Can you use an infinite line of reflectors to send light to the edge of the Universe?

What a good question! Both groups of teachers make very good points. It turns out that there are a few things to consider:

1. Although we like to think of everyday mirrors as "perfect" reflectors, they aren't: a little bit of light is absorbed (and therefore lost) with each reflection. The same is true with transmission through a clear material like glass: in this case, a little bit of the light impinging on the glass is actually reflected instead of transmitted (we've all seen faint reflections against a glass window; that's a manifestation of this effect). Since a little bit of light is lost with each reflection of a normal mirror, we can't "reflect" the light to the edge of the Universe.

But who says that we have to use real-life mirrors? Let's assume that we have access to "perfect" mirrors, that reflect all of the light that we impinge on them. Let's also assume that we can place these mirrors anywhere we want in the Universe with infinite accuracy, that no other objects in the Universe (or light from these objects) contaminates our experiment, and that we can measure the energy of each photon in the light we send out with infinite accuracy at each stage. Now can we reflect it infinitely, as the first group suggests?

2. The second group has a good point about the expansion of a light wave front as it travels: as we get farther away from the source that emitted the light, we have to build bigger surfaces to reflect the latter. It turns out that this is also the case for highly collimated beams of light like those from lasers: they too "spread out" as they propagate through space. So if light spreads out as it travels and you have to keep building a bigger perfect mirror to reflect it all, then you can't propagate the light infinitely since eventually you'd have to build an infinite mirror (which even in our idealized world we'll assume is impossible).

But what if we used perfect curved mirrors instead of flat ones? We could curve the mirrors and make them just concave enough to counteract the spreading of the light from one mirror to the next. Then the size of the mirrors could always be finite, since we would "focus" the light often enough to avoid having really big mirrors. So perhaps we can reflect a signal infinitely and retain all its energy after all...

3. It turns out that the Universe itself has to be taken into account in this experiment, because it's expanding! The expansion of the Universe causes a redshift of light propagating in it - the wavelength of the light expands along with spacetime in the Universe, and that causes the energy of the light to decrease. Even if we bounce the light off perfect curved mirrors as we propagate it through the Universe, we can't avoid the effects of the redshift. This means that although we can preserve the *number* of photons that we emit, we can't preserve their energy - it will always decrease.

All of these things considered, I think a fair answer to your student's question is this: if you use perfect mirrors and if you curve at least some of them to counteract the spreading of the light beam you send out, then you can keep reflecting every single photon you started with indefinitely, and certainly to the end of the Universe and back. However, each of these photons will lose energy because of the expansion of the Universe, and so you can never retain the same amount of energy, just the number of photons.

I hope that this clarifies matters! If you have any additional questions, feel free to write back. It's a pleasure to help teachers give their students a better understanding of physics and astronomy!
366 days ago

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