I How does inertia, a property of mass, arise?

[saddlestone-man]

Doesn't inertia have to do with the fact that all objects in the Universe are being attracted by all the other objects in the Universe. Therefore to change the motion of any object you have to overcome the forces applied by all the others. That's why there can't be an immediate change in motion.

 

[timmdeeg]

This reminds me of Mach's principle which is about rotating objects though. As far as I can tell today it is assumed that inertia is a local phenomenon.

 

[weirdoguy]

Doesn't inertia have to do with the fact that all objects in the Universe are being attracted by all the other objects in the Universe.

No.

 

[PeterDonis]

Doesn't inertia have to do with the fact that all objects in the Universe are being attracted by all the other objects in the Universe.

Not in GR. In GR gravity (which is the only "attraction" that could be in play here) is not a force, it's spacetime geometry. One could say that spacetime geometry determines inertia in GR (and at least one whole textbook, Gravitation and Inertia by Cuifolini and Wheeler, has been written about this), but what that actually means is that spacetime geometry determines which trajectories through spacetime are inertial (geodesics, freely falling) and which are not, and what the path curvature is of the ones that are not. But it doesn't explain why path curvature is felt as weight, which is part of "inertia" as commonly understood; that part just has to be accepted as an axiom, without explanation.

There have been attempts to explain inertia along the lines you describe (for example, Sciama in the 1950s tried it), but these attempts did not use standard GR; they used other theories of gravity. In Sciama's case, he used a simple idealized scalar field model, which is known to be incorrect but which he picked in order to illustrate the basic idea. He planned to write a follow-up paper to try to extend his idea to a tensor theory of gravity, which would have been much closer to GR, but unfortunately it appears he never did.

 

[Paige_Turner]

Well, this university physics dept seems to think that the inertial reaction force is reverse-time gravity from all the galaxies in the distant future reaching backwards in time and pushing back at you.

THE ORIGIN OF INERTIA​

By Dr. James F. Woodward, Fullerton University

It's thought by some folks these days that the cause of inertial reaction forces isn't yet really understood, or that they have just succeeded in figuring out the explanation for these forces with their "new theory." These views are mistaken.

The cause of inertial reaction forces has been understood to be the action of gravity for quite some time now.

Back in 1953, Dennis Sciama showed that gravity could account for inertial reaction forces as long as the interaction of local stuff with the gravity field of distant matter was like the interaction of electric charges and currents with the electromagnetic field. (Monthly Notices of the Royal Astronomical Society, 113, 34-42 [1953]).

It turns out, as a matter of fact, that this is true in general relativity theory, but it took a while to show this. (It was done by D.J. Raine in 1981: Reports of Progress in Physics, 44,1151-1195 [1981]).

The full-blown argument is rather formal and a bit daunting, but it's easy to see that gravity causes inertia in a simple little argument modeled on that presented by Sciama back in 1953.

Full text here.

 

[PeterDonis]

Well, this university physics dept seems to think that the inertial reaction force is reverse-time gravity from all the galaxies in the distant future reaching backwards in time and pushing back at you.

As you were already told in another thread, the article you refer to is the personal opinion of one particular physicist, not a "university physics dept", much less an actual peer-reviewed paper.

Of the two actual papers the article links to, one (the paper by Sciama) was an attempt to account for inertia using a simplified model of gravity (a scalar field) that is known to not be correct. Sciama said he planned to write a follow-up paper extending his idea to a tensor theory of gravity (which GR is), but never actually did so.

The other paper (Raine) does not actually show what the article you quote claims. It does not show that Sciama's idea works in General Relativity (the abstract explicitly says that Mach's principle, which is what Sciama's idea embodies, is not contained in GR). What it does do is propose additional structure that could be added to GR to make it Machian (at least in the author's view). AFAIK this proposal has not gained any traction in the GR community (possibly because many relativists do not share the author's opinion that GR is not Machian; at least one GR textbook, the one by Cuifolini & Wheeler that I referred to in post #54, has been written to justify and expand on the view that it is).

 

[Paige_Turner]

Ahh, thank you! I wondered why I hadn't seen this anywhere else.

> As you were already told in another thread,

I haven't seen it yet.

--lkt

 

[PeterDonis]

I haven't seen it yet.

https://www.physicsforums.com/threads/need-sr-beliefs-integrity-filter.1005129/post-6515561

 

[Paige_Turner]

> Mach's principle, which is what Sciama's idea embodies, is not contained in GR

Yes, but it's not inconsistent with GR.

> What it does do is propose additional structure that could be added to GR to make it Machian

By Machian, I assume you mean that local inertia is determined by faraway mass.

Well, I'm glad you think it's false. I thought I had to believe it because that physics prof said so in the inertia paper.

I never did see what the problem is with the only object in the universe rotating.

...Or do you believe Mach was right? I'm confused. You'd think I'd get used to it.

 

[PeterDonis]

it's not inconsistent with GR.

Agreed.

By Machian, I assume you mean that local inertia is determined by faraway mass.

That's what the references you gave appear to me to mean by it. For example, that's the view that the Sciama paper was proposing.

I'm glad you think it's false.

I didn't say I thought GR wasn't Machian. I only said the abstract of the second paper referenced in the article you quoted said so.

I thought I had to believe it because that physics prof said so in the inertia paper.

This is not a good reason to believe anything. You don't "have" to believe things just because some physicist in some paper says so. At the very least, you should be reading more than just one paper; you should have some sense of the overall literature and where that particular paper fits in. That's one of the biggest advantages of a good textbook (like MTW or Wald for GR): the authors have already done a huge survey of the literature for you, and will put various claims in their proper context.

Or do you believe Mach was right?

Mach himself only had a preliminary and very tentative version of the whole conceptual scheme in question. So the things he himself said weren't really right or wrong; they were initial gropings towards understanding and should not be taken as definite anyway.

My personal view on GR is closer to that of the Cuifolini and Wheeler textbook I referenced, whose tag line is "mass there governs inertia here", i.e., GR is Machian to the extent that such a question even matters. The Einstein Field Equation says that the spacetime geometry at any event is determined by the distribution of stress-energy in the past light cone of that event. That seems pretty Machian to me. The only issue I see with that viewpoint (and I'm certainly not the only one to see it, many physicists have discussed this in the literature) is that many solutions of the EFE require some kind of boundary condition or initial condition, and those conditions can be viewed as something separate from the distribution of stress-energy and hence a non-Machian element.

 

[timmdeeg]

My personal view on GR is closer to that of the Cuifolini and Wheeler textbook I referenced, whose tag line is "mass there governs inertia here", i.e., GR is Machian to the extent that such a question even matters. The Einstein Field Equation says that the spacetime geometry at any event is determined by the distribution of stress-energy in the past light cone of that event. That seems pretty Machian to me.

Doesn't "mass there governs inertia here" imply that the inertial mass of a body depends on the spacetime geometry?

 

[PeterDonis]

Doesn't "mass there governs inertia here" imply that the inertial mass of a body depends on the spacetime geometry?

No. A more precise phrasing would be that mass there governs inertial motion here. Mass there determines the spacetime geometry here, and the spacetime geometry here determines which worldlines here are inertial, and what the path curvature is of worldlines here are not inertial. But path curvature is only proper acceleration; what you feel as weight is proper acceleration times inertial mass. The spacetime geometry does not determine what the inertial mass of a body is.

 

[timmdeeg]

No. A more precise phrasing would be that mass there governs inertial motion here.

Yes this way it makes sense to me and I would prefer to call it just Einsteinian.