3 ms·
Let's try to fool a wave function: Let's take one, run it through a beam splitter, take the two halves, and put one in a lab that is standing still and has a n
by graycat 12y ago
Let's try to fool a wave function: Let's take
one, run it through a beam splitter, take the
two halves, and put one in a lab that is standing
still and has a normal clock and the other half
in a moving lab, a space ship, with a slow clock.
But, we want the wave function to be of a particle
that also has a clock. So, let the wave function
be that of an atom of a radioactive element
with a short half
life.
We get in our space ship and travel at, say,
90% of the speed of light, let the particle
go, let it encounter the beam splitter, let
one half of the wave function continue to
bounce around inside our space ship with a
slow clock and let the other half exit the
space ship through a window, enter the
lab that is standing still, and bounce around there.
Then the question is, what is the half life of the
particle? Is the expected time, in the clock
of the normal lab, to decay different for decays in the
space ship than that for decays in the lab that is
not moving?
I'm sure this is all wet in some sense, but
I'm trying yet another students efforts to
trip up quantum mechanics with special
relativity!
- tjradcliffe 12y agoThe setup you describe doesn't bring QM and SR into conflict because the two split halves of the wavefunction never do anything interestingly "quantum". The radioactive decay process acts as a measurement of "which branch of the beam-splitter did the particle go down?" and so the experiment can be analyzed as if the particle went down one branch of the other in its entirety and was never split. To get at the quantum effects you'd have to consider a case where the two parts of the wavefunction are eventually brought back into interference with each other, but any sort of decay process is going to make them mutually incoherent, so you won't see any interference fringes. You might get something interesting by having a moving mirror in an interferometer, which would redshift the reflected wave in that arm by a bit, and that would result in moving interference fringes due to the resulting frequency difference (you'd need to gate the interference pattern on the position/velocity of the mirror to see this.) But even in that case, nothing very interesting would happen. In any experiment where you can detect which arm a particle goes down it will behave as if it went down that arm, even if your choice is delayed. In any interference experiment it will be impossible to tell which arm it went down. Nature is really good at doing the book-keeping to maintain the quantum veil.
- graycat 12y agoThanks! I suspected I was all wet! I was guessing that there might be tricking some EPR thing due to the two paths being different in SR. Or I was trying to mess up the "bookkeeping"! You seem to want to get the situation back to the Michelson-Morley interferometer! Okay! Or, sure, just Young's double slit. I know; it's not nice and not easy to fool Mother Nature! When I get done with software and business, I want to take a careful pass through SR, GR, and QM looking for just something wrong with the bookkeeping. Wheeler was, so I'll try too! Thanks. I needed that!