Spencer Heath Archive

Item 321.

Nine typed pages by Heath on three-ring binder paper. At the end is appended a   page of penciled equations that opened this piece but is appended separately       because of difficulty of transcription.

Winter 1957-1958

 

 

/THIS OBJECTIVE WORLD/

 

In scientific and in all technical procedures it is the common practice to use established formulas without any necessary understanding of them. Endless instances might be brought to mind. All the processes of mathematics — the simple rules for multiplying and dividing by fractions, the extraction of roots, the manipulation of equations, the use of trigonometric functions, employment of logarithms etc. etc. And, likewise, in the whole realm of practical engineering, the formulas followed need never be understood, nor even capable of being understood, by those who practice them. The whence and whether, the derivations and implications, the origins, whether in pure thought or based on empirical data, and the further rational implications (if any) inherent in the formulae — none of these in current practice need in the least to be understood.

The ego — the self — is experienced only in the consciousness of self, which is subjective, abstract and conceptual. All that is not the self is experienced and enters into con­sciousness only through sensory experiences, the messages of the senses reporting their reactions to impact from and upon the outer world of the not–self. This not–self is the sole and only subject-matter of experience. It is concrete and not abstract, objective and not subjective, experiential and not merely conceptual. And all that can be experienced has three and only three to us sensibly measurable and thereby rational elements, aspects or qualities. These aspects or qualities, being measurable are necessarily in ratios among themselves or one to another. That is how they are related or relative — the fundamental relativity.

     The threefold content of this objective world — this world of mass inversely related to motion (force), motion inversely related to time (velocity) and time inversely relative to frequency (discontinuity) — constitutes what are called, when taken singly (because of their discontinuity), the events, the phenomena, of the objective world (universe). These phenomena, when taken collectively, are called work or action; and the quantity of work or action that is related to and involves a single unit of time is called energy. The rate of work or action, therefore, multiplied by the number of units of time involved is the quantity (quantum_, how much) of work or action involved in any single or uniform series of events. Time is what actualizes mere abstract proportion into concrete objective quantity, capable not only of being symbol­ized and subjectively conceived but also capable of being through the senses objectively experienced.

     Action is dynamic and also discontinuous, that is, repetitional, rhythmic, cyclic, made up of separately distinguish­able events. Events cannot be infinitely distinguishable unless that which distinguishes also has unlimited power to distinguish. But the human capacity for objective experience is always finite. It is confined within an ever-increasing octave, as it were, between zero and Infinity, two impossible or at least unattainable extremes. From this it of necessity follows that any events below or above some certain finite magnitudes, while they may be imagined, symbolized and con­ceived, cannot be within the range of sensory and thereby ob­jective experience. So far as the senses are concerned, they are not indefinitely divisible nor are they indefinitely ag­gregative. The objective human life itself taken objectively is an event of finite dimensions in which it has a rate of action limited and fixed in its over-all quantity, by its dimension of time — the rhythm of its successive generations. Subjectively, in its ego-consciousness (of which all are aware — often called being) it can indefinitely extend, but the individualized objective life of sensory experience is

less than infinite in its quantity or range. In like manner, there is a minimum magnitude in which or in whole-number multiples of which, and not otherwise, any event can be objectively experienced. This unitary event, this almost infinitesimal fraction of an erg-second, (in its physical aspect) is called the quantum of action. Its three elements or aspects — mass, motion and time — can be separately considered, but can be experienced only in their full three-fold unity as an action or event.

The quantity of work or action that is performed or takes place in any event is indicated by the expression ½ mv². This represents a change of relationship, a displace­ment, in terms of motion and time (velocity) between a parti­cular particle or mass and its general environment taken as being unchanged. The physical units involved are the gram for mass, the centimeter for motion and the second for frequency or time. (Time may be taken either as a period — a duration — or     as a frequency, according as it refers to a single event or to a succession of similar events.) Where the event involves but a single unit respectively of mass, motion and time, the product of the first two is called an erg and of the three an erg-second. The erg is the unit of work as though happening without any time being involved, and the erg-second is the unit of work per unit of time it involves.

The erg is the unit of mass (gram) times the unit of motion (centimeter).

The abstract unit of mass (gram) times the abstract unit
of motion (centimeter), taking no account of time, is an
abstract unit of work — a gram-centimeter, called the erg.

The abstract unit of motion (centimeter) times the abstract
unit of time (second), taking no account of mass, is an abstract unit of velocity — a centimeter-second, or centimeter per second.

The abstract unit of work (erg) times the abstract unit of velocity, taking into account the entire three aspects or elements in the composition of an event (mass, motion and time), is a concrete unit of work or action, an erg-second or erg per second.

En-ergy is ergs coming into action.

The term energy signifies either or both a ratio and a quantity:  It is employed to designate the numbers of ergs associated with a single unit of time — the rate of work or action, the ergs per second in an indefinitely extended event. It is used also to designate the product of energy as a rate multiplied by its period or time — the quantity of work or action involved, the over-all dimension, of a definite and particular action or event.

A quantity of energy in contemplation only, and not in action as a continuing or a particular event, is called poten­tial energy.

In radiant energy the mass or particle aspect is in least

possible proportion to the velocity aspect — in most respects

objectively imperceptible.

The energy rate of a particular wave is constant.

     All energy or action is organized in discontinuous events or series of events as cycles or waves. When the mass aspect of a specific quantity of action as an event is at its indi­visible least, the event forms an energy or action wave. The velocity aspect must then be at its highest. Thus there being no velocity higher than that of light is a concomitant of the mass element in a quantum of radiant energy being at its lowest and single unit.

 

Just as, under the quantum principle, there are indivisible units of action compounded of mass, motion and time, so there must be indivisible least units in each of these several com­ponents.

 

In any certain quantity of action as an event, when the mass or particle aspect is at its ultimate least unit, the event takes the form of a wave whose energy rate — mass times velocity — times its period suffices for a whole quantum of action; or the event takes the form of a “train” or packet of waves whose combined energy rate times their period is sufficient to constitute a least unit or quantum of action. In any case, the whole mass element or aspect, being of a single ultimate unit, the motion rate or velocity is identical with the energy rate, and this rate times the period of the wave constitutes in all cases — (waves of all frequencies but of the same velo­city) —  the single least energy unit, the quantum of action. Thus the highest-frequency wave or train of waves, having the shortest durational period, must necessarily have the highest energy rate.

All energy, when in action, actual as objective and not merely potential as subjective, is both dynamic and kinetic, an integration of both force and motion, of dynes and centimeters as ergs; and the element of time as duration, period or frequency is always involved, whether taken account of or not.

When any perceptible mass is moving with respect to its

general environment it is said to possess energy — kinetic

energy — because of its motion. This means that in any change

in its velocity of motion it will impart energy to or accept energy from its environment in proportion to the square of its velocity change. It is customary to take the kinetic energy of a body moving at any given velocity as that quantity of energy which could have given it that velocity or which, con­versely, could diminish it to zero with respect to environment.

The energy (kinetic) of a moving body or particle is taken as that quantity of force and motion . . . 

The force required to accelerate or decelerate a gram mass
at the rate of one centimeter per second is the force of its inertia, called a dyne. And the work (energy-in-action) of a force of one dyne acting through a motion of ½ centimeter is called an erg. An erg (dyne-centimeter/2) of work performed during a period of one second (dyne-centimeter-second/2) is called an erg-second; and any number of ergs of work performed in a period of one second (dyne-centimeters-seconds/2) is called that number of erg-seconds per second. This is the rate at which a body in motion can yield up its energy — commonly called the energy of a body in motion. If the duration or period of the energy in action is more or less than one second, then the quantity of work performed is its rate per second times the number of seconds through which it continues or extends.

Since force does not come into action otherwise than through motion and time

The energy of a particle or moving body is the number of ergs (dyne-centimeters/2) that would be required to accelerate it from a state of rest to its given velocity or to decelerate it to zero velocity, within the duration of one second — the work requisite to be performed in accelerating it to the given velocity or to bring it again to rest.

The number of dynes will be the same as the number of grams, hence M, representing the mass in grams can also repre­sent the force in dynes.

The velocity during acceleration will be only one half the given velocity

And the period of time

The energy of a moving body at a given velocity is the rate in ergs per second at which work must be applied to bring it to rest.

During each second of deceleration each gram of mass will exert a dyne of force. The deceleration will be at the rate of one centimeter per second. And the time required will be the same as the maximum velocity. But the amount of motion required will be only half

Take a single gram. Then each gram must encounter a single dyne of force during each second, to reduce its velocity by one centimeter per second. This will require the same number of seconds as the Initial velocity per second. And the length of motion or distance in centimeters will be one-half the number of seconds because the mean velocity in coming from the initial velocity to zero velocity will be only one half the initial.

The work or energy of one gram, therefore will be one dyne of force acting through a distance that is only one-half as great as if the dyne were acting at a constant velocity.

Take the case of only one gram of the moving mass. It will exert or resist the change of velocity with a force or resistance to force, of one dyne.

This dyne during each second of deceleration

The total time required will be the same as the amount of motion per second at the initial velocity. So, each dyne times the initial amount of motion per second will be the rate of energy, and the time involved will be the same as the amount of motion per second (velocity). But, by reason of the diminishing velocity during this time, the mean velocity will be only one half the initial, and the amount in grams of motion only one half of the amount of time in seconds. Therefore, the whole motion or distance for each dyne will be only one half the ini­tial velocity times a number of seconds that is the same as the initial velocity.

This whole distance can be represented by ½ vt when v is the initial velocity, or vt/2 when v is the mean velocity. And since v and t are always numerically the same, v²/2 repre­sents the amount of motion during the deceleration. Then, since grams and dynes are numerically the same, then for each gram there is a force of one dyne acting through a distance of v²/2 centimeters, which is v²/2 ergs. And, since there are as many dynes of force or inertia acting as there are units of mass, then M (v²/2) represents the total amount of work or energy-in-­action involved in the deceleration.

Hence the customary equation for the amount of energy-in-­action potential in the amount of work capable of being done by a moving body whose velocity is constantly and uniformly diminished is E = M (v²/2) ergs per second? And this is good for any number of grams or any fraction of a gram as a particle.

Now, let us suppose that E is the ergs per second (work rate) in a given quantum of action. Then this quantity of work per second multiplied by the frequency of its wave or packet of waves (which is fractional if more than once per second) will be the quantity of energy-in-action per wave or packet of waves.

Elkridge

Winter 1957-8

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