Spencer Heath Archive

Item 81

Original includes 2 pages of pencilings to be photocopied.

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     A quantum of Action is a very small fraction of an erg-second. An erg-second is the integration into Action of a unit of force (one dyne), a unit of velocity (one centimeter per psecond), and a unit of time or duration (one second) or any other integration of these units of mass, motion and time whose product is unity or one. The product of the first two — force times distance — whenever this product is one, is called an erg — the unit-quantity of energy in Action. The force times distance per unit of time or velocity is the energy rate, and this rate times the number of time units that it endures or con­tinues is the quantity of Action or event in erg-seconds during that time.

     Now, under the quantum principle as now generally accepted, a quantity of Action is not indefinitely divisible. It manifests itself objectively never in any less quantity than an erg-second divided by the enormous number 6.55 x 10^-27 which we will symbolize as H. This exceedingly small quantity of energy in Action is called the quantum or absolute unit of Action — absolute because it is the least magnitude in which force or mass, velocity and time unite as an objective action or actual event.

     Now the quantum theory was founded on the assumption, subsequently proved, that whatever be the composition of an erg-second, whatever the proportions of mass, motion and time that it contains, H is the very largest number of parts into which it can divide. From this it follows that while each least quantity or quantum of action must be uniform with every other as to its gross or over-all magni­tude it still remains possible for them to be as unlike in composition and different from one another as there are ways and proportions in which the three constituents forming any erg-second may be arranged and combined. The question naturally arises whether there is any limit to this possible compositional or qualitative variety within the constant single magnitude of an erg-second. Or, what amounts to the same question, is there any limit to the divisibility of the three constituents of an erg-second just as there is a limit to the divisibility of any erg-second itself. If H is the largest number of parts into which an erg-second can divide, is it also the largest number into which a gram mass and therefore a dyne force can divide? And is H also the highest possible division of the centimeter or of the second?

     The mathematical answer to these questions is no, for, mathematically, if the product of any three factors be divided by any finite number, however large, then any one of its three factors, however small, must be equally divisible by that number. In this view, if any erg-second, as the product of any three factors (mass, motion and time) whose combined product is 1, is divisible by H then any one of these factors, however small, must be equally divisible by that number. H cannot be the highest divisor while there can be still smaller numbers also divisible by H.

     All of this suggests that while the respective factors constituting an erg-second are mathematically and concep­tually divisible to an indefinite extent, there is never­theless a limit or minimum for each of the respective con­stituents of an erg-second below which minimum it cannot be present as an element of objective human experience. (This is due perhaps as much or more to limitations of the concrete human organization than to any limitations affect­ing nature or the cosmos as a whole.) Just as under the quantum theory h is the minimum concrete manifestation of the compound unit of experience that we know as an erg-second, so it seems there must be some corresponding minimum magni­tudes in which the several constituents of a single objective quantum (h) can exist. There must be some minimum magnitudes for the mass, motion and time constituents respectively of h. If there be such indivisible units then one of these units is the least of that kind that can combine in a quantum. And there must also be a maximum number in which any one of them can enter a quantum, for if the number of least mass or force units in any quantum is one then the product of the number of least motion units and the number of least time units in that quantum must be maximum, for the total product cannot exceed h. If, as in this instance, the mass or force constituent of the quantum is single and least, and the time or duration also is but a single least unit, then the motion or velocity units must be of maximum number for each of the other two factors is unity and the total product cannot exceed the value of h. This reasoning seems to establish on rational grounds alone the necessarily uniform velocity of light as it has been inductively observed. The assumption of individual least units for each of the three constituent elements of a quantum necessarily implies a maximum number of units in any one of these constituents when there is only a single unit in each of the other two.

     If the above assumptions are correct then it only remains for physical science to ascertain what are these three least magnitudes in terms of grams, centimeters respectively just as h is the known least magnitude in terms of erg-seconds in which these three combine.