ABSTRACT

The recent surge of interest in the origin of the temporal asymmetry of thermodynamical systems (including the accessible part of the universe itself ) has put forward two possible explanatory approaches to this age-old problem. Hereby we show that there is a third possible alternative, based on the generalization of the classical (‘‘Boltzmann–Schuetz’’) anthropic fluctuation picture of the origin of the perceived entropy gradient. This alternative (which we dub the Acausal-Anthropic approach) is based on accepting Boltzmann’s statistical measure at its face value, and accomodating it within the quantum cosmological concept of the multiverse. We argue that conventional objections raised against the Boltzmann–Schuetz view are less forceful and serious than it is usually assumed. A fortiori, they are incapable of rendering the generalized theory untenable. On the contrary, this analysis highlights some of the other advantages of the multiverse approach to the thermodynamical arrow of time.

EXCERPT

The basic idea of the Acausal-Anthropic approach is that, having already received from (quantum) cosmology a useful notion of the multiverse, we could as well employ it in order to account for the prima facie extremely improbable choice of (local) initial conditions. In other words, we imagine that everything that exists, for which we shall use the term multiverse, represents a ‘‘Grand Stage’’ for the unfolding of—among other things—the thermodynamical histories of chunks of matter. Entropy in the multiverse is high almost everywhere and at all times (‘‘almost’’ here meaning ‘‘everywhere minus a possible subset of small or zero measure’’). In other words, the multiverse is, formally speaking, in the state of ‘‘heat death,’’ as envisaged by classical thermodynamics. Our cosmological domain (‘‘the universe’’) represents a natural fluctuation—presumably of small or zero measure; but the anthropic selection effect answers the question ‘‘why do we find ourselves on an upward slope of such a fluctuation?’’ Hence what needs explaining is not that there are such fluctuations (this is entailed by Boltzmann’s statistical measure); nor the fact that the local initial conditions are of extremely low probability (this results from a distribution over all domains); but the fact that we happen to live in such an atypical region of the ‘‘grand total’’ which is almost always in equilibrium. And that is to be explained by showing why the observed entropy gradient is necessary for our existence as intelligent observers.

The law of non-decreasing entropy is one of the most fundamental in physics. As Eddington proscribed: "...if your theory is found to be against the Second Law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation." Yet in deriving thermodynamics as a limit of statistical mechanics, it becomes clear that the Second Law is not quite inviolable: in an equilibrium system downward excursions in entropy do occur, have been observed in the laboratory, and may indeed be important for the functioning of life at the molecular level . In statistical mechanics, the Fluctuation Theorem quanties the relative probability that an isolated system will evolve upward or downward in entropy . Because an excursion decreasing entropy by ΔS is suppressed by a factor of exp(-ΔS), in macroscopic systems with thousands of particles or more, signicant "miraculous" downward entropy excursions are so rare that they are essentially never important.

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In some cosmological models, however, equilibrium states that hold for arbitrarily long timescales can exist, and in this context signicant downward entropy excursions would, inevitably, occur. In fact, in models of eternal inflation, these excursions may be crucial. They are involved, for example, as intermediate states in the Coleman-de Luccia or Hawking-Moss mechanisms by which transitions occur between metastable inflationary vacua, and are central to process in which the vacuum energy increases, as in stochastic eternal inflation or via the Lee-Weinberg mechanism. They also describe, in eternal thermal spaces, the spontaneous emergence of structures such as black holes or Boltzmann Brains from empty space.