We know that everything in the universe including particles have physical size.
Even so for the past 50 years, the Standard Model of particle physics which many say has given us the most complete mathematical description of the particles and forces that shape our world ignores this fact and treats them all as size less dimensionless mathematical points.
Many physicists feel this way because it predicts with so much accuracy the microscopic properties of particles and the macroscopic ones of stars and galaxies that it must be a correct physical model that even though as was just mentioned it treats all particles and their interactions not in term of their physical size but in terms of mathematic points.
However in 1924 Louis de Broglie’s showed that it cannot be when he theorized that all particle’s have a wave component and that one must take this into account when one defines how they interact with their environments. This fact becomes irrefutable when in 1927 Davisson and Germer observed that electrons were diffracted by crystals. Later it was determined the equation E = hν which defines the wavelength and therefore the physical volume occupied by a particle could be used to calculate the magnitude of that diffraction. In other words one must take into consideration the physical size of a particle to determine how they interact with a crystal.
This means that one cannot assume as the Standard Model does that a particle can be defined as points and expect to develop a complete description of how and why force and particles interact in our observable environment.
In other words one to understand the properties of point particles one must take into consideration their spatial extended properties.
For example in the article "Why is energy/mass quantized?" Oct. 4, 2007 where it was shown the quantum mechanical properties of particles can be defined by extrapolating the laws classical resonance in a threedimensional environment to a matter wave on a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension.
(Einstein gave us the ability to do this when he defined geometric properties of a space time universe in terms of the equation E=mc^2 and the constant velocity of light. This is because it allows one to redefine a unit of time he associated with energy in his spacetime universe to unit of space in one consisting of only four *spatial* dimensions. )
Briefly it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet by a matter wave in four spatial dimensions.
The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.
These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.
The oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in four *spatial* dimensions.
Classical mechanics tells us the energy of a resonant system can only take on the discrete or quantized values associated with its resonant or a harmonic of its resonant frequency
Source: 
Therefore the discrete or quantized energy of resonant systems is responsible for the discrete quantized quantum mechanical properties of particles.
However, it did not explain how the boundaries of a particle’s resonant structure are created in free space.
In other words why is electromagnetic energy not perceived to have the properties of a continues wave moving though space but those of particle
In classical physics, a point on the twodimensional surface of paper is confined to that surface. However, that surface can oscillate up or down with respect to threedimensional space.
Similarly an object occupying a volume of threedimensional space would be confined to it however, it could, similar to the surface of the paper oscillate "up" or "down" with respect to a fourth *spatial* dimension.
The confinement of the "upward" and "downward" oscillations of a threedimension volume with respect to a fourth *spatial* dimension is what defines the geometric boundaries of the resonant system associated with a particle in the article "Why is energy/mass quantized?"
However one can also understand why we perceive there locations in terms of the probabilities associated with quantum mechanics.
The reason why we do not observe energy in its extended wave form is that, as mentioned earlier all energy is propagated through space in discrete components associated with its resonant structure. Therefore, its energy appears to originate from a specific point in space associated with where an observer samples or observes that that energy.
This is analogous to how the energy of water in a sink is release by allowing it to go down the drain. If all we could observe is the water coming out of the drain we would have to assume that it was concentrated in the region of space defined by the diameter of the drain. However, in reality the water occupies a much larger region.
However this also gives one the ability to understand in terms of a physical image the probabilistic interpretation of quantum mechanic interns of where the energy of this matter wave is obverse or measured.
Classical wave mechanics tells us a wave’s energy is instantaneously constant at its peaks and valleys or the 90 and 270degree points as its slope changes from positive to negative while it changes most rapidly at the 180 and 360degree points.
Therefore, the precise position of a particle could be only be defined at the "peaks" and "valleys" of the matter wave responsible for its resonant structure because those points are the only place where its energy or "position" is stationary with respect to a fourth *spatial* dimension. Whereas its precise momentum would only be definable with respect to where the energy change or velocity is maximum at the 180 and 360degree points of that wave. All points in between would only be definable in terms of a combination of its momentum and position.
However, to measure the exact position of a particle one would have to divert or "drain" all of the energy at the 90 or 270degree points to the observing instrument leaving no energy associated with its momentum left to be observed by another instrument. Therefore, if one was able to precisely determine position of a particle he could not determine anything about its momentum. Similarly, to measure its precise momentum one would have to divert all of the energy at the 180 or 360 point of the wave to the observing instrument leaving none of its position energy left to for an instrument which was attempting to measure its position. Therefore, if one was able to determine a particles exact momentum one could not say anything about its position.
The reason we observe a particle as a point mass instead of an extended wave is because, as mentioned earlier the article when we observe or "drain" the energy continued in its wave function, whether it be related to its position or momentum it will appear to come from a specific point in space similar how the energy of water flowing down a sink drain appears to be coming from a "point" source with respect the extended volume of water in the sink.
As mentioned earlier, all points inbetween are a dynamic combination of both position and momentum. Therefore, the degree of accuracy one chooses to measure one will affect the other.
For example, if one wants to measure the position of a particle to within a certain predefined distance "m" its wave energy or momentum will have to pass through that opening. However, Classical Wave Mechanics tells us that as we reduce the error in our measurement by decreasing the predefine distance interference will cause its energy or momentum to be smeared our over a wider area thereby making its momentum harder to determine. Summarily, to measure its momentum "m"kg / s one must observe a portion the wavelength associated with its momentum. However, Classical wave mechanics tell us we must observe a larger portion of its wavelength to increase the accuracy of the measurement of its energy or momentum. But this means that the accuracy of its position will be reduced because the boundaries determining its position within the measurement field are greater.
However, this dynamic interaction between the position and momentum component of the matter wave would be responsible for the uncertainty Heisenberg associated with their measurement because it shows the measurement of one would affect the other by the product of those factors or m^2 kg / s.
Yet because of the time varying nature of a matter wave one could only define its specific position or momentum of a particle based on the amplitude or more precisely the square of the amplitude of its matter wave component.
This shows that one can develop a complete description for how particles can exist as a point as the Standard Model assumes they do while at the same time have the spatial properties need to define our reality
Later Jeff
Copyright Jeffrey O’Callaghan 2017
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Should we let imagination define our reality? If so how much should we allow science to dependent on it?
Most if not all explanatory models of reality rely to some extent on ones imagination because they use unobservable quantities to support them.
For example Einstein used the concept of a spacetime dimension to define gravity. However no one has ever directly observed a spacetime dimension.
Similarly quantum mechanics describes the interactions of particles in terms of the mathematical probabilities associated with a wavefunction which like a spacetime dimension is also unobservable.
In other words both of these theories have imagination as a core component of their explanatory structure.
However there is distinct difference in how they apply it to the environment they are attempting to explain.
For example Einstein in his the "General Theory of Relativity" uses imagination and mathematics to expand a curvature in our observable threedimension environment to define a fourdimensional spacetime universe.
In other words even though its explanatory mechanism is based the existence of a spacetime dimension that can only exist in our imagination he was able by using Riemannian geometry mathematically connect to our observable environment.
Similarly Quantum mechanics also uses imagination and mathematics to very accurately describe the particle interaction based on probabilities.
But unlike Relativity it uses a mathematical construct know as the wavefunction to describe the mechanism responsible for the future position of a particle which has no counterpart in our observable environment.
As Steven Weinberg mentioned in his book "Dreams of a Final Theory" the reason this difference in methodology is important is because mathematics in itself is never the explanation of anything because it is only the means by which we use one set of facts to explain another. This is true even though it may be the only the language in which we express them. In other words mathematics should not be used to justify the mathematics of an explanatory model.
However as was just mentioned quantum mechanics uses the mathematics associated with a wavefunction to explain the mathematical mechanism it assumes is responsible for particle interaction.
Why then when mathematics in itself is never the explanation of anything do so many tell us that the mathematical properties of a wavefunction explain the quantum environment.
They do so because to this date it is the only way available to explain and predict how, among many other things chemical process occur and why the particles that were present in the Big Bang, evolved to create the universe we live in even though its entire theoretical structure is based purely on the imagination of those who developed it.
Some may question using the term imagination to describe the mathematical properties of the wavefunction. However its definition of "being the faculty or action of forming new ideas, or images or concepts of external objects not present to the senses" is applicable to them.
This is true even though science can use its abstract mathematical properties to accurately predict the evolution of particle system.
However as we have shown throughout the Imagineer’s Chronicles there may be more to the wavefunction than just mathematics. In other words by using the imagination one may be able to explain or expand the abstract mathematical properties of the wavefunction to the observable properties of our environment similar to how Einstein was able to expand a curvature in our observable threedimension environment using Riemannian geometry to define a fourdimensional spacetime universe.
For example in the article "Why is energy/mass quantized?" Oct. 4, 2007 it was shown one can understand how and why energy/mass is quantized in terms of the observable properties of resonant systems in our three dimensional environment.
Other articles like "Quantum entanglement: a classical explanation" July 15, 2015 clearly shows that the "spooky action at a distance, as Einstein called it can be explained in terms of the laws of classical causality. In other words it is merely an illusion resulting from a lack of understanding of a classic physicality of a quantum environment
Many of the 250 articles published in the Imagineer’s Chronicles over the past nine years show that one can apply the classical laws of our observable environment to a quantum one to explain hoe the mathematical properties of the wavefunction physically describe how particles interact.
Imagination as was mentioned earlier is a critical component of all modern theoretical models of physics. But we must not allow it to be only the only one because it can result in defining an environment that does not describe the reality we are attempting to define.
In other words similar to how Einstein was able to expand a curvature in our observable threedimension environment to define a fourdimensional spacetime universe one must, as we have tried to do make an effort to expand the physical properties of our observable environment to explain the world of quantum mechanics and the wavefunction that defines its environment.
Later Jeff
Copyright Jeffrey O’Callaghan 2016
The universe’s most powerful enabling tool is not
knowledge or understanding but imagination
because it extends the reality of one’s environment.
However its scientific effectiveness is closely
related to how strongly it is
anchored in the reality it defines.
Anthology of 
The Reality of the Fourth Spatial Dimension Paperback $9.77 Ebook $6.24 

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The Imagineer’s Chronicles Vol. 5 — 2014 Paperback $14.84 Ebook $9.97 
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