We have shown throughout the this blog and its companion book “The Reality of the Fourth spatial dimension” there would be many theoretical advantages to assuming space is composed of four *spatial* dimensions instead of four dimensional space-time.
One of them is that it would allow for a logical explanation of the superposition principal associated with quantum mechanics based on extrapolating our experiences in a three-dimensional environment to a fourth *spatial* dimension.
Quantum mechanics assumes that one can only define the exact position or momentum of a particle in terms of the probabilistic values associated with its wave function. Therefore, according to it one cannot predict future events based on their history. This is in stark contrast to the classical assumption that one can assign precise values of future events based on the knowledge of their past.Â
For example in a quantum system Schrödinger wave equation plays the role of Newtonian laws in that it predicts the future probability distribution of a particles position or momentum by assuming that it simultaneously exists or is superpositioned everywhere in three-dimensional space. On the other hand classical physics derives the future based on the assumption that objects move through time in a unique trajectory based on the forces they experience.
Yet even though these two concepts appear to contradict each other one can as mentioned earlier define the “reality” of quantum superposition by extrapolating the laws of a three-dimension environment to one consisting of four *spatial* dimensions.
The superposition principal states that if a quantum system can be found in one of two state A and B with different properties it may also be found in aA and bB where “a” and “b” are any number. Each such combination is called a superposition and each is, according to quantum mechanics is physically different.Â
In the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown one can derive the quantum mechanical properties of energy/mass by extrapolating the laws of classical wave mechanics in a three-dimensional environment to a matter wave on a continuous “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 will 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 with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.
However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established space.
These resonant structures are responsible for dividing the continuous wave properties of energy/mass and four *spatial* dimensions into their quantum mechanical components.
(In the article “The geometry of quarks” Mar. 15, 2009Â 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 assuming the energy contained in quantum mechanical systems are a result a resonant structure formed by the continuous properties of a wave as was done above allows one to derive the fact that they simultaneously exists or are superpositioned everywhere in three-dimensional space
Earlier it was mentioned the energy/mass of a quantum system is made up of the resonant properties of a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. However, classic mechanics tell us that because of the continuous properties of a wave its energy would distributed throughout the entire volume of three-dimensional space.
In other words the sinusoidal displacements caused by the matter wave on a “surface” of a three-dimensional space manifold which the article Why is energy/mass quantized? showed was responsible for creating the resonant structures it associates with quantum mechanical systems would, similar to Schrödinger’s wave equation be disturbed throughout entire the universe.
This would be analogous to what happens when one vibrates a rod on a rubber diaphragm. The displacement caused by the vibrations would be felt over its entire surface while their magnitudes would be greatest at the point of contact and decrease as one moves away from it.
However, this means if one extrapolates the mechanics of the rubber diaphragm to a “surface” of a three-dimensional space manifold one must assume the displacements associated with each individual quantum system must simultaneously exists everywhere in three-dimensional space. This also means there would be a non-zero probability they could be found anywhere in our three-dimensional environment.
As mentioned earlier the article “Why is energy/mass quantized?†shown 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 the resonance associated with a quantum system 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, it also tells us the point in space associated with a quantum system would be superposed over of every other one because the displacement associated with each individual one is distributed throughout the universe.
Similarly Classical wave mechanics also tell us the distribution of the energy of multiple quantum systems, such as baseballs starts or planets would become more concentrated in a specific point in space as their numbers increased because the interference associated with their multiple wave identities would reduce the dispersion of their energy components.
This tells us the energy distribution of multiple quantum systems, such as baseballs starts or planets would distributed or superpositioned throughout the entire volume of three-dimensional space until someone observes the point in space the waves functions of its individual component reinforce to produce the greatest displacement. When that happens the object or particle will “materialize” or emerge in a specific region of space where that observation was made.
This shows how one can explain the” reality” of quantum superposition by extrapolating the laws of classical wave mechanics to four *spatial* dimensions.
Later Jeff
Copyright Jeffrey O’Callaghan 2011