Heisenberg uncertainty principal: A Classical explanation

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We have shown throughout this blog and its companion book “The Reality of the Fourth *Spatial* Dimension” that if one redefines Einstein space-time universe in terms of four *spatial* dimensions one can seamlessly integrate quantum mechanics into its theoretical structure while at the same time will aid in the development of a theoretical explanation of the Heisenberg’s Uncertainty Principal based on the laws Classical of Physics.

Einstein gave us the ability to do this when he use the equation E=mc^2 and the constant velocity of light to define the geometric properties of space-time because that provided a method of converting a unit of space-time associated with energy to unit of space associated with position.  Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words he gave us the ability to define a theoretical model in terms of four *spatial* dimensions that would make prediction identical to those made by one he defined in terms of four dimensional space time.  Additional it would allow for integration of quantum mechanics into them in terms of either their spatial or time components.

For example the Heisenberg Uncertainty Principle states that certain pairs of physical properties, like position and momentum, cannot both be known to arbitrary precision.  That is, the more precisely one property is known, the less precisely the other can be known.  This is not a statement about the limitations of a researcher’s ability to measure particular quantities of a system; it is a statement about the nature of the system itself as described by the equations of quantum mechanics.  According to the uncertainty principle, it is, for instance, impossible to measure simultaneously both position and velocity of a microscopic particle with any degree of accuracy or certainty.
In the article “Why is energy/mass quantized?” Oct 4, 2007 it was shown one can theoretically derive quantum mechanical properties of a particle by extrapolating the laws governing resonance in a classically three-dimensional environment to a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Additionally, it was showed why all energy exists in these resonant systems and is therefore quantized.

Briefly it was showed the four conditions required for resonance to occur in a classical Newtonian environment, an object, or substance with a natural frequency, a forcing function at the same frequency as its natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would also be found in one consisting of four.

The existence of four *spatial* dimensions would give three-dimensional space 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.

However, these oscillations in a “surface” of a three-dimensional space manifold, according to classical mechanics would generate a resonant system or “structure” in space.  These resonant systems are known as particles.

(In an earlier article “The geometry of quarks” Mar. 2009 it will be shown how and why they join together to form these resonant systems in terms of the geometry of four *spatial* dimensions.)

The energy in a classically resonating system is discontinuous and can only take on the discrete values associated with its fundamental or a harmonic of its fundamental frequency.

However, these properties of a classically resonating system are the same as those found in a particle in that they are made up of discreet or discontinuous packets of energy/mass.  This is the basis for assuming, as was done in the article “Why is energy/mass quantized?” that its quantum mechanical properties are a result of a resonant system in four *spatial* dimensions.

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 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.

In other words by redefining Einstein’s space-time universe in terms of four *spatial* dimension allows of the integration of quantum mechanics in to it because as mentioned earlier they are equivalent.

However, treating the quantum mechanical properties of energy/mass in terms of a resonant system generated by a matter wave in four spatial dimension allows one to derive the validity of Heisenberg’s Uncertainty Principle by, as mentioned earlier extrapolating the laws of a classical three-dimensional environment to a fourth *spatial* dimension.

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 in terms of the peaks and valleys of the matter wave responsible for its resonant structure because those points are the only places 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 its 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 to be observed by another instrument.  Therefore, if one was able to determine precise position of a particle he or she 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 information left to for an instrument which was attempting to measure it.  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 object is because, as mentioned earlier the article “Why is energy/mass quantized?” showed its energy/mass must be packaged in terms of a resonant system.  Therefore, 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.

However, this defines a Classical reason for the validity of Heisenberg’s Uncertainty Principle because it tells us 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 that predefine distance interference will cause its energy or momentum to be smeared our over a wider area.  Similarly, to measure its momentum 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, because of the dynamic interaction between the position and moment component of the matter wave responsible for generating the resonant system associated with a particle defined in the article a ”Why is energy/mass quantized?” the change or uncertainty of one with respect would be defined by the product of those factors.

Another way of looking at this would be to allow a particle to pass through a slit and observe where it struck a screen on the other side.  One could get a more precise measurement of its position by narrowing the slit however classical wave mechanics tell us this will increase the interference of the wave properties associated with its resonant structure.  However this will cause the interference pattern defining its momentum to become more spread out and therefore make it more difficult to accurately determine its value.

Therefore, Classical wave mechanics, when extrapolated to a fourth *spatial* dimension tells us the more precisely the momentum of a particle is known, the less precisely its position can be known while the more precisely its position is known, the less precisely its momentum can be determined if one assumes as we have done in “Why is energy/mass quantized?”that the quantum mechanical properties energy/mass are a result of a resonant system formed by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This shows by redefining Einstein’s space-time concepts in terms of four spatial dimensions one can theoretically derive the mechanism responsible for Heisenberg’s uncertainty principal by extrapolating the laws of Classical Wave Mechanics by a three-dimensional environment to a fourth *spatial* dimension.

Later Jeff

Copyright Jeffrey O’Callaghan 2010

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