Both Einstein’s General and Special Theories of Relativity define macroscopic properties of energy/mass in terms of the continuous properties of four dimensional space-time while quantum mechanics defines its microscopic properties in terms of the discontinuous properties of three-dimensional space.
However finding a way of conceptually integrating them has proven to be extremely difficult for two reasons
The first is that it is impossible to derive a mechanism to explain and predict the continuous properties of four dimensional space-time in terms of quantum mechanics because something that is discontinuous cannot by definition be continuous.
However one can derive the them in terms of the continuous properties of space-time because something that is continuous by definition can be divided into smaller units.
Yet the other reason why it is so difficult is because Quantum mechanics defines its domain in terms of the spatial properties of probabilities while Einstein theories define it in terms of the continuous geometric properties of time.
This suggest we may be able to integrate them if we could find a way defining them in the same terms. In other words redefining the space-time environment of Relativity in terms of the spatial properties of quantum mechanics or redefine the continuous properties of space-time in terms of the quantum properties of quantum mechanics.
However the only realistic option is to redefine the space-time environment of Relativity in terms of the spatial properties of quantum mechanics because as was mentioned earlier it is impossible to derive a mechanism to explain and predict the continuous properties of four dimensional space-time in terms of quantum mechanics because something that is discontinuous cannot by definition be continuous.
Fortunately Einstein gave us the ability to do this when he used he used the velocity of light to define its geometric properties of space time because it allows one to convert a unit of time in his space-time universe to an equivalent unit of space in four *spatial* dimensions. Additionally because the velocity of light is constant means 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 defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.
However as mentioned earlier doing so would also allow one to define a physical mechanism responsible for creating a quantum of space-time in terms of the existence of four *spatial* dimensions.
For example the article “Why is energy/mass quantized?” Oct. 4, 2007 showed it is possible to explain the quantum properties of energy/mass by extrapolating the laws of classical resonance in a three-dimensional environment to a matter wave on the 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 would be meet by a matter wave in four spatial dimensions.
The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a continuous “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.
The oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established in four *spatial* dimensions.
Classical mechanics tells us the energy of a resonant system can only take on the discrete or quantized values associated with its resonant or a harmonic of its resonant frequency
Therefore the discrete or quantized energy of resonant systems in a continuous four dimensional environment would be responsible for the discrete quantized energy quantum mechanics associated with energy/mass.
However, it does not explain the mechanism responsible for quantizing the space containing energy/mass
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 responsible for the quantization of four-dimensional space because it would result in the formation of discrete or quantized volumes associated with the observed quantum properties of energy/mass.
In other words defining space in terms of four *spatial* dimensions allows one to conceptually the integrate the discontinuous quantum mechanical properties of energy/mass into the continuous field properties four-dimensional space in terms of a resonant system created by its wave properties.
Physicists should remember it is impossible to derive a mechanism to explain and predict the continuous properties of four dimensional space-time in terms of quantum mechanics because something that is discontinuous cannot by definition be continuous. However one can understand as was shown above the quantum mechanical properties of space in terms of the continuous properties of space-time because something that is continuous by definition can be divided into smaller units.
Later Jeff
Copyright Jeffrey O’Callaghan 2013