Spencer Heath Archive

Item 60

Penciled by Heath on notepad paper.

January 26, 1952

 

 

Discussion:

 

     The fundamental dimensional units in physical science are those of Mass (inertial or gravitational), Motion and Time.

     These three kinds of units are employed for measuring and thus determining in terms of numbers the respective magnitudes of the three kinds of elements or aspects com­monly called dimensions that constitute an action or event. In scientific research the units most employed are the gram, the centimeter and the second; and the over-all magnitude or dimension of any action or event is the product of its three constituent magnitudes or dimensions. One unit of force (inertial mass of a gram), per one unit of motion (length), per one unit of time — a dyne times a centimeter times a second — is the unit of action or event called an erg-second. The three constituent units may be considered separately and separately measured only by disregarding the actual presence in every act or experience of the other two. They can be conceived and considered as being separate but they can be experienced only as united in actuality as happenings, actions or events.

Introduction:

     Physical science differs from metaphysics and psychology in that it assumes to examine only the objective side of experience, happenings or events. And it deals not only with objects as such but more especially with action or events in which objects, as structures, masses or particles play their component part. Moreover, its methods are objective and impersonal. It is wholly quantitative. It depends on measurement and deals with magnitudes as numerical dimensions in terms of the standardized units with which its measurements are made. Its rationality consists in the ratios between and among its measurements or dimensions as numerical magnitudes. Its relationships are quantitative and rational, therefore mathematical.

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Considered separately and alone, the dyne is the unit of force. The dyne and the centimeter — unit of force per unit of distance, dyne-centimeter — taken together without respect to time constitute the unit of energy or work, the erg.

 

     The erg is a most convenient unit of energy as force times distance (dyne-centimeter) because it admits the use of the simple formula E = MV²/2 for determining the energy of any known mass having any known velocity. This formula presupposes that the given velocity was acquired or accumu­lated by acceleration at the rate of one centimeter per second per each second of time. The number of velocity units and the number of time units under these conditions must have been always the same number. Hence V² is the same as velocity times time, which is distance — the distance the mass would have moved during the elapsed time (number of time units same as number of velocity units) if the given velocity had been constant and not acquired by acceleration from zero and therefore twice the mean velocity from zero. Hence the V² (units of final velocity times units of time) must be divided by two to give the true distance the mass must have been moved to accumulate its given velocity. V²/2 therefore represents distance only. Since a dyne is, by definition, the force required to increase the velocity of each gram mass by one velocity unit per each time unit, there must have been the same number of force units, dynes, as there were mass units, grams. Therefore M in the formula repre­sents in reality not the mass in grams but the number of dynes actuating and accelerating the mass, and the energy, E, in ergs (dyne-centimeters) is the force in dynes into the dis­tance moved in centimeters.

     The centimeter and the second — unit of distance per unit of time — taken without respect to mass or force consti­tute the unit of velocity, centimeter per second. Both of these, the dyne-centimeter and the centimeter-second, are abstractions — drawn away from actuality or action. But the dyne, centimeter and second, all taken together, constitute the erg-second, and this is no abstraction. For it is not abstracted out or away from the field of objective experience. It contains and unites all of the three elements necessary to constitute an objective actuality as action, event or concrete experience.

 

     The erg-second, as a unit of energy-in-action or action is constituted not necessarily of three single or whole units of force, motion and time; it may be constituted of these respectively in any measurable magnitudes or dimensions, so that their combined product be unchanged and remain as one. The respective magnitudes or dimensions and proportions of its several constituents of the erg-second may be varied almost indefinitely without any change in its over-all dimension or magnitude as a quantity, the unit-quantity, of action. Such internal changes of quantity and proportion affect and determine the quality but have no effect on the quantity of action. For example: The energy (dyne-centimeter, ergs) may be exceedingly large, if the time (seconds) be correspondingly small, and vice versa. Similarly the velocity (centimeters-second) may be exceedingly high, if the amount of force (dynes as force or grams as mass) be exceedingly small. Or the velocity low if the force be large. In all cases the quantity of energy-in-action, or action, remains unchanged.

     Now this versatile unit, the erg-second (dyne-centimeter second) is wholly conventional. Neither the erg-second itself nor the measurable quantities of which, in variable proportions, it is composed are discrete and indivisible and in that sense fundamental. The erg-second, in addition to being variably proportioned and composed, is almost indefinitely divisible. It may be divided into almost any number of parts, but there is an exceedingly large number by which being divided it is reduced to a definite magnitude, the least magnitude in which energy-in-action can be measured or otherwise experienced.

 

     The largest number that can be divided into an erg-second without transcending the limits of finite experience is (6.545¹⁰)^-27. This very small and indivisible fraction of an erg-second, called the quantum of action (h), is regarded in physical science as the ultimate unit in which action — as experience, if not in conception — can take place.

     The quantum of action (h) having a definite constant magnitude as a certain fractional part of an erg-second must have the same three kinds of magnitudes or dimensions and other similarities including variability in the proportions of its three constituent elements, force (or mass), distance and time, within the limits below which any one of these will not combine with the other two. That there are such minima is evidenced by the constant velocity of light and other electro-magnetic waves. The constant magnitudes of quanta of action necessitates that, within the quantum, any increase of velocity (centimeters per second times seconds) must occasion a decrease of the mass (or force) dimension. When velocity is less than maximum then mass is obvious and certain, but when velocity is maximum then that must be because mass is at its minimum, uncertain as to particle, at the border line of finite experience. Let the wave-length (distance) and the wave-period or time (inverse of frequency) change as they may, so the velocity is maximum, yet the mass or particle aspect remains equivocal and obscure. Likewise, a maximum of energy, force times distance, implies a minimum of time (highest frequency of a wave) and if there is an ultimate minimum of time this implies the ultimate maximum of explosive power, and a maximum of mass with minimum velocity implies a nearest possible approach to zero tempera­ture.

     These are all ultimate or limiting qualitative changes of proportion within the fixed and least over-all magnitude of the quantum, and since all large-scale phenomena are myriad multiple quanta these qualitative effects are possible to be experienced in magnitudes indefinitely great. The changes of constituent proportions are all qualitative transformations of energy-in-action or action without any necessary change in the quantity of the action. All technological instrumentalities are but devices for re-proportioning the elements of mass, motion and time into action and events that satisfy or contribute towards the satisfaction of desires.