Quantum mechanics states what the universe is made of while not giving an explanation of why it is that way while Relativity give us an explanation of why it is what it is but does not tell us what is it made of.   For example, in a quantum world matter is defined in terms of the wave-particle duality of existence while its interactions with that world are defined in terms of the uncertainty principal which states the momentum and position of a matter cannot both be precisely determined at the same time.  However, it does not give an explanation what existence is or how it interacts with its environment to create the universe we live in.  On the other hand, Relativity explains the existence of the universe in terms of an interaction between space and time without telling us what wave-particle duality of existence is or how it interacts with space and time to create the uncertainty principal.

This suggest one way to unify the quantum world with the universe of Relativity would be to explain how an interaction between space and time is responsible for the wave-particle duality of existence and why one must define its interactions with its environment in terms the uncertainty principal.

We can use the science of wave mechanics along with the fact Relatively tells us wave energy moves continuously through space-time unless it is prevented from moving thru time by someone or something interacting with it.  This would result in its energy being confined to three-dimensional space.  The science of wave mechanics also tells us the three-dimensional "walls" of this confinement will result in its energy being reflected back on itself thereby creating a resonant or standing wave in three-dimensional space.  This would cause the wave energy to be concentrated at the point in space were a particle would be found.  Additionally, wave mechanics also tells us the energy of a resonant system such as a standing wave can only take on the discrete or quantized values associated with its fundamental or a harmonic of its fundamental frequency.

In other words, this shows how one can use the concepts of Relativity and the established science of wave mechanics to validate the wave-particle duality of existence and why it is quantized in terms interaction of space with time as define by Relativity.

For example, it explains why when someone observes or it interacts with something that prevents it from moving through time the particle properties of the wave-particle duality existence become predominate.

Yet, as shows why if allowed to move freely thought space time its wave property will predominant because its energy will not become concentrated in in space-time.

This shows how one can explain in terms of an interaction between space and time the validity of quantum mechanics wave-particle duality of existence.

Next, we must try to explain how the interaction of wave-particle duality of existence in the quantum world interacts with space time to validate the uncertainty principal.

Relativity tell us the energy of the wave component of quantum existence, as was mentioned earlier would be distributed over a length of space-time that correspond to is wavelength.  However, to accurately determine the momentum of a particle one must be able to measure the time it takes for it to move a given distance through it.  Yet because, as was also mentioned earlier the particle component of quantum existence does not materialize until after it is observed one cannot determine the exactly where with respect to the background of space-time the particle was before the measurement was taken. Therefore, one can never know the exact the distance it had moved. Therefore, there will always be an uncertainty in the measurement of the momentum or a particle because the interaction of the wave-particle duality of existence with the properties of space time as defined by Einstein does not allow one to precisely measure the distance it traveled.

In other words, one can validate the uncertainty in determining momentum of a particle in the quantum world in terms of an interaction of space-time with the wave-particle-duality of existence.

However, to fully explain the uncertainty principal or why the more accurately we know either the momentum of the position of a particle, the less accurately we know the other in terms of an interaction between space and time one must examine how the energy of the wave-particle duality of existence interacts with space and time.

Einstein defined energy of a system in terms of a displacement or movement in the "surface" of a three-dimensional space manifold with respect to a time dimension and since energy can nether be created or destroyed the total energy of all systems and their displacements including those of the quantum world must remain constant. 

Earlier we derived uncertainty in determining the momentum of particle in terms of the time properties of the universe. However, the determination of position involves the spatial properties of the universe therefore it should be defined in those terms.

Einstein gave us the ability to do this when he defined the mathematical relationship between space and time in terms of the constant velocity of light because in doing so, he provided a method of converting a unit of time in a space-time environment to its equivalent unit of space in 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 only four *spatial* dimensions.

In other words, according to Einstein the universe is made up of four *spatial* dimensions and or four-dimension space-time.

This tells us the energy of a system can be determined in terms of a displacement or movement in the "surface" of a three-dimension space manifold with respect to either a fourth *spatial* or a time dimension and since energy can nether be created or destroyed the sum of those displacement must remain constant for all system.

However, as was mentioned earlier one cannot explain the position component particle in terms displacement in the "surface" of at three-dimensional space manifold with respect to the time dimension because it is does move through it. However, can one define the position of a particle in terms of a displacement in the "surface’ of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Since the energy of all systems is constant the magnitude of the sum of the displacements associated with the position in four *spatial* dimensional and the one generated by momentum in four-dimensional space-time along with sum of the uncertainties in those displacement must also remain constant. Therefore, the more accurately one measures the momentum of the wave-particle properties of existence the less accurately one can measure its position.

In other words, this this shows how the interaction of space with universe defined by Einstein can explain and validate the uncertainty principal or why the more accurately we know either the momentum of the position of a particle, the less accurately we know the other.

Copyright Jeffrey O’Callaghan 2010

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