One constant in quantum electrodynamics is that it doesn't look right to me, but it seems to work!

Richard Feynman's "QED" is a great read on this.

You can also watch the original lecture. This is one of my very favorite explanations of anything:

http://www.vega.org.uk/video/programme/46

This explanation starts at about 30 minutes, but I highly recommend watching from the beginning.

Thanks! I hadn't seen these. There are 4 Feynman lectures on this page[0], the Douglas Robb Memorial Lectures, of which you linked to the second.

http://www.vega.org.uk/video/subseries/8

1. A gentle lead-in to the subject, Feynman starts by discussing photons and their properties. 2. What are reflection and transmission, and how do they work? 3. Feynman diagrams and the intricacies of particle interaction. 4. What does it mean, and where is it all leading?

The site has many other science videos too:

http://www.vega.org.uk/video/series/5

Update: have now watched 3 of the 4 videos. Can see why you loved it so much! I've watched a lot of Feynman talks and lectures, and read most of his books. ..but this has particularly good explanations of the material, distinctly clearer than a couple of talks of his I'd seen before. Plus a few priceless references to NZ and the NZ national character! (filmed Auckland 1979)

The photon has some amplitude for reflecting in all possible directions, it happens that for certain directions these amplitudes are very close to the same value and so reinforce and become more probable, and at wider angles tend to cancel out and become less probable. When this is not the case and wider angles instead reinforce you can observe this directly in for instance a diffraction grating.

Yes, I agree. But what this has anything to do with the probability of emitting a photon in a specific direction? The parent was speaking about absorption and re-emission, not reflection.

I think the two slit experiments indicate that a photon does exactly have a direction of travel?

Only after it arrives, so the situation's a lot more nuanced than that.

It has enough direction of travel for laser pointers to work.

Conservation of momentum, I think

If the emitted photon always had the same momentum as the absorbed photon, the light would go right through the mirror, passing on its way without changing direction.

Only if the momentum wasn't transferred to the mirror.

Which is, in fact, what happens. Solar sails exploit this fact:

https://en.wikipedia.org/wiki/Solar_sail

If momentum was transferred to the mirror then the emitted photon would not have the same momentum as the absorbed photon.

Conservation of momentum doesn’t mean that the momentum of the emitted photon has to be equal to that of the absorbed photon. It means the sum of the momentum of the emitted photon and the mirror must equal the momentum of the absorbed photon, assuming the mirror had no momentum to begin with.

> Why the photon is then re-emitted in exactly the same direction that it would have if it was reflected rather than a random direction?

That is, the equal and opposite direction, exactly as predicted by conservation of momentum.

Momentum is a vector. The sum of the vectors is preserved.