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I haven't gotten around to reading Hawking's book. That should be my
Mr. Hugh Logan wrote:
In the first place, what do you mean by the total energy of the
universe?
i refer to Hawking in brief history "the TOTAL ENERGY of the universe is exactly zero"-p.136.
In particular, how do you sum the infinitesimal contributions over the entire universe?
may i ask where do all these infinitesimal components come from?
if these are of quantum mechanical origin then we can safely disregard
the component because there is an allowed uncertainty of delE for a >very small time delT such that delE*delT~h.
another point should be
cleared that if stress-energy tensor in GR is conserved as T^jk ;j=o >so why it should not hold for everywhere in the universe?
as inMore generally, if you know the elements of a tensor in any coordinate
tensor we know that if any tensor vanishes in any coordinate system, >so does it in every coordinate system.
To compute a divergence, we need to compare quantities (here vectors) on opposite faces. Using parallel transport for this
leads to the covariant divergence. This is well-defined, because we're dealing with an infinitesimal hypervolume. But to add up
fluxes all over a finite-sized hypervolume (as in the contemplated extension of Gauss's theorem) runs smack into the
dependence on transportation path. So the flux integral is not well-defined, and we have no analogue for Gauss's theorem.
How would this be possible if energy is lost by the universe? The only
thing like creation of matter out of nothing that I have heard of is the
continuous creation theory of Bondi,Gold and Hoyle in which particles
are spontanously created so as to keep the particle density of the
universe constant.
yes, they had devised a so-called c-field theory of such kind.