One can trace contemporary physics back to the suggestion, or intuition, of certain ancient Greeks, especially Democritus and Epicurus, that at bottom reality is composed of atoms, minute indestructible ‘bodies’ that combine with each other to form  objects. The most important addition to this ultra-reductionist picture of reality was Newton’s idea of particular forces operating between bodies composed of atoms, both short-range contact forces and long-range non-contact forces. And forces could only operate because of ‘mass’.  So what exactly is ‘mass’? Newton originally defined it as the “quantity of matter within an object”, an intuitively clear definition but one that physics has largely discarded today. And Newton himself obviously envisaged  mass as something much more elusive and more metaphysical than a mere question of numbers of atoms and how densely packed together they were. Inertial mass was a property that objects possessed which could be measured by their capacity to resist forces that attempted to change their state of motion. And gravitational mass measured a body’s capacity to respond to a particular kind of force operating at a distance.

Now, the starting point of Ultimate Event Theory is the notion that ‘objects’, which are relatively stable and permanent things, consist, not of smaller relatively stable and long-lasting objects such as atoms, but of what I call ‘ultimate events’. And ‘ultimate events’  are inherently unstable in the sense that they appear and disappear almost as soon as they have appeared; also, while some ultimate events occur again and again at successive instants, i.e. repeat, most do not. Instead of being a collection of solid objects, physical reality, according to this view, is rather a sort of cosmic kaleidoscope or cinema show where the successive stills are run through so fast that we can’t keep up and perceive them as continuous movement. In effect, instead of basing our notion of physical ‘reality’ on our perception of solidity and permanence around and inside us, Ultimate Event Theory appeals rather to our  sense of the transience of everything and everyone. Time thus becomes the basic dimension rather than space. This mode of perception seems to be more ‘Eastern’ than ‘Western’ since two of the chief religions/philosophies of the East, Buddhism and Taoism, emphasize transience, indeed make it the cornerstone of the entire conceptual system.

Now, it is my contention, or ‘intuition’ if you like, that a system of physical science could have been developed on such premises especially by certain Indian Buddhists during the first few centuries of our era. That it was not can be ascribed on the one hand to the greater difficulty of experimenting usefully with transient items such as ultimate events (the dharmas of Hinayana Buddhism) rather than relatively permanent solid objects. But there was also a cultural reason:  Buddhist thinkers did develop a sophisticated kind of psychology (Abhidharma) and a form of logic but this was mainly because both these disciplines were useful in making converts and in making sense of their own meditative experiences. But these people had very little interest in the physical world per se, tending to view it, if not as a complete delusion, as at any rate a barrier to ‘deliverance’ and ‘enlightenment’. There was thus insufficient motivation within this particular intellectual milieu for developing a branch of knowledge devoted exclusively to physical matters as happened in the West during the fifteenth and sixteenth centuries.


In any case, all such speculation about what ‘might have happened if…’ is irrelevant. The question I ask myself  is, “Can any sort of a coherent physical system be developed from the premise that the basic elements of existence are not ‘things’ but ephemeral ‘ultimate events’?” And one of the very first sub-questions that arises is: “What is the equivalent of ‘mass’ in this system?”
Returning to the ‘classical’ Newtonian concept of inertial mass, we see that it tends to ‘keep things as they are’, hence the term ‘inertia’ with its largely negative overtones. In Ultimate Event Theory (UET) there can, of course, be no question of ‘keeping things as they are’ in the usual sense, since the innate tendency of ultimate events, is, by hypothesis, to disappear at once, not to remain. But there must, seemingly, be some similar or equivalent ‘property’ for there to be a ‘physical world’ at all, or indeed anything observable and perceptible whether ‘real’ or ‘delusory’.

In UET it is supposed that some ultimate events, by processes at present unknown but probably involving chance repetition, form themselves into event-chains and repeating event clusters. It is the latter, i.e. identically repeating event clusters, that we perceive as objects. The equivalent of ‘mass’ would seem to be persistence since ‘persistence’ is not so strongly associated with continuous existence as mass (Note 1). Note that, in contrast to mass which in the Newtonian system is everywhere, persistence is not a property possessed by all ultimate events but only those of  a certain class ─ though these are the ones we are normally interested in. However, once an ultimate event acquires persistence, it seems to retain it, if not indefinitely at least for a considerable length of time, thus giving rise to an impression of solidity and permanence. And repeating event clusters’ (‘objects’) usually remain ‘where and as they are’ unless interfered with in some way, i.e. made subject to an external ‘force’. Following Newton, one is thus tempted to define ‘force’ as something that stops a persistent  event or event cluster from carrying on repeating identically in the same manner.

Note, however, that in UET, everything is, as it were, pushed one stage further back : it is thus necessary to assume some sort of ‘existence-force’ for event-chains without which there would be nothing but a chaos of momentarily existing ‘ultimate events’.

Elementary or ‘Static’ Persistence

 An ultimate event, then, for reasons unknown ─ but which may have something to do with the pre-occurrence of identical or similar events within a neighbouring region of the Locality ─ repeats identically once and keeps on doing so thus forming an event-chain. Now, since the ‘repeat event’ is not, strictly speaking, the ‘same thing’ as the original ultimate event, there is an extra variable which comes into play in UET and which does not appear in the classical concept of an object, namely the re-appearance rate of an event-chain.

Suppose an ultimate event that has occurrence at one ksana and repeats at the very next ksana. It does not necessarily keep repeating at the same rate which in this case is 1/1 or one appearance per ksana. It might shift to a rate of one appearance every three ksanas, one appearance every five ksanas and so forth, or it might have an irregular repeat rate but for all that still keep repeating. Since ksanas, the ‘ultimate’ temporal intervals, are so small compared to ‘macroscopic’ time intervals, a different repeat rate on the ‘ultimate’ level would not be distinguishable to our senses, or perhaps even to our most accurate current instruments. Nonetheless, in order to keep things simple, I shall start by assuming that an event chain has a 1/1 reappearance rate even though there are all sorts of other possibilities. So the basic ‘persistence’ of an event within an event-chain is set at one occurrence per ksana unless stated otherwise.

In matter-based physics, an object can ‘move’ relative to some other stable easily recognizable object, or relative to a recognizable spot considered the ‘origin’ if we are dealing with a co-ordinate system. But an object cannot meaningfully be said to move ‘relative to itself’ : it is always where it is when it is. However, since an event-chain is by definition discontinuous, being composed of a succession of discrete ultimate events, perhaps with appreciable gaps between such appearances, the situation is rather different. Can we meaningfully consider that a particular ultimate event’s reappearance is shifted to the right or left of its previous position? One’s first inclination is to say, yes, but this immediately gets one into difficulties. An ultimate event is conceived as ‘appearing on’ a backdrop, the Event Locality, or perhaps is better viewed as a ‘localized concretisation’ of this backdrop. Since, by hypothesis, this backdrop (the Event Locality) is ‘neutral’ with respect to what occurs in or on it and is not itself endowed with directions, it makes little sense to speak of the trajectory of an isolated event-chain being ‘straight’ or ‘crooked’ or ‘curved’ with respect to this backdrop ─ although it does still make sense to speak of an event-chain having a certain re-appearance rate. If each ultimate event in an event-chain were conscious, it would consider itself and the entire chain to be ‘at rest’, to be stationary, just as we conceive of ourselves as being stationary and the countryside drifting by when in a train (if it is smooth running). So, if we are to speak of ‘lateral drift’ to right or left at successive ksanas, i.e. to introduce the notion of ‘speed’ into UET, this ‘’lateral  shift’ must be related to some real or hypothetical event-chain which is itself regarded as ‘stationary’, i.e. as composed of ultimate events repeating identically at an equivalent spot at successive ksanas. This issue is by the way not specific to UET since it comes up in classical physics : even in Newton’s own time there was considerable, and often heated, discussion about whether one could meaningfully talk of a body isolated in the middle of space as being ‘at rest’ or ‘in motion’ (Note 2).

Now, although there is no such thing as velocity in the continuous sense usually implied in normal physics and everyday speech, there is in UET a perceptible ‘lateral drift’ of successive ultimate events relative to an actual or hypothetical ‘landmark event-chain’ whose constituent ultimate events form a ‘straight line’, or are supposed to do so. If the successive constituents of an event-chain are randomly situated to right and left relative to this landmark event-chain, the event-chain in question does not have a proper displacement rate ─ though nonetheless the ultimate events are somehow bonded together, one bringing into existence the next. But if there is a clearcut displacement pattern, the event-chain can be said to have a ‘velocity’, or the UET equivalent. And if the pattern of successive appearances resembles a straight line, we have an event-chain with a constant lateral displacement rate. In such a case, we can say that not only does the event-chain have ‘persistence’ but that its displacement rate also has persistence. An event-chain can thus have two kinds of ‘persistence’ : ‘existence persistence’ and ‘lateral displacement persistence’,  roughly the equivalents of the ‘rest mass’ and ‘kinetic energy’ of a particle in Newtonian mechanics. A single ultimate event cannot, of course, have ‘displacement persistence’ if it does not already have ‘existence persistence’ ─  though it can have the latter without the former, i.e. be the equivalent of stationary.

And if we take over Newton’s Laws of Motion and re-state them in ‘event’ rather than ‘object’ terms, we can define ‘force’ as that which affects an event-chain’s persistence, either its ‘displacement persistence’ alone or its ‘existence persistence’. In the latter case, an event-chain is replaced by another event-chain or simply annihilated. The doctrine of the ‘conservation of mass-energy’, if taken over into UET, would forbid complete annihilation without replacement, i.e. the simple disappearance of an event-chain without any sequels. It may, however, turn out not to be the case that event-chains must always be replaced by other ones : at any rate the question is left open. If we do introduce the equivalent of a conservation principle, this would mean that as soon as even a single event-chain formed, there would be an endless succession of events since each time one chain terminated it would give rise to another. Such an ‘event-universe’ would thus be endless, ‘infinite’ if you like. However, my feeling is that nothing physical is endless and that not only can event-chains terminate without giving rise to other ones, but that this must happen eventually for all event-chains, i.e. the ‘event-universe’ will simply disappear and, as it were, return to what gave rise to it in the first place. Indeed, according to the ‘Anti-Infinity Principle’, nothing can continue for ever except the background or origin.


 There does not seem to be any obvious equivalent of ‘energy’ in UET ─ though one must remember that the notion only really entered classical physics during the middle of the 19th century. ‘Energy’ cannot be perceived directly anyway, only inferred, and is, in the framework of Newtonian physics, simply the  “capacity to do work”. One could perhaps view an ultimate event’s  capacity to repeat (or give rise to a different event) as the UET equivalent of ‘energy’, and the reality of repetition as the equivalent of mass ─ though I am not sure this is a meaningful distinction. Clearly, if an ultimate event does not possess the capacity to repeat, it cannot give rise to an  event-chain, while if it does in point of fact repeat, clearly it had the prior capacity to do so. One might also envisage a more general ‘existence capacity’ which covers the two cases of an ultimate event repeating exactly and alternatively  giving rise to a different event (an eventuality we have not treated yet). This would correspond to the generalized notion of ‘energy’ in normal physics where ‘energy’ always exists and passes through different forms. But basically it would seem that there are no obvious exact parallels to the dual concepts of mass and energy in matter-based physics. Had an ‘event-based’ physics ever been developed, or were one to evolve now, it would require  its own concepts and categories, not all of which would necessarily correspond to the familiar ones we have and which themselves required centuries to evolve.          SH   1/1/15

 Note 1  Spinoza apparently believed that the most essential feature of anything real is its ‘striving’ to remain what it is. “Each thing, as far as it can by its own power, strives to persevere in its being….The striving by which each thing strives to persevere in its own being is nothing but the actual essence of the thing” Spinoiza, Ethics Part III quoted by Sheldrake, The Science Delusion.
This is interesting because a ‘striving to persevere’ is not the same thing as a capacity to persevere.

 Note 2  Bishop Berkeley, in criticising Newton, wrote that

Up, down, right, left, all directions and places are based on some relation and it is necessary to suppose another body distant from the moving one… that motion is relative in its nature, it cannot be understood until the bodies are given in relation to which it exists, or generally there cannot be any relation if there are no terms to be related. Therefore, if we imagine everything is annihilated except one globe, it would be impossible to imagine any movement in this globe” (quoted in Rosser, Introductory Relativity p. 276) 



Galileo’s Ship

 It was Galileo who opened up the whole subject of ‘inertial frames’ and ‘relativity’, which has turned out to be of the utmost importance in physics. Nonetheless, he does not actually use the term ‘inertial frame’ or formulate a ‘Principle of Relativity’ as such.

Galileo wrote his Dialogue Concerning the Two World Systems, Ptolemaic and Copernican in 1616 to defend the revolutionary Copernican view that the Earth and the planets moved round the Sun. The Dialogue, modelled on Plato’s writings, takes the form of a three day long discussion where Salviati undertakes to explain and justify the heliocentric system to two friends, one of whom, Simplicius, advances various arguments against the heliocentric view. One of his strongest objections is, “If the Earth is moving, why do we not feel this movement?” Salviati’s reply is essentially this, “There are many other circumstances when we do not feel we are moving just so long as our motion is steady and in a straight line”.

Salviati asks his friends to conduct a ‘thought experiment’, ancestor of innumerable modern Gedanken Experimenten. They are to imagine themselves in “the main cabin below decks on some large ship” and this, given the construction at the time, meant there would have been no portholes so one would not be able to see out. The cabin serves as a floating laboratory and Galileo’s homespun apparatus includes “a large bowl of water with some fish in it”, “a bottle that empties drop by drop into a narrow-mouthed vessel beneath it”, a stick of incense, some flies and butterflies, a pair of scales and so on. The ship, presumably a galley, is moving steadily on a calm sea in a dead straight line. Galileo (via Salviati) claims that the occupants of the cabin would not be able to tell, without going up on deck to look, whether the ship was at rest or not. Objects will weigh just the same, drops of water from a tap will take the same time to fall to the ground, the flies and butterflies will fly around in much the same way, and so on — “You will discover not the least difference in all the effects named, nor could you tell from any of them whether the ship was moving or standing still” (Note 1).

Now, it should be said at once that this is not at all what one would expect, and not what Aristotle’s physics gave one to expect. One might well, for example, expect the flies and butterflies flying about to be impelled towards the back end of the cabin and even for human beings to feel a pull in this direction along with many other noticeable effects if the ship were in motion, effects that one would not perceive if the ship were safely in the dock.

What about if one conducted experiments on the open deck?  It is here that Galileo most nearly anticipates Newton’s treatment of motion and indeed Einstein himself. Salviati specifies that it is essential to decide whether a ‘body’ such as a fly or butterfly falls, or does not fall, within the confines of the system ‘ship + immediate environment’ ─ what we would call the ship’s ‘inertial frame’. Salviati concedes that flies and butterflies “separated from it [the ship] by a perceptible distance” would indeed be prevented from participating in the ship’s motion but this would simply be because of air resistance. “Keeping themselves near it, they would follow it without effort or hindrance, for the ship, being an unbroken structure, carries with it a part of the nearby air”. This mention of an ‘unbroken structure’ is the closest Galileo comes to the modern concept of an ‘inertial frame’ within which all bodies behave in the same way. As Salviati puts it, “The cause of all these correspondences of effects is the fact that the ship’s motion is common to all the things contained within it, and to the air also” (Dialogue p. 218 ).

Now, the claim that all bodies on and in the ship are and remain ‘in the same state of motion’ is, on the face of it, puzzling and counter-intuitive. For one might ask how an object ‘knows’ what ‘frame’ it belongs to and thus how to behave, especially since the limits of the frame are not necessarily, or even usually, physical barriers. Galileo does not seem to have conducted any actual experiments relating to moving ships himself, but other people at the time did conduct experiments on moving ships, dropping cannon balls, for example, from the top of a mast and noting where it hit the deck. According to Galileo’s line of argument, a heavy object should strike the deck very nearly at the foot of the mast if the ship continued moving forward at exactly the same speed in a straight line whereas the Aristotelians, on their side, expected the cannon ball to be shifted backwards from the foot of the mast by an appreciable distance. The issue  depended on which ‘structure’, to use Galileo’s term, a given object belonged to. For example, a cannonball dropped by a helicopter that happened to be flying over the ship at a particular moment, belongs to the helicopter ‘system’ and not to the system ‘ship’. In consequence, its trajectory would not be the same as that of a cannonball dropped from the top of a mast ─ unless the helicopter and ship were, by some fluke, travelling at an identical speed and in exactly the same direction.

By his observations and reflexions Galileo thus laid the foundations for the modern treatment of bodies in motion though this was not really his intention, or at any rate not at this stage in the argument. Newton was to capitalize on his predecessor’s observations by making a clearcut distinction between the velocity of a body which, other things being equal, a body retains indefinitely and a body’s acceleration which is always due to an outside force.

Families of Inertial Frames 

In the literature, ‘inertial frame’ has come to mean a ‘force-free frame’, that is, a set-up where a body inside some sort of a, usually box-like, container remains at rest unless interfered with or, if considered to be already in straight line constant motion, retains this motion indefinitely. But neither Galileo nor Newton used the term ‘inertial reference frame’ (German: Inertialsystem) which seems to have been coined by Ludwig Lange in 1885.

The peculiarity of inertial frames is, then, that they are, physically speaking, interchangeable and cannot be distinguished from one another ‘from the inside’. Mathematically speaking, ‘being an inertial frame’ is a ‘transitive’ relation : if A is an inertial frame and B is at rest or moves at constant speed in a straight line relative to A, then B is also an inertial frame. We have, then, a vast family of ‘frames’ within which objects allegedly behave in exactly the same way and which, when one  is inside such a frame, ‘feel’ no different from one another.

It is important to be clear that the concept of ‘inertial frame’ implies (1) that it is not possible to tell, from the inside, whether the ‘frame’ (such as Galileo’s cabin or Einstein’s railway coach) is at rest or in straight line constant motion, and (2) that it is not possible to distinguish between two or more frames, neither of which are considered to be stationary, provided their motion remains constant and in a straight line. These two cases are distinct: we might, for example, be able to tell whether we were moving or not but be unable to decide with precision what sort of motion we were in ─ to distinguish, for example, between two different straight-line motions at constant speed. As it happens, Galileo was really only concerned with the distinction between being ‘at rest’ and in constant straight-line motion, or rather with the alleged inability to make such a distinction from inside such a ‘frame’, since it was this inability which was relevant to his argument. But the lumping together of a whole host of different straight-line motions is actually a more important step conceptually though Galileo himself did not perhaps realize this.

So. Were Galileo in the cabin of a ship moving at a steady pace of, say, 10 knots, he would, so he claims, not be able to differentiate between what goes on inside such a cabin from what goes on in a similar cabin of a similar ship not moving at all or one moving at a speed of 2 or 20 or 200 or even 2,000 knots supposing this to be possible. Now, this is an extremely surprising fact (if it is indeed a fact) since Ship A and Ship B are not ‘in the same state of motion’ : one is travelling at a certain speed relative to dry land and the second at a quite different speed relative to the same land. One would, on the face of it, expect it to be possible to tell whether a ship were ‘in motion’ as opposed to being at rest, and, secondly, to be able to distinguish between two states of straight line constant motion with different speeds relative to the same fixed mass of land. Newton himself felt that it ought to be possible to distinguish between ‘absolute rest’ and ‘absolute motion’ but conceded that this seemed not to be possible in practice. He was obviously somewhat troubled by this point as well he might be.

 Galileo’s Ship is not a true Inertial Frame

 As a matter of fact, it would not only be possible but fairly easy today to tell whether we are at rest or in motion when, say, locked up without radio or TV communication in a windowless cabin of an ocean liner. All I would need to carry out the test successfully would be a heavy pendulum, a means to support it so that it can revolve freely, a good compass, and a certain amount of time. Foucault demonstrated that a heavy pendulum, suspended with the minimum possible friction from the bearings so that it can move freely in any direction, will appear to swing in a circle : the Science Museum in London and countless other places have working Foucault pendulums. The time taken to make a complete circuit depends on one’s latitude — or, more correctly, the time it takes the Earth to revolve around the pendulum depends on what we choose to call latitude. A Foucault pendulum suspended at the North Pole would, so we are assured, take 24 hours to make a full circuit and a similar one at the Equator would not change its direction of swing at all, within the margins of experimental error. By timing the swings carefully one could thus work out whether the ship was changing its latitude, i.e. moving ‘downwards’ in the direction of the South Pole, or ‘upwards’ in the direction of the North (geographical) pole. On the other hand, a ship at rest, whatever its latitude, would show no variation in the time of swing ─ again within the limits of scientific error.

However, suppose I noted no change in the period of the Foucault pendulum. I would now have to decide whether my ship, galley or ocean liner, was stationary relative to dry land or was moving at constant speed along a great circle of latitude. This is rather more difficult to determine but could be managed nonetheless even with home-made instruments. One could examine  the ‘dip’ of a compass needle which points downwards in regions above the Equator and upwards in regions south of the Equator ─ because the compass needle aligns itself according to the lines of force of the Earth’s magnetic field. Again, any change in the angle of dip would be noticeable and there would be changes as the ship moved nearer the magnetic south or north poles. Nor is this all. The magnetic ‘north pole’ differs appreciably from the geographical north pole and this discrepancy changes as we pursue a great circle path along a latitude : so-called isoclinics, lines drawn through places having the same angle of dip, are different from lines of latitude. There are also variations in g, the acceleration due to gravity at the Earth’s surface, because of the Earth’s slightly irregular shape, its ‘oblateness’ which makes the circumference of the Earth measured along the Equator markedly different from that measured along a great circle of longitude passing through the poles. And so, despite Galileo’s claim to the contrary, there would be slight differences in the weight of objects in the cabin at different moments if the ship were wandering about. Only if the Earth were a perfect sphere with the magnetic poles precisely aligned with the geographical poles, would such tests be inconclusive. But a perfect sphere does not exist in Nature and never will exist unless it is manufactured by humans or some other intelligent species.
Galileo’s claim is thus not strictly true : it is a typical case of an ‘ideal situation’ to which actual situations approximate but which they do not, and cannot, attain.

Einstein’s Generalizations

But, one might go on to argue, the discrepancies mentioned above only  arose because Galileo’s ship was constrained to move on a curved surface, that of the ocean : what about a spaceship in ‘empty space’?

The full Principle of Relativity, Galileian or early Einsteinian,  asserts that there is no way to distinguish from the inside between conditions inside a rocket stationary with respect to the Earth, and conditions inside one travelling at any permissible constant ‘speed’ in a straight line relative to the Earth. It is routinely asserted in textbooks on the Special Theory of Relativity that there would indeed be no way to distinguish the two cases provided one left gravity out of the picture.

Newton made Galileo’s idealized ship’s cabin into the arena where his laws of motion held sway. An object left to its own devices inside a recognizable container-like set-up (an inertial system) would either remain stationary or, if already moving relative to the real or imagined frame, would keep moving in a straight line at constant speed indefinitely. This is Newton’s First Law. Any deviation from this scenario would show that there was an outside force at work ─ and Newton, knowing nothing of interior chemical or nuclear forces, always assumed that any supposed force would necessarily come from the outside. Thus, Newton’s Second Law.

So, supposing I let go of a piece of wood I hold in my hand in this room, which I take as my inertial frame, what happens to it? Instead of remaining where it was when I had it in my hand, the piece of wood falls to the ground and its speed does not stay the same over the time of its trajectory but increases as it falls, i.e. is not constant. And if I throw a ball straight up into the air, not only does it not continue in a vertical line at constant speed but slows down and reverses direction while a shot fired in the air roughly northwards will be deflected markedly to the right because of the Earth’s rotation (if I am in the northern hemisphere). Neither this room nor the entire Earth are true inertial frames : if they were Newton’s laws would apply without any tinkering about. To make sense of the bizarre trajectories just mentioned it is necessary to introduce mysterious forces such as the gravitational pull of the Earth or the Coriolis ‘force’ produced by its rotation on its own axis.

As we know, Einstein’s theory of Special Relativity entirely neglects gravity, and introducing the latter eventually led on to the General Theory which is essentially a theory of Gravitation. Einstein’s aim, even in 1905, was quite different from Galileo’s. Whereas Galileo was principally concerned to establish the heliocentric theory and only introduced his ship thought-experiments to deal with objections, Einstein was concerned with identifying the places (‘frames’) where the ‘laws of physics’ would hold in their entirety, and by ‘laws’ he had in mind not only Newton’s laws of motion but also and above all Maxwell’s laws of electro-magnetism. Einstein’s thinking led him on to a search for a ‘true’ inertial frame as opposed to a merely stationary frame such as this room since the latter is certainly not a ‘force-free’ frame. Einstein, reputedly after speculating about what would happen to a construction worker falling from the scaffolding around a building, decided that a real or imaginary box falling freely under the influence of gravitation was a ‘true’ inertial   frame. Inside such a frame, not only would the ‘normal’ Newtonian laws governing mechanics hold good but the effects of gravity would be nullified and so could be legitimately left out of consideration. Such a ‘freely-falling frame’ would thus be the nearest thing to a spaceship marooned in the depths of space far away from the influence of any celestial body.

A freely falling frame is not a true inertial frame

So, would it in fact be impossible to distinguish from the inside between a box falling freely under the gravitational influence of the Earth and a spaceship marooned in empty space? The answer is, perhaps surprisingly, no. In a ‘freely falling’ lift dropping towards the Earth, or the centre of any other massive body, there would be so-called ‘tidal effects’ because the Earth’s gravitational field is not homogeneous (the same in all localities) and isotropic (the same in all directions). If one released a handful of ball-bearings or a basketful of apples in a freely falling lift, the ball-bearings or apples at the ‘horizontal’ extremities would curve slightly towards each other as they fell since their trajectories would be directed towards the centre of the Earth rather than straight downwards. Likewise, the top and bottom apples would not remain the same distance apart since the forces on them, dependent as they are on the distances of the two apples from the Earth’s centre of mass, would be different and this difference would increase as the falling lift accelerated.

It turns out, then, that, at the end of the day, Einstein’s freely falling lift is not a great deal better than Galileo’s ship ─ although both are good enough approximations to inertial frames, or rather are very good imitations of inertial frames. One can, of course, argue in Calculus manner that the strength of the Earth’s gravitational field will be the same over an ‘infinitesimally small region’ ─ though without going into further details about the actual size of such a region. Newton’s Laws in their purity and integrity are thus only strictly applicable to such ‘infinitesimal’ regions in which case there will inevitably be abrupt transitions, i.e. ‘accelerations’, as we move from one infinitesimal region to another. The trajectory of any free falling object will thus not be fluent and continuous but jerky at a small enough scale.

For that matter, it is by no means obvious that a spaceship marooned in the  middle of ‘empty’ space is a true ‘inertial frame’. According to Einstein’s General Theory of Relativity, Space-time is ‘warped’ or distorted by the presence of massive objects and this space-time curvature apparently extends over the whole of the universe ─ albeit with very different local effects. If the universe is to be considered a single entity, then strictly speaking there is nowhere inside it which is completely free of ‘curvature’, and so there is nowhere to situate a ‘true’ inertial frame.

What to Conclude?

 So where does all this leave us? Or, more specifically, what bearing does all this discussion have on the theory I am attempting to develop ?

In Ultimate Event Theory, the basic entities are not bodies but point-like ultimate events which, if they are strongly bonded together and keep repeating more or less identically, constitute what we view as objects. In its most simplistic form, the equivalent of an ‘object’ is a single ultimate event that repeats indefinitely, i.e. an event-chain, while several ‘laterally connected’ event-chains make up an event cluster. There is no such thing as continuous motion in UET and, if this is what we understand by motion, there is no motion. There is, however, succession and also causal linkage between successive ultimate events which belong to the ‘same’ event-chain.

Although I did not realize this until quite recently, one could say that the equivalent of an ‘inertial frame’ in UET is the basic ‘event-capsule’, a flexible though always finite region of the event Locality within which every ultimate event has occurrence. There is no question of the basic ‘building block’ in Eventrics ‘moving’ anywhere : it has occurrence at a particular spot, then disappears and, in some cases, re-appears in a similar (but not identical) spot a ksana (moment) later. One can then pass on to imagining a ‘rest event-chain’ made up of successive ultimate events sufficiently far removed from the influence of massive event-clusters for the latter to have no influence on what occurs. This is the equivalent, if you like, of the imaginary spaceship marooned in the midst of empty space.

So, where does one go from here? One thing to have come out of the endless discussions about inertial frames and their alleged indistinguishability (at least from the inside), is that the concept of ‘motion’ has little if any meaning if we are speaking of a single object whether this object or body is a boat, a particle, ocean liner or spaceship. We thus need at least two ‘objects’, one of which is traditionally seen as ‘embedded’ in the other more or less like an object in a box. In effect, Galileo’s galley is related to the enclosing dry land of the Mediterranean or, at the limit, to the Earth itself including its atmosphere. The important point is being able to relate an object which ‘moves’ to a larger, distinctive object that remains still, or is perceived to remain so.

In effect, then, we need a system composed of at least two very different ‘objects’, and the simplest such system in UET is a ‘dual event-system’ made up of just two event-chains, each of which is composed of a single ultimate event that repeats at every ksana. Now, although any talk of such a system ‘moving’ is only façon de parler , we can quite properly talk of such a system expanding, contracting or doing neither. If our viewpoint is event-chain A , we conceive event-chain B to be, for example, the one that is ‘moving further away’ at each ksana, while if we take the viewpoint of event-chain B, it is the other way round. The important point, however, is that the dual system is expanding if this distance increases, and by distance increasing we mean that there is a specified, finite number of ultimate events that could be ‘fitted into’ the space between the two chains at each ksana.

This is the broad schema that will be investigated in subsequent posts. How much of Galileo’s, Newton’s and early Einstein’s assumptions and observations do I propose to carry over as physical/philosophic baggage into UET?

To start with, what we can say in advance is that the actual distance (in terms of possible positions for ultimate events) between two event-chains does not seem to matter very much. Although Galileo, or Salviati, does not see fit to mention the point ─ he doubtless thinks it too ’obvious’ ─ it is notable that, whether the ship is in motion or not, the objects inside Galileo’s cabin do not change wherever the ship is, neglecting the effects of sun and wind, i.e. that position as such does not bring about changes in physical behaviour. This is not a trivial matter. It amounts to a ‘law’ or ‘principle’ that carries over into UET, namely that the Event Locality does not by itself seem to affect what goes on there, i.e. we have the equivalent of the principle of the ‘homogeneity’ and ‘isotropy’ of Space-time. As a contemporary author puts it : “The homogeneity of space means that all points in space are physically equivalent, i.e. a transportation of any object in space does not affect in any way the processes taking place in this object. The homogeneity of time must be understood as the physical indistinguishability of all instants of time for free objects. (By a free object we mean an object which is far from all surrounding objects so that their interaction can be neglected.)”  Saxena, Principles of Modern Physics  2.2)   

What about the equivalent of velocity? Everything we know about so-called ‘inertial systems’ in the Galileian sense suggests that, barring rather recondite magnetic and gravitational effects, the velocity of a system does not seem to matter very much, provided it is constant and in a straight line. Now, what this means in UET terms is that if successive members of two event-chains get increasingly separated along one spatial direction, this does not affect what goes on in each chain or cluster so long as this increase remains the same. What does affect what goes on in each chain is when the rate of increase or decrease changes : this not only means the system as a whole has changed, but that this change is reflected in each of the two members of the dual system. When travelling in a car or train we often have little idea of our speed but our bodies register immediately any abrupt substantial change of speed or direction, i.e. an acceleration.  This is, then, a feature to be carried over into UET since it is absolutely central to traditional physics.

Finally, that there is the question of there being a limit to the possible increase of distance between two event-chains. This principle is built into the basic assumptions of UET since everything in UET, except the extent of the Locality itself, has an upper and lower limit. Although there is apparently nothing to stop two event-chains which were once adjacent from becoming arbitrarily far apart at some subsequent ksana provided they do this by stages, there is a limit to how much a dual system can expand within the ‘space’ of a single ksana. This is the (now) well-known concept of there being an upper limit to the speed of all particles. Newton may have thought there had to be such a limit but if so he does not seem to have said so specifically : in Newtonian mechanics a body’s speed can, in principle, be increased without limit. In UET, although there is no continuous movement, there is a (discontinuous) ‘lateral space/time displacement rate’ and this, like everything else is limited. In contrast to orthodox Relativity theory, I originally attempted to make a distinction between such an unattainable upper limit, calling it c, and the highest attainable rate which would be one space less per ksana. This means one does not have the paradox of light actually attaining the limit and thus being massless (which it is in contemporary physics). However, this finicky separation between c s0/t0 and c* = (c – 1) s0/t0 (where s0 and t0 are ‘absolute’ spatial and temporal units) may well prove to be too much of a nuisance to be worth maintaining.  SH 21/11/14


 Note 1  This extract and following ones are taken from Drake’s translation of Dialogue concerning two world systems by Galileo Galilei (The Modern Library)

The Two Postulates of Special Relativity

 If you do not make some assumptions, you can never get started either in physics or mathematics ─  or for that matter in any area of research or endeavour. As stated in the previous post, Galileo kick-started a vast intellectual revolution with his originally rather innocuous suggestion that a man locked up in the  windowless cabin of a ship would not be able to tell whether the ship was in the harbour or proceeding at a steady pace in a straight line on a calm sea (presumably rowed by galley-slaves). Galileo does not seem to have been particularly interested in the topic of inertia as such and only introduced it into his Dialogue Concerning the Two Chief World Systems to meet the obvious objection, ”If the Earth is moving round the Sun, why don’t we register this movement?” In effect, Galileo’s answer was that neither do we necessarily register certain differences of motion here on Earth such as the difference between being ‘at rest’ in the harbour and being rowed at a steady pace on a calm sea. According to Galileo, the behaviour of physical objects inside the cabin would be exactly the same whether the ship was at rest or in constant straight-line motion.
Newton made a good deal more of the principle since it appears as his 1st Law of Motion and provides him with an extremely useful definition of ‘force’, namely something that disturbs this supposedly ‘natural’ state, that of rest or constant straight-line motion. Newton was nonetheless somewhat unhappy about Galileo’s principle because he felt that there ought to be some way of distinguishing between ‘absolute’ rest and constant straight-line motion. However, no mechanical experiment was actually able to decisively distinguish between the two states, either in Newton’s time or in later epochs. At the end of the 19th century, most physicists thought that an optical experiment, provided it was refined enough, ought to be able to distinguish between the two states and the failure of Michelsen and Morley to do so caused a crisis in the physical sciences.
This takes us to 1905 and to Einstein, then a ‘Technical Expert III Class’ in the Zurich Patent Office. Einstein subsequently claimed that the famous null result of the Michelsen-Morley experiment played very little role in what came to be known as the Special Theory of Relativity ─ special because it only applied to ‘inertial frames’ and ignored gravity completely. Einstein does briefly allude to “the unsuccessful attempt to discover any motion of the earth relative to the ‘light medium’ ” on the first page of his 1905 article but seems to be much more impressed by various experiments in electricity and magnetism, some of which he may have conducted himself as a student. In any case, Einstein from the beginning makes ‘relativity’ a matter of principle (rather than a conclusion based on data) though he does state that various ‘examples’ relating to electro-magnetism “suggest that the phenomena of electro-dynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest”.
Thus, in contradistinction to the various other physicists of the time who were anxious to find ingenious explanations for the null result of the Michelsen-Morley experiment, and in contrast to Newton himself who had misgivings on the subject, Einstein makes the ‘Principle of Relativity’ into a postulate  and one to which he is clearly strongly attracted. He immediately adds a second postulate, that “light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body”. Einstein claims that “these two postulates suffice for the attainment of a simple and consistent theory of the electro-dynamics of moving bodies”  

The Third Postulate 

 But do they? Are these two postulates in fact enough? We all take for granted a number of things and debate would be impossible if we had at every moment to state everything we assume to be the case, since this would include the notion that there is such a thing as a physical universe, that there is a ‘person’ who is writing these lines and so on and so forth. Einstein clearly takes on board a certain number of physical assumptions which practically everyone shared at the time, for example that there was such a thing as wave motion, such a thing as a rigid ‘body’, that physics was deterministic, that Maxwell’s equations were essentially correct and so on.
There is, however, one extra principle that is not completely obvious and which does play an important role in the derivation of Einstein’s results. This is the principle of the ‘homogeneity and isotropy of space and time’ as it is rather portentously stated in physics textbooks. Roughly what this means is that any ‘place’ and any ‘time’ is as good as another for carrying out observations or doing experiments. If ‘space’ were not homogeneous, an experiment carried out at a particular spot would not necessarily give the same results as one carried out at another spot (even if the temperature, pressure &c . were identical), nor would an experiment carried out today necessarily give the same result as an identical experiment carried out tomorrow. As for ‘isotropy’ it means “the same in all directions” and is put in to rule out the possibility of our being at the centre of a finite universe ─ for in such a case although each section of ‘space’ might be more or less the same our special position would affect what we saw and how far we saw.
The ‘homogeneity of space and time’ is by no means obvious : indeed, it is astonishing that scientists today feel able to talk confidently about what is happening, or has happened, in places no human being will ever be able to visit (such as distant galaxies). Even the principle is not strictly true ! In General Relativity ‘space’ is not a ‘neutral backdrop’ but is warped and deformed in the neighbourhood of massive bodies, so, in this sense, one ‘spot’ is not the same as another. And one ‘moment’ is not equivalent to another in Quantum Mechanics since exactly the same conditions can (and indeed sometimes must) give rise to different results.
But we can safely ignore such sophistications for the moment. The assumption of the ‘homogeneity of space’ enters implicitly into Einstein’s line of argument at certain points. It is essential that, for example, when he is talking of the velocity of one system relative to another inertial system that the situation is perfectly reversible and symmetric : there is no ‘up and down’, no ‘left and right’ and so forth in space. Whether we consider spaceship A to be moving away from spaceship B at constant velocity, or whether we consider it is spaceship B that is moving away from spaceship A is simply a matter of human convenience ─ and essentially comes down to where the observer, real or imagined, is positioned. This ‘equivalence’ is absolutely essential to Einstein’s thinking and that of his followers. The obstinate refusal to give preferential treatment to any ‘place’, ‘time’ or direction was subsequently extended to a refusal to give preferential treatment to any ‘frame’ and ultimately led on to the rejection (or radical redefinition of) the very concept of an ‘inertial frame’.
In his 1905 paper, Einstein does briefly allude to the homogeneity assumption since he says that “the equations [of motion] must be linear on account of the properties of homogeneity which we attribute to space and time” (Note 2).
Einstein also implicitly appeals to the principle of the conservation of energy in his 1905 paper and explicitly in the subsequent ‘popular’ book “Relativity, the Special and the General Theory”. Here, he writes, “The principle of [special] relativity requires that the law of the conservation of energy should hold not only with reference to a coordinate system K, but also with respect to every coordinate system K′ which is in a state of uniform motion of translation relative to K, or, briefly, relative to every ‘Galileian’ system.”
One could, of course, argue that belief in the conservation of energy was covered by Einstein’s blanket proposition that “the laws of physics take the same form in all inertial frames”. However, at the time very few people realized the full implications of the ‘law’ of the conservation of energy (which was only about fifty years old at the time anyway) so it is certainly worth singling it out for special consideration.

Concepts and Principles inherited from ‘classical’ and 19th century physics  

Since I am now irretrievably embarked on the reckless voyage towards a radically different physical theory, I have had to re-examine the basic concepts of matter-based physics and see what I can (and cannot) incorporate into UET while making only minor changes.
For a start, I am quite happy with the Newtonian concept of a ‘body’ which, redefined in UET terms, simply becomes a massive repeating event-cluster. And I have even less of a problem with the idea of the ‘homogeneity’ and general ‘neutrality’ of ‘Space/Time’ (in Special Relativity). The equivalent of the hybrid ‘Space/Time’ in UET is the Event Locality and it is assumed to be more or less the same everywhere and not to have any observable ‘effects’ on repeating event-clusters ─ e.g. it does not offer any resistance to their progress through or on it. So at least one of Einstein’s basic assumptions, the ‘homogeneity and isotropy of Space/Time’ carries over readily enough into Ultimate Event Theory.
So far so good. What of ‘inertial frames’? Newtonian mechanics considers a frame to be ‘inertial’ if a body inside it either stays put or continues on a straight path at constant speed. No force is required for this and Newton specifically defines a force as an external influence that causes a body to deviate from this ‘natural’ state. An inertial frame is not the same thing as a stationary frame, or rather one perceived as being so. Every ‘observer’  tends to consider him or herself ‘at rest’ firmly anchored to a stationary frame of reference which is why, for example, we still talk about the ‘rising’ and the ‘setting’ of the sun.
So, is it possible to decide whether we are ‘really’ at rest? It is, in many cases, possible to decide that we are not in a state of rest or constant straight-line motion even though at first sight it would seem that we are.  A rotating frame is not an inertial frame and within such a frame Newton’s laws of motion do not hold ─ to make them apply we have to add in so-called ‘fictitious’ forces, centrifugal, Coriolis and so on. Over a short period of time we might ─ and almost always do ─ consider the Earth to be an inertial frame but experiments like Foucault’s Pendulum (on show at the Science Museum, London and elsewhere) demonstrate that the Earth is not an inertial frame since there is, apparently, a force making a free-swinging pendulum move in an arc relative to the floor. Since we have not given the pendulum a push in any direction and can neglect varying air pressure and suchlike effects on a heavy object such as a pendulum, the pendulum should stay put relative to the floor and us. Since it does not stay put, either Newton’s Laws are wrong or what appears at first sight to be an inertial frame, i.e. the Science Museum and the Earth to which it is attached, is not in fact an inertial frame.
But this case is untypical : generally it is not at all easy to decide whether a ‘frame’ is inertial or not. In any case, a building attached to the Earth, even supposing the latter were not rotating on its axis, was, according to Einstein post-1905, not a true inertial frame. For Einstein decided that what had previously been thought of as an ‘inertial frame’ in the sense of it being a ‘force-free frame’ was not in fact inertial. Stand in a room with an apple in your hand and let go of the apple. What happens? It does not stay suspended in mid-air as by rights it ought to according to Newton’s 1st Law, nor for that matter does it fall to the ground at a constant speed. Photographs of astronauts in orbit in conditions that are to all intents and purposes  force-free frames for brief periods of time, or the experiences of parachutists falling from a balloon at great height, have given us a better idea of what a ‘true’ inertial frame is like. A ‘true’ inertial frame is what Einstein called a ‘freely-falling frame’ and in such a frame if you let go of an apple it stays at the same height as you relative to the Earth (Note 3).

Inertial frames in UET 

So, what is the equivalent of an inertial frame in UET? We require at least two ‘entities’, an enveloping structure which is more or less rigid and seemingly permanent, and something inside it which is free to move about. The simplest ‘inertial frame’ ─ and ultimate the only true one in UET ─ is actually the ‘event-capsule’ itself, though I have only recently realized this. Each ultimate event is conceived as being confined inside a certain region that I call an event-capsule. This capsule is ‘flexible’ in shape and form but has a maximum and a minimum size ─ everything in UET has a maximum and a minimum. There are, by hypothesis, c* possible emplacements for an ultimate event ‘inside’ this capsule, though only one emplacement can be occupied at any one ksana.         Why is this the equivalent of an ‘inertial frame’? Because, by hypothesis, nothing can change during the ‘space’ of a ksana so the ultimate event (the equivalent of our apple) has to stay where it is and that is that. Also, although the shape of the surrounding capsule can and sometimes does vary from ksana to ksana its shape, volume and so on does not and cannot vary between the limits of a single ksana.  Thus the image, the schema. It certainly fits all the requirements of an ‘inertial system’ though it is an extremely reduced one, to say the least.
Since nothing lasts in UET (except the Event Locality itself), each ephemeral ‘inertial frame’ either disappears or, if part of an event-chain, re-appears at the next ksana. And if we have a number of event-chains in sync with each other and spatially close, we can easily construct the equivalent of a solid framework which itself contains a smaller repeating event-cluster. However, we very soon run into exactly the same problem as crops up in General Relativity. If repeating massive event-clusters deform the local Event Locality and have observable effects on neighbouring event-chains, any such smaller cluster will change in some way, most likely by changing its overall shape. We can in fact make change of shape a criterion for something not being an ‘inertial’ event frame, with the conclusion that a ‘true’ inertial event-frame, or indeed event-chain, can only exist if it is completely remote from all other clusters.
It transpires that an inertial event-frame, or event-chain, i.e. one where the shape of the capsule and/or the position of the ultimate event inside it do not change, is unrealizable in practice ─ and would certainly be unobservable because any observation would ruin its isolation. There are thus no true inertial event-the frames that last for more than a single ksana, whereas every event-capsule functions as the equivalent of a ‘true’ inertial frame (or ‘freely-falling frame’).
Although you will find this point glossed over in physics textbooks, exactly the same situation applies within General Relativity. To use the terminology of matter-based physics, gravitational fields are not homogeneous ─ certainly that surrounding the Earth is not ─ and even Einstein’s ‘falling workman + lunch-box’ is subject to gravitational forces that are continually changing, to what are known as ‘tidal forces’. The ‘pull’ of gravity on the falling workman’s head will be slightly more than that on his feet, and his body will contract a little widthwise because he is not being pulled straight down but towards the centre of the Earth. As one commentator, Fock,  puts it:

“The equivalence of accelerations and gravitational fields is entirely local, i.e. refers to a single point in space (more exactly to the spatial neighbourhood of the points on a time-like world line.)
(…) One can so transform the equations of motion of a mass point in a gravitational field that in this new system they will have the appearance of a free mass point. Thus a gravitational field can, so to speak, be replaced, or rather imitated by a field of acceleration. Owing to the equality of inertial and gravitational mass such a transformation is the same for any value of the mass of the particle. But it will succeed in its purpose only in an infinitesimal region of space” (Note 3)

         So, really all I am doing in UET is replacing the vague concepts of ‘point’ (which comes from Euclid) and ‘infinitesimal region’ (which comes from Newton and Leibnitz) by the precise image of an ‘event-capsule’.
There are, as far as I can ascertain, no such things as homogeneous gravitational fields : they are useful constructs like the idea of an ‘ideal’ gas and no more. Moreover, the normal physical/mathematical presentation even today involves us in the same sophistries as the infinitesimal calculus : at a certain height above the Earth the gravitational field, though ‘continually changing’, for all that is given a specific value (otherwise we could say nothing of any significance). Any logically coherent theory inevitably ends up with a schema similar to that of Ultimate Event Theory, namely that, within a sufficiently small region there is no change at all, while at different  levels we have  different values for some property such as pressure or gravitational potential. In other words the non-existent continuum of calculus breaks up into a discontinuum of adjacent self-contained regions. We associate a different value of some property with each region but within this region nothing changes. This is what physicists and engineers in effect do, and have to do,  ─ in which case why not lay your hands on the table and dispense with all this continuum nonsense, the lumber of a bygone era?

Upper Speed limit?  

Einstein developed his special theory within the context of electro-magnetism ─ the title of the famous 1905 paper is On the electrodynamics of moving bodies. Light, or rather electro-magnetic radiation, is given a privileged place amongst physical phenomena and the speed of light becomes a universal constant. Einstein is doing two things at once. He is first of all proposing, or rather assuming, that there is an upper limit to the speed of propagation of  all particles/radiation and, secondly, he is assuring us that electro-magnetism actually propagates at exactly this limiting speed. In other words c is not an asymptote ─ a quantity that one can approach closer and closer but never actually attains ─ but a reality.
Now the first assumption ─ that there is a limiting speed for all particles/radiation ─ is entirely reasonable and I cannot myself imagine a universe where this would not be the case. However, the second part, that light actually propagates at this speed, though it sounds at first sight innocuous enough, leads him, and all the physicists who follow him, into deep trouble.  Einstein in effect has his cake and eats it too. He states, “we shall find in what follows that the velocity of light in our theory plays the part, physically, of an infinitely great velocity” (section 4 of the paper). And yet ‘something’, namely light, apparently attains this ‘infinitely great velocity’.
In a later section, he derives an expression for the ‘energy of motion’ of an electron, namely  W =  mc2{(1 – v2/c2)1/2 – 1} and notes that “when v = c, W becomes infinite”. We thus seemingly have to conclude that a photon, or for that matter any other particle that attains c, must be massless. As it happens, photons do have mass in certain circumstances since, in General Relativity, light rays can be bent in the vicinity of massive bodies ─ the bending of starlight observed during a solar eclipse was the first confirmation of Einstein’s later theory. Physics textbooks, realizing there is a problem here, glibly say that photons do have ‘gravitational mass’ but not the inertial variety ─ even though, from the point of view of GR, the two are ‘equivalent’.
Now, conceptually all this is a wretched muddle. An ‘object’ without any mass at all would have strictly no resistance to any attempt to change its state of rest or constant straight line motion, so it is hard to see how it could be anything at all for more than a single instant. In UET terms, such an entity  would lack ‘persistence’, would not be able to maintain itself for more than a single ksana.
Of course, a good deal of this hinges on the strictly mathematical issue of what sense we are to give to division by zero. Whenever v actually is equal to c, the ubiquitous tag known as γ = 1/√1 – (v2/c2)  goes to 1/0 which in the bad old days was actually equated to infinity ─ and many physicists even today speak of a particle’s mass ‘going to infinity’ as v goes to c.
As a matter of fact, this situation can be very easily remedied. We simply prohibit v from attaining c for any particle/radiation and envisage c as an unattainable speed limit ─ the least of such upper limits. Moreover, since everything is ‘quantized’ in UET, this is much easier to do than in continuum physics. We interpret v as a certain number of emplacements for ultimate events in a single spatial direction which are ‘covered’ or ‘skipped’ from one ksana to the next. If c is unattainable and we are dealing in ‘absolute’ units, this means v can be at most (c – 1) which I note as c* (Note 4).
Unfortunately, as any mathematician reading this will see at once, this stratagem makes the usual formulae of SR much more difficult to derive : in effect one has perpetually to deal in inequalities rather than equalities. Though Einstein originally used a rather more tortuous method, he subsequently realized ─ and said so in a footnote to a later edition ─ that the simplest way to derive the Lorentz transformations is to employ the postulate of the ‘absolute’ speed of light in all inertial frames and then express this in two different coordinate systems. We thus have x2 + y2 + z2 = c2t2  in one frame and (x′)2 + (y′)2 + (z′)2 = c2 (t′)2   in the other. Using the Lorentz transformations        x′ = γ(x – vt)   y′ = y   z′ = z    t′ = γ(t –vx/c2)   you will find that this comes out right ─ provided you don’t make a slip ! It can be shown that this is the only solution given the assumptions, or alternatively one can, with some labour, derive these relations by assuming that the transformations are linear. (No one these days bothers much with the derivation since we know that the formulae work.)

Derivation of basic formulae in UET 

There is, dreadful to admit, a great deal wrong with the Special Theory of Relativity ─ despite it being one of the most successful and revolutionary ideas in the history of science. I have mentioned the trouble with c and massless particles, but this is not all. Far too much importance is given to one particular phenomenon (light) and to the traditional way of modelling such phenomena. Coordinate systems are entirely man-made inventions : Nature does not bother with them and seems to cope pretty well considering. As Einstein himself subsequently felt about his theory, it very soon got highjacked by pure mathematicians and removed as far as possible from the plane of reality.
So how would I propose to establish the formulae of SR or something similar? All I can give at present is a very rough plan of campaign. One should certainly not start with coordinate systems or even with velocity as such but with ‘mass’, which certainly for me is not a mathematical fiction but a reality. The equivalent of mass in UET is ‘persistence’. If an event repeats and forms an event-chain, it has persistence, if not not. This is the most basic property of an event-chain and is inherent to it, i.e. does not necessarily involve any other event-chain.  But everything to do with ‘motion’, ‘acceleration’ and so forth is a property of a system of at least two event-chains and there is,  by hypothesis confirmed by experience, a limit to how much a system of two event-chains can expand spatially, so to speak, from one ksana to the next. The ‘persistence’ of each event-chain in the system (as viewed by the other) increases with each expansion and strongly resists further expansion; moreover, this increase is not linear. (We all know how easy it is to go from 5 to 10 mph and how difficult to go from 90 to 100 mph.)
Now, I do not know if it is possible to derive a precise mathematical function on the basis of this and the  current assumptions of Ultimate Event Theory : hopefully it will eventually be possible. But what we can say right now  is that a function of the form p /cos φ   where cos φ = √1 – (v2/c2and  0 ≤ v ≤ c  has desirable properties when confronted with experience. That is, when v = 0 we have just the basic ‘persistence’ which is never lost. As one would expect the ‘persistence’ increases very slowly at first while it rises precipitously as v approaches c (but never attains it). The reason for the complications of the squares and the square root in (√1 – (v2/c2is something that must emerge from the initial assumptions and conclusions drawn therefrom. Once we have established a likely formula for increasing persistence (aka mass) most of the other formulae of SR can be derived employing basic mechanical principles. It should not be necessary to even mention light or electro-magnetism. However, all this is for another day.       SH 


Note 2  (page 44 The Principle of Relativity A collection of original papers Dover edition). The point is that we must, according to Einstein, have equations of motion of the type x′ = Ax + Bt, x = Cx′ + Dt′ where A, B, C, D are constants ─ or at least ‘parametric constants’ involving the relative speed, v. If ‘space/time’ were non-homogeneous, for example ‘patchy’ like the atmosphere or viscous like treacle, so-called linear equations would not work, nor would situations necessarily be ‘reversible’.

Note 3 Apparently Einstein got the idea of a ‘freely-falling frame’ (which became a cornerstone of General relativity) one morning when he was travelling to work and passed by a large building under construction. He wondered what a workman on the scaffolding of the building would feel if he fell off and let go of his hammer and lunch-pack as he fell. Einstein later said that it was “the happiest thought of my life”.

Note 3   The quotation is from Fock’s book Space, Time and Gravitation. It is given in Rosser, Introductory Relativity  p. 263

 Note 4 The ‘speed’, i.e. the ‘lateral’ ratio of emplacements/ksana, for any event-chain with a 1/1 appearance rhythm (one event per ksana), thus has an attainable upper limit of 1/√1 – ((c–1)2 /c2)  = c/√(2c – 1) ≈ √(c/2) . Note that this is in ‘absolute’ limits, not metres per second!

In classical mechanics, the ‘natural’ state of a body is to be at rest or, if in motion, to continue in a straight line at constant speed indefinitely. This is Newton’s 1st Law. Any deviation from this state is to be attributed to the action of a force and, for Newton, all forces were external since Newton knew nothing of  chemical bonding or nuclear reactions.
Similarly, since Newton did not have at his disposal the notion of the field  (which was only invented by Faraday in the 19th century), he assumed that all forces were to be attributed to the action of other bodies : there were contact forces (such as those due to collisions) or distant forces such as those due to gravitational attraction. And for anything to happen at all one needed at least two bodies and the situation was supposed to be symmetric : if A affects B, then B affects A to exactly the same extent ─ Newton’s 3rd Law.
The important point here is that, in the Newtonian scheme, no body is an island but always “part of the main” (to paraphrase Donne) and this ‘main’, because attraction was universal and instantaneous, turns out to be the entire universe. In the Newtonian schema, every atom is enmeshed in a complex net of forces stretching out in every direction and from which there is no hope of escape (Note 1)

Need for an ‘Inertial Frame’  

So, could, in the Newtonian scheme, an entirely isolated body be said to have any properties at all apart from occupying a certain position in space? As Bishop Berkeley observed at the time (Note 2), to speak of a completely isolated body being in ‘motion’ or ‘having a velocity’ is meaningless : we require at least one other body with which we can compare the first body’s changes of position over time. And, in like manner, the ‘second’ body  requires the first.
But a ‘two-body system’ where each body is moving relative to the other is not much of an advance on a single body if we want to work out the successive positions of either, or both, of these bodies, especially if they are circling round each other. What is required is a rigid framework which  encloses our ‘test’ body and which does not itself move around appreciably while the ‘test’ body is free to move inside it. Hence the idea of an ‘inertial frame’  : an absolutely  indispensable concept without which physics would never have developed very far.

Celestial and Terrestrial Inertial Frames  

On the astronomical scale, the required framework was supposed to be provided by the ‘fixed stars’ ─ even though it was already known by Newton’s time that the stars were not completely fixed in their positions relative to each other. But compared to the Earth the stars provided a good enough backdrop.
What of terrestrial frames? Galileo’s ‘inertial frame’ was the windowless  cabin of a ship conceived to be either at rest or moving at a constant speed on a calm sea (presumably rowed by galley-slaves). Today, we have much better ‘inertial frames’, cars, trains, ocean liners, aircraft, spaceships and so on ─ indeed it is remarkable that Galileo and his contemporaries were able to conceive of the idea of an ‘inertial frame’ at all since methods of transport at the time were so jerky.
Of course, not all physical objects are situated inside recognizable ‘inertial frames’, but, if need be, we simply imagine a frame, usually either the classic Cartesian box frame or a spherical ‘frame’ like that of an idealized Earth (without flattening at the poles). If we take one corner of the box as the fixed origin, or the centre of the Earth, we can fix the position of any small body relative to the ‘origin’ using at most three ‘specifications’, i.e. co-ordinates.
Galileo was not particularly interested in inertial frames as such and only introduced the windowless cabin ‘thought experiment’ to meet the standard objection to the heliocentric theory, “If the Earth is moving round the Sun, why do we not register this movement?”  Galileo replied, in effect, that neither do we necessarily register motion here on Earth provided this motion is more or less constant and in a straight line. He challenges a traveller, shut up in the windowless cabin of a ship, to decide whether the ship is at the dock or travelling at constant speed over a calm sea. Galileo argues that no experiment undertaken inside the cabin, would enable the voyager to come to a final decision on the matter. We ourselves know how difficult it sometimes is, when in a train for example, to decide without looking out of the window whether we are in motion (relative to the platform) or are still at the station.
This question of distinguishing between inertial frames has had enormous importance in the history of physics since it ultimately gave rise to Einstein’s Theory of Special Relativity. 19th century physicists, although accepting that no mechanical experiment would be able to distinguish between Galileo’s two situations, reasoned that there ought nonetheless to be a foolproof method of distinguishing between rest and constant straight-line motion by way of optical experiments. The Michelsen-Morley experiment was designed to detect the (very nearly) constant straight-line motion of the Earth through the all-pervading ether. The famous null result caused a crisis in theoretical physics which was only resolved by Einstein. He made it an axiom (assumption) of his theory that no experiment that ever would or could distinguish, from the inside, between different inertial frames. (More precisely, what Einstein assumed  was that “the laws of physics take the same form in all inertial frames”. If identical bodies in similar physical conditions were observed to behave differently in different inertial frames, then this would show either that Einstein’s assumption was wrong or that there were no universally valid ‘laws of physics’.

Absolute Motion and Absolute Rest? 

Newton himself was reluctant to accept what Galileo’s Principle of Relativity implied : namely that there was no such thing as ‘absolute’ motion, or for that matter ‘absolute’ rest, only motion or rest relative to some agreed body or point in space. Instinctively  Newton felt that there ought to be some way of distinguishing between ‘absolute’ and ‘relative’ motion, and consequently between constant straight line motion and rest. But he conceded that, practically speaking, he could not see how this could be achieved ─ “the parts of space cannot be seen or distinguished from one another by our senses, therefore in their stead we use sensible measures of them” (Principia Motte’s translation p. 8).
Newton did, however, point out that we can make an ‘absolute’ distinction when speaking of rotational movement — “There is only one real circular motion of any one revolving body, corresponding to only one power of endeavouring to recede from its axis of motion” (Newton, Principia p. 11) As evidence for this Newton used the ‘bucket and rope’ experiment.
If a bucket of water is suspended on the end of a twisted rope and we leave the rope to untwist, the water climbs up the sides of the bucket which it would not otherwise do. This was, to Newton, an example of ‘absolute rotational movement’ within an ‘absolute’ frame ultimately provided by the fixed stars. In this case, the situation was not symmetrical : one could, by observing the torsion of the rope, conclude that it was the bucket, and not the stars, that was rotating (Note 4).
In much the same manner, one might well expect there to be some inertial frame that was ‘truly at rest’ and against which the motions of all other inertial frames could be judged.

Abandon of the Principle of Relativity in UET

 What is the comparable situation in Ultimate Event Theory? After agonising over this question and related issues for the best part of a year, I have finally taken the plunge and decided to discard one of the most firmly established and fruitful principles in the whole of physical science. So there we are : the Rubicon is crossed.
In UET, the equivalents (sic) of inertial frames are not generally equivalent. In principle at least,  it should be  possible to distinguish between a ‘truly stationary’ event-chain and a ‘non-stationary’ one, as also between event-chains which have different constant displacement rates. Indeed, I aim to propose an axiom which in effect says just this. At present, contemporary experimental methods most likely do not allow one to make such fine distinctions, but this situation may change during this century, and indeed I predict that it will.
Dispensing with the Principle of Special Relativity does not mean we have to abandon all the formulae and predictions based upon it. There exists now a substantial body of evidence that ‘verify’ the formulae Einstein originally deduced on the basis of his particular assumptions, and in the last resort this evidence is the justification of the formulae, not the other way round. It is, for example, a matter of empirical fact that it is  not possible to accelerate a body beyond a certain well-defined limit, and that the closer one gets to this limit, the more difficult it is to accelerate the body.

Assumption of Continued Existence  

In ‘classical’ mechanics and physics generally, it is taken for granted that, once in existence, a ‘solid body’ carries on existing more or less in the same shape and form. Even rocks and mountains get worn down in the end, of course, but their constituent ‘bodies’, namely their atoms, last far longer. For Newton and his contemporaries atoms were indestructible, just as they were for the originators of the atomic theory, Democritus and Epicurus. Although twentieth-century discoveries have overturned this rash assumption ─ most elementary particles are very short-lived indeed ─ there remain plenty of small ‘bodies’ all around and inside us, that we are assured have been in existence for millions, sometimes even billions, of years. The idea that “once in existence an object tends to carry on existing indefinitely” is so deeply ingrained in Western thought that it has  rarely been seriously questioned.
In Western thought but not Eastern. Two of the principal Indian and Chinese systems, Buddhism and Taoism, on the contrary emphasize the transience and ephemerality of all physical (and mental) phenomena. According to Buddhism nothing lasts for more than an instant and even solid objects such as rocks and corpuscles are flickering in and out of existence even as we look at them. It is significant that the ancient Chinese equivalent of the (under normal conditions)  unchanging elements in the Periodic Table are the shifting configurations of the Y Ching, the Book of Changes.
Now, in UET the ‘natural’ state is for every ultimate event to appear and disappear for ever. If an ultimate event reappears and keeps on doing so, thus inaugurating an event-chain, this can only be due to a ‘force’ ─ I have thought of calling it ‘existence-force’. Most ultimate events never become subject to ‘existence force’ ─ never acquire ‘existence energy’ if you like ─  but, once they do acquire this capacity to repeat, they generally retain it for a considerable length of  time. Once an event-chain is established, then, no extra force, inner or outer, is required for it to ‘keep on existing’ : on the contrary effort is required to terminate an event-chain, i.e. to stop the ultimate event or event-cluster repeating. And this is a very important fact.

Why is acceleration so difficult?

Why is it so difficult to make a particular object ‘go faster’? And why, the faster an object is already ‘moving’, is it all the more difficult to make it go faster still?
This state of affairs might appear ‘obvious’, but I do not  believe that it is. Take a bath with a little water in it. Does it become more difficult to add one more teaspoonful as the bath fills up? No, it does not. And even when the bath is full, you can still merrily carry on adding water, though in this case some of the water will spill onto the floor. On the other hand, it is extremely difficult to get a lot of personal objects to fit into a travelling case : we have to fold clothes carefully so that they lie flat, arrange solid objects so they fit together neatly and so on.
What is the difference between the two sets of examples ─  the bath and the travelling case or trunk? It is, of course, simply a matter of the available space. In the case of an ‘open’ container, such as a bath, there is more or less unlimited space; in the case of a trunk, the available space is seriously limited.
Now apply this to ultimate events (which are the equivalent of ‘elementary particles’ in UET). Taking as our starting point the spot where an event occurs at a particular ksana, there is seemingly a built in limitation to how far away the next event in the event-chain can occur. If there is to be only one  ‘next event’, it can only occur in a single spatial direction relative to its predecessor ─ as opposed to all three directions at once. And there is an upper limit to the possible ‘lateral distance’ between successive events if  they are members of an event-chain. This is so because the ‘range’ of the causal connection is finite ─ everything in UET except the Event Locality itself is finite. There may conceivably be relations of some sort between two events that are separated by more than c emplacements at successive ksanas, but, in UET as in the theory of Special Relativity, such relations cannot be causal, at any rate as the term is normally understood (Note 5).
In UET everything is static though one static set-up is constantly being replaced by another. ‘Motion’ in UET simply means the replacement of one ultimate event or event-cluster by another event or event-cluster. Instead of particles in perpetual motion, we must think rather in terms of evanescent point-like ultimate events encased in ‘event containers’. In the proposed schema for UET, each ultimate event has its own particular ‘event-capsule’ of variable dimensions. If we label the  boundary positions in any one spatial direction 0 and c , we can say that there are c* = (c – 1) possible emplacements for ultimate events inside a single capsule in a single direction. (This excludes the two boundary positions.) But only one of these positions or ‘event-pits’ can be occupied at a single ksana (moment).

  • …………………….………………..●

0   ←                        c*                   → c

Now, there is seemingly, also a limit on how far the very next  ultimate event in  an event-chain can be displaced in a single direction. This is a matter of experience and observation though it would be difficult to imagine a ‘world’ in which there was not a limit of some sort. If there was no such limit, something that I do here, wherever ‘here’ is, could have immediate consequences at some arbitrarily distant spot in the universe. The speed of the transmission of causality would be ‘infinite’. This is scarcely conceivable and, in any case, for the purposes of UET, one can  simply rule out any such possibility by invoking the ‘Anti-Infinity Postulate’. Eddington,  rightly in my view, argued that one could decide for strictly a priori reasons that there must be a ‘speed limit’ for the transmission of energy (or information) in any universe, though one could not for a priori reasons decide exactly what this limit must be.
There is, then, a permanent constraint on all event-chains without exception : successive ultimate events cannot be more than c* positions apart in any one direction. And if we have two event-chains where the distance between successive events of each of the two chains regularly increases by, say, d positions (where d < c*) at every ksana, there is a further constraint on this dual system, namely that the greatest possible subsequent increase is (c* – d) emplacements. (Note that I am speaking of event positions or emplacements not distances in the ‘metric’ sense.)
In effect, looming over and above each individual ‘event-capsule’ with its ultimate event, there is a sort of ghostly potential event-container which dictates how far the next ultimate event of an event-chain can be relative to its previous position. If we label the boundary positions of this ‘macroscopic’ event-container 0 and c , we can say that this creature has the  capacity to accommodate c* ultimate events in any one spatial direction but no more. It is, in effect, a scaled-up version of an individual event-capsule since, in the case of an individual event-capsule, there are exactly the same number of possible emplacements for an ultimate event ─ but only one position can be occupied at a time. This parallelism turns out to be extremely significant in UET.
In matter-based physics, we say that a ‘body’ cannot go any faster than c metres per second. The equivalent statement in UET would be : “It is not possible to fit more than c* ultimate events into a causal event container. Once this container is ‘full’, there is no room for any more events and that is that. This question of available space, and the increasing difficulty of cramming events into it, is the crucial issue in UET from which all sorts of  consequences follow. As this available space becomes curtailed, the system as a whole becomes subject to increasing pressure and strongly resists any further constriction. To speak in mathematical terms, any supposed ‘event-packing function’  ─ the equivalent of the acceleration function ─ would not be linear, would start off almost as a straight line but would rise precipitously as v gets nearer and  nearer the maximum possible value c* = (c – 1).

The Inertial Ratchet 

This picture of an event-container and ultimate events inside it is, of course, not quite right. If we are considering an event-chain where each constituent event is ‘laterally displaced’ at each successive ksana, all the intermediate possible emplacements ─ spots where ultimate events could in principle have occurred ─ are not actually occupied. But it is as if they were. There is no way of going back to the previous state of affairs ─ except by applying a completely new force. Galileo’s notion of inertia should not be interpreted negatively, i.e. as showing our personal incapacity to distinguish ‘inertial frames’, but realistically as a sort of ‘valve’ or  ‘space-time ratchet’ which stops an event-chain reverting to its previous occurrence pattern. Not only can the ‘moving finger’ of Omar Khayyam not be lured back to “cancel half a line” but it must inexorably keep on writing at the same rate. If, then, for some reason, an event-chain A suddenly increases its lateral distance from event-chain B by d emplacements at every ksana, it must seemingly keep increasing its distance by this precise amount of d event-emplacements indefinitely.
This property of maintaining a constant ‘speed’ without extra effort is an astonishing and extremely important fact about physical reality which has been glossed over because of the exclusive concentration on the technicalities of how one might  actually be able to distinguish between one ‘inertial frame’ and another. Galileo, foreshadowed by the great medieval thinker Oresme, realized that it is not the distance between two bodies (event-clusters) that is important, but the increase in the distance. Why should this be? Because, as far as we know, there is no built in restriction on how far two event-chains can be apart. But the doctrine of the equivalence of all inertial frames means that conditions within any one of the inertial frames remain exactly the same whether or not the two frames (repeating event-clusters) are right alongside each other or are moving apart at a fantastic speed provided this speed is constant ksana by ksana (and less than the upper limit).
But can one really believe this? One can ─ or I can ─ understand only too well why people (including Newton) were disinclined to accept Galileo’s Principle of Relativity and subsequently at first even more disinclined to accept Einstein’s more extended version. Only repeated experiments of increasing precision made some such acceptance mandatory.

The Systems Axiom  

Let us examine the reasons for this reluctance. It has been argued that velocity has little if any meaning if we are speaking of a completely isolated body, aka event-chain. We thus require at least two bodies that then form a dual system. And although, if we are confined to the point of view of one ‘inertial frame’ (which  we naturally consider to be at rest), we will attribute a certain ‘velocity’ to the other inertial frame (if it seems to be getting further away at each successive moment), this ‘velocity’ really belongs to the dual system ─ and not to either of the components of the system to the exclusion of the other. Very well. Considering the dual system, can we say that a situation where this system is expanding by d emplacements per ksana is ‘equivalent’ to a situation where it is expanding by 2d emplacements per ksana, or for that matter by zero emplacements per ksana? Or even by c* emplacements per ksana? Clearly, the situations or configurations of the dual system are not equivalent, cannot possibly be. However, we are asked to accept that the situations in each of the two components of the system are indistinguishable. Is this reasonable? No.
Why is it not reasonable? Because one would expect conditions of the system as a whole to have repercussions of some sort on all parts of the system : indeed, it is hardly conceivable that it could be otherwise. Certainly in most physical contexts this is what we find. If two bodies are linked by gravitational attraction, this systems situation is detectable in either one of the two (or more) bodies ─ provided we have sensitive enough instruments, of course. Similarly, for components of an electrical circuit. Indeed, one could argue that Newton’s 3rd Law makes something of the kind not just possible but obligatory.
This can be presented as an axiom :

If a system as a whole is subject to certain constraints, then so are all parts of the system and in a similar manner.

        Another statement of the principle would be :

If two or more configurations of a dual event-chain system are distinguishable when considering the system as a whole, then the configurations of each of the two or more components of the system must also be distinguishable considered individually. 

        Now, this axiom is incompatible with the Principle of Relativity, or at any rate what the Principle is taken to imply, namely that there is no way, from the inside, of distinguishing between inertial frames. Let us take a practical example.

The spaceship on the way to the moon

 Once a spaceship bound for the Moon has got sufficiently outside the Earth’s gravitational grip, the rocket motors are turned off. Neglecting minuscule perturbations from other planets, comets and so on, the rocket carries on at the same speed relative to the Earth and in more or less exactly the same direction : it does not drop back to what it was before. To reproduce previous conditions, say when the rocket was momentarily stationary relative to the Earth, it would be necessary to start other motors firing, i.e. to introduce a new force.
Now, so we are assured, astronauts devoid of radio contact, windows and so on, would not be able to tell whether the rocket or spaceship  was ‘in motion’ relative to the Earth or motionless. The dual system ‘rocket/Earth’ is very definitely not  the same in the two contexts. And the same goes for Galileo’s ‘port/ship’ system. If the ship is being rowed by galley-slaves on a calm sea, the distance between the repeating event-clusters we call ‘port’ and those we call ‘ship’ is increasing at every ksana, and so is the distance between the  rocket on its way to the Moon and the Earth.
If now we apply the ‘Systems under Constraint Axiom’, we must conclude that there is, at least  in principle, some way of distinguishing between the two situations. Why so? Because the constraints on the system are not the same. In the case of a stationary dual system, there is the constraint that, at the subsequent ksana, the distance between the two components can be at most c* units. If the system is already expanding by d units of distance, then there is the more stringent constraint that no increase greater than c* – d units of distance is possible. And in the case when the system is expanding at the maximum possible rate, c* positions per ksana, no further increase is possible at all : the constraint becomes a total ban.
So, according to the ‘Systems under Constraint Axiom’, since the system as a whole is under constraint, each component of the dual system is also under constraint and this constraint should in principle be observable. How can this be? Well, first of all, I need to work out a schema that allows such a distinction to be observable in principle; subsequently, it is for experiments to detect such a distinction, or some eventual consequence of such a distinction.
This is why, as stated earlier, I have eventually come to the unwelcome conclusion that the schemas of Ultimate Event Theory and Relativity diverge : they are not ‘homologous’ as mathematicians might put it.    This topic will be pursued in subsequent posts.    SH  1/8/14


Note 1  One is reminded at once of the human (pseudo)individual enmeshed in the web of karma. Except that, according to the Buddha, there is hope of escape.

Note 2   “Up, down, right’ left, all directions and places are based on some relation and it is necessary to suppose another body distant from the moving one ….. so that motion is relative in its nature, [and] it cannot be understood until the bodies are given in relation to which it [a particular body] exists, or generally there cannot be any relation, if there are no terms to be related.  Therefore, if we suppose that everything is annihilated except for one globe, it would be impossible to imagine any movement of that globe.”                              Bishop Berkeley, quoted Sciama

 Note 3  “All things are placed in time as to order of succession and in space as to order of succession. It is from their essence or nature that they are places; and that the primary places of things should be movable is absurd. (…) But because the parts of space cannot be seen, or distinguished from one another by our senses, therefore in their stead we use sensible measures for them. For from the positions and distances of things from any body considered as immovable, we define all places; and then with respect to such places, we estimate all motions….. And so, instead of absolute places and motions, we use relative ones.”                Newton, Principia ‘Scholium’ p.8 Motte’s translation  

Note 4  The late 19th century Austrian physicist Mach argued that the two descriptions, Earth rotating, Heavens fixed and Heavens rotating, Earth fixed, were equally valid and this was also Einstein’s view.

Note 5   Entangled photons and other particles do give rise to event correlations that far exceed c, but asuch associations of distant events are not considered to be causal in the normal sense. The issue bothered Einstein so much that he never accepted Quantum Mechanics in its then current form, nor would he have been any happier with it in its present form.


Note : Recent posts have focused on ‘macroscopic’ events and event-clusters, especially those relevant to personal ‘success’ and ‘failure’. I shall be returning to such themes eventually, but the point has now come to review the basic ‘concepts’ of ‘micro’ (‘ultimate’) events. The theory ─ or rather paradigm ─ seems to  know where it wants to go, and, after much trepidation, I have decided to give it its head, indeed I don’t seem to have any choice in the matter.  An informal ─ but nonetheless tolerably stringent ─ treatment now seems more appropriate than my original attempted semi-axiomatic presentation. SH   26/6/14


It is always necessary to start somewhere and assume certain things, otherwise you can never get going. Contemporary  physics may be traced back to Democritus’ atomism, that is to the idea that ‘everything’ is composed of small ‘bodies’ that cannot be further divided and which are indestructible ─ “Nothing exists except atoms and void” as Democritus put it succinctly. What Newton did was essentially to add in the concept of a ‘force’ acting between atoms and which affects the motions of the atoms and the bodies they form. ‘Classical’, i.e. post-Renaissance  but pre twentieth-century physics, is based on the conceptual complex atom/body/force/motion.

Events instead of things  

Ultimate Event Theory (UET), starts with the concept of the ‘event’. An event is precisely located : it happens at a particular spot and at a particular time, and there is nothing ‘fuzzy’ about this place and time. In contrast to a solid object an ‘event’ does not last long, its ‘nature’ is to appear, disappear and never come back again. Above all, an event does not ‘evolve’ : it is either not at all or ‘in one piece’. Last but not least, an ultimate event is always absolutely still : it cannot ‘move’ or change, only appear and disappear. However, in certain rare cases it can give rise to other ultimate events, either similar or dissimilar.

Rejection of Infinity 

The spurious notion of ‘infinity’ is completely excluded from UET: this clears the air considerably and allows one to deduce at once certain basic properties about events. To start with, macroscopic events, the only ones we are directly aware of, are not (in UET) made up of an ‘infinite’ number of ‘infinitely small’ micro-events: they are composed of a particular, i.e. finite, number of ‘ultimate events’ ─ ultimate because such micro-events cannot be further broken down (Note 1).

 Size and shape of Ultimate Events

Ultimate events may well  vary in size and shape and other characteristics but as a preliminary simplifying assumption, I assume that they are of the same shape and size, (supposing these terms are even meaningful at such a basic level). All ultimate events thus have exactly the same ‘spatio/temporal extent’ and this extent is an exact match for the ‘grid-spots’ or  ‘event-pits’ that ultimate events occupy on the Event Locality. The occupied region may be envisaged as a cuboid of dimensions su × su × su , or maybe a sphere of radius su ,  or indeed any shape of fixed volume which includes three dimensions at right angles to each other.
Every ultimate event occupies such a ‘space’ or ‘place’ for the duration of a single ksana of identical ‘length’ t0. Since everything that happens is reducible to a certain number of  ultimate events occupying fixed positions on the Locality, ‘nothing can happen’ within a spatial region smaller than su3 or within a ‘lapse of time’ smaller than t0. Though there may conceivably be smaller spatial and temporal intervals, they are irrelevant since Ultimate Event Theory is a theory about ‘events’ and their interactions, not about the Locality itself.

Event Kernels and Event Capsules 

The region  su3 t0  corresponds to the precise region occupied by an individual ultimate event. As soon as I started playing around with this simple model of precisely located ultimate events, I saw that it would be necessary to introduce the concept of the ‘Event Capsule’. The latter normally has a much greater spatial extent than that occupied by the ultimate event itself : it is only the small central region known as the ‘kernel’ that is of spatial extent su3, the relation between the kernel and the capsule as a whole being somewhat analogous to that between the nucleus and the enclosing atom. Although each ‘emplacement’ on the Locality can only receive a single ultimate event, the vast spatial region surrounding the ‘event-pit’ itself is, as it were, ‘flexible’. The essential point is that the Event Capsule, which completely fills the available ‘space’, is able to expand and contract when subject to external (or possibly also internal) forces.
There are, however, fixed limits to the size of an Event Capsule ─ everything except the Event Locality itself has limits in UET (because of the Anti-Infinity Axiom). The Event Capsule varies in spatial extent from the ‘default’, maximal size of s03 to the  absolute minimum size of u3which it attains when the Event Capsule has shrunk to the dimensions of the ‘kernel’ housing a single ultimate event.

Length of a ksana 

The ‘length’ of a ksana, the duration or ‘temporal dimension’ of an ultimate event, likewise of an Event Capsule, does not expand or contract but, by hypothesis, always stays the same. Why so? One could in principle make the temporal interval flexible as well but this seems both unnecessary and, to me, unnatural. The size of the enveloping capsule should not, by rights, have anything to do what actually occurs inside it, i.e. with the ultimate event itself, and, in particular, should not affect how long an ultimate event lasts. A gunshot is the same gunshot whether it is located within an area of a few square feet, within a square kilometre or a whole county, and it lasts the same length of time whether we record it as simply having taken place in such and such a year, or between one and one thirty p.m. of a particular day within this year.

Formation of Event-Chains and Event-clusters 

In contrast to objects, a fortiori organisms, it is in the nature of an ultimate event to appear and then disappear for ever : transience and ephemerality are of the very essence of Ultimate Event Theory. However, for reasons that we need not enquire into at present, certain ultimate events acquire the ability to repeat more or less identically during (or ‘at’) subsequent ksanas, thus forming event-chains. If this were not so, there would be no universe, no life, nothing stable or persistent, just a “big, buzzing confusion” of ephemeral ultimate events firing off at random and immediately subsiding into darkness once again.
Large repeating clusters of events that give the illusion of permanence are commonly known as ‘objects’ or ‘bodies’ but before examining these, it is better to start with less complex entities. The most rudimentary  type of event-chain is that composed of a single ultimate event that repeats identically at every ksana.

‘Rest Chains’

Classical physics kicks off with Galileo’s seminal concept of inertia which Newton later developed and incorporated into his Principia (Note 2). In effect, according to Galileo and Newton,  the ‘natural’ or ‘default’ state of a body is to be “at rest or in constant straight-line motion”. Any perceived deviation from this state is to be attributed to the action of an external force, whether this force be a contact force like friction or a force which acts from a distance like gravity.
As we know, Newton also laid it down as a basic assumption that all bodies in the universe attract all others. This means that, strictly speaking, there cannot be such a thing as a body that is exactly at rest (or moving exactly at a constant speed in a straight line) because the influence of other massive bodies would inevitably make such a body deviate from a state of perfect rest or constant straight-line motion. And for Newton there was only one universe and it was not empty.
However, if we  consider a body all alone in the depths of space, it is reasonable to dismiss the influence of all other bodies as entirely negligible ─ though the combined effect of all such influences is never exactly zero in Newtonian Mechanics. Our ideal isolated body will then remain at rest for ever, or if conceived as being in motion, this ‘motion’ will be constant and in a straight line. Thus Newtonian Mechanics. Einstein replaced the classical idea of an ‘inertial frame’ with the concept of a ‘free fall frame’, a region of Space/Time where no external forces could trouble an object’s state of rest ─ but also small enough for there to be no variation in the local gravitational field.
EVENT CAPSULE IMAGEIn a similar spirit, I imagine an isolated event-chain completely removed from any possible interference from other event-chains. In the simplest possible case, we thus have a single ultimate event which will carry on repeating indefinitely (though not for ‘ever and ever’) and each time it re-appears, this event will occupy an exactly similar spatial region on the Locality of size s03 and exist for one ksana, that is for a ‘time-length’ of to.  Moreover, the interval between successive appearances, supposing there is one, will remain the same. The trajectory of such a repeating event, the ‘event-line’ of the chain, may, very crudely, be modelled as a series of dots within surrounding boxes all of the same size and each ‘underneath’ the other.

True rest?

Such an event-chain may be considered to be ‘truly’ at rest ─ inasmuch as a succession of events can be so considered. In such a context, ‘rest’ means a minimum of interference from other event-chains and the Locality itself.
Newton thought that there was such a thing as ‘absolute rest’ though he conceded that it was apparently not possible to distinguish a body in this state from a similar body in an apparently identical state that was ‘in steady straight-line motion’ (Note 3). He reluctantly conceded that there were no ‘preferential’ states of motion and/or rest.
But Newton dealt in bodies, that is with collections of  atoms which were eternal and did not change ever. In Ultimate Event Theory, ‘everything’ is at rest for the space of a single ksana but ‘everything’ is also ceaselessly being replaced by other ‘things’ (or by nothing at all) over the ‘space’ of two or more ksanas. In the next post I will investigate what meaning, if any, is to be given to ‘velocity’ ‘acceleration’ and ‘inertia’ in Ultimate Event Theory.       SH  26/6/14

 Note 1  One could envisage the rejection of infinity as a postulate, one of the two or three most important postulates of Ultimate Event Theory, but I simply regard the concept of infinity as completely meaningless, as ‘not even wrong’.         I do, however,  admit the possibility of the ‘para-finite’ which is a completely different and far more reasonable concept. The ‘para-finite’ is a domain/state where all notions of measurement and quantity are meaningless and irrelevant : it is essentially a mystical concept (though none the worse for that) rather than a mathematical or physical one and so should be excluded from natural science.
The Greeks kept the idea of actual infinity firmly at arm’s length. This was both a blessing and, most people would claim, also a curse. A blessing because their cosmological and mathematical models of reality made sense, a curse because it stopped them developing the ‘sciences of motion’, kinematics and dynamics. But it is possible to have a science of dynamics without bringing in infinity and indeed this is one of the chief aims of Ultimate Event Theory.

Note 2  Galileo only introduced the concept of an ‘inertial frame’ to meet the obvious objection to the heliocentric theory, namely that we never feel the motion of the Earth around the Sun. Galileo’s reply was that neither do we necessarily detect the regular motion of a ship on a calm sea ─ the ship is presumably being rowed by well-trained galley-slaves. In his Dialogue Concerning the Two World Systems, (pp. 217-8 translator Drake) Galileo’s spokesman, Salviati, invites his friends to imagine themselves in a makeshift laboratory, a cabin below deck (and without windows) furnished with various homespun pieces of equipment such as a bottle hung upside down with water dripping out, a bowl of water with goldfish in it, some flies and butterflies, weighing apparatus and so on. Salviati claims that it would be impossible to know, simply by observing the behaviour of the drips from the bottle, the flight of insects, the weight of objects and so on, whether one was safely moored at a harbour or moving in a straight line at a steady pace on a calm sea.
        Galileo does not seem to have realized the colossal importance of this thought-experiment. Newton, for his part, does realize its significance but is troubled by it since he believes ─ or at least would like  to believe ─ that there is such a thing as ‘absolute motion’ and thus also ’absolute rest’. The question of whether Galileo’s principle did, or did not, cover optical (as opposed to mechanical) experiments eventually gave rise to the theory of Special Relativity. The famous Michelsen-Morley experiment was, to everyone’s surprise at the time, unable to detect any movement of the Earth relative to the surrounding ‘ether’. The Earth itself had in effect become Galileo’s ship moving in an approximately straight line at a steady pace through the surrounding fluid.
Einstein made it a postulate (assumption)  of his Special Theory that “the laws of physics are the same in all inertial frames”. This implied that the observed behaviour of objects, and even living things, would be essentially the same in any ‘frame’ considered to be ‘inertial’. The simple ‘mind-picture’ of a box-like container with objects inside it that are free to move, has had tremendous importance in Western science. The strange thing is that in Galileo’s time vehicles  ─ even his ship ─ were very far from being ‘inertial’, but his idea has, along with other physical ideas, made it possible to construct very tolerable ‘inertial frames’ such as high-speed trains, ocean liners, aeroplanes and space-craft.

Note 3  Newton is obviously ill at ease when discussing the possibility of ‘absolute motion’ and ‘absolute rest’. It would seem that he believed in both for philosophical (and perhaps also religious) reasons but he conceded that it would, practically speaking, be impossible to find out whether a particular state was to be classed as ‘rest’ or ‘straight-line motion’. In effect, his convictions clashed with his scientific conscience.

“Absolute motion, is the translation of a body from one absolute place into another. Thus, in a ship under sail, the relative place of a body is that part of the ship which the body possesses, or that part of its cavity which the body fills, and which therefore moves together with the ship, or its cavity. But real, absolute rest, is the continuance of the body in the same part of that immovable space in which the ship itself, its cavity and all that it contains, is moved. (…) It may be, that there is no such thing as an equable motion, whereby time may be accurately measured. (…) Instead of absolute places and motions we use relative ones; and that without any inconvenience in common affairs: but in philosophical disquisitions, we ought to abstract from our senses and consider things themselves, distinct from what are only sensible measures of them. For it may be that there is no body really at rest, to which the places and motions of others may be referred.”
Newton, Principia, I, 6 ff.


“There are more things in earth and heaven, Horatio,
Than are dreamed of in your philosophy.”
Hamlet, I. 2

“Like everyone else I am part of a play whose script is being written as I live it.”
John Conyngham, The Arrowing of the Cane

 In the Beginning…..Jung

Jung did not invent the German term Synchronizität that is translated as ‘synchronicity’ but, on his own admission, he did give it a special meaning, and it is certainly Jung who aroused widespread interest in the topic, an interest  which has continued unabated right up to the present day. So it is only fitting to start with him.
Jung is anxious to distinguish a ‘synchronicity’ from a ‘synchronism’ “which simply means the simultaneous occurrence of two events”. In “Synchronicity : An Acausal Connecting Principle” (Note 1) Jung writes :

“Synchronicity therefore means the simultaneous occurrence of a certain psychic state with one or more external events which appear as meaningful parallels to the momentary state.” (p. 36)

Thus we have (1) a ‘psychic state’;  (2) an objective event; (3) a parallelism between the two and (4) a ‘meaning’ attributed to the association.
But what makes an incident ‘meaningful’? As a psycho-analyst who was also intensely interested in the occult, Jung tended to regard an occurrence as ‘meaningful’  if (1) it gave him a supposed deeper insight into the character of the patient and (2) had ‘mythic’ associations of which the patient was more often than not unaware.
Jung leaves out from this formal definition a crucial element : that the ‘meaningful coincidence’ is what he calls ‘acausal’ (non-causal). He does, however, say this a few lines earlier :

“I am using the general concept of synchronicity in the special sense of a coincidence in time of two or more causally unrelated events which have the same or similar meaning.”


The most famous example of a Jungian synchronicity is the  ‘scarab beetle incident’. In Jung’s own words

“A young woman I was treating had at a critical moment, a dream in which she was given a golden scarab. While she was telling me her dream I sat with my back to the closed window. Suddenly, I heard a noise behind me, a gentle tapping. I turned round and saw a flying insect knocking against the window pane from outside. I opened the window and caught the creature in the air as it flew in. It was the nearest analogy to a golden scarab that one finds in our latitudes, a scarabaeid beetle, the common rose-chafer (Cetonia aurata), which contrary to its usual habits had evidently felt an urge to get into the dark room at this particular moment.”         Jung, Synchronicity p. 31

Note that the beetle was not a figment of the imagination since Jung caught it in his hand. Jung adds later that the young woman in question “was an extraordinarily difficult case to treat” and, appropriately enough, according to Jung, one of her chief problems was that she was ‘over-rational’.
Now, this anecdote does fulfil all the requirements of the definition : there is simultaneity, there is mental/physical parallelism and there is archetypal meaning (since the scarab was extremely important in Egyptian religion). Whether it is sufficiently remarkable to be considered other than a curiosity depends on how likely we consider it to be for a ‘common’ beetle to arrive at this particular moment ─ and I leave you to decide on this.

An ‘Acausal’ Principle 

How does Jung ‘explain’ the incident? He does so by suggesting that there exists in Nature, alongside causality, an ‘acausal’ principle which connects certain events to others in a manner that causality does not permit. For causality, as normally interpreted, is subject to various quite stringent constraints. The two events must not be strictly simultaneous,  there must be a possible physical link, the two systems must have something in common and so on. In particular, there is no known causal mechanism that can link a mental or psychological event directly to an objective physical one. But the ‘acausal’ principle can override all these constraints since ‘synchronistic’ events “prove to be relatively independent of space and time in so far as space in principle presents no obstacle to their passage and the sequence of events in time is [sometimes] inverted, so that it looks as if an event which has not yet occurred were causing a perception in the present” (Synchronicity , p. 144).

Jung does not consider the possibility that his disturbed patient in some way caused the cockchafer beetle to materialize or, alternatively, ‘attracted’ one that already existed to the window. This would save causality but at the cost of accepting the possibility of ‘mind over matter’, at least in certain exceptional circumstances. Seemingly, Jung, acting for once like a straightforward rationalist, thought the cost was too high. So he had to invent a new and different force.
Jung also recounts the case of a woman who has a (correct)  premonition of her husband’s collapse and eventual death when she sees a flock of birds settling on the roof of her house. Apparently, flocks of birds had gathered outside the window at the death of the woman’s mother and grandmother. Jung admits that people in the Romantic era would have spoken of “some ‘sympathy’ or ‘magnetism’ which had attracted the birds to the scene of death but concludes that “such phenomena cannot be explained causally unless one permits oneself the most fantastic ad hoc hypotheses”.
Jung was interested in divinatory procedures and was probably the  first academic to take the Y Ching seriously. He interprets ‘mantic procedures’ including ‘horary astrology’ (where you ask a question and interpret the horoscope of the moment) as examples of synchronicity ─ “the psychic and the physical event (namely the subject’s problems and choice of horoscope) correspond, it would seem, to the nature of the archetype in the background and could therefore represent a synchronistic phenomenon” (p. 80). One fails to see what the ‘archetype in the background’ is doing here : a more natural explanation would be that the subject simply ‘objectifies’ an internal state which shows up in the symbolic system used, in this case astrology.
In conclusion, then, Jung regularly prefers to advance his own complicated ‘acausal’ explanation rather than to relax the rules for the lawful operation of causality to allow for ‘mind over matter’. I am not sure that this is the right choice since his ‘acausal’ explanation is just as far-fetched as the alternative ‘psychic-projection theory’, while it is certainly more difficult to comprehend. Still, Jung may have been on to something for all that.

Madeleine Synchronicity

Do synchronicities necessarily have anything to do with myths and archetypes as Jung suggests? To judge by the ‘synchronicities’ that have happened to me, been recounted to me by friends or are listed in books such as Coincidence by Brian Inglis, the answer is no. Nor do they necessarily reveal anything particular about a person’s character or mental state except perhaps that he or she is highly impressionable. More often than not synchronicities don’t have any  ‘meaning’ at all, archetypal or otherwise, nor do they tell you anything you did not already know. They remain nonetheless perplexing. Take the following example.
During my formative hippie years of drifting aimlessly around Europe, I was temporarily lodged by a woman in a Parisian suburb, Juvisy. This woman had a partner from whom she was separated and who did not live there but visited occasionally. She also had a daughter by a previous marriage, Madeleine by name, who sometimes stayed at the flat. The woman‘s partner was an interesting but somewhat dodgy  character who had twice been in prison and he ended up wanting to get me out of the flat because of a developing relation with the daughter. On one occasion he threatened me with a kitchen knife and I fled from the flat in fear (though probably nothing much would have happened had I stayed.) Running through the streets I was brought up short by an enormous white sheet stretched all the way across a railway bridge with large painted letters in bold red “JOURNEE DE SANG” (‘Day of blood’). This didn’t look a very promising omen and, somewhat unnerved, a few streets on I took refuge in a second-hand shop. I idly took up a battered paperback and opened it at random. The first sentence I saw was the fragment of a conversation “‘Tu dois partir’” (‘You must leave’). The name of the heroine in the novel was Madeleine (the name of the young woman).
The banner ‘Journée de Sang’ turned out to be for a Blood Transfusion Event ─ I don’t take this as a ‘synchronicity’ though it’s a rather amusing detail in retrospect. But the chances of coming across by chance, at that precise moment, a novel with that particular sentence and a heroine of exactly the right name must be trillions to one. And moreover it seems reasonable to suppose that my emotional state had something to do with this.
Excited states do indeed seem to make coincidences of this kind more likely. A woman who eventually became a priest told me that, in her youth, she had had a relation with a married man about which she had always felt uneasy. One day, pondering this, she opened the Bible at random and at once fell on the verse “What God has joined, let no man rent asunder” from Saint Paul. What to conclude? The convinced sceptic dismisses this as pure chance. A believer would see this as the ‘voice of God’ speaking. As far as I am concerned, the woman’s unconscious had directed her to this text (since she was already anxious about the situation). This is, I would claim, by far the most natural explanation. But one fails to see what mechanism could possibly have led the woman to the ‘right’ page and the ‘right’ verse.
Note that I did not gain any new information by opening the novel in  the second-hand shop since I had already more or less  decided not to return to the flat except to pick up my things, nor did the woman glean any new information. The only possible ‘explanations’ of the Madeleine incident are (1) not to attempt to explain it at all but simply dismiss it as an oddity; or (2) to conclude that my emotional state somehow ‘caused’ me to pick up this particular book, open it at precisely that page and read that particular sentence. But how on earth could I know that this sentence was in this particular book in this shop? Brian Inglis’s book Coincidence is choc-a-bloc with even stranger coincidences. 

Objective Synchronicities : Plum Pudding and M. de Fontgibu

Apart from the scarab beetle case, the most famous synchronicity is the M. de Fontgibu plum pudding story. This is a completely different type of synchronicity since the emotional state of the persons involved has no bearing at all on what happened.

“As a schoolboy in Orleans, Emile Deschamps was given a taste of plum pudding ─ then hardly known in France ─ by M. de Fontgibu, one of the emigrés who had fled to England during the Revolution and had returned. Some ten years later, walking along the Boulevard Poissonnière in Paris, Deschamps noticed a plum pudding in a restaurant window, and went to ask if he could have a slice. ‘M. de Fontgibu,’ the dame du comptoircalled out to a customer, ‘would you have the goodness to share your plum pudding with this gentleman?’ (…)

Many years after the restaurant encounter, Deschamps was invited to dine in a Paris apartment and his hostess told him he would be having plum pudding. Jokingly, he said that he was sure M. de Fontgibu would be one of the party. When the pudding was served, and the guests were enjoying the dinner, the door opened and a servant announced: ‘M. de Fontgibu’.
At first Deschamps thought his hostess must be playing a joke on him. He saw it really was Fontgibu when the old man, by this time enfeebled, tottered round the table, looking bemused. It turned out that he had been invited to dinner in the same house, but had come to the wrong apartment.”
Inglis, Coincidence    p. 1        The story was told by Deschamps himself to the French astronomer Flammarion who published it in his book  L’Inconnu (1901).
There is no means of checking its authenticity but it sounds perfectly feasible to me since one could hardly imagine someone making up such a preposterous story. I shall comment on it in a moment.


In 1919, somewhat before Jung wrote his own article, the Austrian zoologist Kammerer published a book called Das Gesetz der Serie where he puts forward the idea that certain events relating to a particular theme ‘repeat’ rather in the way that a main wave creates subsidiary ripples. He gives various examples of this, such as the exact same numbers appearing on tram and cloakroom tickets within a single day, a proper name cropping up in all sorts of unrelated contexts, a tune played on the radio just when you are thinking about it and so on. Note that these phenomena differ from the Jungian scheme since the events are sequential rather than simultaneous (though occurring within a fairly circumscribed time interval such as a day). Also, the mental state of the observer, or ‘experiencer’, does not seem to matter so much ─ but people prone to serial coincidences, in my experience, do tend to be highly strung.
It is open to debate whether there really is a ‘law of series’ as Kammerer believed and the reader must decide for himself on the basis of his own experience. But, for what it is worth ─ and it is worth something ─  folk wisdom throughout the world tells us that “It never rains but it pours”, that “Misfortunes never come singly” and so on and so forth. Gamblers, sportsmen, entrepreneurs, people who live by their wits and adventurers generally almost to a man (or woman) firmly believe in the reality of ‘runs’ and lucky or unlucky breaks, as indeed I do myself. Statisticians despair of ever being able to uproot this irrational prejudice and are reduced to ascribing it to wish fulfilment.
There is another explanation, however : that this is what the data is actually telling you. Scientists and philosophers today are well insulated against the uncertainties of ‘real life’  : they are armchair military theorists who have never been under fire. What they say is not necessarily wrong, but should be treated with some caution. Active people tend to believe in luck, bad or good, and learn to cope with uncertainty rather than try to eliminate it. Nor is this necessarily a matter of believing in guardian angels because this makes you feel good : ‘runs’ are also things to be wary of. My experience tells me that there is something distinctly non-random about random events ─ and the more random, i.e. uncontrolled, the events, the more likely they are to show signs of an intermittent and elusive order lurking in the background. Jung was right at least in this : what order there is, is not the usual sort of clear-cut cause and effect.
Kammerer, who led an unusual life for a career scientist (Note 2), noticed that there was something ‘not quite right’ with the way events evolve into each other, occasionally forming distinct repetitive patterns : it is as if events had a life of their own, or were being manipulated by an  external intelligence for  her or its amusement.  A delusion? Maybe, but maybe not. Einstein, in this respect so much more broad-minded than your normal rationalist/scientist, read Kammerer’s book with interest and pronounced it ‘by no means absurd’.

The Viewpoint of Eventrics 

The theory of Eventrics, of which Ultimate Event Theory is, as it were, the ‘nuclear’ or atomic part, is just as ‘mechanistic’ as Newtonian Mechanics ─ indeed rather more so since Newton at least assumed the existence of a cosmic designer whereas Ultimate Event Theory holds that the universe came about spontaneously, is self-sustaining and up to a point self-correcting.
So what does Eventrics have to say about the sort of ‘synchronicities’ or ‘meaningful coincidences’ mentioned?
Eventrics ─ which is based on the premise that “the world is made up of events and not of things” ─  undoubtedly offers much more leeway for the occurrence of such things (sic) as meaningful coincidences and synchronicities. If Space and Time are continuous, which is the official view, it  is difficult to see how particular streams of events could abruptly change course or be brought under any kind of selective control. But if physical reality is more like a mosaic where there are definite gaps between event-blocks, then it becomes perfectly conceivable that such blocks might sometimes become disarranged, giving rise to apparent causal anomalies. Also, it might not be completely impossible to, as it were, swap one event-block for another.
‘Objective Coincidences’ such as the Fontgibu ‘plum pudding’ synchronicity make perfect sense within the world-view of Eventrics : they are  ‘mismatches’ of pairs of (macroscopic) events, comparable to DNA transcription errors that give rise to mutations. In the M. de Fontgibu saga, two originally unrelated macro-events for some reason got paired off with each other. Event A, the eating of plum pudding in France in Deschamps’ lifetime became systematically connected to event B, the presence of M. de Fontgibu on the scene. Such ‘event mismatches’ might turn out to have a silver lining and give rise to ‘lucky breaks’, but the chances are that they will have no particular importance. Nonetheless, the very  existence of such anomalies implies that the functioning of the colossal event-machine we call the physical universe does not proceed without the occasional glitch ─ though generally extremely reliable, Nature does occasionally mess up. It would be like a skilful mechanic who, on an off day, puts the wrong nut on a screw.
What about Jung’s cases of ‘psycho-physical parallelism’? There is in Eventrics little or no difference between ‘mental’ and ‘physical’ events ─ both are events and are subject to similar or identical ‘laws’ of attraction and association. In consequence, the notion that someone can bring about changes in the material world by projecting out, consciously or unconsciously, a mental state, i.e. by connecting up an emotional event-block to an  external one, is not ruled out a priori. But I do not see the need to drag in a supposed ‘acausal principle’ : causality by itself suffices. The emotionally disturbed person brings about, by a form of event sequencing we do not at present understand, an objective occurrence that otherwise would not take place, that is all. This is surprising but not particularly shocking.
Jung’s simultaneous ‘acausally related’ events, and alleged time-reversals, can be accommodated by broadening the conditions for the operation of causal forces. In earlier versions of Eventrics, where I spoke of ‘Dominance’ rather than Causality,  I introduced the notion of the ‘Equal Dominance’ where each of a pair of events is just as ‘dominant’ as the other  ─ in effect an inseparable dual system suddenly comes into existence. So simultanaous events can still be causally related. This idea does the same work as Jung acausal principle. However, I am no longer sure that this treatment is any better than Jung’s since something other than the events themselves must cause the double-event to appear ─ maybe, after all, there is a universal principle that lies somewhere in between causality and pure chance as Jung surmised.
As for apparent time reversals, they can be accommodated within the framework of Eventrics by supposing that in some cases entire event-blocks, which would normally be composed of separate ‘cause and effect’, get produced ‘at one fell swoop’. In such  cases, the order of occurrence of the constituent events ceases to matter, and the apparent ‘effect’ can precede the ‘cause’. But this is not a true time-reversal since the flow of causality is still uni-directional, from past to future. I consider the idea that a future event can influence a present or past one to be ridiculous : either you have everything happening in an eternal present as Einstein believed towards the end of his life, or you have a single time direction. Nonetheless, because reality is a mosaic, different pieces can get ‘out of step’ as it were and have different time schemes. It seems that we have to accept that there is no single ‘Now’ which applies right across the universe but, certainly, within a particular region there is only one direction for the arrow of time. (Time, of course, in Ultimate Event Theory  is not an arrow but a sequence of stills which gives the illusion of continuity.)

Providential Coincidences 

So, arguably, Eventrics can cope slightly better than contemporary physical theories with some types of synchronicity and  meaningful coincidence. Nonetheless, there remains a large class of phenomena that does not fit into the underlying ‘world-view’ of Eventrics any more than it fits into the various scientific paradigms on offer, classical or modern. This class consists precisely of the most interesting synchronicities and coincidences, those  where the ‘chance’ association of two or more events strongly suggests that there is a (usually benevolent) organizing intelligence at work, either ‘in here’ (in the unconscious) or ‘out there’ (in the universe). In many ways the most puzzling (though the least alarming) synchronicities are those of the ‘Library Angel’  type. Someone is searching for the name of something, a quotation, a particular book : he or she ic opens a book ‘by chance’ and voilà there is what he or she was searching for. Take the well-known de Morgan case, which is almost certainly authentic since de Morgan, a leading Victorian mathematician and logician did not believe in the paranormal.
The exact details need not concern us but the gist is that de Morgan was anxious to trace a paper the physicist Fresnel had sent to England some years previously for translation in the European Review. In de Morgan’s words :

“The question was what had become of the paper. I examined the Review at the Museum, found no trace of the paper, and wrote to that effect at the Museum, adding that everything now depended on ascertaining the name of the editor, and tracing his papers: of this I thought there was no chance. I posted this letter on my way home, at a Post Office in the Hampstead Road at the junction with Edward Street, on the opposite side of which is a bookstall. Lounging for a moment over the exposed books, I saw, within a few minutes of the posting of the letter, a little catch-penny book of anecdotes of Macaulay, which I bought, and ran over for a minute. My eye was soon caught by this sentence: ‘One of the young fellows immediately wrote to the editor (Mr. Walker) of the European Review’. I thus got the clue by which I ascertained that there was no chance of recovering Fresnel’s paper. Of the mention of current reviews, not one in a thousand names the editor.”      de Morgan, A Budget of Paradoxes recounted Inglis, p. 34 

        Note that this is a Jungian synchronicity: there is (1) near simultaneity between the writing and posting of the letter and coming across  the book; (2) a direct connection between a mental state, concern to find the paper, and a physical act, buying and reading the book; (3) ‘meaning’ ─ since de Morgan obtained what was, to him, very valuable in formation.
What is striking about such synchronicities is, firstly, that a ‘random’ act is always involved (“Lounging for a moment over the exposed books… ”) but that this casually unrelated act proves to be far more effective than a systematic search (“Of this [discovering he name of the editor] I thought there was no chance”).

“What is to be done?”  

Basically, when confronted with synchronicities and ‘meaningful coincidences’, there are only two options : either you dismiss  them or you take them seriously. If you take them seriously, this means that there is a genuine rather than an apparent causal process at work ─ or, for Jung, an equally important ‘acausal’ principle.
So what can/should be done with such things? Can this principle be put to good/bad use?
There is certainly potential here. What synchronicities and meaningful coincidences imply is that human beings can (1) do a lot more than they think they can; (2) know a lot more than they think they know and/or (3) that there are entities of some kind ‘out there’ ready and willing to provide assistance, or alternatively to lead people astray.  For scientific rationalists, all three possibilities are unthinkable, therefore all such phenomena must be ascribed to chance.
For  Jungian  ‘psycho-physical’ synchronicities imply that human beings have the power to project outward mental states and turn them into objective realities, as it is claimed Tibetan monks can, or at least could, do. It might thus be desirable to make oneself more prone to synchronicities and the like. Since many (but not all) of such occurrences happen when people are  in  heightened  emotional states (fear, guilt, intense desire, curiosity &c.), one method would simply consist in exposing oneself deliberately to extreme situations. This is what Rimbaud had in mind when he talked of a “systematic derangement of the senses” and plenty of  contemporary cults and the exotic self-help therapies aim to do just this.  The method is, however,  for obvious reasons, hazardous. The difficult part is dosing the derangement so that it is kept within certain bounds ─ which means part of oneself has to remain unaffected. There is also the question of what you are going to do with all the synchronicities when and if they do start occurring nineteen to the dozen.
On a different tack, if one takes the ‘Library Angel’ cases seriously, this means that human beings in principle have access to a much vaster store of information than we think we have : we don’t just have Google but something like the Jungian collective unconscious or the Akashic Records to click onto. Most brain activity consists of sorting out the vast amounts of data streaming in and only keeping near the top for easy access the bits rightly or wrongly deemed important. We know a lot more than what we think we know but we usually don’t know how to access it  : the value of extreme situations is that, when it is a matter of survival, the mind overrides the normal barriers and so has a better chance of  reaching the less accessible areas. This is why there is so much importance given to ‘changing awareness’ in mystic cults. As Strogatz said (in a completely different context) “There are things that are staring us in the face, but we can’t see them because we haven’t developed the conceptual tools to handle them”.
At the end of the day, when considering such matters, one has to tackle the question of what it is ‘in here’ or ‘out there’ that is directing, or at least influencing to some degree, the synchronous current that sweeps one along. Is there a ‘Hidden Hand’? Inhabitants of previous eras had no trouble at this level ─ no conceptual trouble that is ─  since almost everyone believed in “thrones, dominations and powers” as Saint Paul put it. Today, we don’t much believe in these things which means that there are no agents available to do any pushing or redirecting. Worse still, there aren’t really any human wills capable of doing any pushing either. The whole trend of scientific thought and rationalism in the last one hundred and fifty years in the West has been towards a drastic reduction of the scope and range of the human individual : he or she has become  a helpless subject of impersonal deterministic forces that not only he has no hope of controlling, but precious little hope of even remotely understanding unless he has studied (very) advanced mathematics. Nor is Quantum Indeterminacy of the slightest use here, since there is ─ so we are endlessly assured ─ no way to get a handle on the uncertainties and exercise control over them (Note 3).
Synchronicities and meaningful coincidences are chinks in the seemingly impregnable armour of contemporary scientific rationalism and these chinks are inevitably going to be opened. The violent reaction of the scientific establishment towards any straying from the beaten track into paranormal territory only goes to show how threatened at a deep level orthodoxy feels. “Embarrassing questions tend to remain unasked, or if asked, to be answered rudely” writes Medawar in The Future of Man. Yes, quite.
Electricity started off as a fairground amusement : in the eighteenth-century people queued up to be given an electric shock and no one at the time had the faintest idea that this  amusing phenomenon would one day become the principal energy source for a whole country. Maybe something of the sort will happen in this century on a mental level.

 SH   18/6/14

Postscript:  I do not comment on the recent book on Synchronicity by Kirby Surprise because I have not read it yet, but there is an insightful review on the website of EllisNelson that revived my interest in the subject and prompted me to write this post

Note 1 All references are to the Ark Paperback C.G. Jung Synchronicity, an Acausal Connecting Principle which is a translation by R.F.C. Hull of part of Volume 8 of Jung’s Collected Works. This is itself an expansion of the original brief article Über Synchronizität published in Eranos Jahrbuch 1951.    

Note 2  Kammerer eventually committed suicide but not for reasons that had anything to do with a ‘law of series’ as far as we know. He had the  temerity to oppose neo-Darwinian orthodoxy and was accused of fudging his results, see Koestler’s book The case of the Midwife Toad. It has been suggested that a female student or colleague of Kammerer, infatuated with Kammerer,  tampered with the evidence in oestler Today, a m isguided attempt to help him. His biological theories, dismissed because of their alleged Lamarckism, have resurfaced in epigenetics and a Peruvian team has gone so far as to say he was on the right lines.

Note 3  One or two psychoanalysts familiar with quantum theory, notably Ninian Marshall, have  attempted to put telepathy on a quantum footing.
“Marshall’s theory recalls that a sub-atomic system is always, at any given time, a mixture of possibility and actuality, the one tending to give way to the other over a range of probabilities. (..) Each virtual transition is precisely a dip into the future, a future from which the particle ‘comes back’ to live out whichever actual state it has chosen to settle into. The premise on which Marshall based his theory was that precognition could be explained if there was a way that the brain could ‘tune into’ these virtual dips into the future…..”  Danah Zohar, Through the Time Barrier
 The next step from the idea that one can become aware of these ‘virtual futures’ is the notion that one can intervene and make the more attractive options the ones that get realized. If this general schema is correct (which I believe it is), this could give rise to a new form of technology. Instead of breaking down and rebuilding actual substances  — which is essentially what manufacturing does —  one would operate on ‘things’ that are nearly, but not quite, actual.

Two Models of the Beginning of the Universe

 There are basically two models for how the universe began. According to the first, the universe, by which we should understand the whole of physical reality, was deliberately created by a unique Being. This is the well-known Judaeo-Christian schema which until recently reigned supreme.
According to the second schema, the universe simply came about spontaneously: no one planned  it and no one made it happen. It ‘need not have been’, was essentially  ‘the product of chance’. This seems to be the Eastern view, though we also  come across it in some Western societies at an early stage of their development for example in Greece (Note 1).
Although for a long time the inhabitants of the Christian West were totally uninterested in the workings of the natural world, the ‘Creationist’ model eventually led on to the development of science as we know it. For, so it was argued, if the universe was deliberately created, its creator must have had certain rules and guidelines that He imposed on his creation. These rules could conceivably be discovered, in which case many of the mysteries of the physical universe would be explained. Moreover, if the Supreme Designer or Engineer really was all-knowing, one set of rules would suffice for all time. This was basically the world-view of the men who masterminded the scientific revolution in the West,  men such as Galileo, Kepler, Descartes, Newton and Leibnitz, all firm believers in both God and the power of mathematics which they viewed as the ‘language of God’ inasmuch as He had one.
If, on the other hand, the universe was the product of chance, one would not expect it to necessarily obey a set of rules, and if the universe was in charge of itself, as it were, things could change abruptly at any moment. In such a case, clever people might indeed notice certain regularities in the natural world but there would be no guarantee that these regularities were binding or would continue indefinitely. The Chinese equivalent of Euclid was the Y Ching, The Book of Changes, where the very title indicates a radically different world view. The universe is something that is in a perpetual state of flux, while nonetheless remaining ‘in essence’ always the same. According to Needham, the main reason why the scientific and technological revolution did not happen in China rather than the West, given that China was for a long time centuries ahead of the West technically, was that Chinese thinkers lacked  the crucial notion of unchanging ‘laws of Nature’ (Note 2).
Interestingly, there is a noticeable shift in Western thought towards the second model : the consensus today is that the universe did indeed come about ‘by chance’ and the same goes for life. However, contemporary physicists still hold tenaciously onto the idea that there are nonetheless certain more or less unchanging physical laws and rational principles which are in some sense ‘outside Nature’ and independent of it.  So the laws remain even though the Lawmaker has long since died quietly in his bed.

Emergent Order and Chaos

Models of the second ‘Spontaneous Emergence’ type generally posit an initial ‘Chaos’ which eventually settles down into a semblance of Order. True Chaos (not the contemporary physical theory of the same name (Note 3)) is a disordered free-for-all: everything runs into everything else and the world, life, us, are at best an ephemeral emergent order that suddenly occurs like the ripples the wind makes on the surface of a pond ─ and may just as suddenly disappear.
Despite the general triumph of Order over Chaos in Western thinking, even in the 19th century a few discordant voices dissented from the prevailing  orthodoxy ─ but none of them were practising scientists. Nietzsche, in a remarkable passage quoted by Sheldrake, writes:

“The origin of the mechanical world would be a lawless game which would ultimately acquire such consistency as the organic laws seem to have… All our mechanical laws would not be eternal but would have survived innumerable alternative mechanical laws” (Note 4)

Note that, according to this view, even the ‘laws of Nature’ are not fixed once and for all : they are subject to a sort of natural selection process just like everything else. This is essentially the viewpoint adopted in Ultimate Event Theory i.e. the universe was self-created, it has ascertainable ‘laws’ but these regularities need not be unchanging nor binding in all eventualities.

In the Beginning…. Random Ultimate Events  

In the beginning was the Void but the Void contained within itself the potential for ‘something’. For some reason a portion of the Void became active and random fluctuations appeared across its surface. These flashes that I call ‘ultimate events’ carved out for themselves emplacements within or on the Void, spots where they could and did have occurrence. Part at least of the Void had become a place where ultimate events could happen, i.e. an Event Locality. Such emplacements or ‘event-pits’ do not, by assumption, have a fixed shape but they do have fixed ‘extent’.
Usually, ultimate events occur once and disappear for ever, having existed for the ‘space’ of a single ksana only. However, if this was all that happened ever, there would be no universe, no matter, no solar system, no us. There must, then, seemingly have been some mechanism which allowed for the eventual formation of relatively persistent event clusters and event-chains : randomness must ultimately be able to give rise to its opposite, causal order. This is reasonable enough since if a ‘system’ is truly random, and is allowed to go on long enough, it will eventually cover all possibilities, and the emergence of ‘order’ is one of them.
As William James writes:
“There must have been a far-off antiquity, one is tempted to suppose, when things were really chaotic. Little by little, out of all the haphazard possibilities of that time, a few connected things and habits arose, and the rudiments of regular performance began.”

This suggests the most likely mechanism : repetition which in time gave rise to ingrained habits. Such a simple progression requires no directing intelligence and no complicated physical laws.
Suppose an ultimate event has occurrence at a particular spot on the Locality; it then disappears for ever. However, one might imagine that the ‘empty space’ remains, at least for a certain time. (Or, more correctly, the emplacement repeats, even though its original occupant is long gone). The Void has thus ceased to be completely homogeneous because it is no longer completely empty: there are certain mini-regions where emplacements for further ultimate events persist. These spots  might attract further ultimate events since the emplacement is there already, does not have to be created.
This goes on for a certain time until a critical point is reached. Then something completely new happens: an ultimate event repeats in the ‘same’ spot at the very next ksana, and, having done this once, carries on repeating for a certain time. The original ultimate event has thus acquired the miraculous property of persistence and an event-chain is born. Nothing succeeds like success and the persistence of one  event-chain makes the surrounding region more propitious for the development of similar rudimentary event-chains which, when close enough, combine to form repeating event-clusters. This is roughly how I see the ‘creation’ of the massive repeating event-cluster we call the universe. Whether the latter emerged at one fell swoop (Big Bang Theory) or bit by bit as in Hoyle’s modified Steady State Theory is not the crucial point and will be decided by observation. However, I must admit that piecemeal manifestation seems more likely a priori. Either way, according to UET, the process of event-chain formation ‘from nothing’ is still going on. 

The Occurrence Function  

This, then, is the general schema proposed ─ how to model it mathematically? We require a ‘Probability Occurrence Function’ which increases very slowly but, once it has reached a critical point, becomes unity or slightly greater than unity.
The Void or Origin, referred to in UET as K0 , is ‘endless’ but we shall only concerned with a small section of it. When empty of ultimate events, K0  is featureless but, when active, it has the capacity to  provide emplacements for ultimate events ─ for otherwise they would not occur. A particular region of K0 can accommodate a maximum of, say, N ultimate events at one and the same ksana. N is a large, but not ‘infinite’ number ─ ‘infinity’ and ‘infinitesimals’ are completely excluded from UET. If there are N potential emplacements and the events appear at random, there is initially a 1/N chance of an ultimate event occurring at one particular emplacement.
However, once an ultimate event has occurred somewhere (and subsequently disappeared), the emplacement remains and the re-occurrence of an event at this spot, or within a certain radius of this spot,  becomes very slightly more likely, i.e. the probability is greater than 1/N. For no two events are ever completely independent in Ultimate Event Theory. Gradually, as more events have occurrence within this mini-region, the radius of probable re-occurrence narrows and  eventually an ultimate event acquires the miraculous property of repeating at the same spot (strictly speaking, the equivalent spot at a subsequent ksana). In other words, the probability of re-occurrence is now a certainty and the ultimate event has turned into an event-chain.
As a first very crude approximation I suggest something along the following lines. P(m) stands for the probability of the occurrence of an ultimate event at a particular spot. The Rule is : 

P(m+1) = P(m) (1/N) ek    m = (–1),0,1, 2, 3…..

P(0) = 1     P(1) = (1/N)


P(2) = (1/N) (1/N) ek = (1/N2) ek
P(3) = ((1/N2) ek) (1/N) ek = (1/N3) e2k
P(4) = (1/N3) e2k (1/N) ek = (1/N4) e3k
P(5) = (1/N4) e4k (1/N) ek = (1/N5) e4k
P(m+1) = (1/Nm+1) emk  

Now, to have P(m+1) ≥ 1  we require

(1/Nm+1) emk ≥ 1
emk ≥  Nm+1
 mk ≥ (m+1) ln N     (taking logs base e on both sides)
k ≥ ((m+1)/m) ln N  

       If we set k as the first integer > ln N  this will do the trick.
For example, if we take N = 1050   ln N = 115.129….
       Then, e116(m+1)  > (1050)m+1 for any m ≥ 0 

However, we do not wish the function to get to unity or above straightaway. Rather, we wish for some function of N which converges very slowly to ln N  or rather to some value slightly above ln N (so that it can attain ln N). Thus k = f(N) such that ef(N)(m+1) ≥ Nm+1
       I leave someone more competent than myself to provide the details of such a function.
This ‘Probability Occurrence Function’ is the most important function in Ultimate Event Theory since without it  there would be no universe, no us, indeed nothing at all except random ultimate events firing off aimlessly for all eternity. Of course, when I speak of a mathematical function providing a mechanism for the emergence of the universe,  I do not mean to imply that a mathematical formula in any way ‘controls’ reality, or is even a ‘blueprint’ for reality. From the standpoint of UET, a mathematical formula is simply a description in terms comprehensible to humans of what apparently goes on and,  given the basic premises of UET, must go on.

Note the assumptions made. They are that:

(1) There is a region of K0 which can accommodate N ultimate events within a single ksana, i.e. can become an Event Locality with event capacity N;
(2) Ultimate events occur at random and continue to occur at random except inasmuch as they are more likely to re-appear at a spot where they have previously appeared;
(3) ‘Time’ in the sense of a succession of moments of equal duration, i.e. ksanas, exists from the very beginning, but not ‘space’;
(4) ‘Space’ comes into existence in a piecemeal fashion as, or maybe just before, ultimate events have occurrence — without events there is no need for space;
(5) Causality comes into existence when the first event-chain is formed : prior to that, there is no causality, only random emergence of events from wherever events come from (Note 5).

What happens once an event-chain has been formed? Does the Occurrence Function remain ≥ 1 or does it decline again? There are two reasons why the Probability Occurrence Function probably (sic) does at some stage decline, one theoretical and one observational. Everything in UET, except K0 the Origin, is finite ─ and K0 should be viewed as being neither finite nor infinite, ‘para-finite’ perhaps. Therefore, no event can keep on repeating indefinitely : all event-chains must eventually terminate, either giving rise to different event-chains or simply disappearing back into the Void from which they emerged. This is the theoretical reason.
Now for the observational reason. As it happens, we know today that the vast majority of ‘elementary particles’ are very short-lived and since all particles are, from the UET point of view, relatively persistent event-chains or event-clusters, we can conclude that most event-chains do not last for very long. On the other hand, certain particles like the proton and the neutrino are so long-lasting as to be virtually immortal. The cause of ‘spontaneous’ radio-active decay is incidentally not known, indeed the process is considered to be completely random (for a particular particle) which is tantamount to saying there is no cause. This is interesting since it shows that randomness re-emerges and re-emerges where it was least expected. I conceive of event-chains that have lost their causal bonding dwindling away in much the same way as they began only in reverse. There is a sort of pleasing symmetry here : randomness gives rise to order which gives rise to randomness once more.
There is the question of how we are to conceive the ‘build up’ of probability in the occurrence function : exactly where does this occur? Since this process has observable effects, it is more than a mathematical fiction. One could imagine that this slow build-up, and eventual weakening and fading away, takes place in a sort of semi-real domain, a hinterland between K0 and K1 the physical universe. I note this as K01.
I am incidentally perfectly serious in this suggestion. Some such half-real domain is required  to cope, amongst many other things, with the notorious ‘probabilities’ — more correctly ‘potentialities’ — of the Quantum Wave Function. The notion of a semi-real region where ‘semi-entities’ gradually become more and more real, i.e. closer to finalization, is a perfectly respectable idea in Hinayana Buddhism ─ many  authors speak of 17 stages in all,  though I am not so sure about that. Western science and thought generally has considerable difficulty coping with phenomena that are clearly neither completely actual nor completely imaginary (Note 6); this is so because of the dogmatic philosophic materialism that we inherit from the Enlightenment and Newtonian physics. Physicists generally avoid confronting the issue, taking refuge behind a smoke-screen of mathematical abstraction.                                                                SH  8/6/14

Note 1  This tends to be the Eastern view : neither the Chinese nor the Hindus seem to have felt much need for a purposeful all-powerful creator God. For the Chinese, there were certain patterns and trends to be discerned but nothing more, a ceaseless flux with one situation engendering another like the hexagrams of the Y Ching. Consulting the Y Ching involves a chance event, the fall of the yarrow sticks that the consultant throws at random. Whereas in divination chance is essential, in science every vestige of randomness is eliminatedas much as is humanly possible.
For the Hindus, the universe was not an artefact as it was for Boyle who likened it to the Strasbourg clock : it was a ‘dance’, that of Shiva. This is a very different conception since dances do not have either meaning or purpose apart from display and self-gratification. Also, although they may be largely repetitive, the (solitary) dancer is at liberty to introduce new movements at any moment.
As for the Buddhists, there was never any question of the universe being created : the emergence of the physical world was regarded as an accident with tragic consequences.

Note 2 “Needham tells of the irony with which Chinese men of letters of the eighteenth century greeted the Jesuits’ announcement of the triumphs of modern science. The idea that nature was governed by simple, knowable laws appeared to them as a perfect example of anthropomorphic foolishness. (…) If any law were involved [in the harmony and regularity of phenomena] it would be a law that no one, neither God nor man, had ever conceived of. Such a law would also have to be expressed in a language undecipherable by man and not be a law established by a creator conceived in our own image.”
Prigogine, Order out of Chaos p. 48 

Note 3  Contemporary Chaos Theory deals with systems that are deterministic in principle but unpredictable in practice. This is because of their sensitive dependence on initial conditions which can never be known exactly. True chaos cannot be modelled by Chaos Theory so-called. 

Note 4 See pages 12-14 of Rupert Sheldrake’s remarkable book, The Presence of the Past where he quotes this passage, likewise that from Nietzsche. Dr Sheldrake has perhaps contributed more than any other single person to the re-emergence of the ‘randomness/order’ paradigm. In his vision, ‘eternal physical laws’ are essentially reduced to habits and the universe as a whole is viewed as in some sense a living entity. “The cosmos now seems more like a growing and developing organism than like an eternal machine. In this context, habits may be more natural than immutable laws” ( Sheldrake, The Presence of the Past, Introduction).
  Stefan Wolfram also adopts a similar philosophic position, believing as he does that not only can randomness give rise to complex order, but must eventually do so. Both thinkers would probably concur with the idea that “systems with complex behaviour in nature must be driven by the same kind of essential spirit as humans” (Wolfram, A New Kind of Science p. 845)

Note 5.  This idea that causality comes into existence when, and only when, the first event-chains are formed, may be compared to the Buddhist doctrine that ‘karma’ ceases in nirvana, or rather that nirvana is to be defined as the complete absence of karma. Karma literally means ‘activity’ and there is no activity in the Void, or K0. Ultimate events are the equivalent of the Buddhist dharma ─ actually it should be dharmas plural but I cannot bring myself to write dharmas. Reality is basically composed of three ‘entities’, nirvana, karma, dharma, whose equivalents within Ultimate Event Theory are K0 or the Void, Causality (or Dominance) and Ultimate Events. All three are required for a description of phenomenal reality because the ultimate events must come from somewhere and must cohere together if they are to form ‘objects’, the causal force providing the force of cohesion. There is no need to mention matter nor for that matter (sic) God.

Note 6   “ ‘The possible’ cannot interact with the real: non-existent entities cannot deflect real ones from their paths. If a photon is deflected, it must have been deflected by something, and I have called that thing a ‘shadow photon’. Giving it a name does not make it real, but it cannot be true that an actual event, such as the arrival and detection of a tangible photon, is caused by an imaginary event such as what that photon ‘could have done’ but did not do. It is only what really happens that can cause other things really to happen. If the complex motions of the shadow photon in an interference experiment were mere possibilities that did not in fact take place, then the interference phenomena se see would not, in fact, take place.”       David Deutsch, The Fabric of Reality pp.48-9

Comment by SH
 : This is fine but I cannot go along with Deutsch’s resolution of the problem by having an infinite number of different worlds, indeed I regard it as crazy.