That there is no spacelike component of SR
alen
sequences of events, when viewed in a spacelike
separated manner, and whose data is compared in a
spacelike manner, do not display SR effects.
A sequence of events is to be thought to be locally
observable, in a timelike manner, at a location in an
inertial frame.
To view more than one such sequence of events in a
spacelike manner, when spacelike separated, should be
taken to mean that the sequences of events are viewed
by their own separated observers at their own locations in
the inertial frame of the observers.
Sequences of events cannot, of course, be directly examined
and compared in a spacelike manner, but this can be
achieved indirectly, as follows: If all the data associated with
the sequences of events are permanently recorded by their
local observers, such historical records can be examined
and compared at any time, in a manner independent of the
time taken to make the comparison, so that the time taken
could be reduced to a limit of zero, without this making any
difference to the results. This can be taken as the equivalent
of a spacelike comparison of spacelike separated events,
since the result is equivalent to being able to travel from one
event to the other in zero time, as they occur.
For purposes
of comparison, one can make use of the fact that the local
spacelike separated observers are in the same inertial
frame, in the sense that their relative velocity is zero, and
their clocks are synchronised, and identical. Their clock
data can thus be incorporated into the historical record.
As an example of a local sequence of events, consider a
coil plus battery placed opposite a magnet, with the coil and
magnet each having a clock attached to it, and with a local
observer in an inertial frame, such that, on sending a
current for a short time through the coil, a relative
acceleration and final constant velocity is induced between
the coil and magnet, and between both and the local
observer. No force of any kind is applied to the observer,
and all components of the system are initially at rest in
the same inertial frame as the observer. Let the coil and
magnet be considered to have equal masses, if you like.
I make the case that the coil and magnet constitute an
entirely closed and independent system such that, wrt
the observer's inertial frame, the system is translationally
invariant in a spacelike manner. This means that, wherever
it might be initially located in the inertial frame, its local
observer in the inertial frame will record identical results.
From this translational invariance it follows, self-evidently,
that, if the system is duplicated at a second location, a
second local observer will record identical data to that of
the first observer. All the data associated with both
sequences of events, when examined in a spacelike
manner (i.e. as historical records), including all velocities,
accelerations, local time dilations on the system clocks,
and time intervals, will be identical, and no differences
between the sequences of events, due to SR effects, such
as non-simultaneity, will be observable.
If, however, the two systems are sufficiently close together
that the first observer can observe the second system as
well as the first, in a timelike manner, as the events occur,
though at a different spatial distance, this observer will not
record identical data for the two systems. Instead, he will
record different time dilations on the two magnet clocks,
and the two coil clocks, and will calculate foreshortenings
of not only the two magnets but also the distance between
them.
This shows that SR is a timelike phenomenon only, and
cannot involve any global spacetime rotations of inertial
frames, such as to involve spacelike distances as well.
Alen
Dirk Van de moortel
"alen" <al...@westserv.net.au> wrote in message news:01c39d59$de018e80$067ea6cb@default...
[snip]
> For purposes
> of comparison, one can make use of the fact that the local
> spacelike separated observers
Spacelike, lightlike or timelike separation is a possible
property of a pair of events. Not of a pair of observers.
[snip]
> This shows that SR is a timelike phenomenon only, and
> cannot involve any global spacetime rotations of inertial
> frames, such as to involve spacelike distances as well.
I think it shows that you really should start from the
beginning somewhere.
Do yourself a favour and do have a look at Geroch's
book sometime. It is *really* excellent.
Dirk Vdm