How Does the Expansion of the Universe Affect Inertia and Mass?

[chupe1123]

If you have a universe consisting of three bodies; a planet, a truck and a box in the back of the truck what happens when the truck changes velocities- does the box move due to inertia? Because couldn't you view that as the planet changing its speed of rotation and the truck staying still, in which case it seems odd that the box would move at all.

I'm just getting into relativity so I'm sure there's a simple explanation to this that I'm not aware of yet.

Thanks

 

[swapnanil_s]

If you have a universe consisting of three bodies; a planet, a truck and a box in the back of the truck what happens when the truck changes velocities- does the box move due to inertia? Because couldn't you view that as the planet changing its speed of rotation and the truck staying still, in which case it seems odd that the box would move at all.

I'm just getting into relativity so I'm sure there's a simple explanation to this that I'm not aware of yet.

Thanks

Gravity is not only created by heavenly bodies like stars and planets... Ok, don't even bring in that planet, Even then if the truck would change it's velocity, the box would move. It is beacuse of the gravitational field created by the moving truck. Changing velocity of the truck would change the gravitational field, thus the box would move to make itself rest in a stable field.

 

[Passionflower]

If you have a universe consisting of three bodies; a planet, a truck and a box in the back of the truck what happens when the truck changes velocities- does the box move due to inertia? Because couldn't you view that as the planet changing its speed of rotation and the truck staying still, in which case it seems odd that the box would move at all.

I'm just getting into relativity so I'm sure there's a simple explanation to this that I'm not aware of yet.

Thanks

One way of looking at it is what is accelerating. Whether the truck or the planet accelerates is not relevant to the box (we assume the planet is a perfect sphere and we ignore frame dragging). So what makes the box accelerate as well is friction. If the box would be on a frictionless surface it would not accelerate and eventually fall of the truck.

 

[Mike_Fontenot]

Your question is actually quite profound. It is a question raised by Mach: he imagined two blobs of fluid, with NO other mass anywhere in the universe. One of the blobs is "inertial", and is therefore spherical, because of surface tension and symmetry. The other blob is rotating uniformly, about the axis passing through the center of the two blobs. That other blob will not be perfectly spherical ... it will be thicker at its equator, than at its poles ... it will "bulge" at its equator, just like the Earth does, because of its rotational motion.

Mach's question was, if there is NO other mass anywhere, it doesn't make any sense to say one blob is rotating, and one is not. Their rotation must be relative to one another, and not absolute.

Yet, we know that in the real universe, there WOULD be a difference in the blobs. Mach concluded that "inertia" must be caused by the sum total of all the other masses in the universe. The blob that is inertial, is the blob that is not rotating with respect to the general collection of all other masses in the universe.

Mike Fontenot

 

[DreadyPhysics]

In the case where you see the truck standing still and the Earth as rotating under it, to make this frame of reference work you have to see the truck as standing still and the entire rest of the universe rotating, including the box. Hence it would move.

 

[DreadyPhysics]

Mach's question was, if there is NO other mass anywhere, it doesn't make any sense to say one blob is rotating, and one is not. Their rotation must be relative to one another, and not absolute.


Mike Fontenot

This is interesting, I've never heard of it. Was Mach correct in his deduction? It seems like a pretty bizarre way to think of inertia. Is there any sort of modern discussion of this thought experiment? Don't leave us hanging!

 

[Mike_Fontenot]

This is interesting, I've never heard of it. Was Mach correct in his deduction? It seems like a pretty bizarre way to think of inertia. Is there any sort of modern discussion of this thought experiment? Don't leave us hanging!

I think I saw this discussion in Einstein's relativity book by Crown Publishers ("Relativity, the Special and General Theory"). As far as I know, Mach's resolution of his thought experiment is the only explanation of the source of inertia. In Newtonian physics, inertia was easier to at least characterize, because you could think of "space" as being some kind of "stuff" that a body could be rotating with respect to (although even in the Newtonian case, the cause of inertia wasn't explained). In relativity, "space" isn't "stuff" ... there's no underlying "substance" that either of the blobs is rotating with respect to ... in SR, the only rotation that is possible is rotation of one blob with respect to the other blob (when there is nothing else in the entire universe). So inertia becomes even more perplexing.

I think Mach's discussion of this issue profoundly influenced Einstein's thinking as he was originally formulating SR.

[ADDENDUM:] I took a quick look at that Crown book, and didn't see Mach's discussion about the two blobs. I'm drawing a blank right now as to which, of the many relativity books I've studied over the last 30 years or so, contained that discussion.

 

[PAllen]

I believe the conlusion, admitted by Einstein and everyone else, is the while Mach was a philosophic influence on Einstein, the resulting theory (general relativity) is not consistent with Mach's view. No matter what geometry you might ascribe to empty space, there are inertial paths and non-inertial paths a lone object might take, and they are physically distinguishable (while different inertial paths are indistinguishable). General relativity unites inertia in a gravitational field (free fall) with inertia in 'empty space' but does nothing else to explain why it exists in a hypothetically empty universe.

 

[TrickyDicky]

I believe the conlusion, admitted by Einstein and everyone else, is the while Mach was a philosophic influence on Einstein, the resulting theory (general relativity) is not consistent with Mach's view. No matter what geometry you might ascribe to empty space, there are inertial paths and non-inertial paths a lone object might take, and they are physically distinguishable (while different inertial paths are indistinguishable). General relativity unites inertia in a gravitational field (free fall) with inertia in 'empty space' but does nothing else to explain why it exists in a hypothetically empty universe.

Yup, it took Einstein some grieves to realize and accept that after all his theory was not Machian, the first hint came with de Sitter's model, a solution of GR that allowed an empty universe to have inertia and curvature.
After all Mach's philosophy in the form it was formulated is not realized in our universe, except in a twisted sort of way thanks to QFT, if we consider the empty space to have an energy as quantum mechanics implies, and therefore to be a source of gravitational field, since if the equivalence between mass and energy holds this follows, of course Mach died before quantum mechanis was developed, and Einstein never accepted many of the consequences of QM.

 

[gregb134]

I guess wrt Mach's blobs, such a scenario in a causal universe would require that something had set the bulged blob spinning (i.e. there could be no universe with just a blob and a bulging blob spining relative to the first blob and nothing else).

If there was a non-bulged blob there would be at least a 3rd object, say a spaceman that jumped off the side of the blob and set it spinning, or maybe a blob2 and blob3 span off each other and are spinning in opposite directions, conserving momentum.

Maybe Mach's universe is impossible? Or more specifically maybe momentum created out of nothing without any opposite reaction is impossible?

Edit: wrt the truck, I guess you'd regard the box as the bulge on the blob (truck) and the planet as the other blob. Something would have to have set the truck rotating relative to the planet if its box is slipping outwards (I'd just ignore gravity keeping it on the planet and just imagine the truck spinning above the pole of the planet)

 

[DreadyPhysics]

Isn't that kind of hard to say, though? I agree in general that there should have been some force to set the blob in angular rotation... But I just don't know enough about cosmology to say for sure. We're talking about which universes are possible and which are impossible.

 

[gregb134]

Yeah I guess it is hard to say if it's impossible. I sort of tried to turn it into a question/ponder/speculation at the end. I just wonder if we are pondering something that no conceivable universe could have. Maybe it's logically impossible (and maybe logic is the fundamental basis of the laws of physics (oh dear, more lay person speculation)). I have no idea really.

 

[JJRittenhouse]

Yet, we know that in the real universe, there WOULD be a difference in the blobs. Mach concluded that "inertia" must be caused by the sum total of all the other masses in the universe. The blob that is inertial, is the blob that is not rotating with respect to the general collection of all other masses in the universe.
Mike Fontenot

What happens to inertia then as the universe expands? Does this imply that mass may have been "massier" in the past, gradually finding inertia having less and less of an impact as the universe expanded?

If not, then how does the effect of matter on inertia have a limit faster than C?