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Discreteness


Planck - Einstein - Whitehead
At the beginning of the twentieth century, experiments on heat and light led Max Planck to the conclusion that electromagnetic radiation occurred as discrete bundles. Formerly, light of the different frequencies was considered to be waves of continuous energy. Einstein arrived at a similar conclusion which was expressed in his explanation of the photoelectric effect. Light emission occurs as individual bursts. To that extent light is discrete, at least as far as its emission is concerned. This conclusion meant that Nature, at the microscopic level, behaved discontinuously. However, once the discrete bundle of light (photon) was emitted its journey was held to be continuous. Few doubted that in effect Nature's operations, as far as light was concerned, were a mixture of discreteness and continuity.

According to the principle of the inheritance of order and A. N. Whitehead's doctrine of organic realism Nature does everything discretely at the microscopic level of the physical world. Not only is light emitted discretely but its journey is equally discrete and the same lack of continuity is the norm for every process involving all subatomic objects. Just like the movies, where nothing moves, the particles of the microscopic world are all composed of motionless events. The thorough application of discreteness abolishes all continuity and with it all classical motion. Events do not change their geometrical relations.

Over the last seventy odd years, development of Whitehead's process metaphysical scheme, published in 1929 [1], has unsurprisingly shifted some of the original emphasis. His process description of reality placed major stress upon the concept of atomism or discreteness. In that scheme events underlie all nature and they are to be understood as fully atomic. Which is to say, they are separate from each other and cannot be divided into parts ,yet out of that separation grows a subordinate continuity. One gives way to the other. In the continuous space and time framework in which we all find ourselves, that fundamental discontinuity is difficult to both understand and appreciate. It all seems continuous from our standpoint -- but then, so do the movies.

In order to properly understand Whitehead's metaphysics the growth of continuity out of discreteness is absolutely essential. The foundation for continuity is discreteness in both Whitehead's doctrine of organic realism and the present theory of the inheritance of order. In microphysics, which is simply the physics of things too small or too quick to see with the unaided eye, numerous phenomena cannot be satisfactorily explained by continuous theories. Continuous theories are simply those which hold that nature is either mostly or completely continuous and therefore, to that extent, not discrete. The value and hoped-for relevance of Whitehead's scheme is that it will provide some of the explanations which are beyond the scope of continuity theories.

As mentioned above, it was Whitehead who realised that continuity grows out of discreteness. This complicates the issue to the extent that the one theory, his doctrine of organic realism, is therefore both continuous and discrete. Also essential to understanding the doctrine of organic realism is the realisation that discreteness and continuity do not coexist. At first sight this claim seems puzzling, if not downright contradictory. Modern physics has been plagued by attempts to embed discrete entities in continuous background space and time, or spacetime. This problem has, all along, been accentuated by the retention of the block universe concept. However, it may yet be the case that special relativity can retain the block universe in a manner consistent with spacetime not always being everywhere. The claim that the block universe embraces all the time and space that exists as spacetime is fully consistent with the hypothesis that spacetime is not always everywhere.

One of the major problems for discrete theories is causality. If microscopic reality is to be understood as composed of discrete, and therefore separate events in space and time, how is a causal chain to be affected? How can one event contain and transmit causal influence for other events? In continuous theories, by contrast, the question: how is it that this electron was also an electron five seconds ago? is almost meaningless. The answer is that electrons simply keep on being electrons unless they are annihilated or consumed by a destructive process of some kind. In the absence of such intervention things like electrons just keep on keeping on; bringing their own causality with them. It is all tied up with the idea of conservation laws.

No physical process or effect is needed to explain the continuity of the electron's existence, in, for example, quantum field theory where spatially discrete fields move in continuous curved spacetime. In a scheme in which electrons, and everything else, are composed of discrete and motionless events an explanation is needed to convince us that each event in the life of an electron is somehow caused to be like its predecessor(s). The continuous electron is explained by the absence of something going on. By contrast, the discrete electron can only be explained by the presence of something going on.

Whitehead, of course, realised this and supplied the theory of prehensions to explain event-to-event causality. His whole scheme is metaphysical as opposed to physical and so is his theory of prehensions. Modern physical theory, by contrast, is somewhat more particular than metaphysical theory and accordingly its explanations need to be particularly physical rather than generally metaphysical. Whitehead confined himself to the generality of the theory of prehensions whereas the present scheme focuses on the particular, in the form of the theory of the inheritance of order.

In the present scheme, what one event inherits from an antecedent event is not separate from the event itself, and yet the two events are separated in space and time. This is a rather process way of analysing events, which is very important. The event does not reach out and grasp something separate from itself, which is the causal influence to which it is subject. The event is the reception of the causal influence; once received, the event terminates. It does not lie in wait, and it cannot hang about waiting for more.

This contrasts with classical theories in which objects are continuous in time. Events are remarkable occurrances among the accidental adventures to which continuous objects are subject. A major problem with such a scheme arises when trying to equate the temporal separation between objects comparable with their space separations. If space and time are to be treated the same how can a time separation be made formally equivalent to a space separation? How can meaning be given to the statement that two isolated, non-interacting electrons are separated by a definite duration as well as a definite distance?

Hermann Minkowski insisted that the new spacetime concept required that space and time be treated the same. This was achieved by Einstein's Special Relativity in terms of the four dimensional framework used to express the external geometric relations among objects. But what of internal geometric relations? We are told that the distance from one side of a proton to the other is 0.13 fm (its diameter), but what is its duration? In classical physics protons do not have meaningful durations. Is this equal treatment of time and space for a proton? The answer must be no! How is the proton to be described so that its duration did not begin at the big bang and is not continually getting larger? Like its diameter, its duration should be as brief as is consistent with the properties it exhibits. Only then will time and space be treated the same for the proton, at the level of its internal spacetime relations.

How this is to be explained, in terms of the events into which the present theory reduces elementary particles, is a central part of special relativity and quantum physics.

1. A. N. Whitehead. Process and Reality. 1929. Corrected Edition. Ed. David Ray Griffin and Donald W. Sherburne. (New York: Free Press, 1978)

Comments and questions are welcome to pjf@it.net.au

Peter Fimmel 2002-2007

Last page update 14/05/07 

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