Works Cited

It seems, also, that the various observers' aesthetic judgements might well get involved in what they deem to be 'order', rather than 'disorder'. We could imagine some artist taking the view that the collection of shattered glass fragments was far more beautifully ordered than was the hideously ugly glass that once stood on the edge of the table! Would entropy have actually been reduced in the judgement of such an artistically sensitive observer?

In view of these problems of subjectivity, it is remarkable that the concept of entropy is useful at all in precise scientific descriptions--which it certainly is! The reason for this utility is that the changes from order to disorder in a system, in terms of detailed particle positions and velocities, are utterly enormous, and (in almost all circumstances) will completely swamp any reasonable differences of viewpoint as to what is or is not 'manifest order' on the macroscopic scale.

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This is an extraordinary figure. One could not possibly even write the number down in full, in the ordinary denary notation: it would be '1' followed by 10^123 successive '0's! Even if we were to write a '0' on each separate proton and on each separate neutron in the entire universe--and we could throw in all the other particles for good measure--we should fall far short of writing down the figure needed.

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If the photo-cell indeed registers, then it is virtually certain that the photon came from the lamp and not from the laboratory wall! In the case of our time-reversed question, the quantum-mechanical calculation has given us completely the wrong answer!

The implication of this is that the rules for the R part of quantum mechanics simply cannot be used for such reversed-time questions.


Roger Penrose, The Emperor's New Mind