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1kEinstein’s Explanation of the Unexplainable
The cosmological constant problem or vacuum catastrophe is the disagreement between the observed value of the vacuum energy density or the small value of the cosmological constant and the theoretical large value of zero-point energy suggested by quantum field theory.
Depending on the Planck energy cutoff and other factors, the discrepancy is as high as 120 orders of magnitude.
In quantum physics, the vacuum or zero-point energy is the amount of energy in a point “volume” of space as prescribed by Werner Heisenberg’s uncertainty principal. Its existence is derived from that principle which tells us the mathematical point in space quantum mechanics uses to define particles have an inherent fuzziness. Therefore, it is assumed that it oscillates or fluctuate around that point.
One reason for the cosmological constant problem MAY be because Quantum Mechanics states that all fields, such as the electromagnetic one, must be quantized at each and every point in space. It also assumes the evolution of the oscillations associated with the uncertainty principle are defined by wavefunction. Therefore, according to theory, even a pure vacuum has a VERY, VERY, VERY large number of point oscillators each contributing to its energy.
However, this would be true if and ONLY if all fields including an electromagnetic one is quantized at each and every point in space.
BUT THIS MAY NOT BE THE CASE.
For example, Johannes Kepler was able mathematically define the laws of planetary motion in terms of a HYPOTHETICAL point called the center of gravity which defines the evolution of their orbits. This is because in physics, the center of mass is the unique point where the energy of the distributed mass sums to zero.
However, we know a planet has a volume bigger than the unique point which defines its center of gravity,
Similarly, the point in space that quantum mechanics uses to define the evolution of quantum system may ONLY be a hypothetical one which defines the UNIQUE point where its energy distribution of that system sums to zero
This conclusion is supported by the fact the fact particles such as an electron can be diffracted because it is impossible to explain that if was a mathematical point that has no volume. Another observation is that particles are observed to collide in particle accelerators. This could not happen if they had no volume.
However, to understand zero-point energy and why the cosmological constant predicted by quantum mechanics is so high in terms of dynamics of space-time we must first establish a connection between evolution of the wave function which defines a quantum environment and the properties of the space-time. This can be accomplished because in Relativity its evolution is defined in terms of an electromagnetic wave while, as was just mentioned 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.
One can connect them because the science of wave mechanics and Relativity tells us an electromagnetic wave would move continuously through space-time unless it is prevented from moving through time 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” confining the movement of both an electromagnetic wave and point defined by the wavefunction will result in it being reflected back on itself thereby resulting in the creation of a resonant or standing wave in three-dimensional space. Additionally, it tells us its energy can only take on the discrete or quantized values associated with its fundamental or a harmonic of its fundamental frequency of that standing wave while at the same time. Additionally, it tells us the particle defined by the wave function would have an extended volume equal to the wavelength of its standing wave.
Putting it another way if an electromagnetic wave or the wave function is prevented from moving through space either by being observed or encountering an object it will be reduced or “Collapse” to a form a standing wave that would define the quantized energy quantum mechanics associates with a particle.
However, as was mentioned earlier the fact that a particle has an EXTENDED volume suggests the point the wave function uses to defines its evolution MAY ONLY be a hypothetical one which defines where its energy distribution sums to zero similar to how the point called the center of gravity can be used to define the evolution of a planets position.
As was mentioned earlier the discrepancy between the vacuum energy predicted by quantum mechanics and its observed value may be due to the fact that it applies the uncertainty principal to each and every mathematical point in space.
Therefore, to understand why this discrepancy occurs one must show how and why that would NOT define the vacuum energy in quantum system.
As was just shown Relativity and the science of wave mechanics tell us the energy of the standing wave would be distributed over a volume of space-time that corresponds to is wavelength. However, as was also shown earlier the mathematical point quantum mechanics uses to define a particle position MAY only represent where energy of distribution of this standing wave sums to zero.
This means to accurately determine the vacuum energy in a quantum system one must FIRST define why one should NOT repeat NOT apply the uncertainty to the mathematical point defined by the wave function BUT TO energy “volume” of a particle.
The fact that both of these theories assume that energy or information volume of a system can nether be created or destroy provides the basis for the connecting the uncertainty principal to the dynamics of a space-time environment and the cosmological constant.
THIS IS BECAUSE IT DEFINES THE UNCERTAINTY PRINCIPAL AND WHY THE MEASUREMENT OF ANY ONE OF THE PROPERTIES OF THAT VOLUME INCLUDING THE MOMENTUM OR POSITION WILL AFFECT THE OTHER.
As was mentioned before quantum mechanics defines both momentum and position 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 the center of 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 its other component.
For example, as was mentioned earlier because the information volume of a system remains constant the more of it is 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 volume to define its position. 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 volume to define it.
However, the same would be true when measuring either the momentum or position of a particle in a relativistic system because its energy is also conserved. Therefore because, the accuracy of a measurement is directly related to the amount to energy taken out of a system; the measurement of each component of a momentum or position 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.
As was mentioned earlier quantum mechanics define the cosmological constant in terms of the summation of amount of energy in a point “volume” of space has as prescribed by Werner Heisenberg’s uncertainty principal
However as was also mentioned earlier the point in space that quantum mechanics uses to define a system may ONLY be a hypothetical one used to define its evolution similar to how the center or gravity is used to define the evolution of objects in orbit.
This suggest, to define the vacuum energy of a quantum system and the Cosmological Constant one would have to derive it NOT by applying Heisenberg’s uncertainty principal to all mathematical points in space but to the extended volume of space that point represents.
THERE ARE SEVERAL EXPERIMENTAL WAYS OF VERIFYING THIS CONCLUSION.
For example, we can determine the cross section and therefore the volume of a particle by the frequency of their collisions in particle accelerators. Then using that volume determine how many oscillators occupy a given volume and apply the uncertainty principal to them instead of every mathematical point to calculate the how much vacuum energy they would create. Then compare that value with the observed one.
Hopefully this may greatly reduce or eliminate the disagreement between the observed value of vacuum energy density and the one suggested by quantum field theory because it would reduce the number of oscillators in a given volume of space.
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