Our aim is to present a detailed exposition of problems concerning time in philosophy, Newtonian mechanics, relativity, thermodynamics, electrodynamics, quantum mechanics, and cosmology, emphasizing what we do not know.
This is the first part of the exposition and deals with certain preliminary questions regarding time. Age-old attempts to find satisfactory answers to these questions have generated a series of paradoxes. Those elaborated here are the paradox of the vanishing present, the paradox of unreal time, McTaggart’s paradox, Dumett’s paradox, Aristotle’s sea battle, the Master Argument of Diodorus Cronus, Zeno’s paradoxes of motion, and the Thomson lamp. The relevance of these paradoxes to frontier areas of physics, and the subsequent parts of this exposition, is briefly indicated.
KeywordsTruth Table Master Argument National Anthem Successive Moment Choose Event
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Notes and References
- 1.According to Paul Davies, in The Physics of Time Asymmetry,Surrey Univ. Press, London, 1974, the only remaining questions about time are philosophical in nature, and nothing qualitatively new can emerge from a study of the physics of time.Google Scholar
- 2.R. M. Gale, The Philosophy of Time, Macmillan, London, 1968.Google Scholar
- 3.F. Waismann, in Gale, Ref. 2.Google Scholar
- 4.Not every language has three tenses. The Hopi language is tenseless. See B. Whorf Language, Thought and Reality, MIT Press, Cambridge, Mass., 1950.Google Scholar
- 5.Often an order relation is required to be reflexive as well. The usual way of changing from to could well be followed here by replacing ‘earlier than’ with ‘earlier than or simultaneous with’. However, the reflexivity of the temporal relation is usually reserved for describing cyclic time where an event may be earlier than itself.Google Scholar
- 6.Ref. 2, p 67.Google Scholar
- 7.J.M.E. McTaggart , reprinted in Gale, Ref. 2.Google Scholar
- 8.According to the serialist argument of J.W. Dunne, inAn Experiment with lime, Faber, London, 1942, the regress is benign, and an infinite sequence of times provides the natural way of depicting time. Such claims are contrary to the requirement of simplicity (Occam’s razor). Moreover, I find the serialist argument quite irrelevant to the claimed empirical evidence of precognitive dreams developed further by Priestley, Ref. 18.Google Scholar
- 9.It is not clear how much of this impression is due to language. As pointed out earlier, the Hopi language has no tenses so that for the Hopi time does not move!Google Scholar
- 11.M. Dumett, ‘Bringing about the past’, Philosophical Review, 73, 1964. Reprinted in Gale, Ref. 2.Google Scholar
- 12.S.W. Hawking and G.F.R. Ellis, The Large Scale Structure of Space Time, University Press, Cambridge, 1974.Google Scholar
- 15.A detailed account of Zeno’s paradoxes of motion, with possible relevance to quantum mechanics, may be found in A. Grünbaum, Modem Science and Zeno’s Paradoxes, Allen and Unwin, London, 1968.Google Scholar
- 16.A discretized formulation of Newton’s laws, on the other hand, assumes that points of time may be well-ordered, like the natural numbers and unlike the rationals.Google Scholar
- 17.Such as those implicit in the definition of 0. 6, 0 being the Heaviside function and a the Dirac delta, using a formal Fourier transform to express the product as a (divergent) convolution integral.Google Scholar
- 18.J. B. Priestley, Man and Time, Aldus Books, London, 1964. Additional Notes: Chapter IGoogle Scholar
Additional Notes: Chapter I
- 19.A more recent survey of the ancient and medieval philosophy of time may be found in R. Sorabji, Time, Creation and the Continuum, Duckworth, London, 1983.Google Scholar
- 20.Quotations from 8rî Harsa use the translation of Khandana Khanda Khadya by Ganganath Jha, Vol. II, Sri Satguru Publications, New Delhi, , 2nd ed. 1986. At one point where high accuracy seemed absolutely essential I have used the more literal ‘self reference’ in place of Jha’s ‘vicious circle’. I have also modified Jha’s translation of II.1.39 from The Nyaya Sutras of Gautam,Vol II, reprint, Motilal Banrsidass, New Delhi, 1986. Similarly, the translations of Pâninî and Pataiijali incline towards the more literal. The translation of Vyâsa is abridged from J. H. Woods, The Yoga System of Patanjali…,Harvard Oriental Series, Vol 17, Cambridge, Mass., 1927, p 287–88.Google Scholar