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1kWe have shown throughout this blog and its companion book “The Reality of the Fourth *Spatial* Dimension” there are many theoretical advantages to defining the universe in term of the existence four *spatial* dimensions instead of four dimensional space-time.
One of the fundamental difficulties in unifying Quantum Mechanics with Einstein’s General Theory of Relativity is that one is background independent while the other is not.
Einstein tells us the geometry of space evolves with time and the laws of nature have to be expressed in a form that does not assume that space has a fixed geometry. In other words, they are background independent.Â
However, present quantum theories can only be formulated in a fixed geometric background.Â
For example, Quantum Field Theory was unified with Maxwell’s theory of electromagnetism by assuming that electromagnetic energy does not interact with the background geometry of space. In other words, two photons or quanta of electromagnetic energy can move through or past a fixed point in space without interacting with each other.
However, two gravitons or quanta of gravitational energy will interact with each other as they pass a fixed point in space because as mentioned earlier Einstein tells us gravity alters the geometry of space-time.Â
This is why, as mentioned earlier one of the problems physicists encounter in defining quantum gravity is that present quantum mechanical models are background independent while Einstein tells us that gravity is not.
However, as mentioned earlier one can by assuming the existence of four *spatial* dimensions instead of four-dimensional space-time derive a background independent quantum theory.
Einstein gave us this ability when he used the velocity of light to define the geometric properties of time in a space-time environment because it allows one to convert a unit of time in it 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 universe made up of four *spatial* dimensions that makes predictions identical to those he had attributed to four dimensional space-time.
For example the article “Why is mass and energy quantized?” Oct 4, 2007 showed it is possible to explain and predict the quantum mechanical characteristics of energy/mass by extrapolating the laws classically resonance 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.
( Louis de Broglie in 1924 was the first to theorize all particles have a wave component.).
Briefly it was shown 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 a environment 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 in a continuous form of energy/mass.Â
These resonant systems in a continuous form of mass/energy are responsible for the quantum mechanical properties of energy/mass.
However classical wave mechanics tells us because as was shown above all quantum particles are made up of wave means that means that they can move through or past a fixed point in space without interacting with each other for the same reasons wave on the surface of water can..
In other words energy and the internal quantum mechanical structure or energy/mass is fix by the physical properties of four *spatial* dimensions and therefore would be background independent with respect to its geometry.
However, as was shown in the article “Unification of gravity and electromagnetism” May15 2008 gravity would be background dependent on its geometry because as was shown in the article “Gravity” the curvature or changing geometry of a a “surface” of three-dimensional space with respect to a fourth *spatial* dimension is dependent on its energy/mass content. Therefore two gravitons or quanta of gravitational energy will interact with each other as they pass a fixed point in space because of they share a property of that curvature.
In other words one of the fundamental difficulties in unifying Quantum Mechanics with Einstein’s General Theory of Relativity is NOT that one is background independent while the other is not but that we do not have a complete understanding of the mechanism involved in their execution.
Later Jeff
Copyright Jeffrey O’Callaghan 2010
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