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The Imagineer's
Chronicles:
A theoretical blog
Tjipto Juwono contributed the following explanation of a 1935 paper co-authored by Einstein, Podolsky, and Rosen, which presented what has been called the EPR paradox.
"In 1935, Einstein co-authored a paper which was intended to show that Quantum Mechanics could not be a complete theory of nature. The first thing to notice is that Einstein was not trying to disprove Quantum Mechanics in any way. In fact, he was well aware of its power to predict the outcomes of various experiments. What he was trying to show was that there must be a "hidden variable" that would allow Quantum Mechanics to become a complete theory of nature
The argument begins by assuming that there are two systems, A and B (which might be two free particles), whose wave functions are known. Then, if A and B interact for a short period of time, one can determine the wave function which results after this interaction via the Schrödinger equation or some other Quantum Mechanical equation of state. Now, let us assume that A and B move far apart, so far apart that they can no longer interact in any fashion. In other words, A and B have moved outside of each other's light cones and therefore are spacelike separated.
With this situation in mind, Einstein asked the question: what happens if one makes a measurement on system A? Say, for example, one measures the momentum value for system A. Then, using the conservation of momentum and our knowledge of the system before the interaction, one can infer the momentum of system B. Thus, by making a momentum measurement of A, one can also measure the momentum of B. Recall now that A and B are spacelike separated, and thus they cannot communicate in any way. This separation means that B must have had the inferred value of momentum not only in the instant after one makes a measurement at A, but also in the few moments before the measurement was made. If, on the other hand, it were the case that the measurement at A had somehow caused B to enter into a particular momentum state, then there would need to be a way for A to signal B and tell it that a measurement took place. However, the two systems cannot communicate in any way!
If one examines the wave function at the moment just before the measurement at A is made, one finds that there is no certainty as to the momentum of B because the combined system is in a superposition of multiple momentum eigenstates of A and B. So, even though system B must be in a definite state before the measurement at A takes place, the wave function description of this system cannot tell us what that momentum is! Therefore, since system B has a definite momentum and since Quantum Mechanics cannot predict this momentum, Quantum Mechanics must be incomplete.
In response to Einstein's argument about incompleteness of Quantum Mechanics, John Bell derived a mathematical formula that quantified what you would get if you made measurements of the superposition of the multiple momentum eigenstates of two particles. If local realism was correct, the correlation between measurements made on one of the pair and those made on its partner could not exceed a certain amount, because of each particle's limited influence.
This gave physicists the ability verify the quantum theories prediction that particles can instantly influence other particles or are universally connected when they are "spacelike separated" or exist in different local reality.
However, Chapter one postulated that space is composed of a continuous non-quantized form of mass and four *spatial* dimensions instead of four-dimensional space-time which means that all objects and particle are universally connected throught it.
Later in Chapter two, a particle was defined in terms of a resonant system or "structure" formed in space by a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
Chapter three derived the propagation of EM radiation in terms of a matter wave "moving" at the velocity of light on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
Therefore, the existence of a continuous non-quantized form of mass would "make quantum mechanics complete" because
(Louis de Broglie was the first to theorize that all particles have a wave component. His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer. However, this means there must be a continuous non-quantized medium for it to be propagated on because even the smallest possible particle must have a wave component. However, macroscopic observations of wave energy indicate that it can only be propagated on a medium made up of mass. Therefore, the success of Louis de Broglie theory indicates that a continuous non-quantized form of mass exists.)
However, the existence of a continuous non-quantized form of mass may also provide the "hidden variable" defining a mechanism that would allow two particles that are "spacelike separated" to communication.
This mechanism would be analogous to how two pool balls communicate on a pool table.
The pool balls will represent the resonant "structures" in a continuous non-quantized form of mass that defined a quantum particle in Chapter two.
Pool is a game in which a ball. called a cue ball is struck and as a result, it travels on the surface of the pool table until it collides with an object ball. This collision results in the “information" regarding the cue balls momentum to be "communicated" to the object ball. The object ball then begins to travel across the table until it collides with and "communicates" the "information" on its momentum to the next ball in line. The speed at which the "information" is "communicated" between the cue ball and the object ball is, in part, dependent on the time required to travel the distance between the individual balls on the table.
However if the pool balls are physically contacting each other the "communication" or "information" transfer from the first to the last ball in line will be almost instantaneous because the time required for them to travel the distance between them would be minimal.
Chapter three derived the velocity of EM radiation and the information it carries in terms of a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
Therefore, speed of information transfer by electromagnetic energy between two spatial separated particles made up of a resonant system defined in Chapter two would be dependent on the time required for them to travel through the space between them.
This would be analogous to the speed of "communication" or "information" transfer in the earlier example of the pool balls in that the time required for information to be transferred from the first to the last pool ball in the line was dependent on the time required for them to travel through the space between them. This is because speed of the transfer of information by EM radiation would be dependent on the time required for a continuous non-quantized form of mass to "travel the distance" required for it to interact with a continuous non-quantized form of energy.
However, both the EPR paradox and Bells theorem deal with rate at which the information regarding the momentum of particles can be communicated between different local realities.
If space were made up of a continuous non-quantized form of mass as is postulated in Chapter one each resonant "structure" that defined a particle in Chapter two would be interconnect with other particles through the continuous non-quantized form of mass that makes up the space between them. Therefore, the transfer of the information related to their momentum could be almost instantaneous for the same reason as the information transfer between the pool balls in the earlier example that were physically connect or touching was almost instantaneous.
This indicates two particles may be "spacelike separated" with respect to the electromagnetic energy but not with respect to the information carried by a continuous non-quantized mass component of space.
This defines a physical mechanism explaining why Bell's theorem may provide mathematical verification for the instantaneous communication between particles that exist in different local realities in terms of the existence of a continuous non-quantized form of mass and energy.
The universe's most
powerful enabling tool is not
knowledge or understanding but
imagination
because it extends the reality of
one's environment.
Copyright 1995 Jeffrey O'Callaghan