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The Heisenberg Principle
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The Heisenberg Uncertainty Principle Versus "Characterization"

The Heisenberg Uncertainty Principle asserts that the position of fast moving particles cannot be measured accurately (there are various interpretations of this principle that can be found at this Plato link). The uncertainty of the position of a moving particle in space is h-bar divided by the momentum error of measurement of the particle, where h is Planck's constant. Therefore, it was concluded that in order to measure the exact position, the exact momentum or velocity must be known or vice-versa.

As a result, the quantum mechanics model of the hydrogen atom offers only an approximation of the position of the electron. But Heisenberg's Principle was derived mathematically, using matrix theory, and it has been shown that it has no relationship to the real world. Heisenberg's infinite matrices for the position and momentum do not commute. His central result was the canonical commutation relation, and this result does not have a clear physical interpretation ( see Uncertainty Principle Ref.). One must ask: "If a theory has no physical interpretation, what good is it?" Apparently, this theory simply results in a probability function that must be interpreted.

The electromagnetic waves radiating from matter that is traveling at high velocity appear distorted due to the Doppler effect, and the Einstein/Lorentz mass varies with velocity. But just because the velocity and position of a moving object cannot be measured accurately does not mean that the actions of the system (position and momentum) cannot be accurately determined. In electronics, all measurement processes affect both the force and the velocity of electrons, but these errors are nulled out by a process known as "characterization". Electromagnetic waves that move across an antenna wire have been measured very accurately, and they move at the speed of light. In fact, the shape and velocity of these waves have been characterized throughout all space, and no contradictions have yet been discovered.

The process of characterization uses a set of measurements to make a determination. For instance, any instrument used to measure a function produces an error. Through the process of characterization of both the elements of the system and those of the instrument, the errors of measurement are reduced by compensation to the point of insignificance. If the Heisenberg Principle had been adopted for electromagnetic analysis, the assumed inaccuracies would throw the results of all analyses into doubt.

It is also possible to resolve this measurement problem by utilizing two or more measurements to characterize the errors, which is the standard method of the real world.

The delta-function, otherwise known as the "Heaviside impulse function", is a mathematical concept that can only be approximated in the real world. Nevertheless, it is used to easily characterize a system and therefore has tremendous value in producing exact results as confirmed by measurement. This function was conceived by Oliver Heaviside but was not well thought of by mathematicians of the time. The delta function, in the limit, is a pulse that has infinite amplitude and zero width. No such function has ever been measured, and yet it is used profusely in electronics for predicting the responses of electrical circuits and mechanical systems. Some still struggle over this concept, and one approach is to utilize the concept of a "distribution function", which is based on non-ordinary functions that describe a physical quantity. The delta function can be represented by a distribution, which might be an integral equation, a limiting function, or a limit of a sequence of functions (A. Papoulis, "The Fourier Integral and Its Applications").

The energy impulse function (not a distribution) was derived in Chapter 10 of my book "Planck's Columbia Lectures", which correlates with Planck's Radiation Equation, Plancks Energy State Equation and the measured characteristics of white noise. In my opinion, the analytical methods of electronics are well-suited to the analysis of atomic physics as portrayed by Planck. The application of Heaviside calculus to electromagnetic fields yields solutions to the characteristics of white noise and antenna patterns of radiation.

Proof that electromagnetic radiating waves move faster than the speed of light was presented in a previous technical paper, "A Different Picture of Radiation (zipped download). The transverse waves bend as the wave velocity exceeds the speed of light.


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