Archives for category: Causality

“In the last analysis it is the ultimate picture which an age forms of the nature of its world that is its most fundamental possession”
   Burtt, The Metaphysical Foundations of Modern Science

Today, since the cultural environment is so violently anti-metaphysical, it has become fashionable for physical theories to be almost entirely mathematical. Not so long ago, people we now refer to as scientists regarded themselves as ‘natural philosophers’ which is why Newton’s great work is entitled Philosophiae Naturalis Principia Mathematica. When developing a radically new ‘world-view’, the ‘reality-schema’ must come first and the mathematics second, since new symbolic systems may well be required to flesh out the new vision ─ in Newton’s case Calculus (though he makes very sparing use of it in the Principia).
Newton set out his philosophic assumptions very clearly at the beginning, in particular his belief in ‘absolute positioning’ and ‘absolute time’ ─ “All things are placed in time as to order of succession; and in space as to order of situation” (Scholium to Definition VIII). And, as it happened, the decisive break with the Newtonian world-view did not come about because of any new mathematics, nor even primarily because of new data, but simply because Einstein denied what everyone had so far taken for granted, namely that “all things are placed in time as to order of succession” ─ in Special Relativity ‘space-like separated’ pairs of events do not have an unambiguous temporal ordering. The case of QM is more nuanced since the mathematics did come first but it was the apparent violation of causal process that made the theory so revolutionary (and which incidentally outraged Einstein).
The trouble with the current emphasis on mathematics is that, from an ‘eventric’ point of view, the tail is wagging the dog. What is real is what actually happens, not what is supposed to happen. Moreover, mathematics is very far from being so free from metaphysical and ‘intuitive’ assumptions as is generally assumed.         Arithmetic and number theory go right back to Pythagoras who seems to have believed that, at bottom, everything could be explained in terms of whole number relations, hence the watchword “All is Number” (where number meant ‘ratio between positive integers’). And this ancient paradigm received unexpected support from the 20th century discovery that chemistry depends on whole number ratios between the elements (Note 1).
The rival theory of continuous quantity goes back to Plato who, essentially for philosophic reasons, skewed higher mathematics decisively towards the geometrical which is why even those parts of Euclid that deal with (Whole) Number Theory (Books VII ─ X) present numbers as continuous line segments rather than as arrays of dots. And Newton invented his Fluxions (what is now known as the calculus) because he believed reality was ‘continuous, ─ “I consider mathematical Quantities in this place not as consisting of very small parts but as described by a continued Motion…..These Geneses really exist, really take place in the Nature of Things” (Newton, De Quadratura).
The hold of the continuous, as opposed to the discrete, over mathematicians and physicists alike has been extraordinarily strong and held up the eventual triumph of the atomic hypothesis. Planck, the man who introduced ‘quanta’ into physics, wrote “Despite the great success that the atomic theory has so far involved, ultimately it will have to be abandoned in favour of the assumption of continuous matter”.
        Even contemporary branches of mathematics are far from being so ‘abstract’ as their authors claim, witness the excessive importance of the misleading image of the ‘Number Line’ and the general prejudice in favour of the continuous. Only logic is ‘reality-schema free’ and even here, there are systems of ‘deviant logic’ that attempt to make sense of the quantum world. The wholesale mathematisation of physics has itself been given philosophic support by authors such as Tegmark who claim that “at bottom reality is mathematical, not physical”.
All this to say that I make no apology for presenting a broad-brushed reality-schema or ‘world-view’ before attermpting to develop a symbolic model and make predictions. It seems  we need some sort of general ‘metaphysical’ schema if only as a form of intellectual housekeeping, and it is much better to lay one’s cards on the table from the very beginning (as Newton does).
So, what is the schema of Eventrics and Ultimate Event Theory? The fundamental notion is of the ultimate event (an event that cannot be further decomposed). I believe there are such things as events and that they are (at least for the purposes of this theory) more fundamental than ‘things’. I also claim that events must ‘have occurrence’ somewhere ─ hence the need for an Event Locality which either precedes all events or is brought into existence as and when events ‘have occurrence’. Secondly, it since most of the events that I and other humans are familiar with seem to be caused by other, usually preceding,  events, I feel that this needs to be introduced into the theory at the very beginning. There is thus, by hypothesis, a Casual Force operating on and between (most) events. This force I term Dominance in order to emphasize its usually one-sided operation, and perhaps also to be able to extend the sense a little (Note 2).
I have thus already found it necessary in a theory of events to introduce two entities that are not events, namely the Locality and Dominance. Nonetheless, they are very closely tied up with the production of events, since without the first nothing at all could happen (as I see it), and, without the second, all events would be disconnected from each other and reality would be a permanent vast blooming confusion which, reputedly, it is for the new-born infant.
Are all events caused by other events? This is the deterministic view which was for a long time favoured by the scientific community. The 19th century cosmologist Laplace went so far as to claim that if the positions and momenta of all bodies at the present moment were known, the entire future evolution of the universe could be deduced using only Newton’s laws. But, as we know, Quantum Mechanics and the Uncertainty Principle has put paid to such naïve assumptions; the notion of a strictly random event has now become entirely respectable. It can be loosely defined as “an event without causal predecessors” or, in the jargon of UET, “an event that has no passive relation of dominance to any other event that has occurrence on the Locality”. Because of QM and other considerations, I thus found it essential from the very outset to leave some room for ‘undominated’ or ‘random’ events in the general schema. (Not only that, I shall argue that, at one time, random events greatly outnumbered ordinary caused events.)
This naturally leads on to the question of origins and whether we need any. Most ‘origin-schemas’ require the prior existence either of ‘beings of another order’ (Brahman, God, Allah, Norse gods &c.) or of states that are barely conceivable to us mere mortals (Nirvana, the original Tao, the Quantum Vacuum &c.). All such beings/states/entities are other, fundamentally different from the world we (think we) know and the beings within it.
A few ‘origin-schemas’ envisage the universe as remaining basically the same at all times, or at most evolving from something not fundamentally different from the world we now (think we) inhabit. The Stoic cosmology of Eternal Recurrence, Fred Hoyle’s Steady State and perhaps the Hawking-Hartle ‘No Boundary’ theory fall into this  class. For the partisans of these schemas, the present universe is ‘self-explanatory’ and self-sufficient, requiring nothing outside itself for its existence or explication (Note 3).

For a long time modern science adhered to the ‘self-explanatory’ point of view, but current physical orthodoxy is a strange mixture of ‘other-‘ and ‘no-other’ origin-schemas. After dismissing for decades the question of “What was there before the Big Bang?” as meaningless, most current cosmological theories involve pre Big Bang uni- or multi-verses very different from our own but still ‘obeying the laws of physics’ which, though distilled uniquely from observations of this world, have  somehow become timeless and transcendent, in effect replacing the role of God Himself.

Partly for rational and partly for non-rational, i.e. temperamental, reasons I subscribe firmly to the first class of ‘origin theories’. I do not believe the physical universe is ‘self-explanatory’ notwithstanding the amazing success of the natural sciences, and it is significant that present cosmological theorists  have themselves found it necessary to push back into uncharted and inaccessible territory in their search for ultimate origins. The quasi-universality of religious belief throughout history, which, pared down to its essentials, means belief in a Beyond (Note 4) is today explained away as an ingrained habit of wishful thinking, useful perhaps when times are bad but  which humanity will eventually outgrow. However, I don’t find this explanation entirely convincing. There is perhaps more to it than that; this feeling that there is a reality beyond the physical sounds more like a faint but strangely persistent memory that the world of matter and its enforcers have never been able to completely obliterate. (This was the view of the Gnostics.)
Be that as it may, I assume an ultimate origin for events, a  source which is definitely not itself composed of events and is largely independent even of the Locality. This source ejects events randomly from itself, as it were, or events keep ‘leaking out’ of it to change the metaphor. The source is familiar to anyone who is familiar with mysticism, it is the Brahman of Hinduism, the original Tao of Lao Tse, Ain Soph, the Boundless, of the Kabbalah, and what Bohm calls the ‘Explicate Order’. It is  unfashionable today to think in terms of ‘potentiality’ and contrast it with ‘actuality’, but it could be said that this source is “nothing in actuality but everything in potentiality”. Ain Soph is, as Bohm emphasizes, immeasurable in the strong sense ─ measurement is completely irrelevant to it. Since science and mathematics deal only with the measurable and the formal, Ain Soph does not fall within their remit ─ but equally well one can maintain, as all mystics do, that such a thing/place/entity is beyond our comprehension (but perhaps not entirely beyond our apprehension).
What, however, above all one must not do is to mix the measurable and the immeasurable ─ which is exactly what Cantor did, to the great detriment of modern mathematics. Inasmuch as the Unknowable can be known, science and mathematics are definitely not suitable means: ritual, ecstatic dance or directed meditation are traditionally regarded as more suitable ─ and part of their purpose is precisely to quieten or sideline the rational faculty which is, in this context, a hindrance rather than a help.
Ain Soph, or whatever one wants to call the source, should not have any role play in a physical or mathematical theory except at best to function as the ultimate origin of uncaused events. We can, in practice, forgot about it. This means, however, that ‘infinity’, ‘eternity’ and suchlike (pseudo)concepts should have no place in science or in mathematics since they belong entirely to the immeasurable (Note 5).
‘Reality’ thus splits up into two ‘regions’, which I name the Unmanifest and the Manifest. The former is the ultimate source of all events but does not itself consist of events, whilst the latter is ‘manifest’ (to us or other conscious beings) precisely because it is composed of events that we can observe.
These two regions are themselves divided into two giving the schema:
(1) The Unmanifest Non-Occurrent
        (2) The Unmanifest Pre-Ocurrent
        (3) The Manifest Occurrent
        (4) The Manifest Post-Occurrent.

Why do we need (2.) and (4.)?
We need (2) largely because of Quantum Mechanics ─ more precisely because of the ‘orthodox’ Copenhagen interpretation of QM. This interpretation in effect splits the physical world into two layers, one of which is described by the wave function in its ‘independent state’ while the other arises when a human intervention causes the wave function to ‘collapse’ — an interesting metaphor. In the former (pure) state, whatever ‘goes on’ (and something apparently does) lacks entirely the specificity and discreteness of an ultimate event. We are, for example, invited to believe that a ‘photon’ (or rather a photo-wavicle) has no specific location, or momentum, prior to an intervention on our part ─ rather misleadingly termed a ‘measurement’. There is thus a layer of reality, and ‘physical reality’ at that, which does not consist of events but which seemingly does in some sense exist, and is all around and even in us, because QM ‘works’, however crazy it appears. There is thus the need for an intermediary level between the remoteness of the true Unmanifest and the immediacy of the world of actual events we are familiar with (Note 6).
What of (4.), the Manifest Post-Occurrent ? It would seem that there are ‘entities’ of some sort which are not observable, not composed of bona fide observable events, but which are  nonetheless capable of giving rise to observable phenomena. I am thinking of such things as archetypes, myths, belief systems, generalized abstractions such as Nation, State, Humanity, perhaps even the self, Dawkins’s memes and so on. Logic and rational discourse tend to dismiss such things as pseudo-entities: there is the well-known anecdote of the tourist being shown around the Oxford colleges and asking where the university is. But the ‘university’ does have a reality of a sort, something in between the clearcut reality of a blow to the head and the unreality of a meaningless squiggle.
Moreover, it is in (4.) that I place such things as mathematical and physical theories. As far as I am concerned it is not the tourist but people like Tegmark (and Plato) who are guilty of a ‘category mistake’: in effect, they situate mathematics in (1.), the Unmanifest Non-Occurrent, rather than in (4.) the Manifest Post-Occurrent. (1.) is a wholly transcendent level of reality, while (4.) is a manufactured realm which, though giving an appearance of solidity, would not exist, and would never have existed, if there had never been any human mathematicians (or other conscious beings). The Platonic view of mathematics, though tempting, is, I believe, a delusion: mathematics was made by man(kind) and was, originally at any rate, an extrapolation from human sense-impressions, though admittedly it is a very successful one.                                      SH 20/12/19 

 

Note 1. See the chapter on the ‘New Pythagoreanism’ in Shanks’s excellent book, Number Theory, or, for a more accessible treatment, in Valens’s The Number of Things.
Note 2 Dominance is roughly the equivalent of the Buddhist/Hindu concept of karma ─ but applied to all categories of events, not just morally significant ones.
Note 3. Newton granted a small role to God in the evolution of the universe, for example stopping heavenly bodies converging together because of universal attraction, but Leibnitz argued that it was blasphemous to suppose any such intervention was needed since this implied that the Creator had not been a good enough designer in the first place. “No need for miracles” became a principal tenet of the Enlightenment though most thinkers found it necessary to introduce a Prime Mover to ‘get the ball rolling’, so to speak. Even this shadowy deus ex cathedra faded away into nothingness by the time of Laplace who famously informed Napoleon, “I had no need of that hypothesis” ─ the hypothesis in question being the existence of God.

Note 4 The Koran, for example, addresses itself specifically to “those who believe in the unseen”.  

Note 5. This is precisely the point made by Lao Tse in the very first line of the Tao Te Ching which may be translated, “The Tao that can be named is not the original Tao”. Lao Tse was writing at a time when language, not mathematics or physics, was the most advanced human invention and, were he alive today, he would doubtless have written, “The Tao that can be mathematized is not the original Tao”.

 Note 6.    QM is, incidentally, not the only system that posits an intermediary realm between the Limitless and the Limited. Hinayana Buddhism has a curious theory about ‘events’ passing through various stages of progressive ‘realization’ before becoming actual ─ most authors for some reason cite the number 17.

 

 

 

Although, in modern physics,  many elementary particles are extremely short-lived, others such as protons are virtually immortal. But either way, a particle, while it does exist, is assumed to be continuously existing. And solid objects such as we see all around us like rocks and trees are also assumed to carry on being rocks and trees from start to finish even though they do undergo considerable changes in physical and chemical composition. What is out there is  always there when it’s out there, so to speak.
However, in Ultimate Event Theory (UET) the ‘natural’ tendency is for everything to flash in and out of existence and most ultimate events, the ‘atoms’ or elementary particles of  Eventrics,  disappear for ever leaving no trace and even with more precise instruments than we have at present, wouldshow up as a sort of faint permanent background ‘noise’, a ‘flicker of existence’. Certain ultimate events, those that have acquired persistence ─ we shall not for the moment ask how and why they acquire this property ─ are able to bring about, i.e. cause, their own re-appearance and eventually to constitute a repeating event-chain or causally bonded sequence. And some event-chains also have the capacity to bond to other event-chains, eventually  forming relatively persistent clusters that we know as matter.  All apparently solid objects are, according to the UET paradigm, conglomerates of repeating ultimate events that are bonded together ‘laterally’, i.e. within  the same ksana, and ‘vertically’, i.e. from one ksana to the next. And the cosmic glue is not gravity or any other of the four basic forces of contemporary physics but causality.

The Principle of Spatio/Temporal Continuity

Newtonian physics, likewise 18th and 19th century rationalism generally, assumes what I have referred to elsewhere as the Postulate of Spatio-temporal Continuity. This postulate or principle, though rarely explicitly  stated in philosophic or scientific works,  is actually one of the most important of the ideas associated with the Enlightenment and thus with the entire subsequent intellectual development of Western society (Note 1). In its simplest form, the principle says that an event occurring here, at a particular spot in Space-Time (to use the traditional term), cannot have an effect there, at a spot some distance away without having effects at all (or at least most or some) intermediate spots. The original event, as it were, sets up a chain reaction and a frequent image used is that of a whole row of upright dominoes falling over one after the other once the first has been pushed over. This is essentially how Newtonian physics views the action of a force on a body or system of bodies, whether the force in question is a contact force (push/pull) or a force acting at a distance like gravity ─ though in the latter case Newton was unable to provide a mechanical model of how such a force could be transmitted across apparently empty space.
As we envisage things today, a blow affects a solid object by making the intermolecular distances of the surface atoms contract a little and they pass on this effect to neighbouring atoms which in turn affect nearby objects they are in contact with or exert an increased pressure on the atmosphere, and so on. Moreover, although this aspect of the question is glossed over in Newtonian (and even modern) physics, each transmission of the original impulse  ‘takes time’ : the re-action is never instantaneous (except possibly in the case of gravity) but comes ‘a moment later’, more precisely at least one ksana later. This whole issue will be discussed in more detail later, but, within the context of the present discussion, the point to bear in mind is that,  according to Newtonian physics and rationalistic thought generally, there can be no leap-frogging with space and time. Indeed, it was because of the Principle of Spatio-temporal Continuity that most European scientists rejected out of hand Newton’s theory of universal attraction since, as Newton admitted, there seemed to be no way that a solid body such as   the Earth could affect another solid body such as the Moon thousands  of kilometres without affecting the empty space between. Even as late as the mid 19th century, Maxwell valiantly attempted to give a mechanical explanation of his own theory of electro-magnetism, and he did this essentially because of the widespread rock-hard belief in the principle of spatio-temporal continuity.

So, do I propose to take the principle over into UET? No, except possibly in special situations. If I did take over the principle, it would mean that certain regions of the Locality would soon get hopelessly clogged up with colliding event-chains. Indeed, if all the possible positions in between two spots where ultimate events belonging to the same chain had occurrence were occupied, event-chains would behave as if they were solid objects and one might as well just stick to normal physics. A further, and more serious, problem is that, if all event-chains were composed of events that repeated at every successive ksana, one would expect event-chains with the same ‘speed’ (space/time ratio with respect to some ‘stationary’ event-chain) to behave in the same way when confronted with an obstacle. Manifestly, this does not happen since, for example, photon event-chains behave very differently from neutrino event-chains even though both propagate at the same, or very similar, speeds.
One of the main reasons for elaborating a theory of events in the first place was my deep-rooted conviction ─ intuition if you like ─ that physical reality is discontinuous. I do not believe there is, or can be, such a thing as continuous motion, though there is and probably always will be succession and thus change since, even if nothing else is happening, one ksana is perpetually being replaced by another, different, one ─ “the moving finger writes, and, having writ, moves on” (Rubaiyat of Omar Khayyam). Moreover, this movement is far from smooth : ‘time’ is not a river that flows at a steady rate as (Newton envisaged it) but a succession of ‘moments’, beads of different sizes threaded together to make a chain and with minute gaps between the beads which allow the thread that holds them together to become momentarily visible.
If, then, one abandons the postulate of Spatio-temporal Continuity, it becomes perfectly feasible for members of an event-chain to ‘miss out’ intermediate positions and so there most definitely can be ‘leap-frogging’ with space and time. Not only are apparently continuous phenomena discontinuous but one suspects that they have very different staccato rhythms.

‘Atomic’ Event Capsule model

 At this point it is appropriate to review the basic model.
I envisage each ultimate event as having occurrence at a particular spot on the Locality, a spot of negligible but not zero extent. Such spots, which receive (or can receive) ultimate events are the ‘kernels’ of much larger ‘event-capsules’ which are themselves stacked together in a three-dimensional lattice. I do not conceive of there being any appreciable gaps between neighbouring co-existing event-capsules : at any rate, if there are gaps they would seem to be very small and of no significance, essentially just demarcation lines. According to the present theory these spatial ‘event-capsules’ within which all ultimate events have occurrence cannot be extended or enlarged  ─ but they can be compressed. There is, nonetheless,  a limit to how far they can be squeezed because the kernels, the spots where ultimate events can and do occur, are incompressible.
I believe that time, that is to say succession, definitely exists; in consequence, not only ultimate events but the space capsules themselves, or rather the spots on the Locality where there could be ultimate events, appear and disappear just like everything else. The lattice framework, as it were, flicks on and off and it is ‘on’ for the duration of a ksana, the ultimate time interval (Note 2). When we have a ‘rest event-chain’ ─ and every event-chain is ‘at rest’ with respect to itself and an imaginary observer moving on or with it ─ the ksanas follow each other in close succession, i.e. are as nearly continuous as an intrinsically  discontinuous process can be.
According to the theory, the ‘size’ or ‘extent’ of a ksana cannot be reduced  ─ otherwise there would be little point in introducing the concept of a minimal temporal interval and we would be involved in infinite regress, the very thing which I intend to avoid at all costs. However, the distance between ksanas can, so it is suggested, be extended, or, more precisely, the distance between the successive kernels of the event capsules, where the ultimate events occur, can be extended. That is, there are gaps between events. As is explained in other posts, in UET the ‘Space/Time region’ occupied by the successive members of an event-chain remains the same irrespective of ‘states of motion’ or other distinguishing features. But the dimensions themselves can and do change. If the space-capsules contract, the time dimension must expand and this can only mean that the gaps between ksanas widen (since the extent of an ‘occupied’ ksana is cnstant. The more the space capsules contract, the more the gaps must increase (Note 3).  But, as with everything else in UET, there is a limiting value since the space capsules cannot contract beyond the spatial limits of the incompressible kernels. Note that this ‘Constant Region Principle’ only applies to causally related regions of space ─ roughly what students of SR view as ‘light cones’.

The third parameter of motion

 In traditional physics, when considering an object or body ‘in motion’, we essentially only need to specify two variables : spatial position and time. Considerations of momentum and so forth is only required because it affects future positions at future moments, and aids prediction. To specify an object’s ‘position in space’, it is customary in scientific work to relate the object’s position to an imaginary spot called the Origin where three mutually perpendicular axes meet. To specify the object’s position ‘in time’ we must show or deduce how many ‘units of time’ have elapsed since a chosen start position when t = 0. Essentially, there are only two parameters required, ‘space’ and ‘time’ : the fact that the first parameter requires (at least) three values is not, in the present context, significant.
Now, in UET we likewis need to specify an event’s position with regard to ‘space’ and ‘time’. I envisage the Event Locality at any ‘given moment’ as being composed of an indefinitely extendable set of ‘grid-positions’. Each ‘moment’ has the same duration and, if we label a particular ksana 0 (or 1) we can attach a (whole) number to an event subsequent to what happened when t = 0 (or rather k = 0). As anyone who has a little familiarity with the ideas of Special Relativity knows, the concept of an  ‘absolute present’ valid right across the universe is problematical to say the least. Nonetheless, we can talk of events occurring ‘at the same time’ locally, i.e. during or at the same ksana. (The question of how these different  ‘time zones’ interlock will be left aside for the moment.)
Just as in normal physics we can represent the trajectory of an ‘object’ by using three axes with the y axis representing time and, due to lack of space and dimension, we often squash the three spatial dimensions down to two, or, more simply still, use a single ‘space’ axis, x (Note 4). In normal physics the trajectory of an object moving with constant speed will be represented by a continuous vertical straight line and an object moving at constant non-zero speed relative to an object considered to be stationary will be represented by a slanting but nonetheless still straight line. Accelerated motion produces a ‘curve’ that is not straight. All this essentially carries over into UET except that, strictly, there should be no continuous lines at all but only dots that, if joined up, would form lines. Nonetheless, because the size of a ksana is so small relative to our very crude senses, it is usually acceptable to represent an ‘object’s’ trajectory as a continuous line. What is straight in normal physics will be straight in UET. But there is a third variable of motion in UET which has no equivalent in normal physics, namely an event’s re-appearance rhythm.
        Fairly early on, I came up against what seemed to be an insuperable difficulty with my nascent model of physical reality. In UET I make a distinction between an attainable ‘speed limit’ for an event-chain and an upper unatttainable limit, noting the first c * and the second c. This allows me to attribute a small mass ─ mass has not yet been defined in UET but this will come ─  to such ‘objects’ as photons. However, this distinction is not significant in the context of the present discussion and I shall  use the usual symbol c for either case. Now, it is notorious that different elementary particles (ultimate event chains) which apparently have the same (or very nearly identical) speeds do not behave in the same way when confronted with obstacles (large dense event clusters) that lie on their path. Whereas it is comparatively easy to block visible light and not all that difficult to block or at least muffle much more energetic gamma rays, it is almost impossible to stop a neutrino in its path, so much so that they are virtually undetectable. Incredible though it sounds, “about 400 billion neutrinos from the Sun pass through us every second” (Close, Particle Physics) but even state of the art detectors deep in the earth have a hard  job  detecting a single passing neutrino. Yet neutrinos travel at or close to the speed of light. So how is it that photons are so easy to block and neutrinos almost impossible to detect?
The answer, according to matter-based physics, is that the neutrino is not only very small and very fast moving but “does not feel any of the four physical Reappearance rates 2forces except to some extent the weak force”. But I want to see if I can derive an explanation without departing from the basic principles and concepts of Ultimate Event Theory. The problem in UET is not why the repeating event-pattern we label a neutrino passes through matter so easily ─ this is exactly what I would expect ─ but rather how and why it behaves so  differently from certain other elementary event-chains. Any ‘particle’, provided it is small enough and moves rapidly, is likely, according to the basic ideas of UET, to ‘pass through’ an obstacle just so long as the obstacle is not too large and not too dense. In UET, intervening spatial positions are simply skipped and anything that happens to be occupying these intermediate spatial positions will not in any way ‘notice’ the passing of the more rapidly moving ‘object’. On this count, however, two ‘particles’ moving at roughly the same speed (relative to the obstacle) should either both pass through an  obstacle or both collide with it.
But, as I eventually realized, this argument is only valid if the re-appearance rates of the two ‘particles’ are assumed to be the same. ‘Speed’ is nothing but a space/time ratio, so many spatial positions against so many ksanas. A particular event-chain has, say, a ‘space/time ratio’ of 8 grid-points per ksana. This means that the next event in the chain will have occurrence at the very next ksana exactly eight grid-spaces along relative to some regularly repeating event-chain considered to be stationary. On this count, it would seem impossible to have fractional rates and every ‘re-appearance rate’ would be a whole number : there would be no equivalent in UET of a speed of, say, 4/7 metres per second since grid-spaces are indivisible.
However, I eventually realized that it was not one of my original assumptions that an event in a chain must repeat (or give rise to a different event) at each and every ksana. This at once made fractional rates possible even though the basic units of space and time are, in UET, indivisible. A ‘particle’ with a rate of 4/7 s0 /t0 could, for example, make a re-appearance four times out of every seven ksanas ─ and there are any number of ways that a ‘particle’ could have the same flat rate while not having the same re-appearance rhythm. 

Limit to unitary re-appearance rate

It is by no means obvious that it is legitimate to treat ‘space’ and ‘time’ equivalently as dimensions of a single entity known as ‘Space/Time’. A ‘distance’ in time is not just a distance in space transferred to a different axis and much of the confusion in contemporary physics comes from a failure to accept, or at the very least confront, this fact. One reason why the dimensions are not equivalent is that, although a spatial dimension such as length remains the same if we now add on width, the entire spatial complex must disappear if it is to give rise to a similar one at the succeeding moment in time ─ you cannot simply ‘add’ on another dimension to what is already there.
However, for the the time being I will follow accepted wisdom in treating a time distance on the same footing as a space distance. If this is so, it would seem that, in the case of an event-chain held together by causality, the causal influence emanating from the ‘kernel’ of one event capsule, and which brings about the selfsame event (or a different one) a ksana later in an equivalent spatial position, must traverse at least the ‘width’ or diameter of a space capsule, noted s0 (if the capsule is at rest). Why? Because if it does not at least get to the extremity of the first spatial capsule, a distance of ½ s0  and then get to the ‘kernel’ of the following one, nothing at all will happen and the event-chain will terminate abruptly.
This means that the ‘reappearance rate’ of an event in an event-chain must at least be 1/1 in absolute units, i.e. 1 s0 /t0 , one grid-space per ksana. Can it be greater than this? Could it, for example, be  2, 3 or 5 grid-spacesper ksana? Seemingly not. For if and when the ultimate event re-appears, say  5 ksanas later, the original causal impulse will have covered a distance of 5 s0   ( s0 being the diameter or spatial dimension of each capsule) and would have taken 5 ksanas to do  this. And so the space/time displacement rate would be the same (but not in this case the actual inter-event distances).
It is only the unitary rate, the distance/time ratio taken over a single ksana, that cannot be less (or more) than one grid-space per ksana : any fractional (but not irrational) re-appearance rate is perfectly conceivable provided it is spread out over several ksanas.  A re-appearance rate of m/n s0/t0  simply means that the ultimate event in question re-appears in an equivalent spatial position on the Locality m times every n ksanas where m/n ≤ 1. And there are all sorts of different ways in which this rate be achieved. For example, a re-appearance rate of 3/5 s0/t0 could be a repeating pattern such as

 

   ™˜™™™™™™™™™™™™™™™™™™™™™™Reappearance rates 1

 

 

 

 

 

and one pattern could change over into the other either randomly or, alternatively, according to a particular rule.
As one increases the difference between the numerator and the denominator, there are obviously going to be many more possible variations : all this could easily be worked out mathematically using combinatorial analysis. But note that it is the distribution of ™ and ˜ that matters since, once a re-appearance rhythm has begun, there is no real difference between a ‘vertical’ rate of  ™˜™˜ and ˜™˜™ ─ it all depends on where you start counting. Patterns only count as different if this difference is recognizable no matter where you start examining the sequence.
Why does all this matter? Because, each time there is a blank line, this means that the ultimate event in question does not make an appearance at all during this ksana, and, if we are dealing with large denominators, this could mean very large gaps indeed in an event chain. Suppose, for example, an event-chain had a re-appearance rate of 4/786. There would only be four appearances (black dots) in a period of 786 ksanas, and there would inevitably be very large blank sections of the Locality when the ultimate event made no appearance.

Lower Limit of re-creation rate 

Since, by definition, everything in UET is finite, there must be a maximum number of possible consecutive non-reappearances. For example, if we set the limit at, say, 20 blank lines, or 200 03 2000, this would mean that, each time this was observed, we could conclude that the event-chain had terminated. This is the UET equivalent  of the Principle of Spatio-Temporal Continuity and effectively excludes phenomena such as an ultimate event in an event-chain making its re-appearance a century later than its first appearance. This limit would have to be estimated on the  basis of experiments since I do not see how a specific value can be derived from theoretical considerations alone. It is tempting to estimate that this value would involve c* or a multiple of c* but this is only a wild guess ─ Nature does not always favour elegance and simplicity.
Such a rule would limit how ‘stretched out’ an event-chain can be temporally and, in reality , there may not after all be a hard and fast general rule  : the maximal extent of the gap could decline exponentially or in accordance with some other function. That is, an abnormally long gap followed by the re-appearance of an event, would decrease the possible upper limit slightly in much the same way as chance associations increase the likelihood of an event-chain forming in the first place. If, say, there was an original limit of a  gap of 20 ksanas, whenever the re-appearance rate had a gap of 19, the limit would be reduced to 19 and so on.
It is important to be clear that we are not talking about the phenomenon of ‘time dilation’ which concerns only the interval between one ksana and the next according to a particular viewpoint. Here, we simply have an event-chain ‘at rest’ and which is not displacing itself laterally at all, at any rate not from the viewpoint we have adopted.

Re-appearance Rate as an intrinsic property of an event-chain  

Since Galileo, and subsequently Einstein, it has become customary in physics to distinguish, not between rest and motion, but rather between unaccelerated motion and  accelerated motion. And the category of ‘unaccelerated motion’ includes all possible constant straight-line speeds including zero (rest). It seems, then,  that there is no true distinction to be made between ‘rest’ and motion just so long as the latter is motion in a straight line at a constant displacement rate. This ‘relativisation’ of  motion in effect means that an ‘inertial system’ or a particle at rest within an inertial system does not really have a specific velocity at all, since any estimated velocity is as ‘true’ as any other. So, seemingly, ‘velocity’ is not a property of a single body but only of a system of at least two bodies. This is, in a sense, rather odd since there can be no doubt that a ‘change of velocity’, an acceleration, really is a feature of a single body (or is it?).
So what to conclude? One could say that ‘acceleration’ has ‘higher reality status’ than simple velocity since it does not depend on a reference point outside the system. ‘Velocity’ is a ‘reality of second order’ whereas acceleration is a ‘reality of first order’. But once again there is a difference between normal physics and UET physics in this respect. Although the distinction between unaccelerated and accelerated motion is taken over into UET (re-baptised ‘regular’ and ‘irregular’ motion), there is in Ultimate Event Theory a new kind of ‘velocity’ that has nothing to do with any other body whatsoever, namely the event-chain’s re-appearance rate.
When one has spent some time studying Relativity one ends up wondering whether after all “everything is relative” and that  the universe is evaporating away even as we look it leaving nothing but a trail of unintelligible mathematical formulae. In Quantum Mechanics (as Heisenberg envisaged it anyway) the properties of a particular ‘body’ involve the properties of all the other bodies in the universe, so that there remain very few, if any, intrinsic properties that a body or system can possess. However, in UET, there is a reality safety net. For there are at least two  things that are not relative, since they pertain to the event-chain or event-conglomerate itself whether it is alone in the universe or embedded in the dense network of intersecting event-chains we view as matter. These two things are (1) the number of ultimate events in a given portion of an event-chain and (2) the re-appearance rate of events in the chain. These two features are intrinsic to every chain and have nothing to do with velocity or varying viewpoints or anything else.  To be continued SH

Note 1   This principle (Spatio-temporal Continuity) innocuous  though it may sound, has also had  extremely important social and political implications since, amongst other things, it led to the repeal of laws against witchcraft in the ‘advanced’ countries. For example, the new Legislative Assembly in France shortly after the revolution specifically abolished all penalties for ‘imaginary’ crimes and that included witchcraft. Why was witchcraft considered to be an ‘imaginary crime’? Essentially because it  violated the Principle of Spatio-Temporal Continuity. The French revolutionaries who drew the statue of Reason through the streets of Paris and made Her their goddess, considered it impossible to cause someone’s death miles away simply by thinking ill of them or saying Abracadabra. Whether the accused ‘confessed’ to having brought about someone’s death in this way, or even sincerely believed it, was irrelevant : no one had the power to disobey the Principle of Spatio-Temporal Continuity. The Principle got somewhat muddied  when science had to deal with electro-magnetism ─ Does an impulse travel through all possible intermediary positions in an electro-magnetic field? ─ but it was still very much in force in 1905 when Einstein formulated the Theory of Special Relativity. For Einstein deduced from his basic assumptions that one could not ‘send a message’ faster than the speed of light and that, in consequence,  this limited the speed of propagation of causality. If I am too far away from someone else I simply cannot cause this person’s death at that particular time and that is that. The Principle ran into trouble, of course,  with the advent of Quantum Mechanics but it remains deeply entrenched in our way of thinking about the world which is why alibis are so important in law, to take but one example. And it is precisely because Quantum Mechanics appears to violate the principle that QM is so worrisome and the chief reason why some of the scientists who helped to develop the theory such as Einstein himself, and even Schrodinger, were never happy with  it. As Einstein put it, Quantum Mechanics involved “spooky action at a distance” ─ exactly the same objection that the Cartesians had made to Newton. 

Note 2  Ideally, we would have a lighted three-dimensional framework flashing on and off and mark the successive appearances of the ‘object’ as, say, a red point of light comes on periodically when the lighted framework comes on.

Note 3 In principle, in the case of extremely high speed event-chains, these gaps should be detectable even today though the fact that such high speeds are involved makes direct observation difficult. 

Note 4 This is not how we specify an object’s position in ordinary conversation. As Bohm pertinently pointed out, we in effect speak in the language of topology rather than the language of co-ordinate geometry. We say such and such an object is ‘under’, ‘over’, ‘near’, ‘to the right of’ &c. some other well-known  prominent object, a Church or mountain when outside, a bookcase or fireplace when in a room.
Not only do coordinates not exist in Nature, they do not come at all naturally to us, even today. Why is this? Chiefly, I suspect because they are not only cumbersome but practically useless to a nomadic, hunting/food gathering life style and we humans spent at least 96% of our existence as hunter/gatherers. Exact measurement only becomes essential when human beings start to manufacture complicated objects and even then many craftsmen and engineers used ‘rules of thumb’ and ‘rough estimates’ well into the 19th century.

What is time? It is succession. Succession of what? Of events ─ events that take place ‘one after the other’. If there is no succession of events, either nothing happens at all or everything that can happen occurs in an endless, eternal present.
We measure time by referring to two (or more) events which are easily recognizable, themselves having  negligible extension ‘in time’  and which repeat in a fashion we have reason to believe does not change appreciably. Tick-tock. The sounds are sharp, easily recognizable and the old-fashioned pendulum swings fairly regularly ─ though, of course, certain crystals vibrate a good deal more regularly. If we do  not have two  easily recognizable, repeating,  ‘marker events’ which signify the beginning and end of an ‘interval of time’, ‘duration’ is vague and subjective. This shows that duration is a secondary notion compared to succession. Without succession, no duration ─ or at least no accurately measurable duration. One can argue interminably about how long the interval between two events ‘really’ is, or was, but the events themselves either happen/happened, or they don’t/didn’t happen. Occurrence and succession are primary features of physical reality, duration a secondary property.
As I see it, physics ought by rights to be based chiefly on notions of occurrence, succession and causality since all these ‘things’ are primary ─ causality perhaps a shade less fundamental than the other two (since there can be occurrence without causality as in the case of ‘random’ events). In Ultimate Event Theory, the occurrence of an event is absolute in the sense that its occurrence has nothing whatsoever to do with anyone’s location, state of mind, state of motion in relation to other objects, and so on. Also,  since all events are (by hypothesis) made up of a finite number of ultimate events, every event-chain A-B whose first event is A and last event B has an event-number which is a positive integer. But the distances between the successive ultimate events composing the chain are secondary features : they have minimum and maximum values but otherwise are flexible and are legitimately evaluated quite differently according to one’s viewpoint and ‘state of motion’ (Note 1).

Space/Time Event-Capsules and ‘Objects’ 

In the preceding posts, it was hypothesized that the region occupied by the ‘Space-Time Rectangle’ of a single event-chain  or event-complex is constant. In the simplest case of a single repeating ultimate event, we have a repeating unitary four-dimensional  ‘Event Capsule’ successively occupying a region s0 × s0 × s0 × t0 = s03 t0. We, of course, do not ‘see’, or otherwise register, each individual event capsule but run several of them together much as the eye/brain runs together the separate stills that compose a ‘motion’ picture. We eventually become aware of an ‘event block’ which is nonetheless (according to UET) composed of a set of identical unitary event capsules each of them occupying a region s03 t0. This ‘occupied region’ is thus  d s03 × t t0  where d and t are integers. If all the available positions within this region are occupied by repeating ultimate events, we have a repeating  Event Conglomerate of volume d3 × t  in ‘absolute’ units. For simplicity, we shall only consider one of the spatial dimensions and confine ourselves to the Space/Time Event Rectangle of d × t with d and t in ‘absolute’ units. This is the equivalent in UET of a ‘solid object’.
Of course, it is most unlikely that all neighbouring. spatial positions would be occupied by ultimate events which, taken together, constitute Relativity Unitary Capsule Emptythe equivalent of an  ‘object’ or body : there will, almost certainly, be sizeable gaps just as there are ‘holes’ in an apparently solid body. Nonetheless, at least in imagination, we can connect up any two positions on the Locality and construct a ‘Space/Time’ Event Region which, in the simplified case, reduces to a Space/Time Event Rectangle composed of unitary Space/Time Event Rectangles.

 

 

In the following simplified diagram each line represents a section of the Event Locality at one particular ksana (‘moment in time’) and each square a grid-position.

ksana 0  ……..⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐………
ksana 1   ……..⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐……..
ksana 2  ……..⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐………
ksana 3  ……..⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐………
ksana 4 ……..⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐………

Any of these little squares symbolizing two-dimensional grid positions could, in theory, receive an ultimate event and any two arbitrarily selected grid-positions could be connected up, for example those marked in black

……..⅐∎⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐………
……..⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐………
……..⅐⅐⅐⅐⅐⅐⅐⅐∎⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐………
……..⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐………

If we treat these grid-positions as extremities of an ‘occupied region’ equivalent to a perfectly dense ‘object’ occupying the entire rectangle, we have

……..⅐∎∎∎∎∎∎∎∎∎⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐………
……..⅐∎∎∎∎∎∎∎∎∎⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐………
……..⅐∎∎∎∎∎∎∎∎∎⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐………

An object in UET is, then,  an identically repeating event conglomerate that only persists because the individual ultimate events are powerfully bonded both ‘laterally’, within a single ksana, and, more significantly, ‘vertically’, from one ksana to the next. If ultimate events are not bonded ‘laterally’, they do not constitute an ‘object’ : their proximity is entirely coincidental and if one or more of these ultimate events for some reason ceased to reappear, this would have no consequences on the others. And if the ultimate events are not bonded ‘vertically’, i.e. lack the property called persistence, the entire conglomerate does not repeat : it simply disappears without a trace.
Now, since everything in UET is finite (except the extent of the Locality itself), there must be a limit to the possible extent of ‘lateral bonding’ : that is, an ‘object’ cannot exceed certain dimensions at any one ksana. There is presumably also a limit to the number of times any ultimate event can repeat though, to judge by the length of time the present universe has existed and certain elementary particles such as protons, this limit must be inconceivably great. Much more important practically is the ‘lateral displacement limit’. For example, consider two occupied grid positions at successive ksanas

……..⅐∎⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐………
……..⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐………
……..⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐………
……..⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐………

Could these two ultimate events be causally connected, i.e. part of an event-chain? It is quite irrelevant that there are a large number of blank spaces between the two occupied positions since, in UET, it is not necessary for an event chain to fill the intervening space ─ a completely dense repeating event conglomerate is almost certainly a rarity and even perhaps  impossible.
The only problem is thus the extent of the lateral displacement from one  ksana to the next since this has a maximum possible value, traditionally noted as c but  in UET noted as c*. This gives us a test as to whether the two events occupying two squares are, or could conceivably be, causally connected. If the lateral distance covered in one ksana exceeds a certain number of spaces, namely c*,  the events are not causally connected. Of course, it is essentially a matter of convenience, or of viewpoint, which of two regular event chains is considered to be ‘vertical’ and which ‘slanting’, but this does not mean that lateral displacement of events from one ksana to another does not occur. We can imagine the original ultimate event repeating in an exactly equivalent spatial position at the very next ksana, and simultaneously producing a  clone’ of itself so many spaces to the right or left.

……..⅐∎⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐………
……..⅐∎⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐………

If the distance is too great, we can confidently conclude that the red ultimate event has not been produced by the black one since the lateral distance exceeds the reach of a causal impulse emanating from the point of its occurrence (Note 3). All this is, of course, well known to students of Relativity, but it is important to recognize how naturally and inevitably this result (and all that follows from it) arises once we have accepted once and for all that there must, for a priori reasons, be a spatial limit to the transmission of a causal impulse. Someone in another place and time could have (and possibly did) hit upon such a conclusion  purely from first principles centuries before Einstein was even born (Note 4 Galileo…..)and when there would have been no way of carrying out appropriate experimental tests just as there was, in  Newton’s own day,  no way of showing that two small objects suspended in a room and free to move actually attract each other.

Causality and the unitary Space/Time Event Capsule

In normal physics, it is assumed that the ‘natural’ state of a body is to carry on existing more or less in the same state from one moment to the next, and if the  body does change, a fortiori disappear, we conclude that an external (or sometimes internal) force is at work. An ‘object’ does not ‘cause itself to happen’ as it were : the very idea sounds absurd. However, In UET, this is precisely what does prevail since the ‘natural state’ of everything is to appear once and then disappear for ever. The reappearance of an ultimate event more or less in the same position on the Locality is just as much the result of causality as the sudden appearance of a completely new, and, in general, different, event regarded as the ‘effect’. The continued existence of anything is ‘self-caused’ (Note 5 Sheldrake).
So, before examining repeating batches and conglomerates of ultimate events, we should examine exactly what is involved in the reappearance of a single ultimate event since without this happening there will be no repeating conglomerates, no apparently solid objects, no universe, nothing at all except a sort of “buzzing. blooming confusion” (Piaget) brought about by ephemeral random events emerging from the Event Origin and at once disappearing back into it.
For anything to last at all, certain conditions must be met. The first and most important is that the causal influence which brings about the repetition of the ultimate event must at least be able to traverse the distance from the centre of one Event Capsule to another. For, just as the  nucleus of an atom does not extend to the outer reaches of the atom but on the contrary is marooned in a comparatively vast empty area, an ultimate event in UET is conceived as occupying a minute ‘kernel’ at the centre of a Space/Time Event Capsule. When such an ultimate event is isolated or part of an event-chain ‘at rest’, the dimensions of all such capsules are fixed and are always the same. These ‘rest’ dimensions are the ‘true’ dimensions of the capsule and are s0 for the spatial dimension and t0 for the ‘time’ dimension.
‘Distance’, both spatial and temporal, is not absolute in UET but can be legitimately ‘measured’ (or, better, experienced) in different ways — though there are nonetheless, as for everything in UET, minimal and maximal values. What is ‘absolute’ is firstly, the number of ultimate events in an event-chain (or portion thereof) and, secondly, the total extent of the ‘occupied region’ on the Locality. In the simplest possible case which is what we are considering here, we have just a single ultimate event which repeats in the ‘same’ position a ksana later. To accurately model what I believe goes on in reality, it would be necessary not only to have a three-dimensional grid or lattice-frame extending as far as the eye can see in all three directions but also for it to consist of lines of lights which are switched on and off regularly. An ultimate event would then be represented by, say, a red flash inside a rectangular ‘box’ consisting of lines of little lights arranged in series. The whole framework of ‘fairy lights’ representing the Event Locality is then switched on and off, and each time the framework is switched on, a red flash appears inside a lower ‘box’. In the case of two appearances, the ‘vertical displacement’ of the red light would scarcely be noticeable, but if we keep on switching the whole framework on and off and having the red light appear slightly below where it was previously, we obtain a rough  idea of a ‘stationary’ event-chain. To represent ‘lateral displacement’, which is generally what is understood by ‘movement’, we would need to have a second flashing coloured light displacing itself regularly in a slanting straight line relative to the red one. By speeding up the flashings, we would get an impression of ‘continuous movement’ even though nothing is moving at all, merely flashing on and off.
We have then, as it were, arrays of 3- dimensional boxes representing the Event Capsules at a particular ksana, and a  red light, symbolizing an ultimate event, which appears inside first one box and then another below it at the very next ksana.Relativity Rows of capsules

For a ‘rest’ event-chain which we are assuming, the event capsules have fixed ‘rest’ values for both spatial and temporal distances. If we neglect two of the three spatial dimensions we thus have a Space-Time Rectangle of extent s0  by t0.  

 

Minimum and Maximum Displacement Rates 

Imagine then an ultimate event occurring  at a certain spot on the Locality, or rather at the kernel (centre) of an empty grid-space. It remains there for the space of one ksana, disappears, and reappears (or not) at an equivalent spot at the next ksana. How far has the causal influence travelled? If the ultimate event is conceived as occurring at the very centre of a spatial cube of dimension s0

˜Relativity Single event capsule

So the causal impulse must cover very nearly ½ s0 relative to the first grid-space and another ½ s0 relative to the second ksana, in order to  be able to ‘recreate’ a clone of the original ultimate event. The total spatial distance covered is thus (very nearly) ½ s0  + ½ s0  =  1s0 and this distance has been covered  within the ‘space’ of a single ksana. The ultimate event’s ‘vertical displacement rate’ is thus 1s0 /t0 , one grid-space per ksana. And if it keeps re-appearing regularly in the same way, it will keep  the same ‘vertical’ displacement rate — ‘vertical’ because it is not displacing itself either to the left or the right at each ksana relative to where it was previously.
So what happens if the causal influence is not strong enough to traverse such a distance? In such a case, the ultimate event does not re-appear and that is the end of the matter. (I am assuming that the occurrence has taken place at a sparsely populated region of the Locality so that the ultimate event is effectively isolated and not subject to any influence from other event-chains.) Whether or not a causal influence that fails to ‘go the distance’ subsequently completes its work in subsequent ksanas need not concern us for the moment : the point is that during (or ‘at’) the following ksana the ultimate event either does or does not reappear, an open/shut case.
A displacement rate of 1s0 /t0 is thus the minimum (vertical) displacement rate possible. Moreover, the dimensions s0 and t0 are fixed and thus their product, the rectangular ‘area’  s0 × t0 also. It is a postulate of UET that this rectangular area (and equivalent 4-dimensional region) remains constant though the ‘length’ of the ‘sides’ can change, i.e.  for variable ‘sides’  sv and tv, sv tv = s0  t0  = Ω, a constant, and so tvtv /t0 = s0 /sv . It would seem that, in our universe at any rate, s0 is a maximum which makes t0 a minimum. So the vertical displacement rate is maximum spatial unit distance/ minimum temporal unit distance. Note that, since to is a minimum, there is no possible change that can occur anywhere within a smaller interval of time ─ ‘time’ is not infinitely divisible. Also, since there are limits to everything, the minimum spatial distance, which can be noted su (for s ultimate), will be paired off with the maximum ‘temporal length’ of a ksana, tmax and the other extreme ratio will be smin/tmax  = su/tmax where su  ×  tmax  = so × t0 since the area of the rectangle stays the same.  
        But we do not need to pay attention to this for the moment since the sides are not at present going to change. Given that the rate 1s0 /t0  is the least possible, what about the maximum possible rate? Rather surprisingly, this also turns out to be 1s0 /t0 ! For suppose a more powerful causal impulse is able to carry itself over two or more event capsules and recreate the selfsame ultimate event two, four, or a hundred ksanas later. Even if it could do this, the rate would still not exceed 1s0 /t0 since, if the ultimate event were re-created four ksanas later, the causal impulse would have traversed a spatial distance of 4 s0 ­and taken exactly four ksanas to do it.

Relation of vertical displacement rate to ‘speed’ or lateral displacement rate  

In ‘normal’ physics ─ and normal conversation ─ we completely neglect what I term ‘vertical displacement rate’ since we do not conceive of ‘bodies’ appearing and re-appearing. What we are passionately concerned about is what we refer to as ‘speed’, and this in  UET is what I call ‘relative lateral displacement rate’ ─ ‘lateral’ because the ‘time’ axis is usually imagined as being ‘vertical’. Now, it is today (almost) universally recognized that there is a maximum ‘speed’ for all bodies, namely c which is roughly 3 × 108 metres/sec in macroscopic unts. In UET, since everything has a limit, there is a maximum lateral displacement rate for the transmission of causality whether or not light and electro-magnetic radiation actually do travel at exactly this rate. This ‘relative lateral displacement rate’ covers not only cases of ‘cause and effect’ in the normal sense, but the special kind of causality involved when an ultimate event reinvents itself so many spaces to the right or left of its spatial position at the previous ksana. We can thus imagine an ultimate event being re-created (1) in the same position, i.e. zero spaces to the right or left;  (2) one space to the right (or left) of the original position, (3) two spaces to the right, and so on up to, but not exceeding, c* spaces to the right where c* is a positive integer.

……..⅐∎⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐………
……..⅐⅐⅐⅐⅐⅐⅐⅐∎⅐⅐⅐⅐⅐⅐⅐⅐⅐………

←  spaces   →

……..⅐∎⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐………
……..⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐⅐∎⅐⅐⅐⅐⅐………

←                     c* spaces           →

We have, in each case, a ‘Causal’ Space/Time Event Rectangle of dimensions  d spaces × 1 ksana  where d can attain but not exceed c*. Each of these positions could in principle receive an ultimate event and if all are filled (an unlikely occurrence) we will have at each ksana exactly d ultimate events not counting the original one (or d + 1 if we do count the first one). This number of possible ultimate events, brought about by a single ultimate event a ksana earlier, does not and cannot change but, in accordance with the principle of constant area, the distances between events (or rather their positions on the Locality) can and does change. We need not concern ourselves at the moment with the question of whether this change is ‘real’ or essentially subjective : the important  point is to get a clear visual image of the ‘sides’ of the Space/Time Event Rectangle contracting and expanding but nonetheless maintaining the same overall area. Some idea of this is given  by the following diagrams where the blobs represent ultimate events.

Limit of lengths of spatial and temporal ‘sides’ 

Can this process of contraction/expansion be continued indefinitely? In normal physics it can since, with some exceptions and occasional trepidation, contemporary physics still retains a key feature of Leibnitz’s and Newton’s Calculus, namely the usually unstated assumption that ‘space and time’ are ‘infinitely divisible’, incredible though this sounds (Note 2).  In UET on the other hand the spatial contraction has a clearcut limit which is the dimension of the ‘kernel’ of a Space/Time capsule. The precise region where an ultimate event can have occurrence, the equivalent of the nucleus of an atom, does not (by assumption) itself change in size and thus constitutes the ‘ultimate’ unit of distance in UET since everything that we see and hear or otherwise apprehend is made up of ultimate events and each of them (by hypothesis) occupies an equivalent 3-dimensional spot on the Locality whose ‘rest’ dimensions do not change.
Noting the ‘ultimate’ dimension as su, we deduce that there must be a numerical ratio between su and s0, the maximum dimension of a grid-space, which is also that of a ‘rest’ capsule, since everything in UET is basically related by whole number ratios to the complete exclusion of irrationals. So s0 = n su where n is a positive integer ─ i.e. one could in principle fit n ‘kernels’ lengthways and in the other two directions, if we assume a cubic shape, or, if the capsule is conceived as being spherical, we would have a diameter of n kernels.
Now, if the Event Rectangle keeps the same area, it must stay equal to its rest size of  1 s0 × 1 t0  and the spatial distances between ultimate events, or positions where ultimate events could occur, must contract while the temporal distances expand. At the limiting value of c* positions the spatial dimension has shrunk from being s0  to its minimum  size of su , i.e. each grid-position has shrunk to the size of the kernel and it cannot shrink any more since no smaller length exists or can exist. But there are precisely n multiples of su in s0  which can only mean that c* = n. And so the ratio of ‘kernel’, the smallest unit of length that can possibly exist, to the ‘rest’ size of the capsule is the same as the ratio of the ‘rest’ length of a grid-position to the maximum number of positions that can be displaced by a causal impulse within a single ksana. This unexpected result which flows from the basic assumptions of Ultimate Event Theory shows a pleasing symmetry since the constant c* , the limiting displacement rate (‘speed’), also shows up within the structure of the basic Event Capsule, the equivalent in UET of an ‘atom’.

Time Dilation 

When sv , the  variable length of the side of the Event Capsule, reaches its minimum value of su , tv is a maximum since, if  s0 ­is a maximum, t0  must be a minimum. Since  s0 × to  = sv  ×  tv , we have tmax /t0  = s0/su  = c*/1  so  tmax = c* × t0      As sv gets shorter, tv  increases  to keep the ‘occupied area’ constant.  When the spatial distances  d × s0  are large enough to be noticeable, (though the same thing applies if they are small) this gives rise the well-known phenomenon of ‘length contraction’ ─ well-known to students of physics, I mean. And this in turn means that the ‘time dimension’ gets extended to keep the overall area constant.

Relativity Expanding Contracting Rectangles

This is the same as the situation in Special Relativity. But, in UET, the Space/Time Rectangle does not end up with one side becoming ‘infinitely long’ and the other ‘infinitesimally short’ since v can essentially only take integral (or at most rational)  values and peaks at v = c* = (c – 1), i.e. one grid-space short of the ‘unattainable’ value c  ─ unattainable if we are considering a  Causal Space/Time Event Rectangle (Note 3).

Summary    The chief points arising from this discussion are :

(1) Every ultimate event has occurrence at the ‘kernel’ of a Space/Time Capsule of fixed ‘rest’ dimensions
s0 ×  s0 × s0 ×  s0 × t0  

(2) The ratio of the spatial dimension of the kernel su to the spatial dimension s0  is 1 : n ; 

(3) The least ‘re-appearance rate’ of an ultimate event is 1 s0 per ksana which also turns out to be the maximum rate;

(4) The limiting ‘lateral displacement rate’ of a causal impulse is set at c* s0 per ksana ;

(5) The volume of a causal ‘Space/Time Parallelipod’, reduced for simplicity to the area of a causal Space/Time Event Rectangle, is
constant and = s03 t0  or s0 t0  for a rectangle   ;

(6) The number of possible or actual ultimate events within a Casual Space/Time Parallelipod or Rectangle is constant and always a positive integer;

(7) The spatial and temporal distances between possible or actual ultimate events on or inside the Space/Time Parallelipod or Rectangle contract and expand in order to keep the overall volume/area constant;

(8) Spatial distances are submultiples (proper fractions)  of the basic ‘rest’ dimension s0  ;

(9) Temporal distances, i.e. the ‘duration’ of a ksana, the smallest interval of time, are multiples of the basic ‘rest’ temporal unit t0 ;

(10)  The maximum ‘lateral displacement rate’ is c* per ksana (c* a positive integer) where c* = n  

(11) There is a limiting value of the contracted spatial unit distance, namely su  which is the dimension of the kernel ; 

(12) There is a limiting value of the expanded unit temporal  distance, namely tmax =  c* t0   ;

All these features are derived from the basic postulates of Ultimate Event Theory. They differ from the usual features of Special Relativity in the following respects:

(1) Lengths cannot be indefinitely contracted, nor will they ever appear to be, and the same goes for time dilation. Popular books referring to someone falling into a Black Hole suggest that he or she will fall an ‘infinite distance’ in a single mini-second and his or her cry of despair will last for all eternity ─ this does not and cannot happen in UET. It should be possible one day soon to test these predictions (though not with respect to Black Holes): UET says that ‘space contraction’ and ‘time dilation’ will approach but never exceed limiting values, and indeed such observed limits would give us some idea of the dimensions of the Event Capsule.

(2) The actual speed (lateral displacement rate) of event-chains may attain, but not exceed, c* , which means they can be attributed a small but finite ‘mass’ ─ though ‘mass’ has not yet been properly defined in UET (see coming post). A rough definition would be something like the following.

mass :   capacity of an event-chain to resist any attempt to change its re-appearance rate, relative direction of ‘motion’, and a fortiori its very continuing re-appearance.”

(3)  It is in principle possible in UET for an event-chain to eventually exceed the maximum ‘causal displacement limit’ (roughly ‘speed’) but such an event-chain would immediately cease to repeat (having lost persistence or self-causation) and to all intents and purposes would ‘disappear into thin air’ leaving no trace. This would explain the sudden disappearances of ‘particles’ should this be observed. There would be no appreciable energy loss which conflicts with the doctrine of the Constancy of Mass/Energy (energy is as yet undefined in UET).

(To be continued in next Post)

NOTES

Note 1.  One should speak of ‘state of succession’ rather than ‘state of motion’ since continuous motion does not exist in UET (or in reality). But the phrase ‘state of succession’ seems strange even to me and ‘relative state of succession’ even stranger. All this goes to show how strongly we have been marked by the fallacious idea of continuous motion.

Note 2  Hume, the arch sceptic, memorably wrote “No priestly dogma invented on purpose to tame and subdue the rebellious reason of mankind ever shocked common sense more than the doctrine of  infinite divisibility with its consequences” (“Essay on Human Understanding”)

Note 3 We do not get the fantastic picture of someone falling into a Black Hole and being contracted down to nothing while his or her cry of despair lasts for all eternity. That there are definite limits to possible length contraction and time dilation is a proposition that is in principle verifiable — and I believe it will be verified during this century. And once we have approximate values for these limits, we may, by extrapolating backwards, obtain an idea of the dimensions of the basic Space/Time capsule, i.e.  s0 and  t0   .

Pagoda I want to start by expressing my gratitude to MeetUp in general and the London Futurists in particular for enabling this event to take place at all, the first time ever that my ideas have been aired in a public place. I intended to conclude the meeting with an expression of my debt to MeetUp,  the Futurists and founder/organiser David Wood, but unfortunately this slipped my mind as the meeting broke up fairly rapidly after a full hour in the cold. (A summary of my talk will be given in a subsequent post.)
The meeting at the Pagoda on Sunday was, as far as I am concerned, well attended — I did not expect or desire  crowds. All those present seem to have had serious intent and to judge by the thoughtful comments made in the discussion afterwards (drastically curtailed because of the cold) they grasped the main drift of my argument. Some missed the meeting because of the weather or did not find us because we were hidden behind a wall on the south side of the Pagoda.

Two persons have already said they would like to have heard the talk and wondered whether there could be a repeat. However, I feel that my ideas are rather far from the framework and general ethos of the London Futurists — though naturally if asked I would be glad to repeat the talk indoors somewhere at a later date. Instead, I plan to have a monthly series of talks/discussions on various issues arising from ‘Ultimate Event Theory’, the scientific and philosophical system I am currently developing. The place will remain the Peace Pagoda, Battersea Park, South facing wall, at 2 p.m. on a date to be announced, probably the last Sunday of each month — watch this site in January. If no one comes at all, the session won’t be wasted since I will be periodically renewing my contact with the ideas of the Buddha via the beautiful edifice in Battersea Park.

What follows is ‘matters arising’ from the talk:

Three stages

It is said that every new scientific idea goes through three stages : Firstly, they say it is not true, secondly, they say it is not important and, thirdly, they credit the wrong person.
Although I am to my knowledge the first person to have taken the world-view of Hinayana Buddhism seriously as a physical theory (as opposed to a religious or metaphysical doctrine), it is entirely appropriate that the first time Ultimate Event Theory was presented verbally to the public the venue was the Peace Pagoda (built by practising Buddhist craftsmen) since the theory I am developing, “Ultimate Event Theory”, can be traced back to the founder of one of the five great world religions, Buddhism.
Our science stems from the Greeks, in particular the atomist Democritus of Abdera  whose works have unfortunately been lost. He is credited with the amazing statement — reductionist if ever there was one —  “Nothing exists except atoms and void“. These atoms Democritus (and Newton) believed to be indestructile and eternal. Although we now know that some atoms decay, the statement is not so far out : around us are protons and neutrinos that have existed since the Big Bang nearly 15 billion years ago (or very soon afterwards). And as for the void, it is healthier and more vibrant than ever, since it is seething with quantum activity (Note 1).
Dharma    But around the same time when Democritus decided that the ultimate elements of existence were eternal atoms, Gautama Buddha in India reached exactly the opposite conclusion, namely that the dharma (‘elements’) were evanescent and that everything (except nirvana) ‘lasted for a moment only’.  A Buddhist credo summarised the teaching of the Buddha thus: “The Great Recluse identified the elements of existence (dharma), their causal interconnection (karma) and their ultimate extinction (nirvana)” (Stcherbatsky, The Central Conception of Buddhism).
I must emphasize that the theory I am developing, Ultimate Event Theory, is a physical theory (though it has ramifications far beyond physics) and does not presuppose any religious belief, still less is it an underhand way of ‘preaching Buddhism’ or any other form of religion. The Buddha himself founded no Church and spent the latter part of his long life wandering around India giving talks in the open air to anyone who cared to listen. My original interest in Buddhist theory was ‘scientific/philosophical’ rather than ‘spiritual’.  It seemed to me that Gautama Buddha had, through the practice of meditation, intuited certain basic features of physical and mental reality, and concluded correctly that matter, mind, soul, personality and so on are all ‘secondary’ not primary entities — in today’s parlance they are ’emergent’ entities. He also saw, or rather felt, that ‘existence’ was not continuous but that everything (incuding the physical universe) is, as it were, being destroyed and recreated at every instant (the Theory of Instantaneous Being). I do not personally, however, conclude that the personality, consciousness, free will and so on are ‘illusory’ as the Buddhist tradition seems to have inferred, merely not primary, not basic.  At bottom we are seemingly all made up of elementary particles and forces between these particles but at a deeper level still I believe that everything is composed of momentary ‘ultimate events’ flashing into existence and then disappearing for ever. As far as I am concerned the buck stops here : beyond the dharma lies only the Absolute, the ground of all being, and this, though it can perhaps be glimpsed by mystics, is wholly outside the domain of science, rational thought and mathematics. “The Tao that can be named (or measured)  is not the original Tao”.      SH  5 December 2012

Note 1  For the claim that Space/Time is “grainy” see Is Space Digital by Michael Moyer, Scientific American Feb. 2012, also  “How big is a grain of space-time?”  by Anil Ananthaswamy (New Scientist 9 July 2011)

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Genesis of Ultimate Event Theory :  My life could be divided into two periods, the first ending one morning in the late seventies when I came across a curious book with the bizarre title Buddhist Logic in Balham Public Library, Battersea, London.  In this book for the first time I came across the idea that had always seemed to me intuitively to be true, that reality and existence were not continuous but discontinuous and, moreover, punctured by gaps — as the German philosopher Heidegger put it  “Being is shot through with nothingness”. A whole school of thinkers, those of the latter Hinayana, took this statement as so obvious it was hardly worth arguing about (though they did produce arguments to persuade their opponents, hence the title of the book).
This well-written tome of Stcherbatsky, not himself a practising Buddhist, thus introduced me to the ideas of certain Hinayana thinkers during the first few centuries of the modern era (Dignaga, Vasubandhu et al.)  I saw at once how ‘modern’ their views were and how, with a certain ingenuity, one could perhaps transform their ‘metaphysics’ into a physical theory very diffferent from what is taught today in schools. These deep and subtle thinkers, in every way the equal of the Greeks, had no interest in developing a physical theory for its own sake since their concern was with personal ‘enlightenment’ rather than the elucidation of the physical world.  Had they and their followers wished it, quite conceivably the world-wide scientific revolution would have taken place, not in the then backward West, but in India. But maybe the time was has now come for the insights of these men to take root some 1,800 years later on the other side of the world and to eventually become the basis of a new science and a new technology. Matter is getting thinner and thinner in contemporary physics so why not drop it entirely and stop viewing the world as the interaction of atoms or elementary particles ? According to Buddhism the ‘natural’ tendency of everything is not to last for ever (like Newton’s atoms) but to disappear and the relative persistence of certain rare event-chains is to be ascribed to a causal binding force, sort of physical equivalent of karma. There is no Space/Time continuum, only a connected discontinuum which is full of gaps. The universe itself will come to an end and everything will return to the absolute quiescence3 of nirvana — though some later Buddhist thinkers, like some conteomporary cosmologists, envisage a never-ending cycle of emergence/extinction/emergence……

Recommended Reading  Those interested in Buddhism as a ‘way of life’ are recommended to start (and also perhaps finish) with Conze, A Short History of Buddhism. This book really is short (132 small size pages) and so good that I seriously doubt whether anyone really needs to read any other book on the subject (unless they want to follow up a particular aspect of the theory) : the writing is clear, concise, comprehensive, pungent. If I were allowed to take only twenty books on a desert island, this would be one of them.
The Russian scholar Stcherbatsky whose books had such a big effect on me has written three seminal works covering the three main aspects of (Hinayana) Buddhism. The Central Conception of Buddhism concerns what I call ‘ultimate events’ (dharma),  Buddhist Logic deals in the main with causality (karma) and The Buddhist Conception of Nirvana with nirvana as one might expect.  Although it is the second book, Buddhist Logic (Volume 1 only), that influenced me, most interested readers would probably find it forbidding in aspect and would be advised to read the Central Conception of Buddhism first (100 pages only) , and not to bother at all with The Buddhist Conception of Nirvana which I found quite poor.

Newton’s Third Law states rather cryptically that

“To every action there is an opposite and equal reaction.”

This law is the most misunderstood (though probably most employed) Law of the three since it suggests at first sight that everything is in a permanent deadlock !   Writers of Mechanics textbooks hasten to point out that the action and reaction apply to  two different bodies, call them body A and body B.  The Third Law claims that the force exerted by body A on body B is met by an equivalent force, equal in magnitude but opposite in direction, which body B exerts on body A.
Does this get round the problem? Not entirely. The schoolboy or schoolgirl who somehow feels uneasy with the Third Law is on to something. What is either completely left out of the description, or not sufficiently  emphasized by physics and mechanics textbooks, is the timing of the occurrences. It is my push against the wall that is the prior occurrence, and the push back from the wall is a re-action. Without my decision to strike the wall, this ‘reaction’ would never have come about. What in fact is happening at the molecular level is that the molecules of the wall have been squeezed together by my blow and it is their attempt to recover their original conformation that causes the compression in my hand, or in certain other circumstances, pushes me away from the wall altogether. (The ‘pain’ I feel is a warning message sent to the brain to warn it/me that something is amiss.) The reaction of the wall is a restoring force and its effectiveness depends on the elasticity or plasticity of the material substance from which the wall is made — if the ‘wall’ is made of putty I feel practically nothing at all but my hand remains embedded in the wall. As a reliable author puts it, “The force acting on a particle should always be thought of as the cause and the associated  change of momentum as the effect” (Heading, Mathematical methods in Science and Engineering).
In cases where the two bodies remain in contact, a lengthy toing and froing goes on until both sides subside into equilibrium (Note 1). For the reaction of the wall becomes the action in the subsequent cause/event pair, with the subsequent painful compression of the tissues in my hand being the result. It is essential to realize that we are in the presence not of ‘simultaneous’ events, but of a clearly differentiated event-chain involving two ‘objects’  namely the wall and my hand. It is this failure to distinguish between cause and effect, action and reaction, that gives rise to the conceptual muddle concerning  centrifugal ‘force’. It is a matter of common experience that if objects are whirled around but restrained from flying away altogether, they seem to keep to the circumference of an imaginary circle — in the case of s spin dryer, the clothes press themselves against the inside wall of the cylinder while a conker attached to my finger by a piece of string follows a roughly circular path with my finger as centre (only roughly because gravity and air pressure deform the trajectory from that of a perfect circle) . At first sight, it would seem, then, that there is a ‘force’ at work pushing the clothes or the conker outwards  since the position of the clothes on the inside surface of the dryer or of the conker some distance away from my finger is not their ‘normal’ position. However, the centrifugal ‘force’ (from Latin fugo ‘I flee’) is not something applied to the clothes or the conker but is entirely a response to the initiating centripetal force (from Latin peto ‘I seek’) without which it would never have come into existence. The centrifugal ‘force’ is thus entirely secondary in this action/reaction couple and, for this reason, is often referred to as a ‘fictitious’ force — though this is somewhat misleading since the effects are there for all to see, or rather to  feel.
Newton does in certain passages make it clear that there is a definite sequence of events but in other passages he is ambivalent because, as he fully realized, according to his assumptions, gravitational influences seemed to propagate themselves over immense distances instantaneously (and in both directions) — which seemed extremely far-fetched and was one reason why continental scientists rejected the theory of gravitational attraction. Leaving gravity aside since it is ‘action at a distance’, what we can say is that in cases of direct contact, there really is an explicit, and often visible, sequencing of events. In the well-known Ball with Two Strings experiment (Note 2) we have a heavy lead ball suspended from the ceiling by a cotton thread with a second thread hanging underneath the ball. Where will the thread break? According to Newton’s Laws it should break just underneath the ceiling since the upper thread has to support the weight of the ball as well as responding to my tug. However, if you pull smartly enough the lower thread will break first and the ball will stay suspended. Why is this? Simply because there is not ‘time enough’ for my pull to be transmitted right up through the ‘ball plus thread’ system to the ceiling and call forth a reaction there. And, if it is objected that this is a somewhat untypical case because there is a substantial speed of transmission involved, an even more dramatic demonstration is given by high speed photographs of a golf club striking a ball. We can actually see the ball still in contact with the club massively deformed in shape and it is the ball’s recovery of its original configuration (the reaction) that propels it into the air. As someone said, all (mechanical) propulsion is ‘reaction propulsion’, not just that of jet planes.
In Ultimate Event Theory the strict sequencing of events, which is only implicit in Newtonian mechanics, becomes explicit.  If we leave aside for the moment the question of ‘how far’ a ksana extends (Note 3), it  is possible to give a clearcut definition of simultaneous (ultimate) events : Any two events are simultaneous if they have occurrence within the same ksana. A ‘ksana’ (roughly ‘instant’) is a three-dimensional ‘slice’ of the Locality and, within this slice, everything is still because there is, if you like, noit enough ‘time’ for anything to change. Consequently, an ultimate event which has occurrence within or at a particular ksana cannot possibly influence another event having occurrence within this same ksana : any effect it may have on other event-chains will have to wait until at least the next ksana. The entire chain of cause and effect is thus strictly consecutive (cases of apparent ‘causal reversal’ will be considered later.) In effect when bodies are in contact there is a ceaseless toing and froing, sort of ‘passing the buck’ from one side to the other, until friction and other forces eventually dampen down the activity to almost nothing (while not entirely destroying it).
S.H. 21/08/12

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Note 1 Complete static equilibrium does not and cannot exist since what we call ‘matter’ is always in a state of vibration and bodies in contact affect each other even when apparently completely motionless. What can and does exist, however. is a ‘steady state’ when the variations in pressure of two bodies in contact more or less cancel each other out over time (over a number of ksanas). We are, in chemistry, familiar with the notion that two fluids in solution are never equally mixed and that, for example, oxidation and reduction reactions take place continually; when we say a fluid is ‘in equilibrium’ we do not mean that no chemical reactions are taking place but that the changes more or less equal out over a certain period of time. The same applies to solid bodies in contact though the departures from the mean are not so obvious. Although it is practical to divide mechanics into statics and dynamics, there is in reality no hard and fast division.

Note 2  I am indebted to Den Hartog for pointing this out in his excellent book Mechanics (Dover 1948).

Note 3  It is not yet the moment — or maybe I should say ksana — to see how Ultimate Event Theory squares with Relativity : it is hard enough seeing how it squares with Newtonian Mechanics. However, this issue will absolutely be tackled head on at a later date. Einstein, in his 1905 paper, threw a sapnner in the works by querying the then current understanding of ‘simultaneity’ and physics has hardly recovered since. In his latter days, Einstein adhered to the belief that everything takes place in an eternal present so that what is ‘going to’ happen has, in a sense, already been — in my terms already has occurrence on the Locality. I am extremely reluctant to accept such a theory which flies in the face of all our perceptions and would sap our will to live (mine at any rate). On the other hand, it would, I think, be fantastic to consider a single ksana (instant) stretching out across the known universe so that, in principle, all events are either ‘within’ this same ksana or within a previous one. At the moment I am inclined to think there is a sort of mosaic of ‘space/time’ regions and it is only within a particular circumscribed region that we can talk meaningfully of (ultimate) events having occurrence within or at the same ksana. Nonetheless, if you give up sequencing, you give up causality and this is to give up far too much. As Keith Devlin wrote, “It seems to me that there is nothing for it but to take as fundamental the relationh of one event causing another” (Devlin, Logic and Information p. 184)