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1kWe have shown throughout this blog and its companion book “The Reality of the Fourth *Spatial* Dimension” there would be several theoretical advantages to defining the universe in terms of the existence of four *spatial* dimensions instead of four-dimensional space-time.
One of them is that it would allow physicists to derive a physical link between gravity and quantum mechanics in terms of the classical laws of physics.
Einstein defined gravity in terms of a curvature in a space-time manifold while quantum mechanics defines a particles position in space in terms of the probability function associated with Schrödinger’s wave equation.
This suggests the problem of linking gravity with the quantum properties of energy/mass is due to the fact that they are not defined in terms of a common unit. In other words instead of comparing the spatial properties of quantum probabilities to the time properties of gravity we may have more success if we could define them both in terms of a common parameter
Einstein gave us the ability to do this when he used the velocity of light and the equation E=mc^2 to define geometric properties of space-time because it allows one to convert a unit of time in his four dimensional space-time universe to a unit of space in a one consisting of only four *spatial* dimensions.  Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of 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.
In other words it would allow one to define both gravity and the quantum mechanical properties of energy/mass in terms of a common property related to their spatial components.
For example it provides the bases for assuming, as was done in the article “Defining energy?†Nov 27, 2007 that all forms of energy including that associated with gravity and the quantized energy associated with Schrödinger’s wave equation in terms of a spatial displacement in a “surface†of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
For instance as the article “Why is energy/mass quantized?” Oct, 4 2007 showed one could derive the quantum mechanical properties of energy/mass by extrapolating the laws governing resonance in a classical 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 was the first to predict the existence of a matter wave or the physical equivalent to Schrödinger’s wave equation when he theorized that all particles have a wave component. His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer).
Briefly it showed the four conditions required for resonance to occur in a classical Newtonian 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 a four-dimensional environment.
The existence of four *spatial* dimensions would give a “surface” between a third and fourth *spatial* dimensions the ability to oscillate spatially with respect to a fourth *spatial* dimension 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 these oscillations in four spatial dimensions would generate a classically resonating system or “structure” in it because it meets the requirements listed earlier for the creation of one. These resonant structures are responsible for the quantum mechanical properties of energy/mass.
This could not occur in a in a universe consisting of four dimensional space time because time or a space time dimension is only observed to move in one direction forward and therefore could not support the bidirectional movement required to establish classical resonance.
The reason we observe a particle as a point mass instead of an extended object is because, as mentioned earlier the article “Why is energy/mass quantized?†showed its energy/mass must be packaged in terms of a resonant system. Therefore, when we observe or “drain†the energy continued in its wave function, whether it be related to its position or momentum it will appear to come from a specific point in space similar how the energy of water flowing down a sink drain appears to be coming from a “point†source with respect the extended volume of water in the sink.
However, this allows one to form a Classical image why we cannot precisely measure the both the momentum or position of a quantum object associated with Schrödinger’s wave equation. Â
For example, if one wants to measure the position of a particle to within a certain predefined distance “m†its wave energy or momentum will have to pass through that opening. However, Classical Wave Mechanics tells us that as we reduce the error in our measurement by decreasing that predefine distance interference will cause its energy or momentum to be smeared our over a wider area. Similarly, to measure its momentum one must observe a portion the wavelength associated with its momentum. However, Classical wave mechanics tell us we must observe a larger portion of its wavelength to increase the accuracy of the measurement of its energy or momentum. But this means that the accuracy of its position will be reduced because the boundaries determining its position within the measurement field are greater.
However, because of the dynamic interaction between the position and moment component of the matter wave responsible for generating the resonant system associated with a particle defined in the article a â€Why is energy/mass quantized?†the change or uncertainty of one with respect to the other would be defined by the product of those factors.
Therefore, Classical wave mechanics, when extrapolated to Schrödinger’s wave equation in an environment consisting a fourth *spatial* dimension tells us the more precisely the momentum of a particle is known, the less precisely its position can be known while the more precisely its position is known, the less precisely its momentum can be determined. In other words it tells us in terms of a physical image based on a classical environment the reason why we must use probabilities to define a quantum environment is because its physicality prevents us from precisely determining the initial condition of a particle through observation.
This shows one can derive the properties all of the quantum mechanical properties of energy/mass in terms of the continuous properties of four *spatial* dimensions by extrapolating the physicality of three dimensional space to a fourth *spatial* dimension.
However this allows one to define a physical link between gravity and quantum mechanics in terms of the existence of four *spatial* because as was shown earlier there is a one to one correspondence between Einstein’s General Theory of Relativity which define gravity in terms of a universe consisting four dimensional space-time and one consisting of four *spatial* dimensions.
Later Jeff
Copyright 2009 Jeffrey O’Callaghan
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