The Theory of Special Relativity is based on two simple postulates, that “1. the laws of physics take the same form in all inertial frames” and “2. the observed speed of light in a vacuum is constant for all (inertial) observers irrespective of their relative motion”. I shan’t say much about the first postulate now or define an ‘inertial frame’ — basically a ‘frame’ where you can’t say whether you’re moving or not except by looking out of the window — but we need to look at the second.
It is important to realize that (2) is an extremely surprising claim. The speed of a train, for example, is by no means the same for all observers : for the person inside the train the speed is essentially zero since he/she considers himself quite rightly to be at rest unless there is a sudden jolt, but for someone standing alongside the track the speed of the train is, say, 120 miles an hour.  And for an observer in a spacecraft navigating the Earth it is different again (Note 1). Normally, we add speeds together and, if I rolled a marble along the corridor of an unaccelerating train in the direction of travel, the marble’s speed, judged by someone outside would be its speed in the train plus the speed of the train. How is it possible for light to have a constant recorded speed whether the emitter is in a spaceship receding from you or in your own train or spacecraft?
According to Ultimate Event Theory, light, like everything that “has occurrence” is composed of a finite number of ultimate events (Axiom of Finitude). Suppose simply for the sake of argument that the ‘reappearance rate’ of a photon (a specific type of repeating ultimate event) is 1 space/ksana (Note 2). We can represent this by
The blue block represents a repeating event that (rightly or wrongly) we consider to be ‘stationary’from ksana to ksana. My position from ksana to ksana is given by the green blocks and I consider myself to be drifting eastwards away from the blue blocks by one grid-position at each ksana, or, more likely would consider the blue blocks to be drifting steadily away from me westwards. The red blocks represent the positions of some other repeating event that I judge to be moving steadily away from me at a rate of 1 grid-position per ksana. Note that all three coloured blocks joined up give straight lines (they are, in traditional parlance, inertial systems). From the standpoint of the blue blocks, which arbitrarily we take as our ‘landmark sequence’, both the green and red event-chains are moving steadily to the right and the red ‘event-chain’ is moving ‘faster’ since it has a shallower gradient. The ‘speed’ (reappearance rate) of the red line can be calculated by noting the speed of the green blocks relative to the blue and adding on the speed of the green relative to the green. Whereas the green blocks are gaining an extra space each ksana, the red are gaining rather more but the increase (acceleration) is regular. All this is what one would expect.
However, according to Einstein’s Theory of Special Relativity, if light is emitted from the green blocks and the red simultaneously (i.e. within the same ksana), when we eventually pick up the signals at the blue block, compare distances and so on, we do not judge the speed of the light ray from red to be any different from the speed of the light ray from green.  This is extremely unexpected  but will have to be accepted, not because modern physics textbooks say this is so, but because countless actual experiments have (allegedly) failed to detect any difference in the observed speed of light irrespective of the relative movement of the source. Instruments have measured the speed of a light beam projected from an aircraft moving towards the observer and the speed of a light beam projected backwards from the tail of an aircraft moving away ─ and there is no appreciable difference (within experimental error). To see how astonishing this is, imagine a fighter aircraft gunning you down : if it is travelling towards you, the bullets will hit you rather sooner than if you were both travelling at around the same speed. And if the fighter aircraft is moving away from you faster than the ‘muzzle velocity’ of the machine-gun, the bullets from the tail-gun will never reach you at all! Light clearly behaves unlike material objects.
Assuming that Einstein’s prediction about the observed speed of light is substantially correct (which I believe), how can this anomaly be explained in terms of Ultimate Event Theory?  Certainly, there is nothing in my preliminary postulates or my original ‘universe model’ that would lead me to expect anything of the kind, quite the reverse. Since everything that has occurrence is composed of a finite number of ultimate events (the Axiom of Finitude) any and every apparently continuous burst of light is made up of so many individual ‘photonic events’. And the number of these events between two recognizable end-points is fixed once and for all. Also, I absolutely refuse to countenance the notion that the occurrence or not of an ultimate event depends on my personal state of motion or anything else pertaining to me since I consider this the worst kind of subjectivism. If we accept this, we have the absurd consequence that all sorts of things can be conjured into existence just by jumping into a train or a spaceship while they simply never happen at all for someone left behind on the ground !
It is true that I could account for the observed constancy of the photonic event-chain we call light by making the ultimate events themselves larger or smaller according to the relative motion of the observer and observed. But once again I am very reluctant to do this since the advantage of having truly elementary entities is that they have a minumum of attributes and these attributes (such as size) are fixed, are ‘absolute’. It would be equivalent to making the size or charge of a proton changeable in differing situations in ordwer to make certain observations come out right, something one would only wish to do if there was no alternative. The merit of the basic assumptions of Ultimate Event Theory is that they provide a comprehensible, simple framework (or so I would claim) and certainly the simplest and most reasonable assumption is to suppose that all ultimate events are of fixed size (supposing it makes any sense to talk of their having a size) and likewise that the positions available on the Locality are also of fixed size. And finally, for reasons of simplicity and also perhaps aesthetics, I insist on the ‘ksana’, the ‘temporal’ dimension of every event block  as being of fixed size.
If I were stuck with a strictly continuous model of reality, I would now be in an impossible situation. But my Event Locality — which the reader may envisage as, very roughly, the equivalent of ‘Space/Time’ in normal physics — is radically discontinuous, that is, there are gaps. The Locality is not a continuum but a connected dis-continuum, at any rate that section of it that is available to ultimate events. To make Ultimate Event Theory square with Special relativity (which I certainly consider desirable) the only possibility is to consider the ‘gaps’ between events, i.e. the ‘interval’ between co-existing grid-positions and also between successive grid-positions (i.e. between ksanas) as being ‘elastic’, ‘flexible’. These gaps are ‘non-metrical’, have no objective fixed extent and may thus function differently in different event-chains, or rather the same event-chain envisaged from a different perspective (Note 3).

Now, it is possible to maintain the same gradient in the diagram by adjusting the lateral and vertical spacings. Suppose I increase the drift to the right of the red square to represent an increase in speed of the spaceship as perceived by me.  Instead of the original speed of ‘one space to right per ksana’ we have, say, ‘two spaces/ksana’   i.e. we go from





However, if I compensate by spacing out the rows, representing the situation at successive ksanas, we have something more likespeed visuals final

The increased gap between rows, i.e. between successive ksanas,  corresponds to the famous ‘time dilation’ of Special Relativity.
There is, however, still an ‘extra space’ between the red squares in any row, a space which,  by hypothesis cannot be filled ─ since, if so, we would have something travelling faster than light which (according to Einstein) cannot occur. If we want to keep the ‘one space per ksana’ as the maximum ‘speed’ (reappearance rhythm) we can adjust matters by ‘spacing out’ the grid-positions within each ksana, in effect by suppressing the extra black square. This gives something like

c visualwhere the diagonal line red squares has roughly the same slant as in my original diagram ─ the difference is due to the deficiencies of my computer graphics. Spacing out the black squares (which correspond to possible locations of ultimate events) is equivalent to a ‘space contraction’, also a standard alleged effect of Special Relativity.
It must be stressed that there is a significant difference between this model and that of Special Relativity, at least as commonly understood. While the ‘length’ and ‘duration’ of objects (event conglomerates) or trajectories (event chains) are, as in SR, dependent on relative states of motion (reappearance rates), the number of ultimate events in any event chain is not relative but is ‘absolute’. Every trajectory between two marker events will have associated with it an ‘Ultimate Event Number’ which is completely independent of states of motion or material cosntituents or anything else you like to mention. We will not normally know this number — though we will perhaps one day be able to make an informed guess much as we can make an informed guess as to the number of molecules in a given piece of chalk — but it suffices to know that (according to the postulates of UET) this number exists and is unchangeable. I have enshrined this in one of the fundamental assumptions of the theory, the Axiom of Occurrence, “Once an ultimate event has occurrence, there is no way in which it can be altered or prevented from having occurrence : its occurrence is absolute.”
It is not yet entirely clear to me what consequences this principle would have in actual physical situations. It would mean, for example, that the ‘event number’ for the voyage of the twin who goes off on a trip at nearly the speed of light would be the same for both brothers : simply travelling around is not going to conjure into existence events which do not exist for the stay at home brother. If the twin is indeed ‘younger’ when he returns (as Special relativity predicts) this can only be because the gaps between the two twins’ biological events such as heart beats are relatively shorter or longer. Of course, no such experiment could ever be carried out and the occurrence is not in fact covered by the theory of Special Relativity since accelerations are involved when the space traveller takes off, turns round and lands. However, there may be a way to test the independence of the event number in cases of the decay of particles entering the Earth’s orbit, the usual example given of differing time scales because of SR.        SH  26/11/12


Note 1  Zeno of Elea pointed out the relativity of motion in his Paradox of the Chariot. What, he asked, was the ‘true’ speed of a chariot in a chariot race? This differed according to whether you adopt the standpoint of the spectator in the stand or that of the different charioteers in the race. By this thought experiment, Zeno seems to have been attempting to show that there was no such thing as ‘absolute motion’ since the perceived motion depended on the observer’s own state of motion. Newton was deeply bothered by the problem and came to the strange sounding conclusion that ‘absolute motion’ could only mean the motion an object had “relative to the fixed stars”. But today we know that the position of the stars is not at all fixed because of expansion, galactic rotation and so on.

Note 2 This ‘speed’ is, I must emphasize, purely illustrative. The actual speed or rather ‘reappearance rate’ of a photonic event chain would be far, far greater than this : a photonic event would have to shift billions of grid positions to the right or left from ksana to ksana relative to a ‘stationary’ event-chain. It would be interesting to know if there is an event chain whose reappearance rate is exactly 1 space/ksana. This is, incidentally, not the slowest possible rate since, as will be discussed subsequently, I envisage reappearance rates where, during many ksanas, the event does not repeat at all. For example, there could be a reappearance rate of  1 space/7 ksanas or 1 space/100 ksanas and so on. This could be expressed as a reappearance rate of “1/7 spaces per ksana” but this would give the unwary the wrong impression : neither grid positions not ksanas can be subdivided and that is that.

Note 3  This solution would seem to be closest to the spirit of the Special Theory of Relativity. Einstein and his followers continually emphasize that an observer within a given inertial frame would notice nothing untoward : he or she would consider himself to be at rest and the other inertial frame to be ‘moving’. There is only ever a problem when, at a later date, the two observers, one within a given frame and one outside it and in a second inertial frame, confront each other with their meticulous observations. In my terms, each observation is ‘correct’ for the individual concerned because the gaps  between events “have no intrinsic length” and thus may legitimately ‘vary’ according to the standpoint adopted. Are these discrepancies ‘real’ or sim,ply how things appear? There is general agreement that the viewpoint of any and every ‘inertial observer’ is equally legitimate :“there is no truth of the matter” as Martin Gardner put it. I am not sure that this answer is sufficient but I cannot improve on it : I ‘resolve’ the problem by simply positing that the Locality is non-metrical and so all sorts of different metrics can be legitimately ascribed to it provided we keep to the chosen metric.
But what is there between ultimate events? Just the emptiness between adjacent grid-positions. This may remind some readers of the so-called ‘ether’ in which all 19th century physicists believed. It is commonly stated that Einstein ‘did away with the ether’ but this is not strictly true. In a quote that unfortunately I cannot at present trace, he said that “the ether has no physical properties but does have geometrical properties”. By this one should understand that the background ether does not, for example, offer any noticeable resistance to the passage of bodies through it but can (and does) affect space-time the direction of trajectories. After banning mention of the ether for over sixty or so years, the ‘ether’ is well and truly back in physics again, re-baptised the vacuum and far from being empty it is vibrant with quantum energy.  “The modern conception of the vacuum is one of a seething ferment of quantum field activity, with waves surging randomly this way and that. In quantum mechanics waves also have characteristics of particles — photons for the electro-magnetic field, gravitons for the gravitational field and so on — popping out of nowhere and disappearing again. Wave or particle, what one gets is a picture of the vacuum that is reminiscent , in some respects of the ether. It does not provide a special frame of rest against which bodies may be said to move, but it does fill all of space and have measurable physical properties such as energy density and pressure.”    Paul Davies, article NS  19 Nov 2011