Early Childhood

The Newton family belonged to the yeoman class descended from the most modest of the free landholders of manorial England. Socially beneath the esquires and knights, some members of this class had prospered greatly after the fourteenth-century decline of feudalism. Later the dissolution of the monasteries, sheep-farming and inflation had given some yeoman families, like the Newtons, means to enter the gentry class. As small landowners they lived in solid houses of brick or stone, sometimes adjacent to the barns and farmyard, like Newton's birthplace at Woolsthorpe in Lincolnshire. Yeomen, who could not prosper by idleness, constituted a great reservoir of ambition and talent, supplying Church, universities and the law, as well as commerce and industry. They wrote plays for the stage and music for the nobility; they staffed the empire. The father whom Isaac Newton never knew, also Isaac, could not sign his name but his mother and half-sisters were literate after the phonetic style also practised by the greatest ladies. When the posthumous child was three years old his mother, Hannah, remarried Barnabas Smith, rector of nearby North Witham. Smith owned a small library of theological books, works of the Fathers and so on, which passed to his stepson. Thus Isaac was born into the lower limit of landed property and learning alike. When he was old and famous he took pains to satisfy the College of Heralds of his common descent with an established armigerous gentleman, Sir John Newton, who was glad to bring so famous a man among his own kin. Sir Isaac Newton for his part responded to many begging letters from his poor relations.

With the freedom granted to all Lucasian professors to decline holy orders, Newton knew that so long as he retained that office he was assured of the tenure of his fellowship at Trinity College till death or resignation – in fact, he would hold it for another twenty-six years. He did not resign his Cambridge posts until December 1701, still not a Senior in his college though non-resident since 1696. Further, to the best of our knowledge, Newton had carried out no teaching since the Revolution.

His appearances in the public life of his college and university are poorly documented. In March 1673 he joined his relative Humphrey Babington and others, Masters of Arts, in signing a protest against the heads of houses exercising their customary but doubtful powers of nominating two candidates for the post of Public Orator, for the Senate's election. The protest failed. At an unknown date Newton attempted to secure from the commissioners of taxes for Cambridge an exemption from a property tax, on the grounds that the revenue from the Lucasian professorial estate did not belong to his college. (Later, from 1688 to 1695, Newton himself was to be one of these commissioners, a mark of his eminence in the university; the vicechancellor was one of the body ex officio.) In 1676 Newton gave £40 – then a fairly comfortable annual salary – towards the projected new library building proposed by Barrow at Trinity, since famous as the Wren Library closing the rear court of the college. This gift was followed by a loan of £100 made about the end of 1679; Newton also presented a number of books to the library.

A century or so ago, Ludwig Boltzmann and others attempted to explain the temporal asymmetry of the second law of thermodynamics. The hard-won lesson of that endeavour – a lesson still commonly misunderstood – was that the real puzzle of thermodynamics is not why entropy always increases with time, but why it was ever so low in the first place. To the extent that Boltzmann himself appreciated that this was the real issue, the best suggestion he had to offer was that the world as we know it is simply a product of a chance fluctuation into a state of very low entropy. (His statistical treatment of thermodynamics implied that although such states are extremely improbable, they are bound to occur occasionally, if the universe lasts a sufficiently long time.) This is a rather desperate solution to the problem of temporal asymmetry, however, and one of the great achievements of modern cosmology has been to offer us an alternative. It now appears that temporal asymmetry is cosmological in origin, a consequence of the fact that entropy is much lower than its theoretical maximum in the region of the Big Bang – i.e., in what we regard as the early stages of the universe.

The task of explaining temporal asymmetry thus becomes the task of explaining this condition of the early universe. In this chapter I want to discuss some philosophical constraints on the search for such an explanation. In particular, I want to show that cosmologists who discuss these issues often make mistakes which are strikingly reminiscent of those which plagued the nineteenth century discussions of the statistical foundations of thermodynamics.

More them any other topic in the foundations of physics, the problem of the arrow (or arrows!) of time seems to be characterized by a unique ‘slipperiness’: it is not only difficult to find answers to the questions once posed, but difficult to find meaningful questions to ask in the first place. Perhaps this is because an asymmetry with respect to the sense of time is built into us at an even deeper level than other ‘synthetic a priori’ conceptions about the world such as the continued existence of unknown objects. However that may be, in this situation, rather than trying to pose general questions which may turn out in the end to be ill-defined, there may be something to be said for trying to formulate much less speculative, indeed perhaps in retrospect trivial questions to which at least we have a hope of finding a definite answer. This is what I shall do in this essay: to be specific, I shall ask whether a test which is currently being designed concerning the validity of a certain ‘common-sense’ view of the macroscopic world (‘macrorealism’) would be affected if we were to relax our common-sense assumptions about the direction of causality in time.

Let me start with a very brief review of established ideas concerning the formal (a)symmetry of the quantum theory with respect to the direction of time. The classic works on this subject are the paper of Aharonov et al. (‘ABL’) and the book by Belinfante. In these discussions the notion of ‘measurement’ is taken as primitive and undefined.

Does time flow? It will be shown in this chapter that if the spacetime structure of the world has a certain branched dynamic form, then time flows. In addition to the flow and direction of time, two issues in quantum mechanics, those of non-locality and the definition of ‘measurement’, are shown to be illuminated by the hypothesis that the world has the spatio-temporal form described. I call the form the branched model, and the interpretation of quantum mechanics to which it gives rise I call the branched interpretation.

Objective time flow

The branched model is a four-dimensional spacetime model in the shape of a tree, each branch of which is a complete Minkowski manifold in which are located objects and events. The trunk represents the past, the first branch point is the present, and the branches constitute the set of all physically possible futures. The scheme is shown in figure 1.

Of the many possible futures which split off at the first branch point, one and only one is selected to become part of the past. The unselected branches vanish, so that the first branch point moves up the tree in a stochastic manner and the tree ‘grows’ by losing branches. This progressive branch attrition is what in the model constitutes the flow of time.

Suppose for example that 1000 lottery tickets have been sold to 1000 different purchasers. Then at the time of the draw, assuming the procedure is completely fair, there will be at least 1000 different kinds of branch at the first branch point: branches on which A wins, branches on which B wins, etc.

By the expression ‘closed causal chain’ I mean a process (a causally connected sequence of events) that loops back in such a way that each event is indirectly a cause of itself. In this chapter I will explore whether such processes might actually occur and whether certain scientific theories that suggest them might be correct. Since these are questions about what might exist, they are highly ambiguous. For there are various notions of possibility – including, for example, logical consistency, compatibility with the laws of physics, feasibility given current technology, and consonance with known facts – and the status of closed causal chains may be examined with respect to any of these notions. However, since our interest is not confined to just one kind of possibility, there is no need to choose between them, and so we can put our problem as follows. In what senses (if any) are closed causal chains possible, and in what senses (if any) are they impossible?

Another way in which the issue before us is somewhat unclear is with respect to what is to qualify as a closed causal chain – whether the often cited, potential examples really involve causation, strictly speaking. For one might well wonder if any relation that an event can bear to itself could really count as the causal relation, the relation of making something happen. I shall try to mitigate (or, rather, avoid) this problem by raising the questions of possibility, not primarily with respect to the abstract notion, ‘closed causal chain’, but rather with respect to three specific theories, and by construing the expression, ‘closed causal chain’, by reference to the processes they postulate.

The asymmetric nature of time, the radical difference in nature between past and future, has often been taken to be the core feature distinguishing time from that other manifold of experience and of nature, space. The past is fixed and has determinate reality. The future is a realm to which being can only be attributed, at best, in an ‘indeterminate’ mode of a realm of unactualized potentiality. We have memories and records of the past, but, at best, only inferential knowledge of a different sort of what is to come. Causation proceeds from past to future, what has been and what is determining what will be, but determination never occurs the other way around. Our attitudes of concern and our concepts of agency are likewise time asymmetric.

Since the late middle part of the nineteenth century there have been recurrent claims to the effect that all the intuitively asymmetric features of temporality are ‘reducible to’ or ‘grounded in’ the asymmetry of physical systems in the world that is captured by the Second Law of Thermodynamics. The suggestion is, as far as I know, first made by Mach. It is taken up by Boltzmann and used by him in his final attempt to show the statistical mechanical reduction of thermodynamics devoid of paradox. The claim is treated in detail in the twentieth century by Reichenbach, and accepted as legitimate by a host of other philosophers, mostly philosophers of science.

The physical asymmetry to which the asymmetry of time is to be reduced is that which tells us that the entropy of an isolated system can only increase in the future direction of time and can never spontaneously decrease.

Introduction

It is impossible to over-rate the important contribution which statistical mechanics makes to our contemporary understanding of the physical world. Cutting across the hierarchy of theories which describe the constitution of things and related in subtle and not yet fully understood ways to the fundamental dynamical theories, it provides the essential framework for describing the dynamical evolution of systems where large domains of initial conditions lead to a wide variety of possible outcomes distributed in a regular and predictable way. For the special case of the description of systems in equilibrium, the theory provides a systematic formalism which can be applied in any appropriate situation to derive the macroscopic equation of state. Here the usual Gibbsian ensembles, especially the microcanonical and canonical, function as a general schematism into which each particular case can be fit. In the more general case of non-equilibrium, the situation is less clear. While proposals have been made in the direction of a general form or schematism for the construction of non-equilibrium ensembles, most of the work which has been done relies upon specific tactical methods, of validity only in a limited area. BBGKY hierarchies of conditional probability functions work well for the molecular gas case. Master equation approaches work well for those cases where the system can be viewed as a large collection of nearly energetically independent subsystems coupled weakly to one another. But the theory still lacks much guidance in telling us what the macroscopic constraints ought to be which determine the appropriate phase space over which a probability distribution is to be assigned in order to specify an initial ensemble.

Eddington and the running-down of the universe

The phrase ‘time's arrow’ seems to have entered the discussion of time in Sir Arthur Eddington's Gifford Lectures, which were published in 1928. An ‘arrow’ of time is a physical process or phenomenon that has (or, at least, seems to have) a definite direction in time. The time reverse of such a process does not (or, at least, does not seem to) occur. Eddington thought he had found such an arrow in the increase of entropy in isolated systems. He wrote:

Since he held the universe to be an isolated system, he thought that its entropy, which he called its ‘random element’, must ineluctably increase until it reached thermodynamic equilibrium (until it is ‘completely shuffled’), by which point all life, and even time's arrow itself, must have disappeared. He called this process ‘the running-down of the universe’. This vision of the universe is stark, compelling, and by no means hopelessly dated. P. W. Atkins recently wrote:

Introduction

In this chapter the modelling of spacetime is discussed, with the aim of maintaining a clear distinction between the local properties of a model and those attributes which are global. This separation of attributes (into local and global type) logically motivates the construction of the non-Hausdorff branched model for spacetime. Of course, much of the physical motivation for this construction is derived from the stochastic nature of quantum mechanics. The Many-World Interpretation is seen to be (at least, topologically) a consistent and complete interpretation of quantum mechanics.

In any serious inquiry into the nature of spacetime (on either the quantum or cosmological level), mathematical models will be constructed which are in substantial agreement with the collective empiricism of experimental physics. If such a mathematical model is to be more than just a prescription for prediction, then it is necessary to give careful consideration to the appropriate level of mathematical generality of the model. Common sense, as well as the history of science, appear to indicate the need to maintain as general (i.e., unrestricted) a model as possible, constrained only by empirical data on one side, and the limits of our mathematical sophistication and imagination on the other.

In the spirit of generalization, I will construct a model of the time parameter, which extends the usual concept of a time-line, and can be used to model spacetime locally, with the usual product structure of Minkowski spacetime. Our imagination will be constrained only by the mathematical discipline of topology and a clear view of all underlying assumptions.

Introduction

Over the last few years leading scientific journals have been publishing articles dealing with time travel and time machines. (An unsystematic survey produced the following count for 1990–1992. Physical Review D: 11; Physical Review Letters: 5; Classical and Quantum Gravity. 3; Annals of the New York Academy of Sciences: 2; Journal of Mathematical Physics: 1. A total of 22 articles involving 22 authors.) Why? Have physicists decided to set up in competition with science fiction writers and Hollywood producers? More seriously, does this research cast any light on the sorts of problems and puzzles that have featured in the philosophical literature on time travel?

The last question is not easy to answer. The philosophical literature on time travel is full of sound and fury, but the significance remains opaque. Most of the literature focuses on two matters, backward causation and the paradoxes of time travel. Properly understood, the first is irrelevant to the type of time travel most deserving of serious attention; and the latter, while always good for a chuckle, are a crude and unilluminating means of approaching some delicate and deep issues about the nature of physical possibility. The overarching goal of this chapter is to refocus attention on what I take to be the important unresolved problems about time travel and to use the recent work in physics to sharpen the formulation of these issues.

The plan of the chapter is as follows. Section 1 distinguishes two main types of time travel – Wellsian and Godelian. The Wellsian type is inextricably bound up with backward causation.

Introduction

Like the Sirens singing to Ulysses, the concept of entropy has tempted many a thinker to abandon the straight and narrow course. The concept is well-defined for chambers of gases. However, the temptation to extend the concept has been all but irresistible. As a result, entropy is used as a metaphor for uncertainty and disorder. We have nothing against such extensions of usage and, in fact, will indulge in it ourselves. However, we do believe that the price of metaphor is eternal vigilance.

One example of the temptation can be found in R. A. Fisher's Genetical Theory of Natural Selection? In the second chapter of that book, Fisher states a result that he dubs the fundamental theorem of natural selection. The theorem states that the average fitness of the organisms in a population increases under selection, and does so at a rate given by the additive genetic variance in fitness. Fisher then proposes the following analogy:

Fisher then quotes Eddington's famous remark that ‘the law that entropy always increases – the second law of thermodynamics – holds, I think, the supreme position among the laws of nature.’