Spencer Heath Archive

Item 47

Penciled by Heath on a “FLYAWAY Bond Tablet.”

May 7, 1952

 

 

 

On the surface of a sphere —

There are just 8 points corresponding to the 8 apices of the enclosed cube.

Each point is the center of one of 8 equal and similar areas.

 

In an atom —

 

If its nucleus is a sphere, then,

 

Its surface can give equal (and geometrically identical — same size and shape) accommodation to just 8, no more, electrons.

The same is true of any concentric spherical          shell.

 

     If all electrons are so alike that they must occupy equal and similar areas, on a sphere, — most nearly circular

 

     Just for the purpose of illustration let 8 erg-seconds be taken to be the least quantity of kinetic energy, in action, that can be measured or otherwise experienced. And let the dyne, the centimeter and the second be the small­est units that will combine to constitute an erg-second. Then when gram (dyne) and second are at their minimum — unity — then velocity must be maximum at 8, and 1 x 8 x 1 under these suppositions will correspond with the well-known quantum of action, the constant quantity, h. (Period is 1 and Frequency is 1/1.)

 

     Now if velocity is maximum and the frequency of a wave is more than 1, then its period is less than 1, so more than 1 wave will be required to make up the quantum of 8. So, 1 x 8 x i  is the energy of a wave whose fre­quency is 2. Its energy is 4. Energy times frequency equals 4 x 2 = 8 corresponding to h.

          This means that when the energy per wave is less than the quantum it takes a “train” of waves to make up the quantum and the number required will be as many as the period of the wave is contained in the least period that will enter into a non-wave quantum. So, in 1x8x1, 1 stands for the least time period that can come into the quantum 8, and 8 stands for utmost velocity. Any shorter period must be fractional and the frequency larger than l. For example: Suppose frequency is 2, then period is ¹/₂,  then the energy of the wave is 1 x 8 x ¹/₂ = 4 — only a half-quantum. Hence a “train” of two waves is necessary to make the quantum. And frequency 2 x energy 4 = 8, the quantum. Note: While mass (dynes) remains 1, velocity can be 8, period less than 1, frequency more than 1. So the higher the frequency — shorter the wave — the less energy per wave, provided the mass (dynes) is unchanged. But if the mass (dynes) be increased by the same amount, as 2 x 8 x ¹/₂ = 8, then the higher frequency brings no loss of energy. On the contrary, the period being only half as great, the rate of energy per wave is twice as great. In this case, although the frequency is 2 (period ¹/₂), with the mass raised to 2 only one wave is required to make up the quantum of 8.

 

          With velocity constant and maximum at 8, and mass constant and minimum the energy rate per wave is constant, 1 x 8, for any given frequency. But as the frequency increases above one then the shorter period increases the energy rate per wave and at the same time and in the same proportion increases the number of waves requisite to make up the quantum (in this case 8).

     If, however, the mass be increased at the expense of velocity, as 2 x 4 x ¹/₂, then the mass is manifested as particle and shall /still?/ have the properties of a wave — so long as its period is less than one or frequency more than one. — Such as streams of electrons and X-ray particles. And here too there must be enough waves, _________ or particles to make up a full quantum (8) before any effect, as an event, can be objectively experienced or observed. Since the amount of energy of a single wave may be only a fraction of a quantum and radiation can be experienced only as its waves are integrated in quanta it may well be that “action at a distance,” such as the magnetic effect of a stream of electrons, or vice versa, or other action at a distance, such as gravitation and electro-stases are the quantified effects of wave action or similar action taking place in discontinuous units of kinetic energy at magnitudes below the quantum level and thus beyond the realm of our perception or experience. It may be that kinetic energy or energy as “action” operates throughout nature in units of magnitude that are accessible to objective physical experience only as they integrate in sufficient quantum magnitudes and proportions after the manner of the waves that we experience physically only as organized in “packets” or “trains.”

          Once we pursue the hypothesis that just as there is a minimum fraction of an erg-second less than which does not come into objective experience, so also there are minimal units each of the mass, velocity and time that constitute the event, we find a consistent set of proportions and combina­tions among the three that seems to account for at least three otherwise seemingly unrelated physical phenomena. These are: (1) The maximum velocity of electromagnetic waves. (2) The minimum of molecular or atomic activity. (3) The maxi­mum rate of molecular or atomic disintegration (atomic explo­sion).

          For the first, it is only necessary to look where in the organization of the quantum of action the mass, force or inertial element and the period or durational element (increase of frequency) are at their irreducible minimum. Here we find the motion or velocity element necessarily at its maximum; otherwise the over-all magnitude of the quantum as a constant would not be maintained. Such a quantum is well represented in terms of its least compositional units by the constant number 8 (instead of the customary h). The mass, particle, inertia or force element and the time element or period being taken each at its least, then, Mass 1 x Velocity 8 x Time 1 shows the necessarily utmost velocity of least mass or force for the shortest time within the constant quantum.

 

     For the second, if we look where the time period of action is at the maximum, here we must find velocity and mass both at the irreducible minimum — thus: Mass 1, Velocity 1, Time 8 — least energy rate, longest period of time — the best approximation to the conception of absolute zero,

     For the third, we will consider the case of both velocity and time being at the irreducible minimum. This makes mass or force or inertia necessarily at the utmost maximum and since, as in the first instance, only the irreducible minimum of time is involved, velocity would seem converted into mass or equivalent inertia or force.

    It must be kept in mind that in all these cases it is not the rate of kinetic energy nor its period or duration that is constant. It is the constant quantity (or quantum) of action that results from the rate of energy continuing through the period of time. It is not the rate nor the period but their product in action.

     In Case 1 and Case 3 the energy rate and the period are the same; but in Case 1 the energy is stretched out, so to speak, over its utmost length, whereas in Case 3 it is condensed, as it were, into the greatest possible force in the least possible space.

     In Case 2, however, there is the lowest possible rate of energy extended through the greatest possible length of time, the nearest approximation to no energy at all.

 

     The three cases illustrate the extreme qualitative differences between any same quantities of action as energy rate times period or time. In all other and ordinary mani­festations, whether of single quanta (h) or in any multiple of them, the magnitudes of the three elements, mass or force per unit of motion, motion per unit of time and time as the period or duration, must each be greater than its least possible and less than its possible maximum, as for example, Mass or force 2 times Motion or velocity 2 times Period or duration 2. Each of these being above its minimum keeps the other two below their maximum.

     In each of the extreme cases given the two minimums necessitate the third being maximum. Where only one is minimum neither of the other two but only their product can be maximum. When mass (as particle) is minimum, then velocity and period can be of any two whole numbers whose product is 8. When period is minimum, then force and velocity (energy rate) can be any two whole numbers — in this case 4 and 2 — whose product is 8.

          It is worthy of thoughtful consideration that the first two numbers, in the order given, are relative. They are not strictly quantities but, rather, ratios. Mass or force always implies motion and when stated as a quantity always means that number of mass or force units to be taken with each unit of motion. Likewise, any statement of so many motion units must be taken always or reduced to the number of motion units per unit of time. And these two ratios of force to motion and motion to time, when taken together, constitute an energy ratio per unit of time. Time, however, is different. Its quantities are not ratios, not in related [sic] to a unit of anything else. It proceeds in the succession, not in combination or aggregation of its units. Time is what lifts energy from mere conception as the composite of two dimensions, mass or force and length, into the objective actuality of action — from ratio into reality. The ratios of force per unit of motion and of motion per unit of time determine the kind or quality of any event (subjective); only through integration with time does it come into the three-fold dimensionality of objective experience.