QUANTUM CALCULUS MAINSTREAM FALLACY

THE MAINSTREAM FALLACY

AND

THE NEED FOR A REAL QUANTUM CALCULUS

©Edward R. Close, December 22, 2016

A very important fundament fact of nature was uncovered in the year 1900 when German physicist Max Planck discovered that nature metes out energy only in whole numbers of an extremely small amount called a quantum of energy. Within a few years, scientists realized that as a rule, all aspects of physical reality are quantized, and quantum physics was born.

Albert Einstein noted that mass is converted to energy by certain physical processes and energy is converted to mass by other processes. In 1905, Einstein showed that the exact mathematical equivalence of mass and energy is expressed by the equation E = mc². In other words, he discovered that mass and energy are two different forms of the same thing.

In a paper entitled “Does the inertia of a body depend on its energy content?” Einstein concluded:

“It follows directly that: If a body gives off the energy L in the form of radiation, its mass diminishes by L/c². The fact that the energy withdrawn from the body becomes energy of radiation evidently makes no difference, so that we are led to the more general conclusion that the mass of a body is a measure of its energy-content.”

In addition, based on the discoveries of general relativity, Einstein declared that there is no such thing as empty space or eventless time. The space-time continuum has meaning only in relation to mass and energy, which are quantized. In Appendix V of the 15^th Edition of his popular book on Relativity, Einstein says:

“It is characteristic of Newtonian physics that it has to ascribe independent and real existence to space and time as well as to matter, for in Newton’s law of motion the idea of acceleration appears. But in this theory, acceleration can only denote ‘acceleration with respect to space’. Newton’s space must thus be thought of as “at rest’, or at least as “unaccelerated”, in order that one can consider the acceleration, which appears in the law of motion, as being a magnitude with any meaning. Much the same holds with time, which of course likewise enters into the concept of acceleration. Newton himself and his most critical contemporaries felt it to be disturbing that one had to ascribe physical reality to space itself as well as to its state of motion; but there was at that time no other alternative, if one wished to ascribe to mechanics a clear meaning.

Further on in Appendix V, after discussing several historical theoretical concepts of space, Einstein makes the following startling statement concerning “… how far the transition to the general theory of relativity modifies the concept of space”:

There is no such thing as an empty space, i.e. a space without field. Space-time does not claim existence on its own, but only as a structural quality of the field.

The idea that space and time do not exist without the presence of the mass and energy of physical objects is counter-intuitive for us because the everyday picture provided by the neurological processing of pulses of energy entering our consciousness through the functioning of our physical senses seduces us into thinking of space and time, or space-time, as a changeless background within which matter and energy interact to form objects and events. But we now know that this is not true. The illusion of space-time is created by the extension of the substance of physical objects in the form of gravitational and magnetic fields. There is no space-time to be distorted, it is the instruments of measurement (Einstein’s clocks and rods of his thought experiment) that are distorted by motion, not space-time as often depicted by popular presentations by leading mainstream physicists. A simple example will help clarify this point:

A steel ball, rolling across a table in a magnetic field created by the presence of a strong magnet placed under the table, will follow the curvature of the lines of force of the magnetic field. A non-metallic ball, however, unaffected by the magnetic field, will roll straight across the table. With this simple experiment we can see that the idea that the space above the table is warped by the magnet’s field is false. This, of course, is what you would expect if there is no such thing as empty space. In Einstein’s reasoning quoted above, this understanding is extended to space-time.

This shift in our understanding of space and time, made necessary by general relativity, (which, by the way, has been proved correct and accurate by very many, extremely detailed experiments and tests) tells us that there is no space-time independent of mass-and-energy objects and events, which are quantized. This means that the division of space and time, or space-time, into smaller increments than those occupied by a quantum of mass or energy, while theoretically conceivable, has no basis in reality. Thus for any valid mathematical analysis, space-time must be considered as quantized as is mass and energy, and it should not come as a  surprise that ignoring this requirement has resulted in erroneous conclusions about quantum reality and contributed to the perceived “weirdness” of quantum physics.

Newtonian Calculus and Quantum Mathematics

The calculus of Newton and Leibniz, known simply as “the calculus” for more than 300 years, is based on the assumption that the variables measuring objects and events may be divided indefinitely into smaller and smaller “infinitesimal” increments, approaching zero as closely as we please. However, in the real, quantized world of the physical universe, this cannot be done. As pointed out above, Planck’s discovery that energy is quantized, Einstein’s demonstration of the equivalence of mass and energy, and the conclusion that space-time has no independent existence, tells us, in no uncertain terms, that the division of the variables of space-time and mass-energy in the real world cannot approach zero infinitely closely. Therefore, the calculus of Newton and Leibniz, based on the assumption that this can be done, is inappropriate for application to quantum phenomena.

A new calculus, appropriate for application to quantum phenomena, is needed, and the Calculus of Distinctions is that calculus. I am currently working on two rigorously mathematical technical papers for submittal to mathematical physics journals proving this.

REFERENCES:

1. Planck, Max (1899) “Über irreversible Strahlungsvorgänge. Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin. 5: 440–480. pp. 478–80

2. Einstein, Albert (1905) “Does the inertia of a body depend on its energy content?”  Annalen der Physik, 17, 1905. Reprinted in The Principle of Relativity, Dover Pub.

3. Einstein, Albert (1962) “Relativity, the special and general theory, a clear explanation that anyone can understand”, Appendix V, pp. 135, 154 and 155, Crown Publishers, New York