a force that, say, forces Earth to rotate around Sun, while that in the quote above relates to the GR postulate that if a reference frame moves freely - “along a geodesic” when no other [fundamental Nature] forces act, then in this frame – as that is in inertial reference frames in the rest in physics, all physical laws are as they are in the IRFs. I.e. the Galileo - Poincaré [though seems besides Poincaré a lot of other physicists thought so in those times] relativity principle is replaced in the GR by the “strong equivalence principle”.
The strong equivalence principle really wasn’t tested on sufficient confidence level, including since it can be generally true only if a gravity field is uniform – what really don’t exist in practice; though yeah, tables, chairs, cutlets on the ISS at first glance behave as in a Galileo’s cabin in a moving ship and tavern on a beach [besides the static gravity effects, oc course].
Though really that isn’t too essential, since, as that rigorously scientifically shown in the Shevchenko-Tokarevsky’s Planck scale informational physical model, two main papers are https://www.researchgate.net/publication/391209088_The_Informational_Conception_and_Basic_Physics, [ in the paper secton 2.9 “Mediation of the forces in complex systems” can be passed since this is more comprehensively given in section 6.“Mediation of the fundamental forces in complex systems” in other paper below] , and
https://www.researchgate.net/publication/367397025_The_Informational_Physical_Model_and_Fundamental_Problems_in_Physics,
- Matter’s spacetime is fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, spacetime that has metrics (at least) [4+4+1]4D (cτ,X,Y,Z, g,w,e,s,ct), which fundamentally cannot be impacted by anything in Matter and impact on anything in Matter.
Gravity is fundamentally nothing else than some fundamental Nature force - as that at least 3 known now – Weak, Electric, and Strong/Nuclear Forces are , which, as that is quite correctly in physics now, act in/don’t curve the flat spacetime.
More about what are Gravity, Electric and Nuclear/Strong Forces, which on Planck scale act by the same scheme, Matter on this sdcale is rather simple logical system, see the pointed above section 6 in 2-nd link, here also note one really principal point:
Aat static [and till now] the GR “weak equivalence principle”, i.e. the equivalence of fundamentally different inertial and gravitational masses – what was postulated by Newton earlier – holds; why that happens – see the explanation in the reference above,
- but does or not hold this equivalence at large speeds? – when inertial mass is larger the rest mass in Lorentz factor – or the gravitational mass remains be equal to the rest mass at any speed - or something else happen?
For real development of real scientific Gravity theory this point obligatorily must be experimentally clarified.
[Now this thread is indexed in its “Scientific topics” sections - unlike a number of others, where SS posts are; more see section “PS” in SS post April 30 in https://www.researchgate.net/post/Is-it-true-that-physicists-do-not-want-to-understand-quantum-mechanics/329 , page 329]
Cheers
I read as soon as you have a constraint, by by GR. You are on your own with old fasioned newton.
Sergey and Juan,
Thank you for your inputs.
A constraint does not invalidate GR. For example, with or without a constraint, GR predicts the modification of space (spacetime) geometry from the Euclidean (Minkowskian), while Newton's gravitational theory does not. A constraint, by not allowing motion along a geodesic, calls into question only the viewpoint in GR that gravitation is not a force.
That...i cannot get myself to believe.
There would be, to be consistant, some distortian in light ray propagation.
And nature is just not expectant to bend itself each time something flies.
I only half buy GR in astronomical dimensions.
Plus photons do not have rest mass but have momentum.
Magnitude E/c
If may be logical to use F=dp/dt
the F of gravity. I believe the correct ans. follows. This is one of
Effects tauted by GR.
I suppose SR could be used in liew of newton.
However the definition of force in this scheme already starts to show some difficulty.
Jack , from this
“……A constraint, by not allowing motion along a geodesic, calls into question only the viewpoint in GR that gravitation is not a force.…”
- it looks that you didn’t read the SS post above attentively enough. Again - in official physics there exist some a bit vague notion “force”- there exist the “ordinary” force, F, that, say, accelerate something in 3D space in dynamic systems or fixes, say, a PC on a table in statics; in both cases F=dP/dt, P is momentum;
- and “fundamental Nature [ say , Electric] force”, what doesn’t do anything concretely and this only means that in concrete case a force F that , say, accelerate something, is caused at the fundamental force acting. So, including, I write “force” if that is F, and write , say, “Electric Force”, if a fundamental Nature force is mentioned.
So, say, relating to the quote above - at description of what happens in gravitationally coupled system in the GR just “forces” are used, but in official physics - because that the GR is standard theory - Gravity isn’t a Force;
- while all other - Weak, Electric [EM in the official physics. despite that, as that rigorously shown in the SS&VT model [see SS post above], really official “Magnetic Force” [and, say, any magnetic monopoles] doesn’t exist; magnetic interactions and effects really are governed only by Electric Force], and Nuclear/Strong Forces act in fundamentally flat, uniform , and isotropic 4D Minkowski spacetime.
Again – as that rigorously scientifically shown [really proven] in the model – Gravity is fundamentally nothing else than a Force; which , as all other Forces , acts in the absolute Cartesian [4+4+1] spacetime, which fundamentally is nothing else than some fundamentally infinite “empty container”, where everything in Matter exists and happens, emptiness by no means can interact with anything in Matter.
More see in the SS post above, to read a series of SS posts in https://www.researchgate.net/post/NO47What_is_Force_a_Field_Where_is_the_Force_Field_How_does_it_appear_Is_the_Force_Field_a_Regulating_Effect_of_the_Energy-Momentum_Field/2, pages 1,2 , it is useful as well.
Cheers
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