To explain the physicality of the wave function one must connect its wave particle definition of existence along with its probabilistic interpretation to the physicality of our observable universe.

For example, the probability of getting a six on a roll of the dice is related to the physical interaction of the dice with the table where it is rolled. In plain English, the probabilities associated with a roll of dice does not define why a six was rolled the physical properties of table does.

Therefore, to connect the wave particle definition of existence and probabilistic interoperation of the wave function to the physicality of our observable universe one must show how it is responsible for them.

One can accomplish this by using the science of wave mechanics along with the fact Relatively tells us wave energy moves continuously through space-time unless it is prevented from doing so by someone observing or something interacting with it. This would result in its energy being confined to three-dimensional space. The science of wave mechanics also tells us the three-dimensional "walls" of this confinement will result in its energy being reflected back on itself thereby creating a resonant or standing wave in three-dimensional space. This would cause its wave energy to be concentrated at the point in space were a particle would be found. Additionally, wave mechanics also tells us the energy of a resonant system, such as a standing wave can only take on the discrete or quantized values associated with its fundamental or a harmonic of its fundamental frequency. This means one would define the position of a particle in four-dimensional space-time in terms of where this standing wave was located.

This defines the wave particle-duality of existence as define by quantum mechanics in terms of the physical properties of space-time and why a particle becomes reality only when it is prevented from moving through time by and observation.

Additional is also allows us to connect its probabilistic interoperation to the physicality of our observable universe.

This is because is it allows one to understand why the probabilities associated with the wave function does not define the position of a particle, the properties of space-time does. But to do so one would have to show similar to the dice, mentioned earlier why the probabilities associated with wave function does NOT define reason why it will be found in a specific place at a specific time, the universe does.

The physics of wave mechanics and Einstein theories tell us wave energy moves continuously through space-time unless it is prevented from doing so by someone or something interacting. This means (if allowed to move freely it) it would be distributed throughout "surface" a three-dimensional space manifold with respect to time.

For example, the energy of a vibrating or oscillating ball on a rubber diaphragm would be disturbed over its surface while the magnitude of those vibrations would decrease as one move away from the focal point of the oscillations.

Similarly, if the assumption the wave properties of the wave function represent a wave moving through space-time is correct, the oscillations it causes in a "surface" of three-dimensional space, would be distributed over its "surface" while their magnitude would be greatest at their focal point and decrease as one moves away from it.

Earlier, it was shown why one can derive the properties of the wave function in terms of a wave moving through space-time. Additionally, it was shown that a particles position could be derived in terms of where the standing wave created when it was prevented from moving through time was located.

Therefore, as was mentioned earlier to define the physicality of the wave function in terms of space-time one must show how the probabilities it associates with position are caused by it.

This can be accomplished because quantum mechanics defines a particle’s position in terms of a one-dimensional point which could be found anywhere within the volume occupied by that standing wave. Therefore, there is probability it could be found anywhere in that volume before it is observed.

Yet the science of wave mechanics tells us the one-dimensional point that defines a particle position in quantum mechanics would most PROBABLY be found at the focal point were the magnitude of the oscillations was greatest and would diminish as one move away from that point.

In other words, this shows how one can derive the probabilistic interpretation of the wave function in terms of the physical properties of space-time as defined by Einstein.

Copyright Jeffrey O’Callaghan Dec 2020

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