Alfred North Whitehead, the eminent English philosopher, physicist and mathematician collaborated with Bertrand Russell in writing “Principia Mathematica” and made a theory of relativity alternative to that of Einstein before devoting himself completely to the development of his own “organic philosophy.” His major metaphysical work, “Process and Reality” presents a dynamic picture of the universe in which immediate personal experience is conceived in the same terms as the inorganic world, that is as events of experience “actual occasions”. He describes the form of the development of these actual occasions, their growth or “concrescence” at length in “Process and Reality.” Thus the life history of an object is made up of a series of intimately connected events and the traditional logic of substances acting is turned inside out. From this imaginative reconstruction or revision of the world he could and did reconstitute the physics of his day. But what is far more interesting from the point of view of the power of the imagination to grasp the world is that from his metaphysical system the fundamental ideas of quantum physics, which only appeared several years after the book, can be elicited. This paper shows how from his philosophic picture of the world flow naturally the ideas of the physics of his time and also the ideas of quantum mechanics which had not yet been formulated when he wrote “Process and Reality”.
Although the synthesis of the wave and corpuscular theories of light, by which Whitehead illustrates the application of his metaphysical concepts, deals with the corpuscular theory of Newton, it is translatable to more recent science. The corpuscular aspects have, in a sense, been reestablished in optics. It is not observed to be the case, as one might expect on the basis of the wave theory, that just any amount of energy can be emitted by a radiating body or absorbed by another. Only a definite minimal energy or integral multiplies of it can enter into this process. This suggests the integral characteristics of a particle. If Whitehead’s conciliation can be applied to this analogous case, the process would be interpreted as follows: Both the wave and the particle are permanent forms transferred from one actual occasion to another. The particle has personal order, the wave less rigid social order. When a definite quantum of energy – suggesting the particle aspect – is emitted, the dominant order is personal and there are loosely related strands of personal order making up the wave train. After some time the dominant features of the personal order fade because the strands of personal order, which have been prehending each other, have acquired the same features, lost their individuality and become social order. This is an excellent description in more generalized terms of the two physical facts – that only definite quanta of energy are emitted and that light displays wave -like properties such as interference. However, it omits the other fact that only definite quanta of energy are absorbed. The change from personal to social order or from particle to wave is a loss of the stricted kind of order. It suggests, in this respect, an irreversible process. Thus it does not seem possible to stretch the description of Newtonian particle-wave theory of light to the quantum-particle-wave theory.
But a closer analysis of waves will show Whitehead’s principles capable of dealing with wave-and-particle characteristics in matter as well as in light. (I shall talk about transverse waves because they can be diagrammed, but the general characteristics hold (for all waves). A wave is a certain pattern that is repeated over definite intervals of time. It is
governed by the relation: Velocity equals wave length times frequency. A wave of a given velocity in a box of a given length cannot have just any frequency and wave length one might choose. Its possible wave lengths are determined by the condition that the wave length must fit into the box an integral number of times. If this is not the case, different phases of the wave will coincide and interfere with each other, and eventually the wave will die out. So there is a resonance condition belonging to a wave. Also there is the condition that to characterize a wave one must wait for its complete period. Now the Hamiltonian statement for the laws of mechanics – hence of the way matter moves – says that the integral of the difference between the kinetic and the potential energies should be a minimum. The fundamental law of optics is that the time taken to traverse a given path should be a minimum. It was De Broglie who first noticed the similarities in these and derived the equation showing the wave-like properties of matter. Lambda equals h over (m times nu).
Here lambda is the wave length, m is the mass and v is the velocity, h is Planck’s constant given by the equation E = hj;, where v is the frequency of the wave. There are quantization conditions in mechanics corresponding to resonance conditions in optics. The discreteness of the possible energy orbits in the Bohr atom is a consequence of this. Because an electron can only “fall” from one energy level to another and cannot stop anywhere between, energy is emitted in quantities of some integer times the difference in energy levels. Similarly a photon in colliding with an atom can increase its energy only by definite amounts because it can “push” an electron only into the fixed energy levels.
When these physical concepts are translated into metaphysical terms, it is possible to see that they are related as are the generic notions in Whitehead’s system. The resonance conditions in waves which lead to distinct energy levels in the atom have their analogue in the actual occasions. The subjective aim giving unity to the prehensions is represented in the wave by the requirement of a whole period of vibration in order to determine the wave’s shape and by the boundary conditions imposed by the walls of the box. The continuity of e and f, two prehensions, and also their obvious incompleteness, arises from their reference to the subjective aim. Why they take the direction they do take is only apparent upon consideration of the whole pattern. The occasion that is one complete period is divisible into infinitely many prehensions of the original datum and of each other. Hence it is internally continuous.
However the passage from one occasion to another a-g is marked by the change of the second derivative (the rate of change of the curve) from positive to negative. Although there can be no sharp discontinuity, the function has changed directions. Hence “function” might be used as a pun for the mathematical function and also the function of integration and prehension. That g is not a sharp break but a continuous curve represents the conformal inheritance of subjective form. In general the same pattern continues because the low grade mental pole is not active in origination. The physical pole is dominant-hence there is conformation. When there are changes in wave amplitude or pattern they are usually caused by the prehension of some new datum. For instance changes in the velocity of an electron are caused by the creation of a new electromagnetic field near it. Two occasions of the electron are realized at A and B. There is no motion between them. Time consists in the succession of A and B. (This difficult notion has a vague analogy in the gross phenomenon that the particles in the medium of a water wave do not themselves travel with the wave; they only vibrate and transmit the pattern). Thus it appears that the relations between Whitehead’s generic notions correspond to those between the physical concepts in Bohr’s quantum theory. This, however, is hardly surprising since he has obviously spent much thought on this branch of science.
The latter developments of quantum physics, which are not, explicitly mentioned in Whitehead’s writing, provide a better opportunity to test the adequacy of his thought to concepts not involved in its formations.
The fundamental concept that was introduced into quantum mechanics in 1924 in somewhat different terms by both Schrodinger and Heisenberg was that of the theoretical impossibility of determining simultaneously two physical characteristics. In Schrodinger’s treatment the accuracy of the determination of Pi (and indirectly of the determinacy of the position because Pi is a measure of the probability of finding the electron in a given position) is roughly speaking inversely proportional to the accuracy with which the kinetic energy can be determined. When an experiment Jocalizing the electron in one definite point position is performed, the energy becomes infinite, and when the energy is determined with infinite accuracy, the probability of finding the electron anywhere in space is equal. Usually the experiment is not so radical. The electron is localized within a given region, and the energy is determined within a given range. There is a continuous but limited range of possibilities.
This can be translated to the language of metaphysics. The electron is a society of actual occasions. Its position in space is the determinant of the perspective with which these occasions prehend the actual world. The position is closely connected with the physical pole, the passive reception of data and conformance to it. The metaphysical equivalent of energy is emotional intensity which arises from the mental pole. The question is whether the determinateness of these is inversely related metaphysically. The first phase of an actual occasion is completely determined by the physical pole, it is conforming to the data that it prehends from its perspective of the actual world. This perspective on the actual world is taken from a perfectly definite focal position. There is no emotional energy contributed by the mental pole of that occasion. Now during the development of the occasion the perfect certainty about the actual prehended world that accompanied the reality of the first phase is modified. But the mental pole has already begun to operate in the selection for emphasis and suppression of the data in the transmutation. The definite mode in which the mental pole will integrate the prehensions is not yet determined, but it can be partially predicted. As
the occasion concresces propositions and contrasts are introduced. The mental pole overlays the physical prehension of the actual world with consideration of alternatives not actually the case. Valuations and emotions are introduced. By the time all of these feelings have been integrated and the form of emotion made perfectly definite in the final satisfaction what was the original datum is quite obscured.
The terminology of actual occasions can be equally well applied to the alternative formulation of the quantum theory. The uncertainty principle was formulated by Heisenberg. When two mathematical operators are not commutative i.e. the order in which operations are performed on a constant changes the result, determining the value of one completely makes the value of the other completely indeterminate, and in between the extremes the uncertainty about their values is inversely proportional. Delta p delta q~ h and delta E delta T ~ h are the expressions for the uncertainty in Heisenberg’s system. The first says that the uncertainty in the position of the electron times the uncertainty in the momentum is of the order of Planck’s constant, h. The second says that the uncertainty in the energy times the uncertainty in the time interval during which the observation is made is of the order of h. They have the same content as Schrodinger’s equation and are transformable into its terms.
The first uncertainty relation can be interpreted in terms of the prehension of one actual occasion by another. The prehending actual occasion can know its predecessor as a vector with a sense of derivation from the past. This is the analogue of velocity. Or it can prehend the other occasion, not as having emotional intensity and the activity of transference, but as an inactive characteristic of a region of the contemporary world. This is the knowledge of position and geometrical perspectives which arises from sense perception. It is a product of transmutation. That is: The sense of derivation from the past accompanying the prehension of the actual entities in the first phase is ignored and the eternal objects prehended as determinate of the definiteness of the occasion in the datum, are transmuted into the characteristic of some nexus. This nexus is in the world contemporary with the prehending occasion. It has geometrical or spatial relations among its parts. The prehending occasion attributes spatial position to a group of actual entities in its datum as a region of this apparent world. If the analogy with quantum mechanics is to hold, the determinateness of these modes of prehension of previous actualities should be inversely related. In fact, they are so related. The datum is received in the first phase accompanied by a feeling of derivation from the past. Because geometrical relations (hence, position) are a product of the mental pole organizing the data in transmutation and because in the first phase the mental pole is inoperative, the geometrical relations among the prehended entities must be completely indeterminate. During the concrescence the spatial relations of the data develop in the process of transmutation as the mental pole operates. But the sense of derivation from the past fades. By the time the data is transmuted to the characteristics of regions, the active vector quality of it has completely disappeared, and the regions are perceived as inactive. Thus, the inverse relation between knowledge of position and of velocity or feeling of vector derivation holds even in the extreme cases when one is accurately known and the other unknown.
Thus it can be seen that the new concepts of physics introduced by quantum mechanics flow naturally from and into Whitehead’s organic description of the world in experience and as experience.