On Sun, 17 Feb 2008 20:27:24 +1100, bernardZ <BernardZ@[EMAIL PROTECTED]
>
wrote:
:There is a law called the law of conservation of mass and energy under
:QM for short periods of time this law can be broken but for the periods
:we are talking about it must be conserved.
:
:In the scenario where a time traveller suddenly arrives in this time an
:equivalent energy to him must go back to his time.
:
Time travels implies a space-time topology
that is not simply-connected - that is, there can be
two paths connecting two points in space-time that
cannot be continuously transformed from one to the
other. For example, the surface of a sphere is simply
connected - any path between two points can be
smoothly transformed into any other - but the surface
of a torus is not - a path going through the 'hole' of
the torus can't be smoothly transformed to a path
going around the outside of the torus.
Say there's a time-travel event from Los
Angeles in 2029 to Los Angeles in 1984. If you're in
Los Angeles in 1982, you can get to 1984 LA by just
staying where you are for two years, or you can move
to Sacramento, wait 40 years, move back to LA, wait
seven more years, and then travel back to 1984 LA.
But there's no smooth transition from one path to the other.
Global conservation of mass/energy requires a
simply connected space-time topology. To measure
global energy, you have to establish an approximation of
universal simultaneity. Again,. picture space-time as a
sphere, with the beginning of the universe at one point
and the end of it at its antipode. Global conservation of
mass/energy means that along any latitude between these
poles will have the same net mass/energy along it (think of
Cauchy's Integral Formula). It doesn't even matter if these
latitudes aren't perfectly 'horizontal', so long as no point in
the latitude is in the light-cone of any other point. But, if
space-time isn't simply connected, but instead like a torus,
then you can't really define latitudes between the beginning
and end of time, because these latitudes cannot smoothly
transform from one to the other. Not only is global
mass/energy not conserved in a not-simply-connected
space-time topology, it isn't even well-defined, because
there are points that are in each other's light-cones.
--
e^(i*pi)+1=0
George W. Harris For actual email address, replace each 'u' with an 'i'.
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