The genesis of Ultimate Event Theory can be traced back to a stray remark made by the author of popular books on mathematics, W.W. Sawyer. In the course of an exchange of views on contradiction in mathematics, Sawyer threw off the casual remark that “a scientific theory would be useless if it predicted that an event such as an eclipse of the sun would happen at a given place and time, and also that it would not happen at the same time and place”. Such a ‘Law of Non-Contradiction for Events’ was assumed by all the classical physicists and seems to be a necessary (though never stated) assumption for doing science at all. Arguably, Quantum Mechanics does not verify this principle, but this is precisely why QM is so worrisome (Note 1).
Sawyer’s chance remark sounds innocuous enough, but the principle involved turns out to be extremely far-reaching. We have in effect a non-contradiction law for events (not statements), a building block of a physical not a logic theory. Now, it seems of the essence of an ‘event’ that it either happens ‘at a particular time and place’ or it does not: there is no middle ground. There would be little point in announcing that a certain musical or theatrical event was scheduled to take place in such and such a Town Hall on, say, Monday, the 25th of December in the year 20**, but also scheduled not to take place on the given time and date. And certainly once the time and date has passed, the ‘event’ either has occurred or it has not. Moreover, it seems to be of the essence of an ‘event’ to be ‘punctual’, ‘precise’ as to place and time.
An ‘event’, however, is clearly itself made up of smaller events, there are, as it were, macro- and micro-events. Narrowing everything down and ‘taking the limit’, we end up with the eminently reasonable supposition that there are ‘ultimate events’, i.e. events that cannot be further decomposed. Secondly, since like macro-events they are ‘precise as to time and place’, we may presume that they, as it were, occupy a single ‘grid position’ on the Event Locality. This at any rate is the schema I proposed to work with.
There are two philosophic assumptions, one negative and one positive, built into this schema, namely 1. that there is no such thing as infinite regress and 2. that an ‘event’ has to happen ‘somewhere’. Calculus and much of traditional physics has ‘infinite regress’ (or ‘infinite divisibility’ which comes to the same thing) built into it, i.e. it rejects (1). Some contemporary systems such as Loop Quantum Gravity (LPG) are prepared to consider that space-time is perhaps ‘grainy’, but they do not see the need for an ‘event locality’, i.e. they reject (2). In LPG what we call time and space are simply ‘relations’ between basic entities (nodes) and have no real existence. And one could, of course, dispense both with actual infinity and an Event Locality i.e. reject both (1) and (2) — but such a course does not appeal to me. I opted to exclude infinity from my proposed system of the world but, on the other hand, to accept that that there is indeed a ‘Locality’, i.e. a ‘place’ where ultimate events can and do have occurrence.
Dispensing with actual infinity gets rid in one fell swoop of the ingenious paradoxes of Zeno and the reality of Cantor’s transfinite sets in which no one except Cantor himself really believes. Instead of ‘infinite sets’, we have ‘indefinitely extendable sets’ which, as far as I can see, do all the work required of them without us having to (pretend to) believe in ‘actual infinity’. It is tedious to have to explain to mathematicians that so-called infinite sequences can indeed (and very often do) have a finite limit but that this limit is, in the vast majority of cases, manifestly not attained. The terms ‘sum’ and ‘limit’ are not interchangeable and so-called ‘infinite’ series only ever have partial sums, indeed are indefinitely extendable sequences of partial sums. For example the well known series 1 + 1/2 + 1/4 + 1/8 + …. has limit 2 but cannot ever attain it. Most (all?) non-trivial so-called ‘infinite’ series are strictly speaking interminable.
As to (2), the positive requirement, it is to me inconceivable that ‘something that happens’, i.e. an event, does not happen somewhere, i.e. has a precise position on some underlying substratum without which it simply could not occur. The idea of space and time being ‘relations’ between things that exist rather than things that exist in their own right goes back to Leibnitz and is one of the features that distinguishes his mathematics and science from that of Newton who was a great believer in absolute time and space and thus in absolute position. I do not think there is any experiment that can determine the issue one way or the other and doubtless temperament comes into play here, but for what it is worth I believe that Newton’s approach makes much more sense and has been more fruitful. As far as I am concerned, I am convinced that an event, if it occurs at all, occurs somewhere though there is no reason at this stage to attribute any property to this ‘somewhere’ except that it allows events to ‘have occurrence’. It does, however, make the ‘Event Locality’ a primary actor since this Locality seemingly existed prior to any particular events taking place. One could alternatively consider that an event, when and as it has occurrence, as it were carves out a place for itself to happen. In this schema the Locality is an essentially negative entity which does nothing to obstruct occurrence and that is all. This is a perfectly reasonable approach but again one that does not appeal to me for aesthetic or temperamental reasons. However, once I accepted ultimate events and an Event Locality I realized that I had two ‘primary entities’ that henceforth could be taken for granted. A third primary entity was some ‘force of causality’ providing order and coherence to events as they occurred, or rather re-occurred, and so we have the three primary entities of Ultimate Event Theory: ultimate events, the Locality and a kind of causality that I call Dominance. SH
Note 1 It is not, I think, at this stage worth getting involved in interminable discussions about Schrödinger’s dead-and-alive cats though the issue will have to be faced at some stage. Suffice it to say, for the moment, that the wave function, prior to an intervention by a human or other conscious agent does not verify the Law of Non-Contradiction for Events — and one way out is to simply accept that the wave function does not describe ‘events’ at all, though it does deal in ‘potential’ physical entities that are capable of producing bona fide events.
Dharma 