Quantum Decoherence was proposed to justify the framework and intuition of classical physics as an acceptable approximation: it is the mechanism by which the classical limit emerges from a quantum starting point and determines the location of the quantum-classical boundary. Decoherence occurs when a system interacts with its environment in a thermodynamically irreversible way. This prevents different elements in the quantum superposition of the total system’s wavefunction from interfering with each other.
However one may eliminate the need for Decoherence by showing that one can explain how the quantum world emerges from a classical starting point by observing how matter and energy interact in a space-time environment.
But it will be easier if we first transpose or covert Einstein’s space-time universe to one consisting of only four *spatial* dimensions because it will enable us to define the mechanism responsible how this emergence takes place in terms of a geometry which is directly related the position or spatial properties associated with quantum probabilities instead of their non-positional or temporal components.
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 time he associated with energy to a unit of space associated with position. Additionally because the velocity of light is constant it allows for the defining of a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.
In other words the symmetry of the mathematics he use to define his space-time environment makes it possible to define the location of the quantum-classical boundary not only in terms of four dimensional space-time but also in four *spatial* dimensions thereby making it easier to understand how these two worlds interact.
For example 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 allows one, as was done in the article “Defining energy?” Nov 27, 2007 to derive all forms of energy including those associated with quantum systems in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
This will allow as was shown in the article “Why is energy/mass quantized?” Oct. 4, 2007 to understand of the 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 the wave properties of a quantum system 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 spatially 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 its 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.
Yet it also allows one to define the boundary 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 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?“
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 assuming energy is result of a displacement in four *spatial* dimension allows one to derive the most probable position of a particle in terms of its wave function by extrapolating the observations and classical laws associated with a three-dimensional environment to a fourth *spatial* dimension.
Classical mechanics tell us, due to the continuous properties of waves the 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 is correct then classical mechanics tell us 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 decrease as one moves away from it.
As mentioned earlier the article “Why is energy/mass quantized?” Oct. 4, 2007 showed a quantum mechanical system 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 if a particle as was shown earlier is a result of a resonant system formed in space it 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.
However this also defines how quantum probabilities can emerge from an classical interaction of energy/mass with the geometry of four *spatial* dimensions or four dimensional space-time while the same time eliminating the need for Quantum Decoherence because it shows that the different elements in the quantum superposition of a wavefunction are the result of the relative spatial orientation or position of an observer with respect to the its most probable position.
In other words it justifies the framework and intuition of the probabilistic interpretation of quantum mechanics as an acceptable approximation of a classical environment without Quantum Decohernece.
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 by making them applicable to both the spatial as well as the time properties of our universe thereby giving us a new perspective on the causality of the quantum mechanical interaction.
Copyright 2015 Jeffrey O’Callaghan
Understanding what time is and its causality is not easy in part because it is something that cannot be seen or touched. For example some define it only in the abstract saying that is an invention of the human consciousness that gives us a sense of order, a before and after so to speak. In other words most do not perceived time as matter or space but as an irreversible physical, chemical, and biological change in its physical properties.
However this is in direct conflict with how physicists define it in terms of the physical properties of a space-time dimension.
For example Einstein believed as the following quote demonstrates that time was a rigid physical component of a space-time environment defined by both his Special and General Theories of Relatively.
"Since there exists in this four dimensional structure [space-time] no longer any sections which represent "now" objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence."
In other words according to Einstein the structure of space-time is ridge while the changes we perceive are merely an illusion similar to the illusion of change created in a flip book when one rapidly flips through its pages containing series of pictures that vary gradually from one page to the next.
However if one considered blocks of space-time as the pages of the flip book responsible for the illusion of change as Einstein did one still must still define the causality of the change on each page of that book which cannot be related to time if it is a ridge component of a space-time environment.
As mentioned earlier the idea of defining time terms of the physical properties of a space-time dimension conflicts with the abstract properties most associate with change.
Yet one could resolve this conflict while defining why changes occurs in each segment of a space-time environment if one can show that change and therefore time is an emergent property of the physicality most of us including physicists associate with space. In other words if one can define the causality of change in terms of the physical properties of space then one could merge the abstract sense of order that our consciousness feels it has with its physical properties.
However to do this one must be able to understand the causes of change associated with time in terms of the perceive physical properties of space and then determine if one can integrate them into a theoretical model that is consistent with all of the other properties of that environment.
Einstein gave us the ability to do this when he defined the energy associated with change in space-time environment in terms of the equation E=mc^2 and the constant velocity of light because that provided a method of converting a unit time in that environment to its equivalent 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 the equation E=mc^2 allows us to quantitatively derive energy in a space-time environment in terms of four *spatial* dimensions is the bases for assuming as was done in the article “Defining energy” Nov 27, 2007 that all forms of change can be derived in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of one in a space-time manifold.
As mentioned earlier Einstein believed it is more natural to think of physical reality in terms of a four dimensional existence, instead of the evolution of a three-dimensional existence even though he did not define the causality of change in that environment.
However as was shown earlier the symmetry of his mathematics means that he not only defined that "reality" in terms of four dimensional space-time but also in four *spatial* dimensions.
This enables one to derive the causality of change most associate with time in terms of the physical properties of the spatial dimensions instead of its abstract ones.
For example one can observe how a displacement in the geometry of three-dimensional space cases change by watching water flowing over a dam.
Similarly if as was shown above one defines energy in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of four dimensional space-time as was done in the article “Defining energy” Nov 27, 2007 one can define the transfer of energy associated with change in terms of the "level’ each segment of three-dimensional of space has with respect to a fourth *spatial* dimension. In other words change can be defined as an emergent property of four *spatial* dimensions because as one moves though Einstein’s space-time environment each successive section of three-dimensional space would be at a different level with respect to a fourth *spatial* dimension.
Granted due to the symmetrical nature of the arguments presented here one could argue that space is an emergent property of time.
However it is more consistent with observations of our three dimensional environment to assume that the changes most associate with time have their causality in the geometry of space because as was mentioned earlier we can see how that geometry causes change whereas the same cannot be done with respect to time because of its abstract properties.
Copyright Jeffrey O’Callaghan 2015
Vol. 3 — 2012