An infinite universe is necessarily in expansion

[Rip]

What do you think of this argument?

Lets suppose an infinite and eternal universe that is homogenous on a large scale. Since there is no privileged inertial reference frame, regardless of the chosen inertial reference frame, the observed statistical velocity distribution of matter is nearly the same. But that also implies that the maximum observed 4-momentum is unbound, and the only way to avoid collisions liberating an infinite amount of energy is for particles whose observed 4-momentum is infinite to be infinitely far away, and that requires a statistical correlation between position and four-velocity that can also be understood as cosmological expansion. Thus an infinite universe is necessarily in expansion.

 

[Bill_K]

Since there is no privileged inertial reference frame

The laws of physics are the same in every inertial reference frame, but all frames do not have to be observationally equivalent in a given universe. In our universe, for example, the rest frame of the cosmic background radiation is unique.

 

[PeterDonis]

Since there is no privileged inertial reference frame, regardless of the chosen inertial reference frame, the observed statistical velocity distribution of matter is nearly the same.

This does not follow. "No privileged inertial reference frame" just means the *laws* of physics have to look the same in every inertial frame. It doesn't mean that every particular *solution* to the laws has to look the same in every inertial frame. The velocity distribution is a feature of particular solutions, not of the laws themselves.

Also, factually speaking, the quoted statement is false: the observed statistical velocity distribution of matter in our actual universe (which we believe, on our best current understanding, to be spatially infinite) is *not* the same, or even nearly the same, in every inertial frame. There is a particular frame in which the velocity distribution is isotropic; in frames that are moving with a large velocity relative to that frame, the velocity distribution is highly anisotropic.

 

[Rip]

You are right, there is a leap of logic.

It is aesthetically pleasing to imagine a universe that has the same symmetries as the underlying theory, but that need not be the case.

So if we accept as an hypothesis that regardless of the chosen inertial reference frame, the observed statistical velocity distribution of matter is nearly the same, it would follow that such a universe would be in expansion, wouldn't it?

 

[Rip]

The rest frame of the cosmic background radiation is unique.

Is there evidence backing up that statement?
We shouldn't be taking everything in BB theory as a proven fact.

Why should our inertial frame be the special one? Is it by coincidence? Isn't that aspect of BB theory very anti-Copernican and anthropocentric?

I know BB is the theory we have that is most consistent with observations, but how could it not be if thousands of scientists keep fine tuning things such as inflation and dark energy to make it be consistent with observations?

 

[Bill_K]

Why should our inertial frame be the special one?

It is not. Our inertial frame happens to be moving with respect to the rest frame of the CMB by 369 km/sec.

 

[Rip]

Yes of course, you are right. But on a cosmological scale, that is not very a big relative velocity, or is it?

In any case do you agree that a universe that looked the same regardless of the inertial reference frame of the observer would be necessarily in expansion?

My reasoning is that otherwise collisions of unbounded energy would occur as there are no bounds to the 4-velocity of the observer.

 

[marcus]

Is there evidence backing up that statement?
We shouldn't be taking everything in BB theory as a proven fact.

Why should our inertial frame be the special one? Is it by coincidence? Isn't that aspect of BB theory very anti-Copernican and anthropocentric?...

It is not. Our inertial frame happens to be moving with respect to the rest frame of the CMB by 369 km/sec.

Recent detailed confirmation:http://arxiv.org/pdf/1303.5087 (one of the Planck mission reports that came out in March of this year)
==quote, page 1==
Observations of the large cosmic microwave background (CMB) temperature dipole are usually taken to indicate that our Solar System barycentre is in motion with respect to the CMB frame (defined precisely below). Assuming that the observed temperature dipole is due entirely to Doppler boosting of the CMB monopole, one infers a velocity v = (369 ± 0.9) km s⁻¹ in the direction (l, b) = (263.99◦ ± 0.14◦ , 48.26◦ ± 0.03◦ ), on the boundary of the constellations of Crater and Leo (Kogut et al. 1993; Fixsen et al. 1996; Hinshaw et al. 2009).
==endquote==

The Hinshaw et al 2009 article http://arxiv.org/pdf/0803.0732.pdf has it's finding on page11. The dipole (i.e. motion of solar system relative to CMB rest frame) has been well-measured for around 30 years. That is, we've known the approximate 370 km/s speed and direction since roughly 1980. If you google "CMB dipole" one of the top hits is a "history of CMB dipole" by Ned Wright which discusses ground-based measurements going back even before 1980.

The constellation Leo is easy to recognize so I always remember it as a marker of the direction that the solar system is sailing relative to universe-rest. Constellation Crater (the wine cup) is just a bit to the south of Leo, when Leo is overhead. The Wine Cup stars are dim so it's hard to see, but Leo has some bright stars and a distinctive shape.

Nights in April are a good time to see the direction in the sky that we are going (relative to cosmic rest).
When the Big Dipper is on the meridian (the sky's northsouth midline)
http://en.wikipedia.org/wiki/File:Ursa_Major_IAU.svg
look for the two stars Dubhe and Merak that define the west side of the dipper bowl (opposite the handle) and make a line pointing south towards Leo
http://en.wikipedia.org/wiki/File:Leo_IAU.svg

 

[marcus]

... do you agree that a universe that looked the same regardless of the inertial reference frame of the observer would be necessarily in expansion?

My reasoning is that otherwise collisions of unbounded energy would occur as there are no bounds to the 4-velocity of the observer.

Your reasoning assumes the presence of MATTER to have collisions with.

How could a universe containing matter "look the same" to every observer?

I think your reasoning is based on self-contradictory assumptions.

In our universe because we are moving we see a Doppler "hot spot" in the sky.
If we went faster the spot (around constellation Leo) would get hotter. If we went fast enough the CMB radiation would burn us up.

Different observers will see hotspots with different temperatures in different places in the sky. So things will not "look the same" to different observers. So the assumption itself simply does not make sense.

==========
Before 1998 when the cosmological constant was measured and determined to be a small positive curvature, it was believed the constant was zero, and it was considered possible that we lived in a universe that would eventually stop expanding. The Hubble rate H would go to zero and might even (if there was enough matter density) become negative.

Simply by observing CMB one cannot rule out the possibility that expansion has already turned around and the universe is in CONTRACTION---towards a "crunch".

It takes more/different kinds of observations to rule out the possibility that we are in contraction.

So your reasoning is inadequate for two reasons:
1. it is based on a self contradictory assumption (so falls down logically)
2. it is too simple No argument that simple could exclude the case that we are in a universe which HAD been expanding but had gone thru that stage and begun to collapse.

It takes more observational data to rule that out. Based on observations we now think that the universe will, in fact, continue expanding indefinitely and will NOT collapse. But that is not a trivial piece of information. And one needs to have redshift data to conclude that, whatever the future holds, it is currently in expansion.

 

[timmdeeg]

In any case do you agree that a universe that looked the same regardless of the inertial reference frame of the observer would be necessarily in expansion?

My reasoning is that otherwise collisions of unbounded energy would occur as there are no bounds to the 4-velocity of the observer.

In curved space-time you can define inertial reference frames only locally. Which means any collisions will happen with v < c. In other words two masses with relative velocity v > c will never collide. To avoid collisions at all you can think of all masses being in rest with respect to the CMB.

There are other reasons that the universe can't be static, remember Einstein.

 

[marcus]

In curved space-time you can define inertial reference frames only locally. Which means any collisions will happen with v < c. In other words two masses with relative velocity v > c will never collide. To avoid collisions at all you can think of all masses being in rest with respect to the CMB.
...

Yeah. He said " collisions of unbounded energy would occur as there are no bounds to the 4-velocity of the observer."
But I think he meant to say "4-momentum".

But even with that correction, the argument does not make sense.

As you suggest, to good approximation we can think of all the galaxies as at rest w/ respect to CMB. Their motions in their local CMB rest frame are only a few hundred km/s.
So we do NOT see collisions with arbitrarily high kinetic energy. To collide, galaxies have to be in the same local frame, so when we see galaxies colliding it is only with speeds of a few hundred, not arbitrarily high.
Expansion is not required for this to be the case. It would also be true in early stages of contraction

 

[Rip]

Expansion is not required for this to be the case. It would also be true in early stages of contraction

Thanks for your correction. A monotonic dependence of relative velocity as a function of distance seems to be all that is required. Thus I suspect that either expansion or contraction are required to avoid high energy collisions in a hypothetical universe that looked roughly the same regardless of the inertial frame of the observer. If that is what you meant, I fully agree with you. Sorry if I misunderstood.

 

[timmdeeg]

But that also implies that the maximum observed 4-momentum is unbound, and the only way to avoid collisions liberating an infinite amount of energy is for particles whose observed 4-momentum is infinite to be infinitely far away, ...

As Marcus said local relative velocities are small. The reason is the expansion of the universe which increases the distances and thus 'works' against high local velocities.

But how are things in flat space-time? Imagine two bodies which are accelerating from infinity towards each other. Even in this case the kinetic energy of the collision is finite, because according to Special Relativity the relative velocity of two bodies doesn't reach lightspeed.

 

[andrewkirk]

I don't think it is possible for there to be a universe that 'looks the same' from all inertial frames, even if we limit those frames to being in a small neighbourhood of a single point.

In any hypothetical universe at all, even without any CMBR, we can measure the average red-shift of visible objects in different sectors of the sky, just by performing an arithmetic average of the red-shifts over all visible objects (for which we are able to estimate the red-shift) in a given sector . Represent the average red-shift in each sector by a vector pointing to the centre of the sector, of magnitude equal to the size of red-shift, and pointing in the opposite direction if it's a blue shift. We then add those vectors over all sectors of the sky sphere and get an overall red-shift 3-vector in a certain direction. We can then convert that to a notional velocity 3-vector using the formula that would apply if the red-shift was interpreted as purely Doppler effect from relative motion. I suspect that a process something like that is what leads to the figure of 369 km/sec quoted above, except that the process probably uses the CMBR rather than visible objects like stars.

If we use a different inertial frame we'll get a different 3-vector, which will be the vector sum of the previous one and the velocity boost of the new frame relative to the old one. Subjectively, the stars will look bluer in the direction of the boost in the new frame than they did in the old frame.

 

[Rip]

The universe I am imagining would not look the same for arbitrary combinations of position and inertial frame (that is impossible), it would be a universe in expansion that would only look the same for combinations of position and inertial frame such that the immediate environment of the observer is at rest with the observer.

 

[timmdeeg]

I don't think it is possible for there to be a universe that 'looks the same' from all inertial frames, even if we limit those frames to being in a small neighbourhood of a single point.

The point is that the universe looks the same for all Fundamental Observers (provided the Cosmological Principle holds), those which move with the Hubble flow. Inertial observers not at rest with respect to local FO's will see the redshift of galaxies in cosmological distances as a function of the direction.

 

[andrewkirk]

The universe I am imagining would not look the same for arbitrary combinations of position and inertial frame (that is impossible), it would be a universe in expansion that would only look the same for combinations of position and inertial frame such that the immediate environment of the observer is at rest with the observer.

This is not a well-defined concept, and cannot be well-defined in such a way that it leads to the conclusion suggested in the OP. How big is the observer's immediate environment? What if she's in a spaceship moving fast wrt the CMBR? What if she's in a star on the outer rim of a rapidly rotating galaxy? What if she's in a galaxy that is moving rapidly wrt the CMBR? Different definitions of "immediate environment" lead to different co-moving inertial frames. In each of my three examples the observer is at rest wrt her immediate environment, and what changes is that the definition of immediate environment gets larger as we move through the examples - from the walls and contents of the space ship, to the solar system containing the spaceship, to the galaxy containing the spaceship. Yet in every case the observer is moving rapidly wrt the CMBR.