Professor Hawking’s Brief History of Time thoroughly deserves the praise with which it has been widely received.* With only one formula, Einstein’s celebrated E = mc2, which he could just as well have put into prose simply by saying that energy is the arithmetical product of mass and the square of the velocity of light, Hawking gives a more lucid account than any that has yet come my way of such arcane matters as quantum theory and its wave-particle duality, the general and special theories of relativity, the blending of space and time into a four-dimensional continuum, the ways in which physicists measure the age and structure of the universe, the ‘big bang’ with which it is thought to have started, the reasons for holding that it continues to expand, the shrinkage of stars into ‘black holes’.

Just as the failure in the 19th century of established art critics, let alone the general public, to appreciate the works of the French Impressionists has frightened people nowadays from voicing their disapproval of anything that is offered to them under the heading of Pop Art, so the folly of Oxford philosophers sixty or more years ago in rejecting relativity theory and quantum theory, on the mere basis of their a priori intuitions, has made their successors wary of encroaching on the territory of physics in any way at all. Cambridge philosophers, like Russell, Whitehead, Broad and Braithwaite, have not suffered from the same inhibitions, perhaps because they came to philosophy with a training in mathematics and not with the almost exclusively Classical background of the Oxford philosophers of my generation. Wittgenstein, who was drawn to philosophy by his interest in the foundations of mathematics, was schooled as an engineer. Hawking represents Wittgenstein as saying, ‘The sole remaining task for philosophy is the analysis of language,’ and calls this a come-down from ‘the great tradition of philosophy from Aristotle to Kant’. I cannot identify the quotation, but it is a fair enough inference from Wittgenstein’s later practice. What Hawking has overlooked is that it is in the analysis of the language of physics that his own book principally consists. His reproach should have been directed at philosophers like me who have not had the scientific education to relieve him of this task.

Nevertheless I am going not so much to take issue with him as to argue that there are one or two points in his exposition that need to be further clarified, and one or two assertions that have stranger implications than have been explicitly noted by him in his book or, so far as I am aware, by those who have reviewed it.

To begin with, it is not entirely clear whether Hawking takes a realistic or an instrumentalist view of physics. For the most part, his attitude seems to be realistic. Even when he speaks of the function of scientific theories as being that of relating qualities in the world to the observations that we make, the implication appears to be that the qualities are there, independently of our observing them. Moreover many of his accredited hypotheses, regarding the age and size of the universe, and the composition of its many galaxies, are related only tenuously to observation, which is not to say that our observations, such as they are, do not support them. On the other hand, his rejection of absolute time, on the basis of Einstein’s theories of relativity, commits him to the view that an event has no temporal location except in relation to the positions and velocities of its observers, which need not coincide; and he also accepts the Copenhagen interpretation of quantum theory, according to which the impossibility of obtaining a precise measurement of the position and momentum of a particle at any given instant entails that to speak of a particle as being in such an undetectable condition makes no sense.

Hawking’s tendency to oscillate at least between realistic and operational diction has one unhappy consequence for him. After introducing the concept of Euclidean space-time, as something measured by ‘imaginary’ numbers – that is to say, numbers like √-1, which yield negative numbers when multiplied by themselves – and as something that differs from the subject of traditional Euclidean geometry in that it has four dimensions, with no difference between the direction of time and directions in space, Hawking reassures his readers, who may at this point have had some difficulty in following him, by saying that ‘as far as everyday quantum mechanics is concerned, we may regard our use of imaginary time and Euclidean space-time as merely a mathematical device to calculate answers about real space-time.’ On the very same page (135) he initiates a discussion of the initial state of the universe in which his preference for a spatio-temporal surface which is finite but unbounded is based on his plumping for Euclidean space-time. Admittedly, he avoids self-contradiction by associating Euclidean space-time with ‘quantum gravity’ which goes beyond ‘everyday quantum mechanics’, but he just passes over the promotion of Euclidean space-time from a mathematical device to a physical reality. I am not convinced that the reasons he adduces for making this promotion are sufficient.

I am puzzled also by his saying that if he fulfilled Einstein’s hope of unifying relativity and quantum theory he would be furnishing a description of the whole universe. What about the observations which would sustain the theory? They would need to be predictable, within quantum limitations, but would so abstract a theory actually describe them? What about the history of the universe? Would his theory account for the whole course of evolution with its chance mutations? Would they be derivable from quantum probabilities? Surely this needs to be shown.

Hawking distinguishes three arrows of time: the cosmological arrow, which is the direction in which the universe is expanding rather than contracting, the thermodynamic arrow, which is the direction of greater entropy, the passage from less to greater disorder, and the psychological arrow, which is the direction in which we experience the passage of time. He rather surprisingly identifies the thermodynamic and psychological directions, but he has given up his earlier belief in the possibility of our living our lives ‘backward’ because of his refusal to uncouple thermodynamic with cosmological time, his point being that if a reversal of entropy went with a contracting universe, there would be no human beings, since the physical conditions of our existence require us to dwell in an expanding phase.

This does not, however, prevent Hawking from accepting the possibility of time travel. He remarks, in a jocular aside, that it is just as well that ‘cosmic censorship’ would prevent astronauts who avoided falling into black holes from having the power to project themselves into the past. Otherwise, he says, ‘no one’s life would ever be safe: someone might go into the past and kill your father and mother before you were conceived.’ Probably, if he had been speaking more seriously he would have spotted the non-sequitur. In the astronaut’s time, events which occurred, according to an earthbound calendar, in the year in which my parents conceived me might succeed his approach to the black hole, but the events in question could be no more than a selection of the year’s occurrences, arbitrarily chosen so as to define ‘the past’ and none of them entailing his presence, since he was not there. Since I was conceived he could not cause me not to have been. Of course my parents might have been killed before my conception: but for that we do not need an astronaut. A terrestial murderer would do just as well. This is quite an important point, because people are apt to wish that they could foresee the future in order to prevent whatever unpleasant things are going to happen to them. But if these unpleasantnesses do lie in the future they cannot be prevented. This is not fatalism. Perhaps they could be prevented if the proper steps were taken. But the premise that they actually lie in the future entails that they are not not going to be prevented.

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