Abstract
In this chapter I argue that neither the time symmetry of the laws of Newtonian physics nor determinism entails the time symmetry of the order of becoming of events. The time-directionality of individual processes cannot be defined in terms of increasing entropy, nor does it depend on a global direction of time. That process-tokens are future-oriented locally is not a consequence of thermodynamics, but is presupposed by it.
The more closely we examine the association of entropy with ‘becoming’ the greater do the obstacles appear.
—Arthur Eddington, The Nature of the Physical World (1929, 96).
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Notes
- 1.
See, for example, Roberto Mangabeira Unger : “In Newton’s own physics, however, no basis exists on which so to affirm the reality of time. Newton’s laws of motion are time-symmetric, they supply no reason or occasion to distinguish between forward and backward temporal orderings of events” (Unger and Smolin 2015, 165) . On this basis he writes of “the denial of the reality of time in this Newtonian tradition”.
- 2.
The example is taken from Lee Smolin’s Time Reborn, (52), where he is describing the standardly accepted arguments for the unreality of time before proceeding to contest them.
- 3.
- 4.
I refer the reader to George Smith’s excellent article in the Stanford Encyclopedia of Philosophy: “The modern F = ma form of Newton’s second law nowhere occurs in any edition of the Principia even though he had seen his second law formulated in this way in print during the interval between the second and third editions in Jacob Hermann’s Phoronomia of 1716. Instead, it has the following formulation in all three editions: A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed” (Smith 2008, §5).
- 5.
- 6.
See (Arthur 1995, esp. 341–42) for a detailed defence of the claims I make here about Newton’s ontology of space, time and quantity.
- 7.
It was also cryptically alluded to by Locke in the second edition of his Essay Concerning Human Understanding, without attribution to Newton , a circumstance that intrigued Leibniz. See Dempsey’s (2006) for an informative discussion.
- 8.
Cf. John Earman: “a literal notion of flow would presuppose a substratum with respect to which the flow takes place.” (Earman 1989, 7–8).
- 9.
- 10.
As Leibniz explains to De Volder, “You doubt, distinguished sir, whether a single simple thing would be subject to changes. But since only simple things are true things, the rest being only beings by aggregation and thus phenomena, and existing, as Democritus put it, νόμῳ [by convention] not φύσει [by nature], it is obvious that unless there is a change in the simple things, there will be no change in things at all.” (GP II 252).
- 11.
These quotations are from Leibniz’s essay Specimen Dynamicum published in the journal Acta Eruditorum in April 1695 (Leibniz 1998, 155). Cf. also “I also take it for granted that every created thing is subject to change, and therefore the created monad as well; and indeed that such change is continual in every one ” (Monadology §10; Leibniz 1998, 269).
- 12.
Leibniz himself assumed that every event is either before, simultaneous with, or after, every other event, and proposed an “axiom of connectibility” to ensure this (see Arthur 1985). But the asymmetric order of events need not be such a total ordering; it can be a partial ordering, as in Minkowski spacetime (see Chap. 6).
- 13.
Leibniz’s answer to Clarke was that “order also has its quantity; there is in it that which goes before and that which follow; there is distance or intervalv.” (Fifth Paper, §54; Leibniz 1969, 706). An order of successions would be a succession of intervals, or “like states”, each possessing a duration whose length could be determined by comparison with a standard.
- 14.
“The order of things succeeding each other in time, is not time itself: for they may succeed each other faster of slower in the same order of succession, but not in the same time .” (Fourth Reply §41; Leibniz 1969, 695).
- 15.
The clepsydra (literally, “water-thief”) dates back probably thousands of years, but is known to have been used in Aristotle’s time to keep time on clients’ visits to brothels in Athens, and increasingly sophisticated mechanisms (pointers, gears, and escapement mechanisms) were subsequently developed by the Greeks and Romans (as well as, independently, the Chinese) to help improve its accuracy . See Landels (1979, 33).
- 16.
Lest it be thought that the Greeks were technologically primitive, mention should be made of the Antikythera mechanism retrieved from a shipwreck off the coast of the Greek island of that name in 1902. Subsequent analysis has revealed that this was a clockwork device whose 37 gear wheels would have enabled its users to follow the movements of the heavenly bodies, sufficiently for them to be able to predict eclipses. The fact that it could even model the irregular orbit of the moon has led to speculation that the 2nd century BC astronomer Hipparchus of Rhodes might have been consulted in its construction. For a full account , see Jones (2017).
- 17.
For a vivid account of the problem of longitude and John Harrison’s patient (and inadequately rewarded) solution of it through the construction of clocks accurate enough to determine longitude , see Sobel’s (1995).
- 18.
Julian Barbour gives a pellucid and highly informative account of Ptolemy’s contribution to time measurement in his (2001), esp. pp. 175–190. As he observes, this selection of sidereal time by Ptolemy was a major contribution to the scientific revolution, in that it made it “possible to give precise content to the notion of a universal and equable flow of time” (Barbour 2001, 179); “it is only when the one sidereal time is used that all motions can be simultaneously described by simple theories. The time is therefore universal.” (2001, 180).
- 19.
- 20.
In his Pendulum Clock Huygens reports an account of a sea voyage in 1664 by Alexander Bruce, who had been equipped with an early version of his clock. After sailing westward from the island of São Tomé for seven hundred miles in the company of three other ships, then turning south-south-west towards Africa for another two or three hundred miles, they were running out of drinking water. Bruce’s calculations of their position as just 30 miles off the island of Fuego of the Cape Verdi Islands (where they were able to dock the next morning) differed by 80, 100 and more than 100 miles from those calculated by the other three ships lacking his clock (Huygens 1986, 28).
- 21.
The full title of Huygens’s book is The Pendulum Clock, or Geometrical Demonstrations Concerning the Motion of Pendula as Applied to Clocks (Huygens 1986).
- 22.
As Julian Barbour comments, “Huygens could be said to share with the Hellenistic astronomers the credit for the practical application of the way in which the passage of time is manifested in the world” (Barbour 2001, 455).
- 23.
Intriguingly, Barrow’s view can be seen as an anticipation of the situation in canonical quantum gravity. According to the reading of Carlo Rovelli and others, the introduction of a Newtonian universal time parameter is incompatible with general relativity and its quantization, so that the only recourse is to define time in terms of a particular physical process. See Rovelli (2018) and Kiefer (2011).
- 24.
This was established with great precision by Howard Stein in his “Newtonian Space-time ” (Stein 1968).
- 25.
Cf. Brian Greene: “According to Newton , if we knew in complete detail the state of the environment … we would be able to predict (given sufficient calculational prowess) with certainty whether it will rain at 4:07 p.m. tomorrow ” (Greene 1999, 91).
- 26.
Čapek (1971, 111). Cf. Bergson on Laplacian determinism : “Radical mechanism implies a metaphysic in which the totality of the real is postulated complete in eternity, and in which the apparent duration of things expresses merely the infirmity of a mind that cannot know everything at once” (Bergson 1944, 45).
- 27.
The same point of view is expressed rhetorically by G. J. Whitrow, when he asks “if the future history of the universe pre-exists logically in the present, why is it not already present? If, for the strict determinist, the future is merely “the hidden present”, whence comes the illusion of temporal succession ?” (Whitrow 1961, 295); quoted from (Grünbaum 1971, 226).
- 28.
- 29.
Cf. Earman, who argues “that there is a well-defined sense in which Newton’s laws of motion with certain force functions, though invariant under time reversal, allow forward but not backward causation in the sense that past states affect future states but not vice versa. If true, something along this line would be sufficient to account for the asymmetry of traces with respect to past and future” (Earman 1974, 42). See also Earman’s (1986) for a trenchant critique of the usual view of classical physics as deterministic, on various grounds independent of those I discuss here.
- 30.
In one of his unpublished manuscripts on his causal theory dating from the 1680s, Leibniz wrote: “The full cause is a producer that is prior by nature to what is produced, that is, that which involves all the requisites that are sufficient (i.e. from which the remaining requisites follow).” (A VI 4, 564). A “producer” (inferens), on the other hand, is defined as “that which, when posited, the other thing is posited” (C 471). See Futch (2008) and Arthur (2016) for details.
- 31.
(A VI 4, 568); see Arthur (2016) for an exposition of Leibniz’s causal theory of time.
- 32.
See Winnie (1977) for details.
- 33.
As Steve Savitt has reminded me, however, there exists a literature on causation by lack of a particular action, in claims such as “Your not watering my plant while I was away caused it to die”. I will not pursue that here.
- 34.
Torretti gives examples such as “rod contraction” and “particle”. One might add “wave-particle duality ” and the “uncertainty principle”, as we shall see in Chap. 8.
- 35.
Here Bunge approvingly quotes J. D. Bernal : “chance variations or side reactions are always taking place. These never completely cancel each other out, and there remains an accumulation which sooner or later provides a trend in a different direction from that of the original system ” (Bernal 1949, 31; Bunge 1979, 131).
- 36.
Thus if being analytically true means being capable of being demonstrated, then (given Leibniz’s demand that a demonstration be completable in a finite number of steps), only necessary truths are for him analytic, even though all truths have a sufficient reason.
- 37.
Lee Smolin calls this “the standard methodology of physics”, and ascribes it to Newton , calling it the “Newtonian paradigm”. Here a theory is applied to a “subsystem of the universe, idealized as an isolated system”. Its kinematics is described by “a state space, C, giving all the possible states the system may have at any moment of time”; the dynamics then consists in a law governing the evolution of this system from some point in C. “The state space and the law are timeless, while the law evolves the state in time” (Unger and Smolin 2015, 373) . The novelty of Unger and Smolin’s view is that they challenge the idea of timeless laws, holding that the laws evolve in a global time through the evolution of the universe. (See also Unger and Smolin 2015, 19–22, 373).
- 38.
For an eloquent exposition of a similar point of view about accidental factors, the qualitative infinity of nature, and the idealizations of physics, see Bohm’s (1957), esp. pp. 132–160.
- 39.
That “the irreversibility of time is the foundation of the asymmetry between past and future”, and not derived from entropic considerations, is also contended by Roberto Mangabeira Unger (Unger and Smolin 2015, 235).
- 40.
‘‘One can express fundamental laws of the Universe that correspond to the two main laws of thermodynamics in the following simple form: (1) The energy of the Universe is constant. (2) The entropy of the Universe tends to a maximum .’’ (Clausius 1867, 44, as quoted in English by Uffink 2003, 129; see Torretti 2007b, 738).
- 41.
Here I am in complete accord with Mauro Dorato: “physics cannot provide empirical evidence for the reality of absolute becoming because it presupposes it, at least to the extent that it presupposes an ontology of events” (2006, 569).
- 42.
Thus my point of view is directly contrary to that adopted by Huw Price in his provocative (1996). Price insists on a “block universe” view (version 1) which denies the flow of time, so that there is no objective difference between “the two directions of time”. Thus, in his analysis of Popper’s argument, and throughout his book, he assumes that “in changing the perspective [from one sense of time to the other] we do not change anything objective” (56).
- 43.
Here it might be objected that the configuration of all the balls in the first scenario is equally improbable, since it takes an exquisite precision in the velocity and direction of the cue ball to result in precisely that particular break. Carlo Rovelli has made this point, arguing that all such scenarios are equally particular. But in a realistic depiction of the pool break, we cannot ignore the fact that the system of moving balls not isolated from its surroundings: friction cannot be neglected, and some of the balls may have dropped into pockets. This lack of causal isolation is what makes the initial conditions in the reverse case so stupendously improbable.
- 44.
- 45.
“It is impossible for a self-acting machine, unaided by any external agency, to convey heat from one body to another at a higher temperature”—Rudolf Clausius , quoted from Torretti (2007b, 740). Torretti also notes the alternative formulation by Flanders and Swann: “Heat won’t pass from a cooler to a hotter. You can try it if you like, but you far better notter!” —quoted from “At The Drop Of Another Hat” (1964).
- 46.
The objection was raised by Loschmidt in his (1876), and supported by the arguments of Burbury in 1894, and Zermelo in 1896. See Torretti (2007b) for discussion and references to original papers and recent discussion by philosophers of physics. Torretti summarizes the latter as “sufficient to dismiss the popular understanding of the second law of thermodynamics as a law of cosmic evolution, to disqualify thermodynamic entropy as the physical source of universal time order, and to remove the need for deriving Time’s Arrow—per impossibile—from the mechanical or statistico-mechanical principles of thermal physics” (2007b, 739).
- 47.
For example, this is the explanation Sean Carroll gave to journalist Dan Falk, who was covering a conference on Time in Cosmology at the Perimeter Institute in Waterloo, Ontario: “What Boltzmann truly explained is why the entropy of the universe will be larger tomorrow than it is today. But if that was all you knew, you’d also say that the entropy of the universe was probably larger yesterday than today—because all the underlying dynamics are completely symmetric with respect to time .” (Falk 2016).
- 48.
This is related to a reply S. H. Burbury made in a letter to Nature in 1894 in defence of the statistical increase in entropy (Boltzmann’s H-function) against the reversibility objection: “I think the answer to this would be that any actual material system receives disturbances from without, the effect of which, coming at haphazard, is to produce that very distribution of coordinates which is required to make H diminish ” (Burbury 1894, 78).
- 49.
Perhaps (as suggested to me by David Wright in private correspondence) clusters of galaxies can be considered as confined in a gravitational potential well, thus mimicking the effect of confinement by a wall. But for detailed discussion and criticism of these and other assumptions made by Boltzmann, see Earman (2006), Uffink (2007), Butterfield and Earman (2007) and Torretti (2007b).
- 50.
“Then in the universe, which is in thermal equilibrium throughout and therefore dead, there will occur here and there relatively small regions of the same size as our galaxy (we call them single worlds) which, during the relatively short time of eons, fluctuate noticeably from thermal equilibrium, and indeed the state probability in such cases will be equally likely to increase or decrease. For the universe, the two directions of time are indistinguishable, just as in space there is no up and down.” (Boltzmann 1964, 446–47).
- 51.
“However, just as at a particular place on the earth’s surface we call ‘down’ the direction toward the center of the earth, so will a living being in a particular time interval of such a single world distinguish the direction of time toward the less probable state from the opposite direction (the former toward the past, the latter toward the future).” (Boltzmann 1964, 447).
- 52.
For a thorough critique of the “Past Hypothesis ”, see Earman (2006). As he and Torretti (2007b) have objected, the hypothesis of an initial low entropy of the universe is at odds with the stringent condition of homogeneity that must be satisfied by the FLRW models of spacetime (see Chap. 7) on which speculations about the early universe are based. It is “only if the distribution of energy on each hypersurface of simultaneity is absolutely uniform” that the Einstein field equations admit FLRW models as solutions (Torretti 2007b, 751). There are also problems that I will not go into here associated with the fact that the expansion of the universe is accelerating: see Earman (2006, 413). Penrose , however, argues in his recent book that “when gravity is brought into the picture, the CMB must actually have been very far from a maximum-entropy state” (Penrose 2016, 255), even if it issued from a state of thermal equilibrium. This is because “there can be an enormous entropy gain once we allow significant deviation from spatial uniformity, the greatest gain arising from those irregularities leading to black holes ” (2016, 255).
- 53.
This is the methodological principle that the universe must have the properties necessary for the emergence of living, conscious observers, given the obvious fact of their existence.
- 54.
Cf. Torretti , who, on having just seen two swallows flying past his window, asks “Would I see the birds’ heads trail their bodies if I lived in a ‘single world’ in which entropy was decreasing?” (Torretti 1999, 213).
- 55.
Another objection raised by Penrose concerns the formation of black holes with their concomitant massive increase in entropy. If it is assumed that increasing entropy defines the direction of time, then reversing the direction of time would require the reversing of black hole formation, contrary to accepted physics (Penrose 2016, 254).
- 56.
See Earman’s discussion in his (1974). As he notes, if a time direction is supposed for “sufficiently small regions of spacetime” rather than globally, then “this presupposition always holds” (33).
- 57.
In quantum theory, there is the added condition that the time inverse of a state must be the complex conjugate of the original state.
- 58.
Cf. Earman (1974, 37): “We live in only one model, and any given model can be as radically asymmetric with respect to past and future as you like while at the same time all of the relevant laws are time reversal invariant” (italics in the original).
- 59.
It is often held that in relativity theory proper time constitutes such a private time for an observer along its worldline—e.g. “Each observer has his own proper time” (Morris 1985, 157) . But as we shall see in Chaps. 5 and 6, although proper time is specific to a given trajectory in spacetime, it is a constitutive assumption of Minkowski spacetime that processes cannot reverse their temporal orientation.
- 60.
This has been the accepted wisdom for decades. Thus Richard Morris in 1985: “The seemingly paradoxical notion that time-reversed motion might be possible is a consequence of the fact that there is no arrow of time on the subatomic level” (Morris 1985, 126). At least Rovelli , who argues that “In a microscopic description, there can be no sense in which the past is different from the future” (Rovelli 2018, 33), allows that the “thermal time” that he takes to describe macroscopic phenomena also possesses no direction, “and lacks what we mean when we speak of its flow” (142). According to him, “The difference between past and future … issues only from the fact that, in the past, the world found itself subject to a state that, with our blurred take on things, appears particular to us” (194).
- 61.
Thus George Musser writes in a recent edition of Nature concerning descent into a black hole: “The descent is irreversible. That is a problem because all known laws of fundamental physics, including those of quantum mechanics as generally understood, are reversible.” (Musser 2018, S4).
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Arthur, R.T.W. (2019). Classical Physics and Becoming. In: The Reality of Time Flow. The Frontiers Collection. Springer, Cham. https://doi.org/10.1007/978-3-030-15948-1_4
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