Spencer Heath Archive

Item 316

Pencil notes by Heath on lined notepad paper, Elkridge MD. See also Item 318.

December 9, 1957

/e = mc²/

Given:  A number of force units p sufficient to impart a uniform acceleration to a constant number of mass or inertia units m. Then, at any point in time during that acceleration:

 

1. The number of force units f (called dynes) will be the same as the number of mass or inertia units m (called grams)

 

2. The number of velocity units acquired v, motion units per unit of time, will be the same as the number of time units elapsed.

 

3. The mean number of velocity units acquired during the elapsed time will be v/2, one half the number of velocity units acquired during that time.

 

4. The number of motion units l through which the constant force f has acted will be vt. For, 1 = v/2  x  t,  the mean velocity v/2 times t, the number of time units elapsed.

 

5. The total number of work units e (called ergs) — the

energy or action imparted to the mass during the acceleration — will be the number of force or mass units f (in dynes) times the number of motion units l (in centimeters).

 

     This fl is the same as f x v/2 x t or, since the number of force units is the same as the number of mass units, m x v/2 x t.

 

     Since v and t and also f and m are numerically the same, the total action or energy acquired during the acceleration is indicated by the customary formula: e = ½ mv²

 

     This formula, therefore, indicates the total energy of motion (or action) — the kinetic energy — that has been acquired by the acceleration or that can be put out by a corresponding deceleration of any known or given mass having any known or given velocity.

     All of the units referred to above are those of the dyne-centimeter-seconds system, commonly called the CGS system (in which the first two are set in the reverse order from that in which they are most naturally conceived and usually employed).

 

     The three aspects or elements which compose objective energy, action or events, namely, mass, motion and time, are each of them­selves beyond analysis, have no known composition. Subjectively, any one of them or any two together may be separately conceived by simply dis­regarding the presence of the other one or two. It is only in imagination that they can be separately experienced. It is only in their three-fold composite unity as events that they can be objec­tively experienced. However, the first always involves the second in the compounded dyne-centimeter unit of energy or work called the erg. In like manner, the second always involves the third, as in the centimeter-second (or centimeter per second) unit which has not been given any special designation apart from its compound. And the three are always involved together simultaneously in the constitution of any objective action or event, however simple or complex, or a series of them having similar type or form — in the entire subject-matter of objective experience.

 

     Mass is primordial; it has no verb (action) form. Motion, however has a verb form, to move, and mass is always the subject of that verb in its intransitive form. Motion thus is a property of mass. In like manner, motion involves time. It is the subject of the verb to continue or to endure; and being discontinuous it is rhythmic, thus marking time.

     Action is the objective actuality — mass motion and time integrated into concrete events. In all else they are mere abstractions.

     When any quantity of force comes into work or action, it is taken as that number of force units, such as dynes, involved in each single unit of motion. This is the energy or work rate.

     Hence the quantity of work involved in any action, happening or event is found by multiplying the number of force units by the num­ber of motion units. Work thus is composed only of force units and motion units combined, as pounds-feet or dyne-centimeters, which latter are called ergs. Thus its number of ergs is the measure of any quantity of work, energy or action (or of a series of similar events in temporal succession) without any regard to the time that may be required or involved.

 

     Force and motion, and also their compound, work or action, are abstractions from objective experience. They come into action ob­jectively only as they, compounded as work, are further compounded with the third abstraction called time, in precisely the same manner as force is compounded with motion to constitute work.

 

     When any quantity of work comes into action it is taken as that number of work units, such as ergs, that act through or per each unit of time during the time involved.

 

     (Note: The conceptions of force and motion are derived from sensory impressions or experiences, ponderable or inertial, which are called dynamic and compressive or expansive which are spatial and are called kinetic.)

 

     Hence the quantity of action constituting any happening or event (or in any succession of them having the same type, quality or kind — the same internal proportions) is found by multiplying the number of work units by the number of time units involved in the actual and objective event.

 

     If e is taken to represent energy in action as a rate or quantity of work per unit of time, then e = mc² presupposes some previous uniform acceleration of the mass m up to a mean velocity of c, each unit increase of velocity carrying with it an equal unit increase of time. Hence c², c-squared, represents velocity multiplied by time, which is simply distance or length; and if m represents the least possible unit of force that can be objective in a quantum of action (assum­ing mass and force also to be discontinuous) then c must necessarily be the highest velocity that is possible to be objectively exper­ienced. And it must represent also the greatest number of time units through which it is possible for the acceleration to continue or extend.

 

     Thus during the acceleration there is continuous and equal increase of both velocity and time. But the amount of motion, length or distance involved, being the product of velocity and time, in­creases at a much greater rate than they. While velocity increases equally with time, the distance or length increases as the product of velocity and time which is the same as velocity squared, with corresponding attenuation of the quantum force or mass. And since the work or energy in ergs (dyne-centimeters) involved in the actual event is the force in dynes (corresponding to mass in grams) times the whole length in centimeters, therefore c is the velocity at which there is the greatest possible attenuation of the quantum force or mass. When this velocity is attained the energy has the form of the least possible force acting through the greatest possible length.

 

     Since during uniform acceleration velocity and time go hand in hand, the time required for a single quantum unit of mass in grams (having a single unit of inertia in dynes) to be accelerated to the velocity of light is the same number of time units as the number of units of velocity attained, and the length traversed as motion will be the square of that number.

 

     This increase in velocity and length will be discontinuous. It will have a periodicity governed by the magnitude or least change in magnitude of the force or mass (accompanied by inverse change in motion or time or both). So there will be as many periods each second as there are fundamental mass units in the gram which, being widely different for different kinds of atoms will determine the frequency periods of their several rays. Correspondingly, the recip­rocals of these known frequencies will be the magnitudes (in grams or dynes) of their least and indivisible dynamic units. Hence the frequency will be the number of waves (package or train) necessary to constitute a single quantum of action — and the smaller the number of waves the greater their length and the fewer per packet.

     In radio-activity there are two kinds of motion, longitudinal or rectilinear and transverse, and thus two kinds of velocities and two kinds of energy or action. And these are inter-convertible, much as a fish’s tail converts transverse into rectilinear motion or as, conversely, a flag flutters in a breeze.

 

     Rectilinear velocities are well known, but transverse velocities have not been examined or ascertained. The transverse velocity of a wave, therefore, may be taken, provisionally at least, as being the same as the rectilinear.

 

     Applying this hypothesis to a quantum particle at its highest velocity, it may be said that its mass has been converted into the frequency of reversal of its transverse motion to and fro with re­spect to its axis of rectilinear propagation. Thus, for any ampli­tude the length of the transverse motion in any group or packet of waves will be directly proportional to their frequency. A quantum group consisting of many waves having the same amplitude and energy-in-action as another group comprising fewer waves would have a longer path of transverse motion and thus a higher transverse velocity and from this a higher transverse energy than the otherwise corre­sponding group composed of fewer waves. This transverse energy therefore must be a function of the frequency of the waves, as is experimentally well known.

 

     Thus it appears that the difference in actinic and other chemical effects between high and low frequency quanta of waves is due to the unlikeness in their transverse energies, which is due to their differing frequencies, arising from the unlike dynamic compo­sition of the atoms from which the waves proceed. Atomic decompo­sition thus through radiation may be in part balanced by atomic recomposition, the “negative entropy” so called, which includes the positive phenomenon of evolving life.

     In its employment of the formula, e = ½ mv², physical science accepts the fundamentally metaphysical nature of physical phenomena or events — of the subject matter of objective and sensory experience, as distinguished from purely subjective and metaphys­ical experience.

 

     The formula refers only to energy-in-action; not to potential energy nor to kinetic energy, in neither of which is there occur­rence of any action or event. It deals with the three elementary abstractions, mass, motion and time, as such. It shows in what relation these three abstract elements invariably combine to constitute any concrete action or event — how these three elements, each in itself abstract and metaphysical, are related in a concrete physical event.

 

     This relationship is one of proportion. It is expressed therefore in numbers. And these numbers, whole or fractional, are based on units such as gram, centimeter and second. These units are treated as fundamental in that in purely physical phenomena there are none other than these, including such as are derived from and are di­rectly proportional to them.

 

     The formula sets up a constant relationship e = mc²