6. Understanding the Uncertainty Principle in terms of the dynamics of space-time.
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Quantum mechanics states what the universe is made of while not giving an explanation of why it is that way in terms of the observable properties of our universe while Relativity gives us an explanation of why it is what it is but does not tell us what it is made of.
For example, the quantum world is defined by how the mathematical properties of the wave function interact with the wave-particle duality of existence. However, it also tells us that one can NOT precisely determined both the momentum and position of a particle at the same time. But does NOT provide an explanation for why this uncertainty exists in terms of the OBSERVABLE properties of our universe. On the other hand, Relativity explains the existence of the universe and the particles it contains in terms of an interaction between space and time without telling us what wave-particle duality of existence is or how it interacts with it to create the Uncertainty Principal as defined by quantum mechanics in terms of observations.
Therefore, to understand its dynamics in terms of space-time we must first establish a physical connection between the mathematical evolution of the wave function and the observable properties of space-time.
One can accomplish this by using the fact that in Relativity the evolution of space-time is defined in terms of an electromagnetic wave while, as was mentioned earlier the mathematical properties of the wave function defines how a quantum environment evolves to the point where it is observed.
This commonality suggests the wave function could be a mathematical representation of an electromagnetic wave in space-time.
This means one MAY repeat MAY be able to explain the wave particle duality existence associated with the wavefunction in terms of interaction between space and time. This is because the science of wave mechanics and Relativity tell us an electromagnetic wave would move continuously through space-time unless it is prevented from doing so by someone or something interacting with it. This would result in it 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 energy of an electromagnetic wave 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 that the wave function associates with a particle.
Putting it another OBSERVATION OF A RELAITISIC ENVIROMENT tell us when an electromagnetic wave that was earlier associated with the wave function is prevented from moving through space-time either by being observed or encountering an object it is reduced or “Collapses” to a form a standing wave that would define the quantized energy quantum mechanics associates with a particle.
(The boundaries or “walls” of its confinement would be defined by its wave properties. If an electromagnetic wave is prevented from moving through space-time it will be reflected back on itself. However, that reflected wave still cannot move through it therefore it will be reflected back creating a standing wave. Therefore, the wave itself defines its boundaries.
This shows how based on observation of a relativistic environment if an electromagnetic is prevented from evolving through space by an observation or encountering an object its wave properties collapse or is “reduced” and presents itself as a particle.)
Yet, this is also consistent with the observations of quantum environment in that the mathematical properties associated with the wave function will continue to evolve similar to how electromagnetic wave continues to evolve through a space-time universe and that it only “collapses” to a particle when it is observed or encounters an object.
Putting it another way it shows how one can explain and predict the evolution of a quantum environment BASED ON OBSERVATIONS of a relativistic one.
Next, we must explain how the energy or information “volume” of a system is responsible for both the uncertainty involved in measurement of the CONJUGATE PAIRS such as the momentum and position of an object or particle in both a relativistic and quantum environment.
Relativity and the science of wave mechanics tell us the energy of the standing wave which earlier defined a particle would be distributed over a volume of space-time that corresponds to is wavelength.
However, to measure the CONJUGATE PAIRS OF A SYSTEM INCLUDING THE MOMENTUM OR POSITION in both quantum and relativistic environment one must determine where relative to the information or energy volume of system the measurements are being taken. Therefore, there will ALWAYS repeat ALWAYS be an uncertainty if one cannot determine where those points are with respect to a systems information or energy volume.
The fact that both of these theories assume that energy or information of a system can nether be created or destroy provides the basis for the connecting the uncertainty principal to the space-time environment of Relativity.
THIS IS BECAUSE IT MEANS THE MEASUREMENT OF ANYONE ONE OF THE CONJUGATE PAIRS OF A SYSTEM INCLUDING THE MOMENTUM OR POSITION WILL AFFECT THE OTHER.
As was mentioned earlier quantum mechanics defines both the momentum and position of particle with respect to a one-dimensional point in the mathematical field of the wave function. However, the accuracy of the information as to where that point is in relation to its information volume is directly related to how much of it is taken from the system. This means the more accurate the measurement the more information regarding it must be removed from the system and the less is available to measure the other component of its Conjugate pair.
For example, as was mentioned earlier because the information “volume” of a system remains constant the more of it taken out regarding its momentum means there will be less to define its position. This makes the determination of its position more uncertain because there is less information left in its information “volume” to define it. While the more information taken out of it regarding its position will result in there being less to define its momentum. This makes this determination of its momentum more uncertain because less information left in that in its information volume to define it. This would be true for all Conjugate pairs.
However, the same would be true when measuring either the momentum or position of a particle in a relativistic system because as was mentioned earlier its energy is also conserved. Therefore because, the accuracy of a measurement is directly related to the amount to energy is available to define a system; the measurement of each component of momentum or position of a system will affect the other. For example, the added energy required to make a more accurate measurement of a systems momentum will result in there being less to define its position. This makes the determination of its position more uncertain because there is less energy in that system to define it. While the more additional energy required to make a more accurate measurement of its position will result in there being less to define its momentum. This makes this determination of its momentum more uncertain because less energy left in the system to define it.
This shows how one can the explain the existence of the Uncertainty Principle and understand why it must be used in a quantum environment in terms of the dynamics of space-time.