Time Elapsed Through Earth's Tunnel: Clock Drop Experiment

[Count Iblis]

Suppose someone drops a clock and it tunnels through the Earth. What time will have elapsed according to the clock when it emerges on the other side of the Earth?

 

[country boy]

Is it only tunneling in space or can it also tunnel in time?

 

[genneth]

Time is one of those annoying issues in quantum mechanics. In non-relativistic QM, time isn't even a state of the system -- there is no operator that corresponds to measuring it. In relativistic QM, you've got a multiplicity of time and proper times are difficult to acertain without resorting to rather advanced applications of statistical mechanics and QM together. The basic idea is that time flow is always determined, in some sense, by the statistical state, and not just by the background structures or even just the dynamics.

Rather hazily, I might try to understand the situation via the Feynman paths method -- the initial state is propagated in spacetime via all possible routes, and the result of a measurement will have a probability distribution given by the interference possible. Assuming that the clock is a fundamental particle (it doesn't explode as it interacts with the Eath), and measures its proper time, the answer would be some inference pattern, in time.

 

[GleefulNihilism]

As I understand it, and I claim no more authority then an interested amatuer, if the clock does true quamtum tunneling then it will reappear on the other side of the Earth instantly.