I appended a conclusion to my original reply from last night.
Stephen,
thank you for the answer. It appears relativistic velocities like
the muon are not as common as I imagined but even these lesser velocities
you mention would accumulate into time dilation like the protracted decay of
the muon just on a smaller scale. Normally this dilation is intangible as
the atoms must exist in a different inertial frame only briefly passing our
frame of observation. If we can accept time dilation due to mass
acceleration relative to the time axis then we should also allow for the
opposite case of a moving time frame relative to a stationary mass. I think
this is already the case for equivalent acceleration when a crushproof
spacecraft sits on a collapsed star but instead of inhibiting the flow of
time like the dead star, the Casimir cavity takes that same sort of
inhibition (accumulated pressure) and exhausts it out of a tiny cavity too
small to exhaust the reservoir. This creates a steady stream many times
faster than the isotropic field it is breaching. My point is this represents
a difference in acceleration between inhabitants of the cavity vs outside
the cavity such that "velocity" accumulates -I put velocity in quotes since
from our perspective it is time dilation but from the local perspective of
the gas atoms inside the cavity it is feeling equivalent acceleration and
sees the cavity walls shrinking away into the distance even though its
spatial coordinates are unchanged. This makes time dilation tangible in that
We can use gas atoms in a stationary catalyst/reactor to exploit this
environment.
In conclusion the temporal "rate" of the Casimir cavity by virtue of its
vector should be considered immediately "relativistic". It doesn't have to
achieve a right angle relationship on the scale of C because it is directly
altering the time axis. Relative to the isotropic time flow outside the
cavity there is an absolute difference in "equivalent" acceleration meaning
that gas atoms diffusing between the 2 frames will experience abrupt changes
in time and gravity we refer to as catalytic action (change in Casimir
force).
Best Regards
Fran
