B Where does the energy of gravity come from?

[PeterDonis]

My point is that you cannot transform away a true "gravitational field", i.e., a curved spacetime doesn't become flat by any coordinate transformation.

Of course not.

In this sense gravity is not merely an "inertial/fictitious force".

The "gravity" that is sometimes called a "fictitious force" is not spacetime curvature. Spacetime curvature is tidal gravity.

In MTW you find the expression "tidal gravitational forces" a zillion of times!

Yes, but none of them are referring to the "force of gravity" that is sometimes called a "fictitious force". They are referring to the tidal stretching and squeezing of objects, for example as the singularity of a black hole is approached. When you look closely at such cases, the actual forces involved are the internal forces between the parts of the object (which are electromagnetic) that try to resist the tidal effects, and ultimately fail.Objects moving solely under the influence of tidal gravity, with no non-gravitational interactions present, feel no force and are in free fall.

 

[vanhees71]

Ok, that's again a semantic discussion. The tidal gravity is what I meant when I said that there is a "true interaction".

 

[PeterDonis]

The tidal gravity is what I meant when I said that there is a "true interaction".

The issue is whether "true interaction" is an appropriate term for that. I have given reasons why it isn't, and referred to a classic textbook that makes that same case in great detail.

 

[vanhees71]

Where in this textbook?

 

[PeterDonis]

Where in this textbook?

Pretty much everywhere. MTW is well known as a classic exposition of the "gravity is not a force" geometric viewpoint, as well as the viewpoint that all physics is contained in invariant or covariant objects (which does not include the various "gravitational energy" pseudotensors). The fact that they often happen to use the expression "tidal forces" does not contradict this, for reasons I have already explained in post #51.

 

[vanhees71]

But in #51 you admitted that there is "tidal stretching and squeezing of objects". So there is an interaction. It's of course not a force. There are no forces in relativistic physics, only local field descriptions, but that's also semantics...

 

[PeterDonis]

in #51 you admitted that there is "tidal stretching and squeezing of objects".

I stated that, yes. But such objects, in the absence of non-gravitational interactions, feel no force due to tidal gravity and are in free fall. Just like any other objects that are moving solely under the influence of the spacetime geometry, with no non-gravitational interactions present.

So there is an interaction

If an object subjected to tidal gravity feels a force (or an interaction, if you prefer), the interaction it feels is non-gravitational--internal non-gravitational interactions between the parts of the object that, as I said, are trying to resist the effects of tidal gravity. The stretching or squeezing is what is left over after those non-gravitational interactions have done as much as they can. The tidal gravity itself is not felt at all. Which, once again, is a key reason why gravity is not considered to be a force or an interaction in classical GR.

 

[vanhees71]

Of course, a free point particle moves along a geodesic, and you can say that "free fall" is the analogue to force-free motion in Newtonian and special relativistic physics, as long as you only look locally. Already a cloud of "dust" may collapse under its own gravity, as you've just nicely described in your recent Insights article. I'd call this an interaction, but I can live with just saying "gravity".

 

[Demystifier]

In all current physical theories, energy comes from initial conditions. Where do energy conditions come from, that's a question that current theories don't answer.

 

[haushofer]

In classical GR, the only "local field" you can use is the metric itself or some tensor derived from it (such as the Riemann tensor or the Einstein tensor). But the metric doesn't describe an "interaction"--it describes the spacetime geometry. That is why it is commonly stated that gravity is not a force in classical GR.

In classical GR. But classical GR is equivalent to classical Fierz-Pauli theory, i.e. an interacting spin-2 theory on flat spacetime. So in that sense the metric field does introduce an interaction.

 

[PeterDonis]

But classical GR is equivalent to classical Fierz-Pauli theory, i.e. an interacting spin-2 theory on flat spacetime.

As long as the global topology of spacetime is $\mathbb{R}^4$. Otherwise the assumption of a flat background spacetime won't work.

 

[member 728827]

What does the Equivalence Principle have to do with energy?

I don't know, is just this guy that at least at the beginnings thought than has something to do with it.

 

[PeterDonis]

I don't know, is just this guy that at least at the beginnings thought than has something to do with it.

This is an early paper on what would eventually become General Relativity. Many of the things in it were later found not to work. If you are studying the history of how Einstein discovered GR, these papers are very interesting and useful. But they can be worse than useless if you try to use them to understand the physics. You should be looking at the latest modern treatments, not historical attempts that have long since been superseded.

 

[Wes Tausend]

"Where does the energy of gravity come from?"
If Einstein is at all correct, and I believe he is, the energy of gravity simply comes from e=mC², as do all other energies, including all accelerations, the Big Bang, Dark Energy etc. --wes

 

[PeterDonis]

If Einstein is at all correct, and I believe he is, the energy of gravity simply comes from e=mC²

No, that is not correct.

as do all other energies, including all accelerations, the Big Bang, Dark Energy etc. --wes

That is not correct either.

 

[Wes Tausend]

In my 1960's physics class, our book stated something to the effect that, in our universe, "The total energy equaled the the total mass times the speed of light squared and that energy and the mass were constant & interchangeable throughout the universe." I tend to believe this, following along the lines of https://en.wikipedia.org/wiki/Zero-energy_universe. The whole thing seems simple enough to me.

Peter stated that my post was not correct with no reason given. I am interested what his theory is, or that of another theory is, that accounts for his apparent claim that Einstein's theory is not correct in the above respect.

In dlgoff's post, the wiki link given includes the phrase , "In general relativity gravitational energy is extremely complex, and there is no single agreed upon definition of the concept." This line is offered at the beginning of the General Relativity section (https://en.wikipedia.org/wiki/Gravitational_energy#General_relativity). In that, the given link is not so helpful other than it is admittedly not well understood. -wes

 

[jbriggs444]

In my 1960's physics class, our book stated something to the effect

That is not an acceptable reference in these forums.

 

[PeterDonis]

In my 1960's physics class

We've learned a lot about this subject since the 1960s.

our book

What book?

I tend to believe this, following along the lines of https://en.wikipedia.org/wiki/Zero-energy_universe.

Wikipedia is not a valid reference. But even leaving that aside, that article does not say what you were saying in the post that I said was wrong.

In @dlgoff's post

I'll respond to that separately.

 

[haushofer]

As long as the global topology of spacetime is $\mathbb{R}^4$. Otherwise the assumption of a flat background spacetime won't work.

That's a good point, but does the interpretation of gravity as an interaction then depend on the global topology of spacetime?

E.g., how is that done in string theory? There you quantize a string on a flat background, and after a lot of calculations (conformal invariance etc.) you show that there are gravitons as vibrational modes obeying the Einstein equations (plus corrections). Would you call gravity an interaction in string theory, or only within certain topologies? To me that sounds a bit overcomplicated.

To be honest, I've never understood the problem here, but that could be my deficit understanding. You start out in Fierz Pauli theory on, say, Minkowski spacetime, use gauge invariance to include non-linear terms, and in the end you end up with the full Einstein equations, which show that you could have started from every background you wanted as long as it is a solution to the obtained field equations. I.e., to me that shows how one can obtain a backghround independent theory by starting from a background dependent theory, and I've used this argument sometimes when string theory critics complained that string theory is not background independent.

 

[vanhees71]

Gravitation can be described as gauging the Poincare symmetry of SRT. In this sense it's an interaction as all the other (known) ones. Of course, you can also reinterpret it in the sense of geometrodynamics. I'd not make a religion of either point of view.

 

[Vanadium 50]

Have we abandoned the B-level?

 

[PeroK]

Have we abandoned the B-level?

@vanhees71 doesn't do B-level!

 

[PeterDonis]

does the interpretation of gravity as an interaction then depend on the global topology of spacetime?

In the sense that finding that the global topology of our actual spacetime was not $\mathbb{R}^4$ would rule out the spin-2 field on flat spacetime interpretation, yes.

In fact, finding a different global topology might not even be necessary. One can argue that for the spin-2 field on flat spacetime interpretation to work, the actual spacetime must be asymptotically flat, so that the field goes to zero at infinity. But the spacetime of our actual universe is not asymptotically flat. So one can argue that that in itself is sufficient to rule out the spin-2 field on flat spacetime interpretation.

 

[PeterDonis]

in the end you end up with the full Einstein equations, which show that you could have started from every background you wanted

Not if you started by assuming a particular background. Then it doesn't matter that the field equations you end up with would, taken in isolation, allow other backgrounds--because on this interpretation the field equations can't be taken in isolation. They have to be taken in conjunction with the background assumption you made to derive them; any solution to the field equations that is not consistent with that background assumption cannot be allowed if you adopt this interpretation.