In sci.physics, DARTH VADER

wrote
on 17 Aug 2005 10:07:34 -0700
.com:
What exactly is space time ?
Why cant we travell through the 4th dimention (time axis)?


Spacetime is simply the cross-product of the spatial
dimensions (of which there are three, usually expressed
in Cartesian coordinates (x,y,z)) and the time dimension,
which is measured by clocks (or attempted, given that
clocks have annoying tendencies to drift, become erratic,
and, if not regularly supplied with energy, stop).

The conventional representation of spacetime is with
four coordinates (x,y,z,t). The first three are the
aforementioned spatial coordinates, in meters; the last
is in seconds and represents time. This makes for a
rather strange metric, at least in SR; the quantity
x^2 + y^2 + z^2 - c^2t^2 is readily verified to be
invariant under the Lorentz Transformation.

Visualization of spacetime has some issues, mostly
because we can only see three dimensions. One could
visualize a hypersphere x^2+y^2+z^2+t^2 = r^2 as
an expanding, then contracting, soap bubble; that's
arguably the best one can do. Other methods include
slicing the object with a 3-space (the analogue of
a plane in regular 3-D euclidean geometry) and see
the results.

As for traveling through space-time, we do it without
any effort at all, at least in the time direction.
Seconds tick regardless of one's desires. :-) (There
are some issues regarding perception, but those are
more properly handled in neurobiological contexts,
not physics-oriented ones.)

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