Is Gravity Really a Force? A Look at General Relativity's Perspective

[Ibix]

I would say that the layman thinks of gravity as "what makes this ball fall if I let go of it". That's precisely the bit of the interaction (equivalent to the force $mg$ in Newtonian physics) that can be transformed away by an appropriate choice of coordinates, so is reasonably called an "inertial force".

In a broader sense, of course, not all effects that we attribute to gravity can be transformed away. With sufficient precision you can detect tidal effects in a small room, and you cannot make those vanish by picking a free falling frame. Non-uniform gravitational fields (such as the Earth's on a relatively large scale) are the explanation for orbits, tides, the shape of celestial bodies, galaxies, and more. It's still not a force (at least not in the usual sense of the word), but it isn't explicable as a coordinate transform (i.e. it's not an inertial force) either.

This is, I think, a restatement of @Dale's #20 in less mathematical terms.

 

[Dale]

Once more:

I am pretty sure that nobody here either disagrees or is unaware of all of this (in particular @A.T. understands). Do you have a specific reason why you are repeating it?

 

[Frodo]

I don't think that a semi-infinite slab would not be subject to tidal forces. Do you have a concrete model in mind?

I apologise profusely as my fingers did not type what my mind was thinking.

I meant an infinite plate of zero thickness and of uniform mass density.

The gravitational force is then uniform throughout the region and there are no tidal forces either parallel or perpendicular to the plate. The proof is given directly or by the equivalent electrical analogy with charge - eg Feynman 5–6 A sheet of charge; two sheets

IIRC your objection was, essentially, that a gravitational force cannot be made to disappear by a change of reference frame because tidal forces are always present. This example is one which disproves your assertion as the gravitational force here can be made to disappear merely by using a frame in free fall and there are no tidal forces.

Again, sufficiently small means a region small enough such that tidal forces can be neglected.

I also questioned "point" and extended "region". Here you can have a region as large as you wish without tidal forces.

Anticipating a possible objection, an infinite plane of zero thickness and uniform mass density is just as valid for analysis as is a light inextensible string passing over a frictionless pulley.

 

[vanhees71]

Sure, that's what (not only) I said above several times.

So the short answer simply is: Gravitation is a fundamental interaction and thus a "true force" and not (only) an "inertial force".

It's even clear in Newtonian mechanics: You can transform away a homogeneous gravitational field by just using the free-falling reference frame. The proof is very simple. If you have a gravitational field $\vec{g}$ that can be considered homogeneous the equation of motion is
$$m \ddot{\vec{x}}=m \vec{g}=\text{const}.$$
Now transform to the freely-falling reference frame, for which
$$\vec{x}=\vec{x}'+\frac{1}{2} \vec{g} t^2$$
you get
$$m \ddot{\vec{x}}=m \ddot{\vec{x}}' + m \vec{g}=m \vec{g} \; \Rightarrow \; m \ddot{\vec{x}}=0.$$
In this sense a homogeneous gravitational field is inertial, because it can be transformed away by going to an accelerated reference frame.

Of course, the true gravitational field of the Earth is not homogeneous and this field cannot be transformed completely away by changing to an accelerated reference frame.

 

[Frodo]

We are in violent agreement.

 

[Halc]

I meant an infinite plate of zero thickness and of uniform mass density.

Why the zero thickness? If the field it produces is uniform then it is not a function of distance from the mass, so the field is a function only of the mass per unit area, not mass per unit volume. That means an zero thickness plate of a million kg/m² (infinite density) exerts the exact same force (at any positive altitude) as a slab of 10,000 km thick foam with mass of a million kg/m² which is a density of 0.1kg/m³

 

[vanhees71]

Well, yes. You can always invent some highly idealized academic example, which cannot be realized in nature ;-)).

 

[Frodo]

Well, yes. You can always invent some highly idealized academic example, which cannot be realized in nature ;-)).

And I thought I had anticipated that objection

First, I'm just following Feynman, someone for whom I have great respect.

Secondly, in what sense is "a light inextensible string passing over a frictionless pulley" not a "highly idealized academic example"? It, and a "point mass" and "a smooth frictionless surface" appear in countless excercises.

I was attempting to validate my assertion that gravity was a virtual force against all those who quibbled with me.

Remember this is a B, or High school level thread.

 

[vanhees71]

I've also the highest respect for Feynman, but what has this to do with the argument that gravity is an interaction and not just an inertial force? Does Feynman make the statement gravity was just an inertial force? How is this then consistent with his marvelous "Feynman lectures on gravitation"?

 

[Dale]

The OP was long since answered and, since this has now degenerated into the semantic argument I had tried to avoid, it is time to close the thread.

It is simply not necessary that everyone use the same terminology, as long as we are all using terminology that is consistent with the literature.