Gravitational attraction on the cosmic scale?

[Chalnoth]

I am afraid I don't agree. No pressure means no (ex)change of energy. i.e. pressureless particles can still carry constant kinetic energy>0. With no forces acting on them this energy is indeed constant.

What do you mean by a "pressureless particle"?

Pressure is not a function of an individual particle, but instead of a fluid of particles.

 

[Vincentius]

Ok. I mean radially moving particles (Hubble flow) which do not collide. I suppose this is a pressureless fluid.

 

[Chalnoth]

Ok. I mean radially moving particles (Hubble flow) which do not collide. I suppose this is a pressureless fluid.

If your particles' only motion is the Hubble flow, then those particles are not moving with respect to the Hubble flow, and thus have no kinetic energy compared to said flow and produce no pressure.

 

[Vincentius]

Indeed, no pressure. But no kinetic energy? That depends on the definition of kinetic energy, but I don't know the answer. There must be kinetic energy in the receding masses. Imagine what would happen if everything moves at the same speed but inward. Kinetic energy is a relational property between masses, hence this favors a Machian definition of kinetic energy between every pair of masses (Schrödinger!). Kinetic energy relative to an imaginary frame is physically meaningless.

Again I don't know the answer. The point though is that if there is kinetic energy stored in the cosmic recession of matter (by whatever definition), then it is conserved since net force is zero.

 

[Chalnoth]

Indeed, no pressure. But no kinetic energy? That depends on the definition of kinetic energy, but I don't know the answer. There must be kinetic energy in the receding masses. Imagine what would happen if everything moves at the same speed but inward. Kinetic energy is a relational property between masses, hence this favors a Machian definition of kinetic energy between every pair of masses (Schrödinger!). Kinetic energy relative to an imaginary frame is physically meaningless.

Again I don't know the answer. The point though is that if there is kinetic energy stored in the cosmic recession of matter (by whatever definition), then it is conserved since net force is zero.

You have to use the definition that's relevant to the situation at hand. In this case, the relevant frame of reference is the co-moving frame of reference.

It's easier if you think of it as an expanding gas than as a set of individual particles.

 

[Vincentius]

Exactly: relevant for kinetic energy is relative motion between particles. Nothing else. Speed, and so kinetic energy, of an object in otherwise empty space is non-observable and (therefore) physically meaningless. It needs a second object to become physically meaningful.

 

[Vincentius]

Don't you recognize it? It's a standard paradox. Nothing to do with cosmology or general relativity, it results from attempting to apply theorems relating to Laplace's Equation to a source with an infinite uniform distribution. It can be the Newtonian gravitational potential of a mass distribution, the electrostatic potential of a charge distribution, etc. (a) of course is the correct answer.

Bill_K, could you elaborate on this? What standard paradox are you referring to? Any references?

 

[Chalnoth]

Exactly: relevant for kinetic energy is relative motion between particles. Nothing else. Speed, and so kinetic energy, of an object in otherwise empty space is non-observable and (therefore) physically meaningless. It needs a second object to become physically meaningful.

Nope. Especially not in a curved space-time (e.g., an expanding universe), where the definition of the relative velocity of two far-away particles is arbitrary.

Here the only reason kinetic energy was brought up in the first place was in the context of a thermal fluid where the pressure of the fluid is proportional to the average kinetic energy of the particles that make up said fluid. The average motion of the fluid plays no role whatsoever in determining this pressure: it is only the relative motions of the individual particles. So the correct frame of reference is the comoving frame.

 

[Vincentius]

The universe appears flat, not? GR is a local theory, therefore may have/has difficulties with non-local relationships. The ambiguity this causes in concepts like kinetic energy and gravitational potential make some people make statements like these concepts do not exist on cosmic scales. Or become nill, as you see it wrt kinetic energy. At what distances these elementary concepts cease to exist or vanish? There is no clear transition between bound and unbound matter.

I understand pressure of a fluid is related to the average kinetic energy of the particles, but this is thermal (random) motion. Uniform recessional motion like in the universe is without collisions, i.e. no thermal pressure. But why would this not carry kinetic energy? Again, imagine what happens in a big crunch. No energy?

 

[Chalnoth]

The universe appears flat, not?

Flat space, curved space-time. The curvature that we see manifests itself as the expansion of our universe.

GR is a local theory, therefore may have/has difficulties with non-local relationships.

That's not really relevant to the issue. All of our theories of physics are local (or can be written down in a local manner). They usually don't have this peculiar issue of not being able to compare velocities of far-away objects.

I understand pressure of a fluid is related to the average kinetic energy of the particles, but this is thermal (random) motion. Uniform recessional motion like in the universe is without collisions, i.e. no thermal pressure. But why would this not carry kinetic energy? Again, imagine what happens in a big crunch. No energy?

And that's why recession velocity doesn't play a part in pressure.

Again, context. Sure, you can define a kinetic energy that these particles would have, but it's a definition that is meaningless in the context of this discussion.

 

[Vincentius]

Again, consider a finite sphere of matter, instead of the force a single particle feels.

Chalnoth, this coincides with view b) in my original post, if I am right. I suppose you also agree with view a) (net force zero)? Then would you state that both views hold, i.e. there is no paradox?

 

[Chalnoth]

Chalnoth, this coincides with view b) in my original post, if I am right. I suppose you also agree with view a) (net force zero)? Then would you state that both views hold, i.e. there is no paradox?

Sorta kinda. It coincides with the statement that there is no net force from the point of view of the particle in the center of your coordinate system.

If you think about it, this must be the case: the particle in the center doesn't move at all. It has zero acceleration, so it must have zero net force, from that perspective. This statement is unchanged no matter which particle you choose to be at the center of your coordinate system.

The statement does not hold, however, for particles away from the center of the coordinate system, as you can see by examining the force of the atoms on the surface of a hypothetical sphere which is centered at the origin in that particular coordinate system. Those particles will have a net force.

If it seems odd that those particles would have a net force in one frame and not another, bear in mind that these reference frames are accelerated relative to one another, so of course the forces are going to be different as well.

 

[Vincentius]

Chalnoth, I can imagine both a) and b) hold, but still am not sure about b).

Bill_k, Marcus and Mordred reject b), so no consensus. Anyone to comment?