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1kIs it possible to define the “reality†behind the quantum world of probabilities in terms of the physical concepts of causality in the space-time environment defined by Einstein?
Quantum theory defines the existence of particles in terms of a mathematically generated probability function created by Schrödinger’s wave equation and assumes that particles do not exist until a conscience observer looks at it. In other words it assumes the act of observation or measurement creates their reality.
However because it is based on probabilities it also assumes that the predictability associated with the laws of causality that govern our macroscopic universe do not apply to a quantum world.
In other words in quantum theory, everything is unpredictable.
Einstein hated this uncertainty, famously dismissing it when he said “God does not play dice with the universe” even though he was unable to give a reason.
However he gave us a clue as to why God must play dice when he said “If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless”
In other words we may be able to understand why a quantum environment lacks causality if we can transform the abstract or non-physical aspects or the probabilities associated with Schrödinger’s wave equation to one that more closely resembles the physical properties of our classical world.
For example Einstein told us that our physical environment is made up of four dimensional space-time however no one has ever observed the physicality of time or a space-time dimension.
Therefore it is extremely difficult to form a physical image of the quantum world or any other based on the existence of time or a space-time dimension because it is not part of our sensory environment.
Granted Einstein’s theories give us a detailed and very accurate description of how an interaction of time with the three *spatial* dimensions is responsible for the “reality” of the sensory world we inhabit and he was able to give us a clear physical image how a curvature in space-time can be responsible for gravity.
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For example the most common physical image use to explain gravity does not use time but instead extrapolates the image of an object moving on a curved two dimensional “surface” in a three dimensional environment to four dimensional space-time. However this image only contains reference only to the sensory reality of the spatial dimensions and not a time or space-time dimension.
Yet, the fact that most humans define our physical “reality” in terms of the spatial dimensions instead of a time or space-time dimension suggests that one may be able to form a physical image of how and why the quantum world is what it is by viewing our universe in terms of its spatial instead of its time properties.
Einstein gave us the ability to do this when he used the velocity of light to define the geometric properties of space-time because it allows one to convert a unit of time in his four dimensional space-time universe to a unit of a space identical to those of our three-dimensional space. Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.
In other words by mathematically defining the geometric properties of space-time in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry 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 gravity in terms of four *spatial* dimensions allows one to form an image of its causality in terms of the physical properties of the spatial dimension instead of the non-physical ones most of us associate with time or a space-time dimension.
As was mentioned earlier one of the advantage to redefining Einstein space-time concepts in terms of four *spatial* dimensions is that it not only allows one to understand gravitational energy in more direct terms but also allows on to form a physical image in terms of a classical environment for the unpredictability of the quantum world.
For example in the article “Why is energy/mass quantized?†Oct 4, 2007 it was shown one can derive the 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 therefore must be quantized.
Briefly it was 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 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 substance with a natural frequency) 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 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, treating the quantum mechanical properties of energy/mass in terms of a resonant system generated by a matter wave also allows one to form a physical image of its unpredictability by extrapolating the laws of our classical three-dimensional world 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 quantum mechanics associates Schrödinger’s wave equation with 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 it’s 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 allows one to form a physical image of the unpredictability of a quantum environment because it give us a Classical reason why we cannot precisely measure the both the momentum or position of a quantum object because the measurement of one effects the measurement of 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 â€Why is energy/mass quantized?†the change or uncertainty of one with respect to the other 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 Schrödinger’s wave equation in an environment consisting 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. In other words it tells us in terms of a physical image based on a classical environment the reason why God must play dice is because the physicality of a quantum environment prevents us from precisely determining the initial condition of a particle through observation.
Later Jeff
Copyright Jeffrey O’Callaghan 2014
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