Gravity: Exerting Force or Warping Spacetime?

[Jehannum]

TL;DR

Looking for a definitive answer to pedantic arguments about whether gravity is a force or not.

In Einstein's theory, gravity is caused by the warping of spacetime. This leads some people to object to gravity being referred to as a force.

However, to me it is correct to say that a paperweight resting on a desk is exerting a force on the desk (and vice versa). Is this a correct statement at every level of physics- that, whatever the cause of gravity, forces are being exerted in this situation?

 

[A.T.]

In Einstein's theory, gravity is caused by the warping of spacetime. This leads some people to object to gravity being referred to as a force.

In General Relativity you can have a force of gravity, but it is an inertial force in non-inertial coordinates, rather than an interaction over distance like in Newton's model of gravity. And conversely, you can reformulate Newtonian gravity using spacetime geometry.

However, to me it is correct to say that a paperweight resting on a desk is exerting a force on the desk (and vice versa).

The contact force between the paperweight and desk is not gravity. Neither in Newton's nor in Einstein's theory.

 

[jbriggs444]

Looking for a definitive answer to pedantic arguments about whether gravity is a force or not.

That would not be an argument about physics. It would be an argument about word meaning.

 

[pervect]

Summary:: Looking for a definitive answer to pedantic arguments about whether gravity is a force or not.

In Einstein's theory, gravity is caused by the warping of spacetime. This leads some people to object to gravity being referred to as a force.

However, to me it is correct to say that a paperweight resting on a desk is exerting a force on the desk (and vice versa). Is this a correct statement at every level of physics- that, whatever the cause of gravity, forces are being exerted in this situation?

Several aspects of gravity in General relativity simply do not fit well into the model of a force, at least not the sort of force that a paperweight exerts.

My favorite example are gravitational time dilation, and the Shapiro effect (gravitational time delay, see for instance the wiki article by the same name).

 

[PeroK]

However, to me it is correct to say that a paperweight resting on a desk is exerting a force on the desk (and vice versa). Is this a correct statement at every level of physics- that, whatever the cause of gravity, forces are being exerted in this situation?

Your question, ultimately, has no simple, single answer. Let's look at your scenario of a paperweight resting on a desk.

In Newtonian mechanics there are two forces acting on the paperweight: gravity acting downwards; and, a force from the desk acting upwards. The two forces are equal and opposite, resulting in the paperweight remaining at rest.

In General Relativity there is only one force on the paperweight: the force from the desk. Because of the shape of spacetime around the Earth the natural path of the paperweight is towards the centre of the Earth. It requires a force from the desk to prevent the paperweight following that path and keep it at rest relative to the Earth.

I might lean towards saying gravity is not a real force, but can be modeled as a force - as it is in Newtonian mechanics.

PS If you understand Newtonian mechanics and General Relativity, then this is not a question to get worked up about. Only non-physicists, I suggest, think it's an important question.

 

[timmdeeg]

Looking for a definitive answer to pedantic arguments about whether gravity is a force or not.

As I understand it gravity in General Relativity doesn't deal with forces but with objects in free fall. Search 'geodesic deviation' which describes relative acceleration of neighboring geodesics.

 

[Jehannum]

PS If you understand Newtonian mechanics and General Relativity, then this is not a question to get worked up about. Only non-physicists, I suggest, think it's an important question.

Yes, the people who have been dwelling on this argument are very much non-physicists.

 

[phinds]

Is this a correct statement at every level of physics- that, whatever the cause of gravity, forces are being exerted in this situation?

The paperweight is free-falling on a geodesic towards the center of the Earth and the desk is exerting a force pushing back against that motion, impeding the movement of the weight. In Newtonian physics, you have to say that the weight is exerting an equal and opposite force, but in GR, that's not the case.

EDIT: I wrote this reply before there were others but somehow neglected to hit "post"

And I agree w/ @jbriggs444 that you are concerned about words, not physics. Pick your model (Newton or GR) and be happy.

 

[vanhees71]

Your question, ultimately, has no simple, single answer. Let's look at your scenario of a paperweight resting on a desk.

In Newtonian mechanics there are two forces acting on the paperweight: gravity acting downwards; and, a force from the desk acting upwards. The two forces are equal and opposite, resulting in the paperweight remaining at rest.

In General Relativity there is only one force on the paperweight: the force from the desk. Because of the shape of spacetime around the Earth the natural path of the paperweight is towards the centre of the Earth. It requires a force from the desk to prevent the paperweight following that path and keep it at rest relative to the Earth.

I might lean towards saying gravity is not a real force, but can be modeled as a force - as it is in Newtonian mechanics.

PS If you understand Newtonian mechanics and General Relativity, then this is not a question to get worked up about. Only non-physicists, I suggest, think it's an important question.

I'm a bit puzzled, why you call gravity not a force but the electromagnetic interaction between the paperweight and the table a force. On a relativistic level of understanding there are no forces but only local interactions. At least nobody has found an as convincing description in terms of forces as the now established standard picture provides, and this standard picture is that all dynamics is described as local field equations. Gravity can be reinterpreted as a dynamically interacting space-time pseudometric of a pseudo-Riemannian manifold (or most probably an Einstein-Cartan manifold since there's spin).

 

[PeroK]

I'm a bit puzzled, why you call gravity not a force but the electromagnetic interaction between the paperweight and the table a force.

Gravity can be reinterpreted as a dynamically interacting space-time pseudometric of a pseudo-Riemannian manifold (or most probably an Einstein-Cartan manifold since there's spin).

There's no mystery. It's an "I" level thread and what you've written is considerably beyond my understanding of physics.

There must be a place for B-level and I-level explanations; otherwise, nothing can be said outside the mathematical foundations of physics.

 

[Herman Trivilino]

Summary:: Looking for a definitive answer to pedantic arguments about whether gravity is a force or not.

No, it's not. And the reason is because gravity is a naturally-occurring phenomenon and the notion of using a force to explain it is a matter of which man-made explanation you wish to use. None of those explanations, by the way, is complete. In other words, gravity is a phenomenon and force is part of a study of that phenomenon. Forces are an invention of the human mind, used to explain the nature of attractions and repulsions between objects. Interaction is a better term.

 

[PeterDonis]

I'm a bit puzzled, why you call gravity not a force but the electromagnetic interaction between the paperweight and the table a force.

Because gravity obeys the equivalence principle, while the other interactions do not. This allows us to construct a model--General Relativity--in which gravity is not a force but just a manifestation of spacetime geometry.

Or, if you don't like that answer, here's another: the "force" of gravity is never felt; objects moving solely under gravity are weightless. Objects affected by any other interaction are not weightless. So there is a simple physical test for the presence of other interactions, but there is no simple test for the presence of gravity--you have to make more complicated measurements over extended regions of space or time or both. That's why we call those other interactions "forces"--the simple physical test for them matches our intuitive sense of what a "force" is. There is no such test for gravity.

 

[vanhees71]

Sure, it's the specific nature of gravity, that it can be reinterpreted in terms of dynamical spacetime geometry, and I think we are discussing semantics here anyway.

It depends on the framework within which you describe the phenomena, whether you consider interactions as forces (Newtonian level of description, where you have gravitational and electromagnetic forces) or as local interactions "mediated" through fields (classical relativistic theory). Of course the point-particle concept is somewhat problematic in relativistic theories (there's no fully consistent theory of a system of point particles interacting via the electromagnetic and/or the gravitational interaction, though approximations are quite successful thanks to the weakness of both interactions). There's no such problem with continuum descriptions of matter. Than everything is described on the same footing in terms of field descriptions.

 

[timmdeeg]

I think we are discussing semantics here anyway.

Wouldn't limit semantics to the minimum saying GR is about geodesics, so no forces are involved.

 

[vanhees71]

Sure, after having reinterpreted the gravitational field potentials as a spacetime pseudometric the worldlines of test particles are geodesics in this curved spacetime.

In relativistic theories there are no forces; at least nobody has found a satisfactory theory of interacting entities with action-at-a-distance forces as in non-relativistic dynamics. The closest I'm aware of might be the Wheeler-Feynman absorber theory of electromagnetic interactions which you get by eliminating the electromagnetic field from the dynamics in a specific and quite complicated way. The trouble with this is that it works only in the classical realm but neither Feynman nor Wheeler nor anybody else has been able to successfully quantize it. That's why today we still use the concept of local relativistic (quantum) field theories to describe interacting entities.

 

[timmdeeg]

Sure, after having reinterpreted the gravitational field potentials as a spacetime pseudometric the worldlines of test particles are geodesics in this curved spacetime.

Thanks