Spencer Heath Archive

Item 406

Working draft for a letter from Heath to Alfred Landé, dictated to Spencer MacCallum. Some pencilings by Alvin Lowi. No date, but after Foundations of Quantum Theory which was published in 1955

 

 

Dear Professor Landé:

 

As a mere non-mathematical layman, I find a great deal of interest in your recent Foundations of Quantum Theory. For it prompts me to the expression of some points of view regarding the quantum itself which seem to be implicit in your technical presentation and in most of your predecessors, notably Professor Eddington’s chapter on Quantum Theory in his Nature of the Physical World.

 

The basic subject matter seems to be “observables.” This seems to mean some kinds of objective entities — subject matter of experience. Most frequently, these entities are referred to as particles, but in a broader and more general sense, as on your pages ______, they seem to be recognized as happenings, or events. Now the quantum of action, I take it, falls within this class — is an observable, not merely a particle but a happening or event having three characteristic dimensions of mass, velocity and time, precisely as Eddington describes it as a very definite and precise and very small fraction of an erg-second.

 

/Penciling by Alvin Lowi: “Heath’s charter of purpose.”/ It seems to me, as a layman, that it could be profitable to examine fully what this very specific definition necessarily implies.

 

First, we must recognize that the quantum under this definition can be in no wise different from an erg-second in any way but in respect to its magnitude. The difference must be quantitative alone. Whatever are the fundamental elements of the erg-second, must be the elements of the quantum of action as well. And whatever varieties of composition the erg-second may exhibit, must be reflected in the composition of the quanta of which it is composed.

The erg, of course, is an amount or quantity of work. It is that quantity of work which if performed at the energy rate of one dyne-centimeter per second, and continued through any number of seconds, then constitutes an objective event that is so many erg-seconds. Correspondingly, the energy rate in a quantum of energy multiplied by its frequency (as a wave) constitutes the quantum of action as a very specific objective event.

It seems significant to observe that the quantum of action, like its multiple, the erg-second, is composed of three distinct, measurable elements, which are called (1) force or inertia, (2) motion as velocity and (3) frequency as periods of time. Its force or mass (inertial) is stated in terms of dynes — so many dynes per each unit of motion, stated in centimeters. The total force units, therefore, is the given force times the number of centimeters through which it acts. The velocity is, of course, the number of motion units per single unit of time; and the energy rate is the number of force units multiplied by this velocity. However, it seems necessary to note that this energy rate is not any specific quantity of energy or work, but only the rate of work per unit of time — an abstract ratio between work and time. In order to measure any specific event, quantum or other, we must multiply this abstract ratio by a specific period of time. When, in any objective event, this ratio of work to time has been by measurement ascertained, and the time through which it acts likewise observed, the product of these three measurements (which are abstractions from, distinguishable aspects of an actual concrete event) is the over-all magnitude of the given measured and experienced event. This last is not merely an abstract ratio or rate but a concrete actuality — the objective side of experience. That seems to be why we call it energy (at a rate) in action, or, simply, action — that to which we react subjectively as experience.

If the above be accepted, the quantum of action, h, is to be seen as a specific objective event. But specific and precise as to its over-all magnitude, it still remains variable as to the energy rate and the frequency or period through which its energy acts at the particular rate. And the rate itself also is variable according to how the energy itself is proportioned as between its force, inertia or particle aspect and the velocity at which it moves. The quantum of action is thus an event having a specific over-all magnitude, yet susceptible of extreme variations in the ratios or proportions of the three elements of which it is composed.

Let us now try to answer the question, “Why is the action constant h so very small?” or “Why are we ourselves and other living beings so very large?” (page 84).

Let us examine ourselves. Clearly we, as biological units, are not infinite or absolute in any of our properties and powers. Our frequency range of sight and sound is narrowly limited, and we must at least infer similar limitations as affecting all our capacities including our capacity to react in any manner to the events which constitute the “otherness” of our objective world. It is equally obvious that there is an objective world. Everything that we experience in it appears to be absolute and infinite. We are always finding more and more, and there is nothing in all our experience that speaks of or even intimates limitations in any of its characteristics, save only those appertaining to the many kinds of units or individuals of which it is composed. It were arrogant indeed to suppose that we in our finite constitution could have experience co-extensive with the absolute whole. It is only reasonable to suppose, therefore, that in our reaction to events which we call experience, that there should be some necessary minimum event below which our experience cannot extend, however far our abstract and mathematical reasoning may range. The quantum event, therefore, need not necessarily be the least unitary event of which the universal phenomena is composed. It may be that this almost infinitesimal fraction of an erg-second is only the least dimension of all the events that come within the range of human experience. It may thus be said to occupy the border land of experience for the human individual as he has, so far, at least, physically conditioned and evolved — at the boundary between the physical and the meta-physical world.

/Aside during dictation:/ I’m getting into mighty deep water here — but it’s the water; I didn’t make it, I’m only exploring it.

 

It is to be noted that force, velocity and time are the physical characteristics of the universe to which we react and with which we interact. ..

 

/Aside:/ We’re actors ourselves, not just recipients, you see. That’s where we differ as living things from the inorganic, which have no purpose. That’s what is highlighted so nicely by Sinnott.

 

.. Doubtless that is why the gram, centimeter and second are called the “fundamental units of physical science.” They are not the fundamental units of biological science. This gives us the cell as our living unit in place of the inorganic atom, and this cell exhibits properties and powers, by reason of its organization, not possessed by any or all of the atoms or molecules of which it is otherwise composed.

 

The cell has a potentiality of purpose towards specific design. And, in its higher integrations, of imagination and achievement both within itself and outwardly upon its objective world — the capacity to dream and design and to create what it has dreamed.

 

This imagination, characteristic of none but living things, ranges far beyond the limitations of the physical structure through which it acts, and of the physical world which it inhabits. We need not be surprised, therefore, that the mathematical and imaginative is not confined within the limits of experience to which the physical body is limited in its objective world. The experiences of the mind are free-ranging, not only within the field of objective physical experience, which it can so wonderfully rationalize, but also in realms of magnitude both minimal and maximal far beyond the physical within which physical and objective experience is bound. It conceives in terms of zeroes and infinities as well as quantities between those two unattainable extremes. It has words and symbols such as its quantum terminology, its differential quantities, and geometrical “points,” in its quantitative understandings of the fundamental aspects of its physical world.

 

Limiting ourselves to the physical world, it appears that every event is a unitary complex of lesser and lesser events at descending levels of magnitude, until experience is abruptly stopped at those events which, however variably composed, exhibit no less over-all magnitude than the minute portion of an erg-second that is called the quantum of action. These minimal events, however, are not simple but complex — a complex of force, velocity and time. In quality and character, they are highly variable, according to the proportions in which their three elements are combined. This is discoverable by the analysis of any event. Such analysis reveals to the human mind the ratios in which its constituent units are composed. It is discovered to be rational, and the mind thereby takes on a rational understanding of what is physically experienced. Such understanding is quantitative and thereby strictly scientific and pre-determined. But the mind of man is not objectively determined. ..

 

/Aside:/ The event forces itself on the mind, but the mind can put these events together in different proportions according to its own inner urge.

 

.. It can conceive of events proportioned and composed in ways it has never experienced — hypothetical events determined by its own inner nature and processes. And further, it can imagine ways and means of bringing its hypothetical events to pass. This is the whole function of science, to analyze events in their fundamentals and re-organize them into new events determined by the imagination and realized in experience. Such is the entire field of fundamental analysis on the one side and creative synthesis on the other — the whole field of scientific technology as we know it today, which consists in the re-proportioning of mass, motion and time in the events (and thereby the structures) which constitute the thereby increasingly habitable environing world.

 

This process of re-proportioning the fundamental constituents of events seems to explain the most beneficent results that have been achieved by men in cooperation rebuilding and thereby better and longer living in their world; and it also seems to explain the extreme limits in the proportioning of events that come within his experiential realm. Accepting that all greater events are integrations of lesser, and that the quantum of action is the final atom of physical experience, human events must be seen to range between all the extremes of proportion in which its constituent elements can be composed.

 

Just as chemical elements do not react or combine except in multiples of their least unit, the atom, so it may well be supposed that there is a minimum unit for each of the three constituent elements of which the quantum of action is composed, and below which units in magnitude the respective elements of force, velocity and time do not unite or integrate themselves into the quantum unit.

There must always be some proportion of the three constituents — some rational proportion. These proportions can only be true proportions through being numerical. And they cannot be numerical unless each of them in turn is composed of least units of its own.

Assuming necessity for such units, /Penciling by Alvin Lowi: Why is this not just a property of – numbers – mind and not the concept itself?/ we can see that when the force or particle element is at its minimum, then velocity must be maximum — as in the velocity of light. When velocity is at its minimum, inertness must be at its extreme, as in absolute temperature. When time, or duration, is at its minimum, then each quantum of action must possess the highest possible rate of energy, as (apparently) in nuclear or atomic explosions.

It is surprising to find such wide variety and extremes of physical events all seemingly accounted for upon the simple basis of the character and composition of the quantum of action of which all the events of the physical world are more and more thought to be composed. It is suggested by a non-mathematical layman, who views things and events in their most profoundly fundamental aspect, and who with all his lack of other qualifications has succeeded in looking beyond the complicated mathematical constructions which, though of vast value in the interpretation of less generalized phenomena, is sometimes in danger of being fundamentally mis-applied.

It is coming to be recognized by many physical scientists, slowly and almost unawares, that the real subject matter of their investigations can best be thought of as events rather than as physical things. The materialistic approach is more definite as we go back in time to the more primitive conceptions. Recent advances have carried us far beyond the old, purely materialistic conceptions. Perhaps we are now on the horizon where physical science, with its predominately materialistic conceptions, may, by aid of the quantum generalization, lay the foundation in which to discover mass with its attributes of force and inertia as only one of the three measurable aspects of nature and of events of which the whole phenomenon of the physical world is comprised. Quite possibly, the three kinds of dimensions, such as gram, centimeter and second, may be found sufficient to take the dimensions of all the events which constitute the phenomena of the physical world.

___________