John Clark wrote:
On Sun, Oct 26, 2014 at 1:35 AM, Bruce Kellett
> he [Krauss] appears to have overlooked the simple fact that in a
closed universe, light cannot go right round and back to the
starting point before the universe re-contracts to zero size.
You appear to have overlooked the simple fact that in a universe that is
getting smaller and smaller the time it takes to circumnavigate that
universe becomes less and less.
That is true, but it is relatively simple to calculate the time for a
light beam to go round a closed universe and also the lifetime of such a
universe before it re-contracts to zero. You find that if the universe
is dominated by radiation, then light can get round exactly once. If it
is dominated by matter, then light can only ever get half way round. If
there is more that a very small amount of dark energy, then a beam of
light can never get right round the universe (the universe does not
re-contract in that case -- it expands for ever even though closed). So
you can never see the back of your own head.
The calculations are in Misner, Thorne and Wheeler (MTW).
Bruce
> Krauss's argument by analogy with the total charge in the universe
fails
I don't see why, it seems like a pretty good analogy to me. Krauss's
argument is about electric field lines joining up and a electric field
moves at exactly the same as light does, so if it works for one it
should work for both.
John K Clark
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