Poincaré vs. Einstein

every thing has been obscured by the "flipbook school,"
taking the extreme of saying that space is the same as time,
just because of a graph ... although,
one should have no loop-de-loops in one's graph
of "1+1 phase-spaces;" is it not a standard function,
if time is on either axis?

Am 13.04.2011 02:24, schrieb rasterspace:
every thing has been obscured by the "flipbook school,"
taking the extreme of saying that space is the same as time,
just because of a graph ... although,
one should have no loop-de-loops in one's graph
of "1+1 phase-spaces;" is it not a standard function,
if time is on either axis?

No, not this way.
But how do we measure time?
By something, we assume to behave the same way everywhere.
So we could do a transport of this clock-device to somewhere else in
space and it has the same rate.

In the spacetime-view, this is a 'parallel-transport' of the clock. This
means, 'same rate' *defines* parallel and that defines space, because
this 'same rate' contains a definition.

But lets assume a 'curved transport', meaning: not the same rate of
ticks of our clock-device.
Since we would still assume the clock to be a valid time-piece, the
space shrinks - because of constancy of c.

This is difficult, but possible to understand: space is measured by
light, since that is, what we *see*. If the tick rate of our clock is
altered, the space we see is affected, because the light speed stays the
same. But what doesn't stay the same is, what we actually see (and not
where we see that). So time could be turned a bit into space - with
'morphing' of its content.

The anchor is time and from this we derive our understanding of space.
This space is space, because it has no frequency and that is an inverse
to time. This is infinitely large (size goes to infinity) and eternal
(frequency goes to zero).

But what we regard as the universe and what as matter depends on our own
clock, since this device is what *defines* space. Since devices are made
from matter, our view is locked to our universe.

But we could perform a very difficult 'curve in spacetime', where these
relations are altered. Than we always have a valid universe and a valid
measure of time, but not the same universe and not the same time.

This is a common experience and we call that light. This light is a wave
in our view, but not in its own, because in its own FoR it is
stationary. In this view, we (the observers), are the light.


Thomas Heger

well, due to the fact that time goes slower,
with respect to a (say) orbiting clock,
there is no problem ... like,
use quaternions for "3+1 = what ever."