Talk:Time's arrow and Boltzmann's entropy

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    The article discusses the emergence of the thermodynamic arrow of time. Here are some possible suggestions and thoughts over what is written:

    1) For the subject "Arrow of time" one could also expect a short description or inclusion of the standard arrows, as they are typically discussed, being besides the thermodynamic arrow, for example the causal arrow, the psychological arrow, the electrodynamic or radiative arrow and the cosmological arrow (direction in time in which the universe is expanding). It seems worth pointing out how they are all related to or even just consequences (with the possible exception of the cosmological arrow) of the thermodynamic arrow.

    2) Related to the previous comment "to broaden" the discussion, one could think to include more general comments or some extra standard references (lifting it historically beyond quotes from Brian Greene). E.g. the expression "arrow of time" appears to go back to Arthur Eddington in "The Nature of the Physical World" (Gifford Lectures 1927-1928). Other example, the notion of "block universe" was, I believe, introduced by Hermann Weyl ("the objective world simply is, it does not happen"). Other example, the electrodynamic arrow was discussed on at least to well-known occasions, being (1) the Ritz-Einstein exchanges of 1908-1909, and (2) the Wheeler-Feynman work (absorber theory) of the 1940's. Final example on the influence of relativity on our notion of time: Schroedinger (Tarner Lecure 1956) speaks about "the dethronement of time as a rigid tyrant imposed on us from outside, a liberation from the unbreakable rule of "before and after"."

    3) One could perhaps also add critical remarks to the proposal by Roger Penrose, such as formulated by various authors (like Hawking 1985): (i) why does it appear natural (not ad hoc) to associate a zero Weyl tensor with past singularities (not future ones)? (ii) Penrose's proposal appears heavily based on the prediction of singularities (of classical general relativity) but perhaps these are not there in quantum gravity. Perhaps here is truly a place where quantum effects matter for the appearance of the arrow. That last remark would in fact probably be also defended by Penrose himself, though for other reasons.

    4) Is it not strange to have Planck's constant appearing in the Liouville volume, especially after emphasizing somewhat that the discussion can be entrirely carried out in Newtonian sense. It only appears as some normalization but it is probably within the spirit of Boltzmann to emphasize the possible discretization of phase space.

    5) what is "Augustine's view?" (past and future unreal) mentioned in the paragraph following the description of Huw Price? Augustine is actually much known for emphasizing that the creation of the world was "with" time, not "in" time.

    6) some typo's: "is as" in the 5th paragraph of Matter in Space-time; "equalibrium" in the paragraph on initial conditions.

    Christian Maes

    Reviewer C: Comments

    Reviewer C

    I think the article is basically on the right track, and worth accepting.

    Some bigger-picture comments:

    1) The article gets technical pretty quickly (as is often true of Wikipedia articles as well). I would prefer to see a more accessible introduction to Boltzmann entropy and the Second Law near the beginning of the article. But this is just a preference.

    2) The third paragraph under "Initial Conditions," beginning "Put differently," was a bit confusing to me. The quotes from Boltzmann were very nice, although there appear to be some quotation marks missing -- it was unclear when the first quote ended. (It would also be preferable to have a citation to the precise original source.) However, the two quotes seem mutually contradictory; first he is saying "assuming a very improbable initial state...", and then he is saying "we do not have to assume a special type of initial condition..." This is at the very least confusing, and may represent an inconsistency on Boltzmann's part -- over the years he was known to take different views on the matter of initial conditions. It would be good to explain this all more clearly.

    3) The Penrose discussion was also slightly confusing. I'm not sure what "far from proven" means in this case, but it seems quite clear that the early universe was in a low-entropy state, far from equilibrium; I don't think that is very controversial. (The controversial part is why it might have been like that.) On the other hand, the discussion of uniformity and entropy in the presence of gravity seems a bit too credulous toward Penrose. It is true that a collapsed system will have a higher entropy than a uniform gas of constant density (at least on scales larger than the Jeans length). However, this is not the endpoint of gravitational evolution, as Jennifer Chen and I have emphasized ( In a universe dominated by a positive cosmological constant, collapsed structures will evaporate, leaving behind nearly empty space as the state of maximum entropy. It should at least be stated clearly that the nature of equilibrium states in the presence of gravity is a nontrivial issue, and involves cosmological considerations as well as local ones.

    Sean Carroll

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