Quantum mechanistic defines our observable environment only in terms of the probabilistic values associated with Schrödinger’s wave equation.

Many interpret this as meaning a particle and all other objects exists in a world of probabilities and only become connected to the environment when observed.  Additionally it assumes that a particle is distributed or simultaneous exists form one edge of the universe to the other because it tells us there is a probability it can be found anywhere in it.

However it is extremely difficult to define a set of statements which explains how those probabilities can be physically connected to that environment even though it has held up to rigorous and thorough experimental testing.

Yet Einstein gave us a an explanation for this connection in his relativistic formulas for length contraction L = L0((1 – v2/c2))1/2 because it tells us the distance between every point along the trajectory of all forms of energy which are moving at the speed including that associated with the wavefunction is zero for an observer who is outside of its reference frame.  In other words since the energy associated with Schrödinger’s equation which is moving at the speed of light the distance between the each end of the universe for it relative to an outside observer is zero.

However because the probabilities associated with Schrödinger’s equation involve the spatial properties of position, to fully understand the ramifications of that equation to our understanding of quantum mechanics one must transpose it to the spatial equivalent.

Einstein gave us the ability to do this when he defined the geometric properties of space-time in terms of the constant velocity of light and a dynamic balance between mass and energy because that  provided a method of converting a unit of time in a space-time environment of unit of space in four *spatial* dimensions.  Additionally because the velocity of light is constant he also defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions is one bases for assuming as was done in the article “Defining energy?” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However this would allow one to physically the connect the probabilities associated Schrödinger’s equation to our observable environment in terms of a physical or spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension as was done in the article "Why is energy/mass quantized?" Oct. 4, 2007.

Briefly that article showed that the observable properties of particles can be caused by the formation of a resonant system on a "surface" of a three-dimensional space manifold with respect to fourth "spatial" dimension.  This is because the four conditions required for resonance to occur in a three-dimensional 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 occur in one made up of four.

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* dimension 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 three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established on a surface of a three-dimensional space manifold.

Yet the classical laws of three-dimensional space tell us the energy of resonant systems can only take on the discontinuous or discreet energies associated with their fundamental or harmonic of their fundamental frequency.

However, these are the similar to the quantum mechanical properties of energy/mass in that they can only take on the discontinuous or discreet energies associated with the fundamental resonate  frequency of space defined by the equation E=hv where "E" equals the energy of a particle "h" equal Planck’s constant "v" equals the frequency of its wave component.

Yet it also allows one to define the physical boundaries of a quantum system in terms of the geometric properties of four *spatial* dimensions.

For example in classical physics, a point on the two-dimensional surface of a piece of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space.

Similarly an object occupying a volume of three-dimensional 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 three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries associated with a particle in the article "Why is energy/mass quantized?" Oct. 4, 2007

As mentioned earlier in the article “Defining energy?” Nov 27, 2007 showed all forms of energy can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However as mentioned earlier assuming the probabilities associated with Schrödinger’s equation are the result of a displacement caused by a matter wave moving on a "surface" of a three-dimension space manifold with respect to a four *spatial* dimension allows one to connect them to the physicality of the observable environment we all live in.

Classical mechanics tell us that due to the continuous properties of the wave energy the article "Why is energy/mass quantized?" Oct. 4, 2007 associated with a quantum system would be distributed throughout the entire "surface" a three-dimensional space manifold with respect to a fourth *spatial* dimension.

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

Similarly if the assumption that quantum properties of energy/mass are a result of vibrations or oscillations in a "surface" of three-dimensional space caused by matter wave is correct then classical mechanics tell us that those oscillations would be distributed over the entire "surface" three-dimensional space while the magnitude of those vibrations would be greatest at the focal point of the oscillations and decreases as one moves away from it because

However, as was mentioned earlier Einstein in his formula for length contraction L = L0((1 – v2/c2))1/2 tells us that a particle would simultaneously exist everywhere throughout the entire universe because of the fact that wave energy is continuous it would extend to each end of the universe.  Therefore the distance between the each end of the universe relative to an observer outside of that reference frame would be zeroAdditionally because time stops for anything traveling at the speed of light it would appear to exist simultaneously at every point in the universe of an outside observer.

As mentioned earlier the article “Why is energy/mass quantized?” shown a quantum particle is a result of a resonant structure formed on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Yet Classical Wave Mechanics tells us resonance would most probably occur on the surface of the rubber sheet were the magnitude of the vibrations is greatest and would diminish as one move away from that point.

Similarly a particle would most probably be found were the magnitude of the vibrations in a "surface" of a three-dimensional space manifold is greatest and would diminish as one move away from that point.

In others words one can explain how the probabilities associated with Schrödinger’s equation are connected to our physical world and the fact that particles simultaneously exist everywhere in the universe before it is observed by applying the concepts of Einstein Theory of Relativity to the quantum environment.

It should be remember Einstein’s genius allows us to choose to define a quantum system in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories thereby giving us a new perspective on the probabilistic properties of a quantum environment and how they physically connected to our observable universe.

Later Jeff

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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 three-dimensional environment to a matter wave on a "surface" of a three-dimensional 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 space-time 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 three-dimensional 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

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 two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space.

Similarly an object occupying a volume of three-dimensional 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 three-dimension 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 270-degree points as its slope changes from positive to negative while it changes most rapidly at the 180 and 360-degree 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 360-degree 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 270-degree 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 in-between 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