Tube Alloys IIXaX: January 2021

Wednesday, January 20, 2021

Boltzmann on relativity of time's arrow

From Barbour online re Boltzmann 1897:

Of his two proposals, the first—that the universe as a whole rather than only “a very large part of it which surrounds us”—has by far been taken more seriously for several decades. Boltzmann’s second proposal, later in the same paper, develops the suggestion he had made in Nature in 1895 and attributed there to Dr Schuetz. What he now said in 1897 was that in a sufficiently large universe which is in thermal equilibrium as a whole and therefore dead, there must be

here and there relatively small regions of the size of our galaxy (which we call worlds), which during the relatively short time of eons deviate significantly from thermal equilibrium. Among these worlds the state probability increases as often as it decreases. For the universe as a whole the two directions of time are indistinguishable, just as in space there is no up or down. However, just as at a certain place on the earth’s surface we can call “down” the direction toward the centre of the earth, so a living being that finds itself in such a world at a certain period of time can define the direction of time as going from the less probable to more probable states (the former will be the “past” and the latter the “future”) and by virtue of this definition he will find that this small region, isolated from the rest of the universe, is “initially” always in an improbable state. This viewpoint seems to me to be the only way in which one can understand the validity of the second law and the heat death of each individual world without invoking an unidirectional change of the entire universe from a definite initial state to a final state.⁴⁴

It was through passages like these that Boltzmann persuaded scientists that the experienced direction of time is aligned with the direction of entropy increase. The 1895 letter to Nature did not include the argument that the less probable state will be taken to be the “past”. This is one of the ideas for which Boltzmann is famous; it seems have been his own addition to Schuetz’s original idea. I think it is clear that neither Thomson in 1874 nor Boltzmann in 1877 had been capable of shedding the instinctive feeling that, whatever may be happening in the world, time flows forward inexorably. Also, I am not aware that Boltzmann ever made it fully explicit that intelligent beings could exist on both sides of a single localized entropy dip and would therefore live in a spatially and temporally part of the universe with bidirectional arrows of time.

44. The ‘only way’ in this last sentence seems to me to imply that Boltzmann’s preference for explanation of the entropic arrow was through fluctuations that, without violating time-reversal symmetry, would create transiently existing worlds of low-entropy dips.

Tuesday, January 19, 2021

N13 (20210120_175411...20210119_201616)
Entropy, Barbour

Barbour quotes Gibbs as saying that a system of particles dispersing through infinite space cannot attain equilibrium. Yet in many cases, one may argue, the net vector of the particles reaches approx. 0 and stays that way as the particles disperse. For that, we would expect the system to have been "physically connected" when dispersion was initiated.