San José State University
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Entanglement: A Contrived Enigma

The purpose of this piece is to point out how contrived are the puzzlements of the conventional notion of entanglement. The detailed history of the notion of entanglement is given elsewhere.

Supposedly according to the Copenhagen Interpretation (CI) of quantum physics particles generally do not have a physical existence. Instead they exist only as probability density distributions. These probability density distributions are determined as solutions to Schrödinger's equations.

According to the CI particle have a physical existence only when they are subjected to observation. Observation causes the probability density distribution of a particle to collapse into a spiked distribution at a specific location. The Uncertainty Principle says that since there is no uncertainty as to the particle's location the uncertainty of its velocity must be infinite.

Entanglement involves a pair of particles. According to the conventional view, when the pair is created neither has a physical existence and their characteristics such as spin are not specified. But if they are separated and one of the pair is subjected to observation then its characteristics become definite. When the other particle is subjected to observation its characteristics are found to correspond appropriately to what was found for the first particle. This is interpreted as evidence that the two particles have some sort of link, called an entanglement, such that specific characteristics found for the first particle are communicated to the second particle.

This interpretation creates a number of puzzlements. If the particles are separated by a significant distance and the second particle's characteristics are observed just after the observation of those of the first then it appears that the information from the first was communicated at a speed faster than light.

Or, if the characteristics of the second particle are not observed until sometime after those of the first there is the puzzlement of how the information of the first particle is retained until it is needed for the determination of the characteristics of the second particle. It cannot be communicated at the time of observation of the first particle because, according to the theory, there is no way for it to be retained. Supposedly then the first particle would be in constant communication with the second particle until its characteristics are observed.

Then what would happen if the first particle is annihilated before the second particle's characteristics are observed? What a puzzlement!

But all of these puzzlements are eliminated if the corresponding characteristics of the of the two particles are determined at the time the pair is created and this information is retained throughout their lifetimes. Thus the puzzlements are contrived.

The notion that information can be communicated between two particles at a speed greater than that of light should have immediately been rejected and along with it the CI notion that particles do not have a physical presence.

An alternate interpretation of the solutions to Schrödinger's equation is that they represent the dynamic appearance of particles executing periodic trajectories. Those trajectories are executed at such fantastically high rates that there is little possibility of observing anything other than the dynamic appearance of the periodic motion unless observation halts the periodic motion. The rate of revolution of electrons in atoms is on the order of 7 million billion times per second. This is fantastically high but much slower than the rates of rotation of nuclei, which are on the order of a hundred billion billion times per second.

It is as though the CI interprets the translucent disk of a rapidly spinning fan as a single unchanging "particle" in which the material of the fan is smeared over disk and the fan is nowhere or simultaneous everywhere over the disk. In such an interpretation the fan is said to not exist materially until a wrench is stuck into the spinning fan and Clang! the fan comes into material existence. The solutions to Schrödinger's equation have to do with dynamic appearance of particles in motion and not their physical existence.

Consider a massive charged particle execting a periodic path. At any point in space the time average of the effect of that particle is the same as if its mass and charge were smeared over its path in proportion to the amount of time it spends throughout the path. With the path being repeated much more than billions of times per second there is nothing other than time averages that can be observed. For more on this topic see Simple but Irrefutable.

The CI belief in the absence of. a physical presence of particles derived originally from the notion that the uncertainty principle requires it. This is not true. The time-spent probability distributions for a harmonic oscillator satisfy the uncertainty principle while still applying to material particles. It only takes one example to show that the uncertainty principle does not require the absence of material existence.

The absence of material existence for particles was initially simply an interpretation of quantum theory; i.e., the Copenhagen Interpretation. Bell's Theorem offered the possibility of empirical verification of that interpretation. The testing using photons seemed to confirm it, but photons are quite different in their nature from electrons, protons and neutrons. Photons do not have a material presence. We know from the studies of solitons and solitary waves that a wave may have particleness as well as being a wave.

So the experimental results concerning the testing of Bell's Theorem must be carefully examined to see if there is an alternate interpretation from the conventional one. If some factor important in the physical world has been left out of the derivation then it would not be surprising that a physical experiment does not give results based on a derivation that leaves out that factor.

Consider the situation before Bell's work. An obvious theorem could have been articulated; i.e.,

The Ante-Bell Theorem:
If a pair of material partcles is created with corresponding characteristics the throughout their subsequent lives if a characteristic of one particle is observed the other particle will be found to possess the corresponding characteristic even if the observation of the second particle takes place at exactly the same instant as the observation of the first.

The predictions of the this theorem would have been confirmed inumerable times. These confirmations of this theory were dismissed and its place taken by the implausible apparatus of the Copenhagen Interpretation and the Bell Inequality with the communication between paired particles taking place at speeds faster than that of light, even at infinite rates. If such an alternative is considered acceptable then there should not be much difficulty in coming up with an alternate explanation for any experimental violations of Bell's Inequality.

The dilemma is that there are two apparent discrpancies between theories and empirical measurements. One is based upon Bell's Theorem is as shown below.

The classical case shown corresponds to material particles having a continual material presence with the characteristic of a pair of particles fixed at the time of the formation of the pair. The quantum case shown is for a pair of particles not to have a material presence until a characteristic of one of the particles is measured. There is a remarkably small difference. On the other hand there is the very great difference between the implied speed of communication between the two paired particles. The speed of communication classically is the speed of light. And there is communication between the paired particles through their gravitational and electromagnetic fields and this wouls seem to constitute something in the nature of measurement. The speed of communication implied by the Copenhagen Interpretation has no upper bound.

Which of the following seems more likely to resolve the discrepancy between theory and measurement? On the one hand there could be an expansion of the Bell Theorem analysis to take into account such factors as the gradients in the ambient electrical and magnetic field in the vicinity of the measring apparatus. It was afterall the gradient in a magnetic field in the Stern-Gerlach experiment in 1922 that produced the first evidence of atomic spin.

On the other hand there could be the search for some mechanism that would account for communication between paired particles at speeds greater than the speed of light and perhaps at infinite rates. There seems to have been no attempt to pursue this later goal. That perhaps is a manifestation of the exasperationg true-believer-hood of those who believe in the Copenhagen Interpretation.

In the CI the observation and measurement of a particle takes on some metaphysical aspect of there being a conscious observer. Meaurement is simply the disruption of the periodic motion of a particle.

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