Trapped light: redshift or not?

[Yoo]

If light from billions of years ago were trapped within a perfectly reflecting mirrored box, will it be redshifted in a way comparable to light from galaxies billions of light-years away? I had made up this http://blog.chungyc.org/2009/03/redshift-puzzle/" as a supposed illustration of how the redshift in distant galaxies is not due to them moving away but rather because of the expansion of the universe itself, but I worry that it doesn't work out the way I think it would. (Although I should have probably mentioned that the box should be very far away from any significant concentrations of mass.)

I can only think of two real reasons why light trapped in such a box won't be redshifted:

1. Even in principle, the gravity from the box itself or even the photons themselves would be sufficient to locally cancel out any expansion.
2. Even with a sufficiently large box, say a hundred kilometers on each side, quantum mechanics will prevent any significant shifting in the frequency of the trapped light.

I don't think that the couple of possible objections above would really apply, but I'm not sure (I'd probably have to spend a year absorbing the background and working it out). How does everyone else think the thought experiment would work out?

 

[v2kkim]

During each travel of light from one side to the other, it will have a tiny redshift. Therefore it will have a regular redshift as a light coming from a remote star. The redshift amount will depends on how much space expansion has proceeded from the time light emitted to present. I agree the box will be in the same size but it does not matter.

 

[Yoo]

The size of the box shouldn't matter much (I think), but keeping it the same size would prevent confusion over the redshift being due to Doppler shift as the walls move away from each other. It would highlight how the redshift is due to the expansion of the universe itself rather than because distant galaxies are "moving away" by showing that the light is still redshifted even when nothing is moving.

Or at least I think it would: if the thought experiment doesn't work out the way I think it does, I can't use it as a clue stick on people who misunderstand the expansion of the universe (who also often wonder how anything could move faster than light).

 

[cesiumfrog]

The size of the box shouldn't matter much (I think), but keeping it the same size would prevent confusion over the redshift being due to Doppler shift as the walls move away from each other.

But now the walls of the box aren't inertial; they are locally being pulled toward one another to prevent their separation from increasing along with the universe's expansion.

I'm inclined to guess that if the walls were allowed to expand, the red-shift would be the same as if the walls were not there. Therefore, I wonder if your box may actually cancel the effect.

 

[v2kkim]

... the expansion of the universe (who also often wonder how anything could move faster than light).

The space expansion is a quite strict and a kind of high level principle which defy even special relativity application. You can try a new theory but in general people simply do not apply special relativity to space expansion matter. Universe expansion is just an expansion happening, for which we may try to consider more fundamental reason and some relationship with other parameters like mass, dark matter etc. But this expansion affects light propagation since the road itself expands while the light travels, causing redshift.

 

[Chronos]

Redshift due to expansion is indistinguishable from redshift due to the doppler effect. The problem arises for objects with redshifts greater than z = 1. Expansion is the only suitable alternative explanation at present.

 

[cesiumfrog]

The problem arises for objects with redshifts greater than z = 1.

What problem is that?

 

[Yoo]

But now the walls of the box aren't inertial; they are locally being pulled toward one another to prevent their separation from increasing along with the universe's expansion.

I'm inclined to guess that if the walls were allowed to expand, the red-shift would be the same as if the walls were not there. Therefore, I wonder if your box may actually cancel the effect.

Great point. Now that I think about it again, another way to look at the problem is to realize that the expansion of space could be modeled as stuff simply moving away for short distances, so keeping the walls of the box still would result in no redshift. So much for my attempt to illustrate how the expansion of the universe shouldn't be viewed as everything just moving away from each other ...

Then again, modeling the expansion of space as just stuff moving away from each other might not be a good approximation for large time. I'm getting confused again ...

 

[Yoo]

The space expansion is a quite strict and a kind of high level principle which defy even special relativity application. ... But this expansion affects light propagation since the road itself expands while the light travels, causing redshift.

I understand this, but I wanted something that clearly shows that "expansion of the universe" is not quite "stuff just moving away from each other" without going into the subtleties of distances and speeds over large scales.

Unfortunately, it seems my efforts are futile in that anything local won't be able to show the difference. And anything over large distances would have to go into the subtleties over what distance, speed, etc. might mean for distant objects, and how the speed of light limit doesn't apply, something I had hoped would have been avoided in the thought experiment with my mirrored box. :(

 

[Ich]

That's a tricky question.

If the universe were "free floating", i.e. the expansion neither accelerating nor decelerating, there would be no redshift at all.
Now, if there is matter between the walls (technically: $$T^{\alpha}_{\alpha}>0$$), and the walls were each free floating, they would approach each other due to the "attraction" of said matter. Keeping them at a fixed distance means that at least one of the walls must feel an outward proper acceleration.
If the box is symmetric, both walls are accelerated the same amount, and no redshift is observed.
If, by asymmetric construction or an external force, one of the walls (A) is not accelerating, i.e. comoving (free floating), the other wall (B) is constantly accelerated away. In this case, B sees the light coming from A as redshifted, A sees light coming from B as blueshifted. Both see light that they send out and observe after it comes back from the other wall as not shifted at all.

The outcome of the experiment is not dependent on whether the global energy/pressure density implies an accelerating or decelerating universe, but only on local energy/pressure density. If it is performed near a galaxy with a high dark matter density, it will show the above result, despite the universe as a whole being subject to accelerated expansion.

If the energy density varies significantly during the experiment, it becomes even more complicated.

 

[cesiumfrog]

If [..] the expansion [were] neither accelerating nor decelerating, there would be no redshift at all.

Are you sure?

 

[Ich]

Are you sure?

Quite sure. There may be errors in my post, but this particular statement should be correct.

 

[cesiumfrog]

I thought we called it the Hubble redshift because we explained it long before we discovered the expansion might be accelerating?

 

[George Jones]

Quite sure. There may be errors in my post, but this particular statement should be correct.

It's not.

The cosmological wavelength shift is the ratio of the scale factor at the time of reception to the scale factor at the time of emission. As long as there is expansion (linear, accelerating, decelerating, etc.) between the two times, there will be a redshift.

 

[chronon]

It's not.

The cosmological wavelength shift is the ratio of the scale factor at the time of reception to the scale factor at the time of emission. As long as there is expansion (linear, accelerating, decelerating, etc.) between the two times, there will be a redshift.

Sorry, this is just wrong. Whatever myths may have grown up about the 'expansion of space', linear expansion is precisely equivalent to objects moving apart in special relativity, and in this case it is clear that light in a non-expanding box would not show redshift.

 

[George Jones]

Sorry, this is just wrong. Whatever myths may have grown up about the 'expansion of space', linear expansion is precisely equivalent to objects moving apart in special relativity, and in this case it is clear that light in a non-expanding box would not show redshift.

By "linear," I meant that the FRW scale factor is proportional to cosmological time, and, in this case, there most definitely is a redshift.

 

[chronon]

By "linear," I meant that the FRW scale factor is proportional to cosmological time, and, in this case, there most definitely is a redshift.

That's what I meant too, a(t)=t, and I say there definitely isn't a redshift.

 

[George Jones]

That's what I meant too, a(t)=t, and I say there definitely isn't a redshift.

Then your view is very non-mainstream.

I just picked at random three general relativity texts off my shelf, and they all corroborate what I wrote.

 

[Ich]

The cosmological wavelength shift is the ratio of the scale factor at the time of reception to the scale factor at the time of emission. As long as there is expansion (linear, accelerating, decelerating, etc.) between the two times, there will be a redshift.

Hi George,

your analysis applies to comoving observers only. In this Gedankenexperiment, the walls are thought to stay at a constant distance, i.e. not comoving - at least one of them.