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A sealed cavity full of light weighs more than an empty one. So consider a cavity consisting of parallel mirrors, with a pair of beams bouncing between the mirrors. The question is whether that weight will change if we arrange for the beams to completely cancel one another at every point along their length?

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How do you achieve that? – gatsu May 2 '13 at 8:28
By making the mirror separation an odd multiple of the half-wavelength. But it doesn't have to be precise; we don't need to get into spectral purity or Heisenberg, etc. Partial cancellation is enough for us to still be able to ask whether the weight changed or not. – Andrew Palfreyman May 2 '13 at 9:24
There is no such thing as pure cancellation of two existing waves everywehere in a cavity. What happens is that you form a standing wave[] where the energy is zero at the nodes and double at the anti-nodes. Overall, the energy and therefor ethe mass is unchanged – gatsu May 2 '13 at 10:38
Yes, good; I knew that and temporarily forgot it. So how can this be done? How about 2 collinear beams 180 degrees out of phase? – Andrew Palfreyman May 2 '13 at 16:30
That's equivalent to a beam with zero intensity. – Colin K May 2 '13 at 20:50

You're not being very careful about your terminology. Instead of weight I think you're really talking about the total mass-energy of the sealed cavity. If you want to discuss weight the it would be better to think of that as the force on the total mass-energy in a gravitational field.

Thinking about it in terms of mass-energy makes the question much easier. Then it's obvious that the massless photons still add energy to the system (already acknowledged in your question) and (hopefully!) it's obvious that no constructive or destructive interference or absorption of the photons will change the total mass energy.

That is, due to the conservation of energy, nothing that happens to the photons inside of the sealed cavity will change the total mass-energy of the system.

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