Einstein’s Explanation of the Unexplainable
Quantum mechanics assumes the mathematical evolution of the wavefunction is responsible for quantization of ALL mass and energy. Additionally, it assumes it exists in a superposition of several eigenstates and only reduces or collapses to a particle ONLY repeat ONLY when it interacts with its environment or an observer.
Therefore, many feel detecting gravitons, the hypothetical quanta of gravity, would prove gravity is quantized. The problem is that gravity is extraordinarily weak and for that reason, detecting them is extremely difficult.
However, Einstein in his General Theory of relativity defined gravity in terms of the energy density of space. Therefore, one way of defining quantum gravity would be to show how and why it is quantized in terms in terms of his theory in a manner that is consistent with the mathematical foundations of Quantum mechanics.
The fact gravitational waves have been observed suggests it has properties similar to other energy waves, such as electromagnetic with one very important difference: they do NOT interact with it environment or an observer in the same way. This suggests the reason a graviton is so hard to detect while the photon or quantum electromagnetic energy is MAY NOT be related to its weakness but to how it interacts with its environment.
But before we can understand why we need to establish a connection between the evolution of the wavefunction, its collapse and electromagnetic waves. This can be accomplished because in Relativity evolution of a space-time environment is defined by an electromagnetic wave while, as was mentioned earlier the mathematics of the wave function defines how a Quantum environment evolves to create a particle.
This commonality suggests the wave function MAY BE a mathematical representation of an electromagnetic wave in space-time. However, if this is true one should be able to derive the reason for its collapse in a manner that is consistent with the mathematical foundations of Quantum mechanics.
This can be done by using the science of wave mechanics and the fact that Relativity tells us an electromagnetic wave moves continuously through space-time unless it is prevented from moving through space 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 its energy to COLLAPSE or 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.
(The boundaries or “walls” of its confinement would be defined by its wave properties. If an electromagnetic wave is prevented from moving through space it will be reflected back on itself. However, that reflected wave still cannot move through space therefore, it will be reflected back creating a resonate standing wave.)
In other words, if an electromagnetic wave 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 create a QUANTIZED repeat QUANTIZED increase the energy density of the space it occupies.
However gravitational waves do not interact or exchange energy with their environment in the same way as an electromagnetic one therefore their energy will not be confined to three-dimensional space and quantized as is the case with electromagnetic waves.
For example, gravity waves have only been observed when they squeeze and stretch space. However, that observation does not result in an exchange of energy between it and the observer.
However, quantum mechanics assumes the wave function reduces to a quantized unit of energy ONLY repeat ONLY when it is observed or interacts with its environment.
This suggests the reason why a graviton is so hard to detect MAY NOT be because it is weak but MAY be related to how we are trying to observe it.
This is because gravity waves, as was just mentioned do NOT interact with either the environment they are moving through or the equipment used to observe it. Therefore, according the rules of quantum mechanics the wave function SHOULD NOT and WILL NOT collapse to create a graviton unless we can find a way to get it to interact with its environment.
Putting it another way Quantum mechanics tells us just watching it pass by will not produce a graviton.