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
There are many theories that attempt to explain what we observed in our three dimensional environment in terms of higher dimensions. However they all suffer from the same problem in that the existence of those higher dimensions are primarily based on abstract on mathematical models. The reason is because we as three dimensional beings are only able to observe objects in the three-dimensional environments we occupy. Therefore we must rely on mathematics to guide us in understanding how their existence influences what we observe in our world.
Many feel the most promising is called string theory, which attempts to define all of the observed properties of our universe in as many as ten dimensions.
However, as is pointed out on page 51 of Lee Smolin book "The Trouble with Physics" all attempts at unifying physics through extra dimensions suffer from the same problem. There are a few solutions that lead to the world we observe but there are many which do not. One has to set the initial conditions, which are found by observing our world to determine which solutions define what we observe. The use of this circular methodology means its validity is not based on its theoretical structure but on its flexibility.
In other words its validity is not based on connecting the observed properties of our environment to it but the randomly picking which the ones do the best job.
Einstein’s theories are very different in that they make specific predictions based on the existence of a single space-time environment that if found not to occur would invalidate it.
For example his theory tells us that light should bend as it passes by a massive object.
If this was not observed his theory would have to be discarded.
However 1919 Arthur Eddington lead an expedition to photograph the Total Eclipse of the Sun. The photographs revealed stars whose light had passed near sun had been bent exactly as Einstein had predicted. The experiment was repeated in 1922 with another eclipse with the same confirmation.
Additionally in past century since he proposed his theory there has not been any observations of our macroscopic universe that disagree with any of its predictions.
Even so this does not mean that we should assume that our universe is physically made up of four dimensional space-time because as with all multidimensional theories when Einstein derived the geometric properties of a space-time universe in terms of the constant velocity of light he also define another one with identical properties in terms of four *spatial* dimensions.
In other words by defining the geometric properties of space-time in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining its time related properties in terms of only four *spatial* dimensions.
As was mentioned earlier the fact that light bends as it passes by massive objects doers not mean our universe is made up of four dimensional space-time because the symmetry of equations used to make that prediction also predicts one made up of only four *spatial* dimensions will do the same.
Therefore the fact that light bends as it passes by a mass cannot be used to eliminate that possibility.
However there is a experiment very similar to the one Arthur Eddington preformed that would resolve this ambiguity.
Einstein’s Theory of General Relativity tells that objects that create gravitational field cause time to "move" slower. However due to the symmetry of his equations one could also say that time slowing down results in the formation of a gravitational field. Therefore one must assume that a gravitational field must always be attractive because observations indicate that time only moves in one direction forward.
However the fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the energy he associated with gravity in terms of four *spatial* dimensions is one bases for assuming as was done in the article “Defining energy?” Nov 27, 2007 that it 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 as well as one in a space-time dimension.
However unlike time which is observed to only move in one direction forward observations tell us that we can move in spatially in two directions up down backwards and forwards.
Therefore if the universe was made up of four *spatial* dimensions there should exist a form of mass that posses a negative gravitational potential.
One candidate for such a mass is antimatter. We know from observations that in it posses an opposite electrical charge than its matter counterpart. Therefore it is logical to assume that it posses a gravitational field that is oppositely directed from that of matter.
An experiment has be proposed that could determine if this is indeed true.
As describe in the New Scientist article "Antimatter mysteries 3: Does antimatter fall up?" Apr 29, 2009, it involves using uncharged particles to prevent electromagnetic forces from drowning out gravitational effects. It will first build highly unstable pairings of electrons and positrons, known as positronium, then excite them with lasers to prevent them annihilating too quickly. Clouds of antiprotons will rip these pairs apart, stealing their positrons to create neutral antihydrogen atoms.
Pulses of these anti-atoms shot horizontally through two grids of slits will create a fine pattern of impact and shadow on a detector screen. By measuring how the position of this pattern is displaced, the strength – and direction – of the gravitational force on antimatter can be measured.
In other words there is an experiment that could determine if our universe is physically composed of four dimensional space time or four *spatial* dimensions because as was mentioned earlier a universe physically composed of four dimensional space-time cannot support a negative gravitational potential while one made up of four spatial dimensions can.
Yet if found to be true it does not mean that Einstein’s theories are invalid because his theories and predictions were based on pure mathematics and as mentioned earlier a universe consisting of four dimensional space-time and four spatial dimensional are mathematically are equivalent in every respect.
However it would require us to rethink our understanding of the physical geometry of our universe and the causality of gravitational forces.
Copyright 2015 Jeffrey O’Callaghan