Yes, agreed 100%. In this case, though, it's an impossible situation. That impossibility is what insures the conservation laws will hold. It's sort of like saying "what do the laws of physics predict would happen if you could extract path information from the double slit experiment, yet maintain the interference pattern?" The problem is that the situation is impossible within the current framework of the physical laws so the laws don't apply anymore. In your case, setting up the perfect situation is impossible given the current framework, so analyzing it in the same framework gives results that no longer agree with experiment.Originally Posted by Mike Henderson
The other way of looking at it is that the photon always ends up SOMEWHERE. It never goes poof. When you analyze it on a photon by photon basis, the conservation of energy becomes obvious. The photon goes somewhere. You never end up with no photon. It's only when you analyze it using a wave treatment that you have the problem of purely destructive interference, but then when you do that and take everything into account you find that it's impossible to actually setup a situation that gives you that pure destructive interference. it's not just a matter of technology or "hardness". It's a matter of there's no arrangement that's possible in the current framework that could ever give you that without also giving you enough constructive interference elsewhere to make up for it.
Schrodinger's cat can, in principle, be setup. We can't really do it in real life right now, but presumably that's just a technological hurdle. The case you're trying to setup can't be setup even in principle, no more than a measurement could ever be taken that violates the uncertainty principle. It's deeply unsatisfying, and it was deeply unsatisfying to Einstein and Shrodinger himself as well, but that's all there is at the moment.
BTW, I use this stuff everyday. Whenever my inlays don't fit perfectly, I always blame Heisenburg
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