This recognition was left to Einstein (and several others, H. A. Lorentz, Poincaré, Minkowski, for example). The mighty impact of their discoveries on philosophers, men-in-the-street, and ladies in the drawing-room is due to the fact that they brought it to the fore: even in the domain of our experience the spatio-temporal relations are much more intricate than Kant dreamed them to be, following in this all previous physicists, men-in-the-street and ladies in the drawing-room.
The new view has its strongest impact on the previous notion of time. Time is the notion of ‘before and after’. The new attitude springs from the following two roots:
(i) The notion of ‘before and after’ resides on the ‘cause and effect’ relation. We know, or at least we have formed the idea, that one event A can cause, or at least modify, another event A, so that if B were not, then B were not, at least not in this modified form. For instance when a shell explodes, it kills a man who was sitting on it; moreover the explosion is heard at distant places. The killing may be simultaneous to the explosion, the hearing of the sound at a distant place will be later; but certainly none of the effects can be earlier. This is a basic notion, indeed it is the one by which also in everyday life the question is decided which of two events was later or at least not earlier. The distinction rests entirely on the idea that the effect cannot precede the cause. If we have reasons to think that B has been caused by A, or that it at least shows vestiges of A, or even if (from some circumstantial evidence) it is conceivable that it shows vestiges, then B is deemed to be certainly not earlier than A.
(2) Keep this in mind. The second root is the experimental and observational evidence that effects do not spread with arbitrarily high velocity. There is an upper limit, which incidentally is the velocity of light in empty space. In human measure it is very high, it would go round the equator about seven times in one second. Very high, but not infinite, call it c. Let this be agreed upon as a fundamental fact of nature. It then follows that the above-mentioned discrimination between ‘before and after’ or ‘earlier and later’ (based on the cause-and-effect relation) is not universally applicable, it breaks down in some cases. This is not as easily explained in non-mathematical language. Not that the mathematical scheme is so complicated. But everyday language is prejudicial in that it is so thoroughly imbued with the notion of time – you cannot use a verb (verbum, ‘the’ word, Germ. Zeitwort) without using it in one or the other tense.
Fig. 3.
The simplest but, as will turn out, not fully adequate consideration runs thus. Given an event A. Contemplate at any later time an event B outside the sphere of radius ct around A. Then B cannot exhibit any ‘vestige’ of A; nor, of course can A from B. Thus our criterion breaks down. By the language we used we have, of course, dubbed B to be the later. But are we right in this, since the criterion breaks down either way?
Contemplate at a time earlier (by t) an event B′ outside that same sphere. In this case, just as before, no vestige of B′ can have reached A (and, of course, none from A can be exhibited on B′).
Thus in both cases there is exactly the same relationship of mutial non-interference. There is no conceptual difference between the classes B and B′ with regard to their cause-effect relation to A. So if we want to make this relation, and not a linguistic prejudice, the basis of the ‘before and after’, then the B and B′ form one class of events that are neither earlier nor later than A. The region of space-time occupied by this class is called the region of ‘potential simultaneity’ (with respect to event A). This expression is used, because a space-time frame can always be adopted that makes A simultaneous with a selected particular B or a particular B′. This was Einstein’s discovery (which goes under the name of The Theory of Special Relativity, 1905).
Now these things have become very concrete reality to us physicists, we use them in everyday work just as we use the multiplication table or Pythagoras’ theorem on right-angled triangles. I have sometimes wondered why they made such a great stir both among the general public and among philosophers. I suppose it is this, that it meant the dethronement of time as a rigid tyrant imposed on us from outside, a liberation from the unbreakable rule of ‘before and after’. For indeed time is our most severe master by ostensibly restricting the existence of each of us to narrow limits – seventy or eighty years, as the Pentateuch has it. To be allowed to play about with such a master’s programme believed unassailable until then, to play about with it albeit in a small way, seems to be a great relief, it seems to encourage the thought that the whole ‘timetable’ is probably not quite as serious as it appears at first sight. And this thought is a religious thought, nay I should call it the religious thought.
Einstein has not – as you sometimes hear – given the lie to Kant’s deep thoughts on the idealization of space and time; he has, on the contrary, made a large step towards its accomplishment.
I have spoken of the impact of Plato, Kant and Einstein on the philosophical and religious outlook. Now between Kant and Einstein, about a generation before the latter, physical science had witnessed a momentous event which might have seemed calculated to stir the thoughts of philosophers, men-in-the-street and ladies in the drawing-room at least as much as the theory of relativity, if not more so. That this was not the case is, I believe, due to the fact that this turn of thought is even more difficult to understand and was therefore grasped by very few among the three categories of persons, at the best by one or another philosopher. This event is attached to the names of the American Willard Gibbs and the Austrian Ludwig Boltzmann. I will now say something about it.
With very few exceptions (that really are exceptions) the course of events in nature is irreversible. If we try to imagine a time-sequence of phenomena exactly opposite to one that is actually observed – as in a cinema film projected in reversed order – such a reversed sequence, though it can easily be imagined, would nearly always be in gross contradiction to well-established laws of physical science.
The general ‘directedness’ of all happening was explained by the mechanical or statistical theory of heat, and this explanation was duly hailed as its most admirable achievement. I cannot enter here on the details of the physical theory, and this is not necessary for grasping the gist of the explanation. This would have been very poor, had irreversibility been stuck in as a fundamental property of the microscopic mechanism of atoms and molecules. This would not have been better than many a medieval purely verbal explanation such as: fire is hot on account of its fiery quality. No. According to Boltzmann we are faced with the natural tendency of any state of order to turn on its own into a less orderly state, but not the other way round. Take as a simile a set of playing cards that you have carefully arranged, beginning with 7, 8, 9, 10, knave, queen, king, ace of hearts, then the same in diamonds, etc. If this well-ordered set is shuffled once, twice or three times it will gradually turn into a random set. But this is not an intrinsic property of the process of shuffling. Given the resulting disorderly set, a process of shuffling is perfectly thinkable that would exactly cancel the effect of the first shuffling and restore the original order. Yet everybody will expect the first course to take place, nobody the second -indeed he might have to wait pretty long for it to happen by chance.
Now this is the gist of Boltzmann’s explanation of the unidirectional character of everything that happens in nature (including, of course, the life-history of an organism from birth to death). Its very virtue is that the ‘arrow of time’ (as Eddington called it) is not worked into the mechanisms of interaction, represented in our simile by the mechanical act of shuffling. This act, this mechanism is as yet innocent of any notion of past and future, it is in itself completely reversible, the ‘arrow’ – the very notion of past and future – results from statistical considerations. In our simile with the cards the point is this, that there is only one, or a very few, well-ordered arrangements of the cards, but billions of billions of disorderly ones.
Yet the theory has been opposed, again and again,
occasionally by very clever people. The opposition boils down to this: the theory is said to be unsound on logical grounds. For, so it is said, if the basic mechanisms do not distinguish between the two directions of time, but work perfectly symmetrically in this respect, how should there from their co-operation result a behaviour of the whole, an integrated behaviour, that is strongly biased in one direction? Whatever holds for this direction must hold equally well for the opposite one.
If this argument is sound, it seems to be fatal. For it is aimed at the very point which was regarded as the chief virtue of the theory: to derive irreversible events from reversible basic mechanisms.
The argument is perfectly sound, yet it is not fatal. The argument is sound in asserting that what holds for one direction also holds for the opposite direction of time, which from the outset is introduced as a perfectly symmetrical variable. But you must not jump to the conclusion that it holds quite in general for both directions. In the most cautious wording one has to say that in any particular case it holds for either the one or the other direction. To this one must add: in the particular case of the world as we know it, the ‘running down’ (to use a phrase that has been occasionally adopted) takes place in one direction and this we call the direction from past to future. In other words the statistical theory of heat must be allowed to decide by itself high-handedly, by its own definition, in which direction time flows. (This has a momentous consequence for the methodology of the physicist. He must never introduce anything that decides independently upon the arrow of time, else Boltzmann’s beautiful building collapses.)
It might be feared that in different physical systems the statistical definition of time might not always result in the same time-direction. Boltzmann boldly faced this eventuality; he maintained that if the universe is sufficiently extended and/or exists for a sufficiently long period, time might actually run in the opposite direction in distant parts of the world. The point has been argued, but it is hardly worth while arguing any longer. Boltzmann did not know what to us is at least extremely likely, namely that the universe, as we know it, is neither large enough nor old enough to give rise to such reversions on a large scale. I beg to be allowed to add without detailed explanations that on a very small scale, both in space and in time, such reversions have been observed (Brownian movement, Smoluchowski).
To my view the ‘statistical theory of time’ has an even stronger bearing on the philosophy of time than the theory of relativity. The latter, however revolutionary, leaves untouched the undirectional flow of time, which it presupposes, while the statistical theory constructs it from the order of the events. This means a liberation from the tyranny of old Chronos. What we in our minds construct ourselves cannot, so I feel, have dictatorial power over our mind, neither the power of bringing it to the fore nor the power of annihilating it. But some of you, I am sure, will call this mysticism. So with all due acknowledgment to the fact that physical theory is at all times relative, in that it depends on certain basic assumptions, we may, or so I believe, assert that physical theory in its present stage strongly suggests the indestructibility of Mind by Time.
CHAPTER 6
The Mystery of the Sensual Qualities
In this last chapter I wish to demonstrate in a little more detail the very strange state of affairs already noticed in a famous fragment of Democritus of Abdera – the strange fact that on the one hand all our knowledge about the world around us, both that gained in everyday life and that revealed by the most carefully planned and painstaking laboratory experiments, rests entirely on immediate sense perception, while on the other hand this knowledge fails to reveal the relations of the sense perceptions to the outside world, so that in the picture or model we form of the outside world, guided by our scientific discoveries, all sensual qualities are absent. While the first part of this statement is, so I believe, easily granted by everybody, the second half is perhaps not so frequently realized, simply because the non-scientist has, as a rule, a great reverence for science and credits us scientists with being able, by our ‘fabulously refined methods’, to make out what, by its very nature, no human can possibly make out and never will be able to make out.
If you ask a physicist what is his idea of yellow light, he will tell you that it is transversal electro-magnetic waves of wave-length in the neighbourhood of 590 millimicrons. If you ask him: But where does yellow come in? he will say: In my picture not at all, but these kinds of vibrations, when they hit the retina of a healthy eye, give the person whose eye it is the sensation of yellow. On further inquiry you may hear that different wave-lengths produce different colour-sensations, but not all do so, only those between about 800 and 400 μμ. To the physicist the infra-red (more than 800 μμ) and the ultra-violet (less than 400 μμ) waves are much the same kind of phenomena as those in the region between 800 and 400 μμ, to which the eye is sensitive. How does this peculiar selection come about? It is obviously an adaptation to the sun’s radiation, which is strongest in this region of wave-lengths but falls off at either end. Moreover, the intrinsically brightest colour-sensation, the yellow, is encountered at that place (within the said region) where the sun’s radiation exhibits its maximum, a true peak.
We may further ask: Is radiation in the neighbourhood of wave-length 590 μμ the only one to produce the sensation of yellow? The answer is: Not at all. If waves of 760 μμ, which by themselves produce the sensation of red, are mixed in a definite proportion with waves of 535 μμ, which by themselves produce the sensation of green, this mixture produces a yellow that is indistinguishable from the one produced by 590 μμ. Two adjacent fields illuminated, one by the mixture, the other by the single spectral light, look exactly alike, you cannot tell which is which. Could this be foretold from the wave-lengths – is there a numerical connection with these physical, objective characteristics of the waves? No. Of course, the chart of all mixtures of this kind has been plotted empirically; it is called the colour triangle. But it is not simply connected with the wave-lengths. There is no general rule that a mixture of two spectral lights matches one between them; for example a mixture of ‘red’ and ‘blue’ from the extremities of the spectrum gives ‘purple’, which is not produced by any single spectral light. Moreover, the said chart, the colour triangle, varies slightly from one person to the other, and differs considerably for some persons, called anomalous trichromates (who are not colour-blind).
The sensation of colour cannot be accounted for by the physicist’s objective picture of light-waves. Could the physiologist account for it, if he had fuller knowledge than he has of the processes in the retina and the nervous processes set up by them in the optical nerve bundles and in the brain? I do not think so. We could at best attain to an objective knowledge of what nerve fibres are excited and in what proportion, perhaps even to know exactly the processes they produce in certain brain cells – whenever your mind registers the sensation of yellow in a particular direction or domain of our field of vision. But even such intimate knowledge would not tell us anything about the sensation of colour, more particularly of yellow in this direction – the same physiological processes might conceivably result in a sensation of sweet taste, or anything else. I mean to say simply this, that we may be sure there is no nervous process whose objective description includes the characteristic ‘yellow colour’ or ‘sweet taste’, just as little as the objective description of an electro-magnetic wave includes either of these characteristics.
The same holds for other sensations. It is quite interesting to compare the perception of colour, which we have just surveyed, with that of sound. It is normally conveyed to us by elastic waves of compression and dilatation, propagated in the air. Their wave-length – or to be more accurate their frequency – determines the pitch of the sound heard. (N.B. The physiological relevance pertains to the frequency, not to the wave-length, also in the case of light, where, however, the two are virtually exact reciprocals of each other, since the velocities of propagation in empty space and in air do not differ p
erceptibly.) I need not tell you that the range of frequencies of ‘audible sound’ is very different from that of ‘visible light’, it ranges from about 12 or 16 per second to 20,000 or 30,000 per second, while those for light are of the order of several hundred (English) billions. The relative range, however, is much wider for sound, it embraces about 10 octaves (against hardly one for ‘visible light’); moreover, it changes with the individual, especially with age: the upper limit is regularly and considerably reduced as age advances. But the most striking fact about sound is that a mixture of several distinct frequencies never combines to produce just one intermediate pitch such as could be produced by one intermediate frequency. To a large extent the superposed pitches are perceived separately – though simultaneously – especially by highly musical persons. The admixture of many higher notes (‘overtones’) of various qualities and intensities results in what is called the timbre (German: Klangfarbe), by which we learn to distinguish a violin, a bugle, a church bell, piano … even from a single note that is sounded. But even noises have their timbre, from which we may infer what is going on; and even my dog is familiar with the peculiar noise of the opening of a certain tin box, out of which he occasionally receives a biscuit. In all this the ratios of the co-operating frequencies are all-important. If they are all changed in the same ratio, as on playing a gramophone record too slow or too fast, you still recognize what is going on. Yet some relevant distinctions depend on the absolute frequencies of certain components. If a gramophone record containing a human voice is played too fast, the vowels change perceptibly, in particular the ‘a’ as in ‘car’ changes into that in ‘care’. A continuous range of frequencies is always disagreeable, whether offered as a sequence, as by a siren or a howling cat, or simultaneously, which is difficult to implement, except perhaps by a host of sirens or a regiment of howling cats. This is again entirely different from the case of light perception. All the colours which we normally perceive are produced by continuous mixtures; and a continuous gradation of tints, in a painting or in nature, is sometimes of great beauty.
What Is Life (Canto Classics) Page 16