Dear Colleagues,I have a brief response to Bill Phillip's question about why a smooth big
bang is surprising. Some years ago Roger Penrose tried to quantify the
degree of specialness associated with a smooth early universe by comparing
the observed entropy of the universe with the maximum possible entropy. The
latter he assumed would be associated with the most clumpy state, namely,
gigantic black holes. Using the Hawking-Bekenstein area formula for the
entropy of a black hole, Penrose found that the observed universe has an
entropy thirty powers of ten less than the maximum permissible value. If one
interprets entropy as a measure of expectedness (low-entropy states are
surprising and rare, high entropy states numerous and unremarkable) then the
probability of the observed smooth initial state is infinitesimal.
A simpler way of arriving at the same conclusion is that a smooth,
uniformally expanding state implies that almost all the available energy of
expansion is concentrated in a single dilatory mode, rather than being
distributed evenly among the myriad degrees of freedom available to cosmic
dynamics. This arrangements is therefore highly ordered, and has very low
entropy.
Either way, smooth means surprising!
Regards,
Paul Davies
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