Kant and Einstein

The new view has its strongest impact on the previous notion of time. Time is the notion of ‘before and after’ with 2 roots:

1. 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 B, so that if A 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. 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 7 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 preju- dicial 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. 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. ~rhus 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 onB’).

Thus in both cases there is exactly the saOle relationship of mutial non-interference. There is no conceptual difference between the classes Band 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 Band 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).

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 philos- ophers. I suppose it is this, that it meant the dethronement of time as a rigid tyrant imposed on us from outside, a liberatton from the unbreakable rule of ‘before and after’.

For 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 though t.

Einstein has not 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.

The Statistical thermodyanmics of the Willard Gibbs and Ludwig Boltzmann created a change nearly as much as Relativity.

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.

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.

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.

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 shuffiing. 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 2 directions of time, but work perfectly sym- metrically 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 momen- tous 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. )

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 worthwhile arguing any longer.

Boltzmann did not know what to us is at least extremely likely, namely that the universe 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 presup- poses, 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 assump- tions, we may, or so I believe, assert that physical theory in its present stage strongly suggests the indestructibility of Mind by Time.