There can be no doubt the probabilistic interpretation of Schrödinger’s wave equation predicts with amazing precision the results of every experiment involving the quantum world that has ever been devised to test it.
However this interpretation is at odds with the reality of the classical or deterministic world most of us appear to live in because it assumes that for a given set of initial conditions there can only be one outcome while the probabilistic interpretations of quantum mechanics assumes there can be an infinite number.
However many of the standard interpretations of quantum mechanics assume that probability is the fundamental property of the universe, while alternative interpretations explain it as an emergent or a second-order consequence of various limitations of the observer or the environment he or she is occupying when making an observation.
Determining which is the correct way of interpreting it is difficult because due to the limitation imposed on observers by uncertainty principle we can never be sure what is happening on the quantum scale when an observation is made.
Yet that does not mean that we cannot extrapolate what we can learn from observing our four dimensional space-time environment to the quantum world to help us understand what happens when we make an observation.
However we will find it beneficial to redefine Einstein space-time model of the universe into its equivalent in four spatial dimensions.
(The reason for this will become obvious later on)
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 it provided a method of converting a unit of it he associated with energy to unit of space we feel he would have associated with mass. 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.
As mentioned earlier Quantum mechanics assumes one can only determine the future evolution of a particle in terms of the probabilistic values associated with its wave function which is in stark contrast to the Classical “Newtonian” assumption that one can assign precise values of future events based on the knowledge of their past.
In other words in a quantum system Schrödinger’s wave equation plays the role of Newtonian laws in that it predicts the future position or momentum of a particle in terms of a probability distribution.
This accentuates the fundamental difference between quantum and classical mechanics because the latter defines the reality of future events in terms of pervious events whereas quantum mechanics defines them based on the “non-classical” reality of the sum total of all possible events that can occur.
However as mentioned earlier one may be able to understand the physical reason why these two theories define the reality of events differently if, as was done earlier one redefine Einstein’s space-time concepts in terms of four spatial dimensions.
In the article “Why is energy/mass quantized?†Oct. 4, 2007 it was shown one can understand the physicality of quantum properties energy/mass by extrapolating the laws of classical wave mechanics 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.
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 occur in one consisting of 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 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 space.
Therefore, these oscillations in a “surface” of a three-dimensional space manifold would meet the requirements mentioned above for the formation of a resonant system or “structure” in four-dimensional space if one extrapolated them to that environment.
Classical mechanics tells us the energy of a resonant system can only take on the discrete or quantized values associated with it fundamental or a harmonic of its fundamental frequency.
Hence, these resonant systems in four *spatial* dimensions would be responsible for the discrete quantized energy associated with the quantum mechanical systems.
(In the article “The geometry of quarks” Mar. 15, 2009 the internal structure of quarks, a fundament component of particles was derived in terms of a resonant interaction between a continuous energy/mass component of space and the geometry of four *spatial* dimensions.)
However, if a quantum mechanical properties of particle is a result of a matter wave on a “surface†of three-dimensional space with respect to a fourth *spatial* dimension, as this suggests one should be able to show that it is responsible for the uncertainties and probabilistic predictions made by Schrödinger and his wave equation regarding the position and momentum of particles.
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 it’s 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 â€Why is energy/mass quantized?“ showed energy must be packaged in terms of its discrete resonant properties. 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.
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 that 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 “mâ€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 defines the physical reason in terms of four *spatial* dimensions for why we are unable to measure the exact position and moment of a quantum system.
However it also defines the reason why the probably functions of quantum mechanics are an emergent or a second-order consequence of various limitations of the observer or the environment and not a fundamental property of our universe because as was just shown the physicality of four *spatial* dimension places limitations on our ability to define the initial conditions or momentum and position of a quantum system we are measuring.
In other words the reason quantum mechanics can only predict the probability of an event occurring is because of the limitations the physical properties of four *spatial* dimension places on an observer.
This shows why we should view the probabilistic properties of quantum mechanics as an emergent or a second-order consequence of the limitations of the four *spatial dimension or space-time environment he or she is occupying when making an observation and not a fundamental property of the universe.
Later Jeff
Copyright Jeffrey O’Callaghan 2014