Abstract
Studies of time by scientists have often been concerned with the multifaceted problems of measuring time intervals in atomic, geophysical, biological, and astronomical contexts. It has been claimed that in addition to exhibiting measurable intervals, time is characterized by a transiency of the present, which has often been called ‘flux’ or ‘passage’.
A Louis Clark Vanuxem Lecture, delivered at Princeton University on March 2, 1967. This paper includes a revised version of Chapter I of my Modern Science and Zeno’s Paradoxes, Wesleyan University Press, Middletown, 1967; 2nd ed., Allen & Unwin Ltd., London, 1968.
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References
G. J. Whitrow, The Natural Philosophy of Time,Thomas Nelson and Sons, Ltd., London, 1961, p. 88.
For example, consider the events in the careers of human beings or of animals who return to a spatially fixed terrestrial habitat every so often. These events occur at space points on the earth which certainly do not exhibit the betweenness of the points on a Euclidean straight line.
For details, cf. Adolf Grünbaum, Philosophical Problems of Space and Time,Alfred A. Knopf, Inc., New York, 1964, pp. 214–216. Hereafter this work will be cited as PPST.
This noncommittal character of the term ‘initial state’ seems to have been recognized by O. Costa de Beauregard in one part of his paper entitled ‘Irreversibility Problems’, Logic, Methodology and Philosophy of Science,Proceedings of the 1964 International Congress (ed. by Y. Bar-Hillel), North-Holland Publ. Co., Amsterdam, 1965, p. 327. But when discussing my criticism of Hans Reichenbach’s account of irreversibility (PPST,pp. 261–263), Costa de Beauregard (ibid.,p. 331) overlooks that my criticism invokes initial states in only the noncommittal sense set forth above.
Thus, it is erroneous to maintain, as Milic Capek does, that the distinction between temporal betweenness and irreversibility is ‘fallacious’ in virtue of being ‘based on the superficial and deceptive analogy of “the course of time” with a geometrical line’, The Philosophical Impact of Contemporary Physics,D. Van Nostrand Co., Inc., Princeton, New Jersey, 1961, p. 349; see also pp. 347 and 355. If Capek’s condemnation of this distinction were correct, the following fundamental question of theoretical physics could not even be intelligibly and legitimately asked: Are the prima facie irreversible processes known to us indeed irreversible, and, if so, on the strength of what laws and/or boundary conditions are they so? For this question is predicated on the very distinction which Capek rejects as ‘fallacious’. By the same token, Capek errs (ibid.,p. 355) in saying that when Reichenbach characterizes entropically counterdirected epochs as ‘succeeding each other’, then irreversibility ‘creeps in’ along with the asymmetrical relations of before and after. For all that he needs to assume here to speak of ‘before’ and ‘after’ is a time coordinatization which reflects the assumed kind of betweenness and simultaneity.
On the basis of a highly equivocal use of the term ‘irreversible’, M. Capek, ibid.,pp. 166–167 and 344–345 has claimed incorrectly that the account of the space-time properties of world lines given by the special theory of relativity entails the irreversibility of physical processes represented by world lines. He writes: ‘The world lines, which by definition are constituted by a succession of isotopic events, are irreversible in all systems of reference’ (ibid.,p. 167) and the relativistic universe is dynamically constituted by the network of causal lines each of which is irreversible;... this irreversibility is a topological invariant’ (ibid.,pp. 344–345). But Capek fails to distinguish between (1) the non-inversion or invariance of time-order as between different Galilean frames which the Lorentz-transformation equations assert in the case of causally connectible events, and (2) the irreversibility of processes represented by world lines in the standard sense of the non-restorability of the same kind of state in any frame. Having applied the term ‘irreversibility’ to (1) no less than to (2) after failing to distinguish them, Capek feels entitled to infer that the Lorentz transformations attribute irreversibility within any one frame to processes depicted by world lines, just because these transformations assert the invariance of time order on the world lines as between different frames. That the Lorentz equations do not disallow the reversibility of physical processes becomes clear upon making each of the two replacements t → — t and t ’ → — t’ in them: these replacements issue in the same set of equations except for the sign of the velocity term in each of the numerators, i.e., they merely reverse the direction of the motion. Therefore, these two replacements do not involve any violation of the theory’s time-order invariance as between different frames S and S’. By contrast, different equations exhibiting a violation of time-order invariance on the world lines would beobtained by replacing only one of the two variables t and t’ by its negative counterpart in the Lorentz equations.
For a discussion of the various kinds of irreversible processes which make for the anisotropy of time and furnish specified criteria for the relations of temporal precedence and succession, see Costa de Beauregard, op. cit.,p. 327; and A. Griinbaum, PPSTCh. 8, and ‘The Anisotropy of Time’, in The Nature of Time (ed. by D. L. Schumacher and T. Gold), Cornell University Press, Ithaca, 1967, pp. 149–186.
Some have questioned the possibility of stating what specific physical events do occur in point of fact at particular clock times without covert appeal to the transient now. Cf. Hermann Weyl, Philosophy of Mathematics and Natural Science,Princeton University Press, Princeton, 1949, p. 75. In their view, any physical description will employ a time coordinatization, and any such coordinatization must ostensively invoke the now to designate at least one state as, say, the origin of the time coordinates. But I do not see a genuine difficulty here for three reasons. Firstly, it is not clear that the designation of the birth of Jesus, for example, as the origin of time coordinates tacitly makes logically indispensable use of the now or of tenses in virtue of making use of a proper name. Secondly, in some cosmological models of the universe, an origin of time coordinates can clearly be designated non-ostensively: in the ‘big bang’ model, the big bang itself can be designated uniquely and non-ostensively as the one state having no temporal predecessor. And thirdly, any two descriptions of the world which differ only in the choice of the origin of time coordinates while employing the same time metric and time topology are equivalent with respect to their factual physical content. Thus such descriptions differ only in regard to the way in which they numerically name or label particular simultaneity classes of events. Hence, let us grant for argument’s sake that tacit use of the now or of tenses is logically indispensable to designating the origin of any one particular time coordinatization. Even if this is granted, it does not follow that past, present, and future have a mind-independent status in the temporal structure of the physical world.
The claim that the now advances in the direction of the future is a truism as regards both the correspondence between nows and physically later clock times and their correspondence with psychologically (introspectively) later contents of awareness. What is not a truism, however, is that the introspectively later nows are temporally correlated with states of our physical environment that are later as per criteria furnished by irreversible physical processes. This latter correlation depends for its obtaining on the laws governing the physical and neural processes necessary for the mental accumulation of memories and for the registry of information in awareness. (For an account of some of the relevant laws, see A. Grünbaum, PPST,Ch. 9, Secs. A and B.) Having exhibited the aforementioned truisms as such and having noted the role of the empirical laws just mentioned, I believe to have answered Costa de Beauregard’s complaint (in ‘Irreversibility Problems’, op. cit.,p. 337) that ‘stressing that the arrows of entropy and information increase are parallel to each other is not proving that the flow of subjectivistic time has to follow the arrows!’
A very illuminating account of the logical relations of Minkowski’s language to tensed discourse is given by Wilfrid Sellars in ‘Time and the World Order’, Minnesota Studies in the Philosophy of Science,vol. III (ed. by H. Feigl and G. Maxwell), University of Minnesota Press, Minneapolis, 1962, p. 571.
Quoted from G. J. Whitrow, op. cit.,pp. 129–130.
For a searching treatment of the ramifications of the contrast pertinent here, see Wilfrid Sellars, ‘Philosophy and the Scientific Image of Man’, Frontiers of Science and Philosophy (ed. by Robert G. Colodny ), University of Pittsburgh Press, Pittsburgh, 1962, pp. 35–78.
It will be noted that I speak here of the dependence of nowness on an organism M which is mind-possessing in the sense of having conceptualized or judgmental awareness, as contrasted with mere sentiency. Since biological organisms other than man (e.g., extra-terrestrial ones) may be mind-possessing in this sense, it would be unwarrantedly restrictive to speak of the mind-dependence of nowness as its ‘anthropocentricity’. Indeed, it might be that conceptualized awareness turns out not to require a biochemical substratum but can also inhere in a suitably complex ‘hardware’ computer. That a physical substratum of some kind is required would seem to be abundantly supported by the known dependence of the content and very existence of consciousness in man on the adequate functioning of the human body.
The distinction pertinent here between the mere hearing of something and judgmental awareness that it is being heard is well stated by Roderick Chisholm as follows: ‘We may say of a man simply that he observes a cat on the roof. Or we may say of him that he observes that a cat is on the roof. In the second case, the verb “observe” takes a “that”-clause, a propositional clause as its grammatical object. We may distinguish, therefore, between a “propositional” and a “nonpropositional” use of the term “observe”, and we may make an analogous distinction for “perceive”, “see”, “hear”, and “feel”‘. ‘If we take the verb “observe” propositionally, saying of the man that he observes that a cat is on the roof, or that he observes a cat to be on the roof, then we may also say of him that he knows that a cat is on the roof; for in the propositional sense of “observe”, observation may be said to imply knowledge. But if we take the verb nonpropositionally, saying of the man only that he observes a cat which is on the roof, then what we say will not imply that he knows that there is a cat on the roof. For a man may be said to observe a cat, to see a cat, or hear a cat, in the nonpropositional sense of these terms, without his knowing that a cat is what he is observing, or seeing, or hearing. “It was not until the following day that I found out that what I saw was only a cat”’. Theory of Knowledge,Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1966, p. 10. I am indebted to Richard Gale for this reference.
The judgmental awareness which I claim to be essential to an event’s qualifying as now may, of course, be expressed by a linguistic utterance, but it clearly need not be so expressed. I therefore consider an account of nowness which is confined to utterances as inadequate. Such an overly restrictive account is given in J. J. C. Smart’s otherwise illuminating defense of the anthropocentricity of tense, Philosophy and Scientific Realism,Routledge andKegan Paul, London, 1963, Chapter vii. But this undue restrictiveness is quite inessential to his thesis of the anthropocentricity of nowness. And the non-restrictive treatment which I am advocating in its stead would obviate his having to rest his case on (1) denying that ‘this utterance’ can be analyzed as ‘the utterance which is now’,and (2) insisting that ‘now’ must be elucidated in terms of ‘this utterance’ (ibid.,pp. 139–140).
Hans Reichenbach, The Direction of Time,University of California Press, Berkeley, Calif., 1956, p. 16.
Paul Fraisse, The Psychology of Time, Eyre & Spottiswoode, London, 1964, p. 73.
A. Grünbaum, PPST,p. 325.
M. Capek, op. cit.,p. 337.
On the basis of such a misunderstanding, M. Capek incorrectly charges the thesis with a ‘spatialization of time’ in which ‘successive moments already coexist’ (ibid.,pp. 160–163) and in which ‘the universe with its whole history is conceived as a single huge and timeless bloc, given at once’ (ibid.,p. 163). See also p. 355.
G. J. Whitrow, op. cit.,p. 228 (my italics). For a criticism of another such misconstrual, see A. Grünbaum, PPST,pp. 327–328.
G. J. Whitrow, ibid.,p. 88.
Ibid.,pp. 227–228.
J. J. C. Smart, op. cit.,p. 139.
G. J. Whitrow, op. cit.,p. 88, n. 2 (my italics).
Ibid.,p. 293.
Ibid.,p. 88, n. 2.
Bertrand Russell, ‘On the Experience of Time’, The Monist 25 (1915), 212.
The need to deal with this question has been pointed out independently by Donald C. Williams and Richard Gale.
Mental events, as distinct from the neurophysiological counterpart states which they require for their occurrence, are not in our heads in the way in which, say, a biochemical event in the cortex or medulla oblongata is.
Thus a conscious state of elation induced in me by the receipt of good news from a telephone call C 1 could be temporally between the physical chain C 1 and another such chain C 2 consisting of my telephonic transmission of the good news to someone else.
J. J. C. Smart, op. cit.,p. 135.
I am indebted to Richard Gale for pointing out to me that since the term ‘psychological’ is usefully reserved for mind-dependent attributes which are private, as specified, it would be quite misleading to assert the mind-dependence of tense by saying that tense is ‘psychological’. In order to allow for the required kind of intersubjectivity, I have therefore simply used the term ‘mind-dependent’.
Hans Reichenbach, The Philosophy of Space and Time,Dover Publications, Inc., New York, 1958, pp. 138–139.
Hans Reichenbach, ‘Les Fondements Logiques de la Mécanique des Quanta’, Annales de l’Institut Poincaré 13 (1953), 154–157.
Ibid.
Cf. H. Bergmann, Der Kampf um das Kausalgesetz in der jüngsten Physik,Vieweg & Sohn, Braunschweig, 1929, pp. 27–28.
H. Bondi, ‘Relativity and Indeterminacy’, Nature 169 (1952), 660.
I am indebted to Professor Wilfrid Sellars for having made clarifying remarks to me in 1956 which relate to this point. And Costa de Beauregard has reminded me of the pertinent French dictum Ce qui sera, sera.
Yakir Aharonov and David Bohm have noted that time does not appear in Schrödinger’s equation as an operator but only as a parameter and have pointed out the following: (1) The time of an energy state is a dynamical variable belonging to the measuring apparatus and therefore commutes with the energy of the observed system. (2) Hence the energy state and the time at which it exists do not reciprocally limit each other’s well-defined status in the manner of the non-commuting conjugate quantities of the Heisenberg Uncertainty Relations. (3) Analysis of illustrations of energy measurement (e.g., by collision) which seemed to indicate the contrary shows that the experimental arrangements involved in these examples did not exhaust the measuring possibilities countenanced by the theory. Cf. their two papers on ‘Time in the Quantum Theory and the Uncertainty Relation for Time and Energy’, Physical Review 122 (1961), 1649, and Physical Review 134 (1964), B1417. I am indebted to Professor A. Janis for this reference.
A helpful account of the difference relevant here between being determinate (i.e., intrinsically attribute-specific) and being determined (in the relational sense of causally necessitated or informationally ascertained), is given by Donald C. Williams in Principles of Empirical Realism,Charles C. Thomas, Springfield, Ill., 1966, pp. 274 ff.
Capek, op. cit.,p. 340.
Capek writes further: ‘As long as the ambiguity of the future is a mere appearance due to the limitation of our knowledge, the temporal character of the world remains necessarily illusory’, and ‘the principle of indeterminacy... means the reinstatement of becoming in the physical world’ [ibid.,p. 334]. But granted that the indeterminacy of quantum theory is ontological rather than merely epistemological, this indeterminacy is nonetheless relational and hence unavailing as a basis for Capek’s conclusions.
Ibid.,pp. 334–335, cf. also p. 164.
G. J. Whitrow, op. cit.,p. 295.
M. Capek, op. cit.,p. 165.
Accordingly, we must qualify the following statement by J. J. C. Smart, op. cit.,pp. 141–142: ‘We can now see also that the view of the world as a space-time manifold no more implies determinism than it does the fatalistic view that the future “is already laid up”. It is compatible both with determinism and with indeterminism, i.e., both with the view that earlier time slices of the universe are determinately related by laws of nature to later time slices and with the view that they are not so related’. This statement needs to be qualified importantly, since it would not hold if ‘indeterminism’ here meant a macro-indeterminism such that macroscopic causal chains would not exist.
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Grünbaum, A. (1969). The Meaning of Time. In: Rescher, N. (eds) Essays in Honor of Carl G. Hempel. Synthese Library, vol 24. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1466-2_8
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