B Could accelerating expansion be caused by a "spinning" universe?

[metastable]

The subject of the thread summarizes my question: Could the accelerating expansion be explained by a "spinning" universe?

 

[Ibix]

That would imply a special axis about which it is spinning, which would seem to lead to anisotropy even if we lie on the axis. The sky is remarkably isotropic on large scales, so I don't think this is plausible.

 

[PeterDonis]

Could the accelerating expansion be explained by a "spinning" universe?

Why would you expect a spinning universe to lead to accelerated expansion?

 

[metastable]

Why would you expect a spinning universe to lead to accelerated expansion?

If I have a bowl full of jello and suspended coffee beans, and I spin the bowl fast enough, I'd expect the beans to accelerate away from the rotation axis...

 

[PeterDonis]

If I have a bowl full of jello and suspended coffee beans, and I spin the bowl fast enough, I'd expect the beans to accelerate away from the rotation axis...

But that's because you're assuming the bowl is embedded in flat spacetime. For the universe as a whole, spacetime is not flat, so the effects of rotation will not be what your intuition expects.

For example, consider the Godel universe:

https://en.wikipedia.org/wiki/Gödel_metric
It describes a universe full of matter which is rotating, but not expanding (see the "Cosmological interpretation" section of the article).

 

[metastable]

I believe it’s thought there is no “preferred rest frame” in the universe... ie if i’m weightless in a closed elevator I can’t tell whether I’m accelerating in a gravitational field or just coasting through empty space.

On the other hand if the elevator is “spinning” I believe I can infer or measure this from inside the elevator without seeing the rest of the universe.

If the universe has no preferred frame of reference, why am I able to observe that the elevator spins while I’m weightless in the closed elevator? What is the elevator spinning relative to?

 

[PeroK]

I believe it’s thought there is no “preferred rest frame” in the universe... ie if i’m weightless in a closed elevator I can’t tell whether I’m accelerating in a gravitational field or just coasting through empty space.

On the other hand if the elevator is “spinning” I believe I can infer or measure this from inside the elevator without seeing the rest of the universe.

If the universe has no preferred frame of reference, why am I able to observe that the elevator spins while I’m weightless in the closed elevator? What is the elevator spinning relative to?

It's a good question.

You need to be careful with what these phrases actually mean. "Equivalence principle" and "no preferred reference fame" are useful sound bites but in a way they are just that and there is more detail behind what they actually mean.

If we take Newton's first law. That essentially defines inertial reference frames. And those are preferred reference frames. It's that no specific inertial reference frame is preferred.

The same applies in SR.

Moreover, you are able to measure forces on an object. And these forces are independent of the inertial reference frame. So, you could say that an accelerating or spinning object is accelerating or spinning relative to all inertial reference frames.

You could say in fact that acceleration is equivalent to changing your inertial reference frame. That's what acceleration does.

The situation is slightly more subtle in GR, but you can still measure forces and define (proper) acceleration of an object.

One description of proper acceleration in GR is that your worldline is not a geodesic of the spacetime geometry. And that statement is completely independent of any reference frame.

Spinning would be a particular case of proper acceleration and a particular case of a non geodesic worldline.

 

[metastable]

Spinning would be a particular case of proper acceleration and a particular case of a non geodesic worldline.

Would the particles that make up the elevator which are located directly along the free-falling-through-empty space-elevator’s axis of spin also be considered to be in a state of proper acceleration? If not, what are these spinning relative to?

 

[PeroK]

Would the particles that make up the elevator which are located directly along the free-falling-through-empty space-elevator’s axis of spin also be considered to be in a state of proper acceleration? If not, what are these spinning relative to?

If we are talking microscopic particles here then a rigid body is not really a contiguous rigid body. The particles will have thermal motions and quantum mechanical properties.

In addition, the axis of rotation would in general be empty space!

 

[metastable]

If we are talking microscopic particles here then a rigid body is not really a contiguous rigid body. The particles will have thermal motions and quantum mechanical properties.

In addition, the axis of rotation would in general be empty space!

So if the elevator spins at 1000rad/sec, and discharges a single electron into the vacuum, will the electron retain any of the elevator’s classical angular speed or will the electron’s spin be the entirely quantum-mechanical concept of spin? If the emitted electron does retain some or all of the elevator’s 1000rad/sec classical spin, what would this additional spin (above and beyond the intrinsic quantum mechanical spin) be relative to?

 

[metastable]

That would imply a special axis about which it is spinning, which would seem to lead to anisotropy even if we lie on the axis. The sky is remarkably isotropic on large scales, so I don't think this is plausible.

If the universe as a whole were not only spinning, but precessing as well, and both spin rate and precession rate were increasing, can this lead to isotropic accelerating expansion? The thought of a spinning ice skater bringing in their arms leading increased angular speed comes to mind... or a spinning precessing ball which is shrinking in size as it cools.

 

[Bandersnatch]

By anisotropy @Ibix meant that a spinning thing, be it skater or a universe, looks different along the axis of rotation than perpendicular to it. Whether it also precesses makes no difference in this regard.

 

[PeterDonis]

If the universe as a whole were not only spinning, but precessing as well, and both spin rate and precession rate were increasing, can this lead to isotropic accelerating expansion?

No. There is no way for any kind of spinning to look the same in all directions.

 

[metastable]

By anisotropy @Ibix meant that a spinning thing, be it skater or a universe, looks different along the axis of rotation than perpendicular to it. Whether it also precesses makes no difference in this regard.

No. There is no way for any kind of spinning to look the same in all directions.

I guess I'm confused because I thought that adding a second axis of rotation would alter the vectors of the centrifugal forces experienced by particles in a reference frame with both accelerating rotation and accelerating precession...

For example suppose I have a large spherical tank of jello on a two axis motorized gimbal with evenly dispersed coffee beans within the jello. One of the coffee beans somewhere in the middle represents myself and the other coffee beans represent distant galaxies.

In the first test I only spin up the tank to 10,000rad/sec along the vertical axis. In this test, from the rest frame of the tank I expect to see all beans move away from the single axis of rotation (but some of the beans appear to be moving roughly in parallel). In this case, from my perspective as a bean, many of the beans appear to be moving away from me but the beans directly vertically above and below me appear stationary relative to myself, because "we" are experiencing roughly the same centrifugal force along the roughly the same angle vector away from rotation axis.

In the second test I not only spin up the tank to 10,000rad/sec along the vertical axis, but I also accelerate the rotation of tank with the same acceleration rate to the same 10,000rad/sec along the second horizontal axis.

I have to admit I don't know exactly what would happen, but based on intuition, from the rest frame of the tank, rather than seeing all beans move away from the single axis of rotation, I expect I would see the beans radiate away from the "center" of rotation. In this case, from my perspective as a bean, I now expect ALL of the beans to appear to be moving away from me, because I expect the vector and/or magnitude of the centrifugal force should be different at all points in space within the tank-- and from my rest frame as a bean, I expect it would appear that ALL beans are accelerating away from me (except the ones that reach the edge of the tank), with the beans that are farther away appearing to accelerate faster. If this is not what would happen exactly in the jello-tank analogy please let me know as it is an entirely intuition-based assessment.

 

[Ibix]

I guess I'm confused because I thought that adding a second axis of rotation would alter the vectors of the centrifugal forces experienced by particles in a reference frame with both accelerating rotation and accelerating precession...

It will change the axis. But it will never make the universe look isotropic. It just gives you a time-varying anisotropy.