Basic questions about general relativity concepts

[bcrowell]

No, this is extremely misleading. There is no "expansion of space" in that sense,

If you like that interpretation, that's fine, but it is a minority interpretation. This is basically an issue of pedagogy and personal preference.

A well-known paper against the expansion interpretation is this one: E.F. Bunn and D.W. Hogg, "The kinematic origin of the cosmological redshift," American Journal of Physics, Vol. 77, No. 8, pp. 694, August 2009, http://arxiv.org/abs/0808.1081v2

Here is a paper that makes the case for the expansion interpretation: http://arxiv.org/abs/0707.0380v1

It is a serious drawback of the "expanding space" idea that it leads to the assumption that everything has a tendency to be stretched somehow. This is not true.

That's an important pedagogical issue, but it doesn't mean that the expansion interpretation is wrong.

 

[Ich]

As I've been saying in this thread, I think there would be a tendency for everything to get stretched if mass had actually been distributed homogeneously.

I agree. You can trace this tendency back to a repulsive acceleration due to DE. Generally, if ä>0 in an exactly homogeneous universe, there is a tendency to expand. If ä<0, there's a tendency to contract. The important thing - and my point - is: this tendency is totally independent of H. It doesn't matter if the universe is contracting or expanding. What matters is if it does so in an accelerated way.

For example, the solar system isn't expanding because its distribution of matter is nothing at all like in a FLRW solution.

There are two inhomogeneities involved: If you removed all normal matter (and stopped the thest planets' motion for simplicity), there'd still be a tendency to contract, because we have a very high DM density here. Its gravity is more than enough to counter the DE "push".
Which is my second point: in a non-homogeneous universe, the behaviour of test particles is completely determined by the effective energy density (trace of T, including DE) in the interesting region. You don't have to know anything about the rest of the universe, as long as said rest is approximately spherycally symmetric. Again, the expansion of the universe is irrelevant.

 

[Ich]

Hi If there is no expansion of space in the sense of an expanding matrix or medium
then how do you explain the expansion of wave length??

Explaining means to trace back to well-know physics. In order to do so, you use a static coordinate system instead of the expanding one. Then, redshift is seen to be a combiantion of Doppler shift and gravitational redshift.
The problem is that it's hard to have a static coordinate system if everything is changing. It will always work for a region of a few Gly and Gy, but not for the whole universe all the time.
So you'll still want to use expanding coordinates, but remember that these don't introduce any new physical effects to small scale physics.

On peculiar velocities; are you suggestin that two stars at rest wrt each other would not expand with the rest of the universe?

Yes. Depending on where they are, they will accelerate either towards each other or away from each other, but never follow the expansion of the rest of the universe. (with the exception of an exponentially expanding universe)

 

[Ich]

If you like that interpretation, that's fine, but it is a minority interpretation.

Let me emphasize some parts of the passage you're referring to, this time including the context:

As far as I understand it the redshift due to expansion theory is based on the assumption that light waves are expanded and have longer wave lengths due to the expansion of space(matrix) as a medium .

No, this is extremely misleading. There is no "expansion of space" in that sense

I don't think I'm advocating a minority interpretation here. You'll find very few papers advocating the expansion of space as a medium, dragging things with it. The paper you cited is especially clear about that point.

This is basically an issue of pedagogy and personal preference.

Of course.

It is a serious drawback of the "expanding space" idea that it leads to the assumption that everything has a tendency to be stretched somehow. This is not true

.
That's an important pedagogical issue, but it doesn't mean that the expansion interpretation is wrong.

It didn't say it is wrong. I said it's extremely misleading, that's a statement about pedagogics and heuristics. A statement that's easy to defend, IMHO.
Example:
The paper "Expanding Space: the Root of all Evil?" is a good one. And it's written by experts. Still, it contains one factual (mathematical) and one connected pedagogical/heuristical error which, I condend, would not have happened if the authors had checked against static coordinates, where we all actually understand what we're doing and don't have to rely on the abstract mathematical result alone. Can you spot it?

 

[Ich]

Hi Fredrik, bcrowell,

I'd very much appreciate if you'd comment on what I've written. This is not exactly the first time I describe my point of view, and not for the first time the discussion then ends abruptly. This could mean that I'm saying something obvious but failed to express myself clearly, that I'm misguided in a way that further discussion is useless, that it's not interesting, or that you agree.

 

[Fredrik]

Hi Ich. Sorry about that. I have to do something else right now, but I'll try to write something a few hours from now. I think I just forgot about this thread because I have a lot of other things on my mind, and also other threads going on.

 

[Fredrik]

I agree. You can trace this tendency back to a repulsive acceleration due to DE. Generally, if ä>0 in an exactly homogeneous universe, there is a tendency to expand. If ä<0, there's a tendency to contract. The important thing - and my point - is: this tendency is totally independent of H. It doesn't matter if the universe is contracting or expanding. What matters is if it does so in an accelerated way.

This looks wrong to me. I would say that there's a "tendency to expand" even when $\ddot a=0$. The reason is the geometry in the solar system is much better approximated by something like a Schwarzschild solution (where there is no expansion of space) than by a FLRW solution, because matter isn't distributed homogeneously and isotropically at these scales. This implies that measuring devices don't expand and that intergalactic distances do. It's precisely the fact that measuring devices don't expand (or that they at least do it at a much smaller rate) that makes redshift observable.

After taking a quick look at the papers bcrowell linked to and the discussion between you and him, I would say that the answer to the question of what causes the redshift depends on what coordinate system we're using. If we're using a FLRW system, the cause is indeed that the light expands along with the cosmological expansion (while measuring devices don't). If we're using our local inertial frame (in which the simultaneity lines are geodesics that are tangent to a hypersurface of constant FLRW time), the cause is a doppler shift.

 

[Ich]

This looks wrong to me. I would say that there's a "tendency to expand" even when $\ddot a=0$.

Ok, I'll derive my points of view here, it's just a few lines.
Take the radial equation of free motion in a FRW universe (slow speed limit is enough):
$$2\dot a \dot r + a \ddot r = 0$$
Pick an origin and switch to "proper distance coordinates" $x=a\,r$ where
$$\ddot x = \ddot a r + 2\dot a \dot r + a\ddot r$$
Combined you get
$$\ddot x = r\ddot a$$
which becomes zero for $\ddot a = 0$. With this equation it's easy to calculate the effect of expansion on bound systems. This is my first point.

Next step is not to take $\ddot a$ as the cause of that perturbation term in the equation of motion, but to look for a common cause of the perturbation and $\ddot a$. Insert the second Friedmann equation,
$$\frac{\ddot{a}}{a} = - \frac{4\pi G}{3}(\rho + 3p)$$
you get
$$\ddot x = -x\frac{4\pi G}{3}(\rho + 3p)$$
which shows that the perturbation is nothing else than the gravitation of an effective mass density $\rho + 3p$. This is not surprising:
Birkhoff's theorem tells us that, if we regard a ball around an arbitrary origin, the dynamics inside the ball is completely unaffected by the outside universe ($\dot a, \ddot a$ cannot alter the dynamics). Any changes have to come from within the ball.
To calculate the dynamics, remove all the matter/energy inside the ball. You're left with flat space. Then add local energy again as a perturbation, you get the complete dynamic behaviour, with the Newtonian approximation sufficient for almost every purpose. This is my second point.
It's as if the outside universe doesn't exist, which is a necessary consequence of Birkhoff's theorem.