The problem of time's arrow historico-critically reexamined

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Abstract

Responding to Hasok Chang's vision of the history and philosophy of science (HPS) as the continuation of science by other means, I illustrate the methods of HPS and their utility through a historico-critical examination of the problem of “time's arrow”, that is to say, the problem posed by the claim by Boltzmann and others that the temporal asymmetry of many physical processes and indeed the very possibility of identifying each of the two directions we distinguish in time must have a ground in the laws of nature. I claim that this problem has proved intractable chiefly because the standard mathematical representation of time employed in the formulation of the laws of nature “forgets” one of the connotations of the word ‘time’ as it is used in ordinary language and in experimental physics.

Section snippets

The continuation of science by other means

Hasok Chang's (2004) book Inventing Temperature offers in its last chapter a view of the history and philosophy of science (HPS) as “the continuation of science by other means”. The need for supplementing normal scientific research in this fashion was impressed on Chang by his personal experience as a philosophical historian of science, which he describes as “a curious combination of delight and frustration, of enthusiasm and skepticism, about science”. His delight in the beauty of conceptual

The problem of time's arrow

The phrase “time's arrow” was coined by Eddington (1929, p. 69) presumably on the analogy of the arrows placed on street corners to indicate the direction of traffic. The idea that time flows—where? in another time?—is senseless, but it is old and popular. In an otherwise beautiful line, Vergil (Georg. 3.284) wrote that “time flies away”, without bothering to specify the medium in which this feat occurs. In the professional literature about time's arrow, the expression does not usually refer to

Meanings of ‘time’

When faced with the problem, a philosophically minded person will ask, in the first place, what the word ‘time’ means and how it is being used. Since ‘time’ is a noun it is plausible to ask for its referent. Reading some philosophers one even gets the impression that the word designates a unique entity and therefore ought to be regarded as a proper name (although in English we seldom capitalize it). Its purported denotatum is, however, hard to pin-point. In everyday conversation, ‘time’ is most

The mathematical structure T

Classical mathematical physics took an interest in most of the said connotations of ‘time’, which it succeeded in representing as features of a one-dimensional differentiable manifold. The concept of a differentiable manifold is, of course, a creature of the 20th century, but the classical differential equations of physics make no sense unless the time variable that occurs in them ranges over a domain that we can bring under this concept. Classical physico-mathematical time is topologically

Time asymmetry and the laws of physics

The world we experience teems with readily discernible processes that display time-asymmetric patterns of succession. However, the craving for unity that was still so very much alive in the 19th century did not favor the dispersion of explanatory grounds over a dappled collection of sources, but would rather focus on a single unidirectional universal law of becoming, from which one would then hope to derive the entire array of temporally oriented patterns. Since the 1860s, almost all

The second law of thermodynamics

The second law of thermodynamics can be traced back to Sadi Carnot's groundbreaking thoughts about heat engines (1824). A heat engine is a device by which heat is transferred from a hot reservoir—the furnace (foyer)—to a cooler one—the refrigerator (réfrigerant)—and which through this process yields mechanical work. According to the caloric theory of heat, which Carnot took for granted, heat is an indestructible substance, so that, if the process is carried out adiabatically, that is, in

The kinetic theory of heat and Boltzmann's H-theorem

Although Clausius and Kelvin embraced the conception of heat as a kind of motion, initially they did not agree on what kind of motion it was. While Kelvin was inclined throughout his life to view matter as being ultimately continuous,17

Loschmidt's reversibility objection and Boltzmann's defense

The two main objections to Boltzmann's H-Theorem are the reversibility objection, soon raised by Joseph Loschmidt (1876),25

The low entropy Big Bang

The currently fashionable reply to this question has been chiefly promoted by the great Oxford mathematician Roger Penrose (1979), Penrose (1989), Penrose (2005).32 It runs as follows. In the light of astronomical evidence, the universe can be represented to a good approximation (in the large) by an expanding

Concluding remarks

Let us recapitulate what we have done. First I reviewed the meanings and uses of ‘time’ and proposed a moderately systematic summary of those I judged relevant in the present context. I noted that theoretical physics excludes from its mathematical representation of time the trichotomy of times now, which we can all take stock of whenever we are awake. Suppressing it serves the scientist's pursuit of universality, but does not favor the treatment of our problem, for it leaves out the one feature

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