Alberto said:
[The relativity of simultaneity]
> Is this valid for all spacelike events?
Yes, it's valid for all pairs of events separated by spacelike
intervals. Similarly, for all pairs of events separated by spacelike
intervals there will be an inertial frame in which they occur at the
same place at different times. The "proper distance" or "proper time"
between two events is the "length" of the interval between them, and is
the distance between the two events in the frame in which they're
simultaneous or the time between the two events in the frame in which
they're at the same place. The metric is the gadget that converts
coordinate changes in a given frame to intervals of proper distance or
proper time. Once again, I refer you to my Very Brief History of Time
http://www.mrao.cam.ac.uk/~rcdb100/physics/vbht/
for more details.
Rich, who notes that things are a bit more subtle in general relativity
but that basically the same conclusions hold.
