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Re: [Phys-l] slowing time




Kenny Stephens wrote:

"A student asked if "time slows down as you approach absolute zero
temperature." I responded that the molecular vibrations decrease and
if you measure time according to that, then yes."


The question is tricky and a little ambiguous (at least I have a
problem trying to understand what the student meant when saying
"time slows down"). The amplitude and velocity of molecular vibrations
decrease with cooling, and in this sense the molecules slow down.
On the other hand, if there is a process that could be used as a
microscopic clock within an atom (e.g. the oscillating atom has a
radioactive nucleus), its decay rate increases when measured by the
laboratory-based observer. You can think of it as a rehash of the twins
paradox: one of the twins is stationary, the other is moving back and
forth together with the atom. With each cycle the moving twin comes
back having aged a little less than its stationary twin. If the atom
slows down, this time discrepancy decreases, that is the moving twin
starts aging faster. But of course this effect is ridiculously small
at low temperatures.


">My question for the list: does a particle's lifetime increase if its
temperature is reduced in a roughly analogous way to how its lifetime
increases (relative to a stationary observer) if it is moving near the
speed of light?"

No. The particle's lifetime measured by stationary clock decreases with
decresing temperature, - its aging rate is fastest when at rest in an
inertial reference frame.


">I realize that molecular vibrations will slow. But is that related to
the particle's lifetime?"

As I said before, as the particle's translational motion slows down,
its inner evolution speeds up (to its proper limit), and if the
translational motion accelerates to the speed of light, then the
particle's inner evolution (as observed by a stationary observer!) slows
down until it freezes at v -> c. This effect is very pronounced at one
limit (v -> c), but totally negligible at the other limit (v -> 0).


Moses Fayngold,
NJIT