In the 1920's it became accepted that at the quantum level the dynamics of a particle were given by Schrödinger's equations. Max Born in Göttingen, Germany communicated to Niels Bohr and Werner Heisenberg in Copenhagen his belief that the solutions to Schrödinger's equations determine probability density distributions for a particle's location and velocity. They replied that they never thought those solutions were anything else. Because of the notion that a particle has a probability density distribution they concluded that a particle does not have a material existence until it is subjected to measurement/observation. This became known as the Copenhhagen Interpretation.

However this conclusion is unjustified for particles having mass such as electrons, protons and neutrons. Any particle undergoing repetitive motion has a probability density function for its location based upon the proportion of the time spent in the various intervals of its path. Call this probability density function the time-spent probability density function for the location of the particle. There is likewise a time-spent probability density function for the velocity of a particle and hence also for its momentum.

In 1927 Heisenberg published his article on what came to be known as the Uncertainty Principle. Niels Bohr was not ln agreement with Heisenberg on this matter and did not want Heisenberg to publish that article, but Heisenberg did so anyway. Because, according to this principle, the location and momentum for a particle cannot both be known to arbitrary precision Heisenberg concluded that subatomic particles cannot have material existence and trajectories. This conclusion is also unjustified. For simple physical systems for which explicit mathematical solutions are known the time-spent probability density functions easily satisfy the Uncertainty Principle.

The Correspondence Principle

Niels Bohr in the 1920's articulated the Correspondence Principle; i.e., in order for quantum analysis to be valid it has to be consistent with classical analysis as the energy level of the physical system increases without bound. Bohr's Correspondence Principle has to be modified slightly. It is the spatial average of the quantum level probability density function that must be consistent with the results of classical analysis. The time average of the result of the quantum level analysis is a probability density function. What probability density function of classical analysis can the result of the quantum analysis asymptotical approach? It can only be the time-spent probability density function. Mathematical analysis of the solution to the time independent Schrödinger's equation for a particle moving in a potential field shows its time average asymptotically approaches the time-spent probability density function from classical analysis.

The time-spent probability density function for a physical system is its dynamic appearance; it says nothing about the static appearance of the system. The blurred unchanging appearance of a physical system in motion does not imply the immateriality of the particles making it up. Thus the Copenhagen Interpretation is wrong because its based upon Bohr and his associates jumping to unjustified conclusions.

The Bell Theorem supposedly provided empirical support for the Copenhagen Interpretation but an analysis of the logic of the testing of Bell's Theorem reveals a shortcoming. Bell derived a prediction based upon a set of assumptions, one of which was the materiality of charged particles. Another of which is that a charged particle in a beam of charged particles travels in a strictly straight line; i.e., there are no transverse oscillations due to repulsions between nearby charged particles. When Bell's prediction was found to not hold it was held to imply that the materiality of charged particles is not true. Logically that is not valid. It only implies that one or more of the assumptions do not hold, but not necessarily the assumption concerning the materiality of charged, massive particles. (Much of the testing of Bell's involves photons and photons' immaterialty was never in question.)

The Copenhagen Interpretation
and its Origin

The Copenhagen interpretation is an expression of the meaning of quantum theory that was largely devised in the years 1925 to 1927 by Niels Bohr and Werner Heisenberg in Copenhagen, Denmark. It is commonly thought to be the dominant interpretations of quantum theory] According to the Copenhagen interpretation, physical systems generally do not have definite properties such as mass and charge prior to being measured. Prior to that measurement the particles of physical systems exist only as probability distributions. Quantum theory can only predict the probabilities of what measurements will produce. The act of measurement affects the system, causing the probability distribution, after the measurement, to reduce to only one of the possible values This phenomenon is known as wave function collapse.

Niels Bohr achieved a tremendous break-through in 1913 in quantum theory with his solar system model of the atom. In Bohr's 1913 model electrons orbit the atom's nucleus as the planets orbit the Sun. When an electron drops to a lower energy orbit a spark of electromagnet radiation is given off. The wavelengths of those sparks of radiation is called the spectrum of the element.

Bohr's model achieved an amazingly accurate explanation of the spectrum of hydrogen. It could be extended to other atoms which have a single electron in the outer shell of electrons. It did not work for atoms with multiple electrons in the outer shell such as helium atoms.

Bohr with his great prestige and authority in the world of quantum physics commenced a program in Copenhagen to extend quantum analysis. He brought younger physicists such as Werner Heisenberg from Germany to help in his program. These younger physicists were in their early 20's and known as the Wunder Kinder (wonder children). Heisenberg developed a new system of quantum analysis, called matrix mechanics, based upon square matrices of infinite order. But just after Heisenberg's great success in the development of matrix mechanics seemingly out of nowhere came a superior formulation by an Austrian physicist, Erwin Schrödinger, based upon partial differential equations. Schrödinger was in his late 30's and had never before done anything in quantum theory. His specialty was optics. He was inspired to investigate quantum theory by the work of Louie de Broglie. De Broglie argued that just as radiation waves have a particle aspect particles have a wave aspect. The whole dramatic story is told in Quantum Drama.

Schrödinger developed an equation that was accepted by Bohr as the foundation for quantum theory despite there being serious problems. One of those problems is that the equation is not derived from first principles. Instead it is merely constructed by a definite procedure. However the solutions to Schrödinger's equation seemed to fit the physical quantum world so that it was accepted as "a justification". However Schrödinger's equations were often solved by a mathematical technique called separation of variables. The problem with this procedure is that separation of variables is not compatible particleness. Therefore the solutions found by this technique may be mathematically valid but physically irrelevant.

Schrödinger's equation involved a variable the nature of which he did not specify. He thought it was analogous to a variable involved in the equations of optics. It was labled the wave function. The terminology of interpretation originally referred to the interpretation of the wave function. Max Born in Göttigen, Germany concluded that the squared magnitude of wave function was the probability density. As noted previously, when he communicated this interpretation to Bohr and Heisensenberg in Copenhagen Bohr responded that they never considered it to be anything else. Thus was born the Copenhagen Interpretation of quantum theory.

There is a metaphysical offshoot of the Copenhagen Interpretation that talks about the need for a consciousness to observe the measurement of a partcle. This notion is unjustified. All that is involved in the measurement of a particle is that its motion is ended and its dynamic appearance is merely its static appearance.

Links to Specific Studies

• The Time-Spent Probability
  Density Distributions
• The Correspondence Principle
• The Satisfaction of the Uncertainty
  Principle by the Time-Spent
  Probability Distributions
  for a Harmonic Oscillator
• The Satisfaction of the Uncertainty
  Principle by the Time-Spent
  Probability Distributions
  for More General Physical Systems
• The Asymptotic Limit of the Probability
  Density Function for a Particle Moving in a
  Potential Field in 2D Space
• The Invalidity of the Tests
  of the Bell Theorem
  for Charged Particles
• The Successive Histories of the
  Notions of the Nature of the
  Fundamental Bits of Matter

(To be continued.)

Conclusion

The tenet of the Copenhagen Interpretation that charged particles have no material existence until they are subjected to measurement has no justification. It is based upon the false notion that if a particle has a probability distribution then it does not have a material existence. Any particle in motion has a time-spent probability distribution based upon the proportion of the time it spends in its various allowable locations and velocity intervals. The probability density distribution of a physical system asymptotically approaches the time-spent probability distribution of the system as its energy increases without bound.

Likewise the Uncertainty Principle does not imply the immateriality of particles. Time-spent probability distributions for material particles can satisfy the Uncertainty Principle perfectly well.

Thus the Copenhagen Interpretation notion of the immateriality of massive, charged particles was never justified.