A cosmologically redshifting puzzle in a box

In the comments for another blog post about cosmological distances, I suggested a thought experiment that would highlight how the redshift from distant galaxies is not due to a Doppler shift, that is, light from very distant galaxies is not redshifted because of the movement of the galaxies, but rather because the intervening space itself is expanding:

If someone managed to trap light when the universe first became transparent, about 300,000 years after the Big Bang, inside a perfectly reflecting mirrored box such that the light is contained in perpetuity, what would have happened to the wavelength of the trapped light by now?

We'll allow ourselves the reasonable assumption that the size of the mirrored box does not change because the electromagnetic, strong, or weak forces that maintain its shape overwhelms any tendency for the box to grow along with the expansion of space.

If the redshift seen in the light from distant galaxies is really just due to a Doppler shift as they speed away from us, then there should be no reason for the light trapped in the mirrored box to shift wavelength. However, the redshift in light from distant galaxies is mostly not due to their movement away from us: it is mostly due to the light being stretched along with the expansion of space. For the same reason, the light in the mirrored box should also be redshifted as the expansion of space stretches the light while it bounces around inside the box. If we were to open the box today, we should see light that has been redshifted by an amount comparable to what the cosmic microwave background has gone through. The result should emphasize how the redshift from distant galaxies is not a Doppler shift.

Or at least this is what I think would happen. Different responses could be:

  1. I completely misunderstand the expansion of the universe.
  2. Quantum mechanical behavior prevents light from being stretched within an enclosed space.
  3. When the light interacts with the walls of the mirrored box, something happens that prevents the redshift.
  4. Any physical enclosure with fixed size necessarily "shields" the space inside from the expansion that goes on in the rest of the universe.
  5. There can be no such thing as a perfectly reflecting mirror box: the thought experiment does not even make sense.
  6. The entire universe is only several thousands of years old: it only looks like it's billions of years old and expanding.

I don't think any of the objections above are valid, but I could be missing something vital, and neither does it mean that I may have missed some other fatal flaw in my reasoning. Anyone else want to take a stab at what they think would happen in the thought experiment?

5 thoughts on “A cosmologically redshifting puzzle in a box”

  1. "Anyone else want to take a stab at what they think would happen in the thought experiment?"

    Um ... no??!! Mai brainz still hurtz. :-(

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