Something occurred to me that some of our professional physicists might be able to answer.
So, virtual particles. What happens if we measure the Casimir Effect in various frames? For instance- at rest, accelerating, rotating, etc? I assume that the answer is: nothing. Always the same. So - does this lead to, or is another way of getting to, some useful conservation laws via Noether’s theorem?
Not a good assumption. Even without any Casimir plates at all, accelerating reference frames will observe different things with respect to real and virtual particles. If you take an inertial observer, and plunk him down in a vacuum, she will observe zero real particles, but if you then put an accelerated observer in the exact same space, the accelerated observer will observe real particles, in an effect analogous to Hawking radiation.
OK, wow. So - what should I be looking at to learn a bit more? I can sort of see this as you say - analogous to Hawking radiation, but whilst that is pretty well known, this is on the surprising side for this bear of little brain.
They would explain it as their inability to come up with a globally conserved quantity that coincides with their local measurements of energy.
A Kerr black hole is stationary, which means that at infinity there is a time-translational symmetry and Noether’s theorem famously relates the conservation of energy to time-translational symmetry. However in the ergosphere of a Kerr black hole the Killing vector field which represents this symmetry becomes spacelike, which means that, in the ergosphere:
i) the “Killing energy”, which is the globally conserved quantity related to the symmetry, of a particle can be negative. NB negative Killing energy particles always have trajectories such that they fall into the black hole.
ii) there are no observers “at rest” wrt to the Killing vector field representing asymptotic time-translational symmetry, so their local measurement of energy cannot be made to coincide with the globally conserved Killing energy.
In more mundane terms, i) just means that to bring a negative Killing energy particle to rest at infinity you have to increase its energy by more than its rest energy and ii) just means that particles in the ergosphere must either gain or lose energy to be at rest at infinity.
Thank you! I’ve been trying to recall that for a long time. Should’ve just asked in Café.
Found a PDF and I just read it- thanks for the tip.
You’re welcome (both of you)