Many believe the ability of a particle to penetrate through a potential energy barrier that is higher in energy than its kinetic energy can only be explain by assuming it is a quantum mechanical phenomenon.
But before begin we must first establish a physical connection between the mathematical evolution of the wave function and the properties of an electromagnetic wave in space-time. This can be accomplished because in Relativity the evolution of space-time is defined in terms of an electromagnetic wave while, 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 relatively tells us an electromagnetic wave moves 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” 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.
As was mentioned earlier the mathematical properties of the wave functions defines the evolution of a quantum system in terms of its wave particle duality. However, as was shown above one can understand why if one assumes that it represents an electromagnetic wave in a space-time because if it is prevented from evolving through space by an observation it presents itself as a particle.
As was also mentioned earlier many believe the ability of a particle to penetrate through a potential energy barrier that is higher in energy than the its kinetic energy can only be explain by assuming it is a quantum mechanical phenomenon.
However, one can use the science of wave mechanics to show that MAY NOT be true.
It and observations of waves tell us when the crests of two waves collide will produce a wave with more energy. This means if crests of the standing wave responsible for a particle mentioned above collide, they will produce a wave which MAY have enough kinetic energy to go over a potential energy barrier that is higher than that associated with the original wave.
One could validate this conclusion in terms of the physical connection mentioned above between the mathematical evolution of the wave function and the properties of an electromagnetic wave in space-time. Because if it is true one should be able to use it to define PROBABILITY of where and when the crests of the two waves associated with wave function would most likely interact to produce one with enough energy overcome the kinetic energy barrier. If that probability agrees with the observed number that passes through the barrier it would support that assumption.
This question is especially relevant for the scientists who struggle on daily basis to help us understand the “inner” reality of our universe.
Some define it based on a quantitative mathematical analysis of observations.
For example, Quantum mechanics defines the “reality” or the state of a quantum system in terms of the mathematical probability of finding it in a particular configuration when a measurement is made. However, defining reality in terms of probabilities means that each probabilistic outcome of an event becomes a reality in the future. This is why some proponents of quantum mechanics assume the universe splits into multiple realities with every measurement.
This also may be why Niels Bohr, the father of Quantum Mechanics said that
“If quantum mechanics hasn’t profoundly shocked you, you haven’t understood it yet.”
However, others define reality in terms of deterministic proprieties of cause and effect.
For example, Isaac Newton derived the laws of gravity by developing a causal relationship between the movement of planets and the distance between them. He then derived a mathematical equation, defining a reality which could predict their future movements based on observations of their earlier movements.
Both the wave function of quantum mechanics and Newton’s gravitational laws are valid definitions of reality because they allow scientists to predict future events with considerable accuracy.
However, this does not mean that they accurately define the environment responsibility for those realities.
For example, at the time of their discovery Newton’s gravitational laws allowed scientists to make extremely accurate predictions of planetary movements based on their previous movements, but they did not explain why those those laws exist.
However, Einstein, in his General Theory of Relativity, showed there was room for an “alternative reality” that could explain them in terms of a distortion in space-time. However, it did not alter or change the validity of Newton’s gravitational laws when the velocities were small with respect to the speed of light, they are still valid.
This shows, just as there was room for an alternative “reality” which could explain Newton’s laws there could be one that defines the predictive powers of quantum probabilities that would not affect the validity of those predictions. This is true even though many physicists feel there is no room for alternatives because modern experiments, combined with quantum theory’s mathematics give us the most accurate predictions of events that have ever been achieved.
As mentioned earlier quantum mechanics defines reality in terms of probabilities, which means each probabilistic outcome becomes a reality in the future. However, it also means one must assume separate realities are created for the possible outcomes of every event.
However, this would not be true if those probabilities can be derived in terms of an interaction between a quantum system and the physical properties of the universe.
For example, when we role dice in a casino most do not think there are six of them out there waiting for the dice to tell us which one we will occupy after the roll. This is because the probability of getting a six is related to or caused by its physical interaction with the properties of the table in the casino where it is rolled. In other words, what defines the reality getting a six is not the probability of getting one but physical properties of how the dice interacts with casino it occupies. Putting it another way. the probabilities associated with a roll of the dice does not define the casino, the casino defines those probabilities.
As was mentioned earlier many proponents of quantum mechanics assume the universe splits into multiple realities because it describes the interactions of a quantum system with the universe in terms of probabilities, rather than definite outcomes. This means there must a separated universe for all possible outcomes of an event.
However, even though the reality that appears when a dice is rolled in a casino can be determined in terms of a probably does not mean all possibilities appear in their own separate casino. This is because as was mentioned earlier the probabilities involved in the roll of dice does not define the reality of the casino but that the casino defines those probabilities. In other words, the fact that casino define the probability of the role of dice tells us that it will have definite outcome in the casino
Similarly, just because quantum mechanics describes the interactions of a quantum system in terms of probabilities, we should not assume they define the reality of the universe because it is possible the universe defines those probabilities.
This also shows how one defines reality depends on if all you care about is that a six appears on the roll of dice or if you want know why you rolled it.
Copyright Jeffrey O’Callaghan 2021
Recently it has been suggested a force called Dark Energy is needed to account for the observations suggesting the universe’s expansion is accelerating. However, there is another reason which is related to effect gravity has on time.
Einstein told us and it has been observed the rate at which time passes is perceived to be slower in all environments where the gravitational potential is greater with respect where it is being observed. This means the further we look back in time, where the gravitational potential of the universe’s was greater due to the more densely pack matter, the estimate of its rate of expansion would be slower than it actually was if that were not taken into consideration.
However, we also know the gravitational potential has a slowing effect on the universe’s expansion and because that potential decreases as its volume increase, the rate of that slowing also decreases.
This means the rate of its expansion would be faster than it appeared to be from the perspective of present due to the effects gravity has on time while its actual rate of slowing would be declining due to its decreasing gravitational potential as it expands.
Yet, because of the non-linear effects between the slowing of time created by universe’s differential gravitational potential and the effects it has on its rate of expansion there will be a point in its history where one will APPEAR to overtake the other.
IN OTHER WORDS, IT IS POSSIBLE THE OBSERVATIONS SUGGESTING ITS EXPANSION IS ACCELERATING MAY BE THE RESULT OF THE EFFECTS ITS GRAVITATIONAL POTENTIAL HAS ON TIME WHICH WOULD CAUSES IT TO APPEAR MOVE SLOWER IN THE PAST THAN IT ACTUALLY DID.
One could verify this conclusion by using the observation that about 4 billion years ago the universe’s expansion appears to have change from decelerating to an accelerated phase. This is because one could derive its actual rate of expansion in the past by using Einstein equations to determine how much time would have been slowed due to the differential gravitational potential between the past and present. If it was found that about 4 billion years ago that actual rate of expansion was faster than it is now it would suggest that the its expansion is NOT accelerating
Some may say the slowing of time slowing would not affect its expansion because it is expanding along with the entire universe. However, Einstein define the time dilation only in terms of the affects a differential gravitational potential has on it therefore it would not be affected by its expansion. Some have also suggested that because it is expanding the gravitational potential is expanding and weakening at the same rate therefore when we look back the effects it will have on the timing of its expansion will cancel. However, Einstein tells us the timing of events that cause the universe to expand is locked in the past along with its gravitational potential at the time the expansion took place. Therefore, one must take into account the differential gravitational potential between the past and present universe when defining its expansion.
Some have also suggested Relativistic properties gravity has on time already been already been accounted in the Friedman model that was used in part by scientist to define the accelerated expansion of the universe. However, that is NOT the case because when someone in the past measures its rate of expansion he or she would NOT need to use the slowing effects gravity has on time because his entire spatial slice of the universe would be at the same gravitational potential. However, this would NOT be the case for someone looking at it from the future. He would have to use it because due to its expansion a differential gravitational potential would have developed between the past and present. Yet as was mentioned earlier the effects gravity has on time tell us from the perspective of the present its expansion rate would be moving slower than it actually was from the perspective of someone who is present at the time when that expansion was taking place. In other words, since Friedman’s equation does not consider the effects the differential gravitational density has on time it would predict it to be slower in the past than it actually was.
Copyright Jeffrey O’Callaghan 2021
Mass is both a property of a physical body and a measure of its resistance to acceleration (a change in its state of motion) when a net force is applied.
Physicists who are proponents of the Standard Model realized in order for it to agree with observations it was necessary to imagine a new field called the Higgs which must exist everywhere in the universe to explain what mass is and its resistance to acceleration. However, shoring up existing theories by inventing new theoretical components to the universe is dangerous, and in the past led physicists to hypothesize a universal aether but the more math they did, the more they realized that the Higgs field simply had to be real. The only problem? By the very way they’d defined it, the Higgs field would be virtually impossible to observe.
However, if they had spent the time to analyze the conceptual foundations of Einstein, they would have realized that he had already explained mass and its resistance to motion in terms of his math and observations.
He was able to explained the physicality of mass in terms of an increase in the energy density of space while defining its resistance to a change in motion terms of it occupying a “flat” region in space-time. This is because he showed us the increase in the energy density caused by mass results in the “surface” of space-time to be curved. Therefore, one can assume a mass moving at a constant velocity MUST be moving through “flat” region of it whose energy level is constant because if it was not, it would be accelerated.
Yet this also allows one to define relative motion in terms of the different energy levels they occupy in space-time. For example, Einstein’s equation E=mc^2 that defines the equivalence
between mass and energy tells us the magnitude of them would be directly related to mass. In other words, a large mass that is not in relative motion with respect to smaller one would occupy a higher energy level.
However, if they were in relative motion one would have to add the energy associated with its motion to determine their relative energy levels. Putting it another, way the difference between the energy levels of two objects in motion would not only be related to their mass but also to their relative velocities. Therefore, according to Einstein relative motion occurs when the difference between their energy levels in space-time exceeds what is associated with their masses. Additionally, it tells us to change motion of mass one must also change its energy level.
(The reason all motion is relative is because as was just shown Einstein defined it only in terms of the difference in the energy level between masses in space-time.)
This conclusion is supported by the fact that Einstein derived the force of gravity in terms of a change in the energy levels occupied by a mass as it moves along a curvature in the “surface” of space-time.
This provides an explanation of the resistance, force, or energy required to change the motion of a mass that is consistent with Einstein definition of gravity because as was mentioned earlier the change in motion or acceleration of objects in a gravitational field is a result of them moving through different energy level in space-time. This suggests the resistance or force required to overcome the resistance or a change in motion of a mass is a result of the energy required to change the energy level it is occupying in space time.
This means that one may not have to as some have suggested “invent new theoretical components” to define mass and its resistance a change in its state of motion because as was shown above Einstein equation E=mc^2 defines its physicality in terms of the energy density of space-time while he showed that one can derive its resistance to a change in motion in terms of the force required to change the energy level it occupies in space-time.
Copyright Jeffrey O’Callaghan 2021
Entanglement provides a VERY SIMPLE experimental way of determining if Quantum mechanics or Einstein’s Relativistic theories define why our universe is what it is.
This is because it is one of the central principles of quantum physics. In short it assumes two particles or molecules share on a quantum level one or more properties such as spin, polarization, or momentum. This connection persists even if you move one of the entangled objects far away from the other. Therefore, when an observer interacts with one the other is instantly affected.
However, it contradicts the central core Einstein’s theory of Relativity which states that no information can be transmitted instantaneously or faster than the speed of light.
Since these two concepts are diametrically opposite, if one can define the mechanism responsible for entanglement in terms of either one it would invalidate the other will help us to understand why our universe is what it is.
This is because there is irrefutable experimental evidence the act of measuring the state of one of a pair of photons instantaneously affect the other even though they are physically separated from each other.
As was mentioned earlier quantum physics, assumes ALL entangled particles, not only photons remain connected so that actions performed on one immediately affect the other, even when separated by great distances.
While Einstein tells us that instantaneous or faster than light communication between to particles is impossible. However, he also told us the distance between two objects or points in space is defined by their relative motion and that there is no preferred reference frame by which one can define that distance.
Therefore, he tells the distance between the observational points in a laboratory, can also be defined from the perspective of the photons moving at the speed of light.
Yet, his formula for length contraction (shown below) tells us the separation between those observational points from the perspective of two photons moving at the speed of light would be ZERO no matter how far apart they might be from the perspective of an observer in that laboratory. This is because, as was just mentioned according to the concepts of Relativity one can view the photons as being stationary and the observers as moving at the velocity of light.
Therefore, according to Einstein’s theory all photons which are traveling at the speed of light are entangled no matter how far they may appear to be someone who is looking at them. Additionally, it also tells us information exchange between two entangle photons does not travel faster than the speed of light because from their perspective the distance between the observation points where information was read is zero.
In other words, entanglement of photons can be explained and predicted terms of the relativistic properties of space-time as defined by Einstein as well as by quantum mechanics.
HOWEVER, AS WAS MENTIONED EARLIER ONE OF THE CORE PRINCIPALS OF QUANTUM MECHANICS IS THAT ALL PARTICLES SHARE ON A QUANTUM LEVEL ONE OR MORE PROPERTIES SUCH AS SPIN POLARIZATION OR MOMENTUM.
This gives us a way of experimentally determining which of these two theories define why entanglement occurs because if it is found that some particles that are NOT moving at the speed of light experience entanglement it would validate one of the core principals of quantum mechanics and invalidate Relativities assumption that information cannot be exchange instantaneously or faster that the speed of light.
However, one MUST ALSO use another core principle of quantum mechanics defined by De Broglie that particle are made up wave with a wavelength defined by ? = h/p to determine if it or Einstein’s theories define how the universe works. This is because it tells us all material particles have an extended volume equal to there wavelength
Yet because ALL particles have an extended volume equal to their wavelength there will be an overlap or entanglement if the distance separating them is less than their volume as defined by De Broglie.
This tells us some particles moving slower than the speed of light CAN BE entangled if the relativistic distance between the observation points from the perspective of the particles is less than their extended volume is because from their perspective they are in physical contact.
This means that both relativity and quantum mechanics tell us that all particles CAN be entangled if the distance between the end points of the measurements of their shared properties is less than their wavelength or volume as defined by De Broglie.
However, this gives us a way to DEFINITIVELY determine which one of these theories defines the reason for entanglement because we can precisely define the wavelength and therefore the volume of a particle by, as mentioned earlier using De Broglie formula ? = h/p while one can determine the relative distance between the observation points from the perspective of the particles being observed by using Einstein formula for length contraction. If it is found entanglement DOES NOT occur if that distance is greater than a particles volume then it would invalidate the core principles of quantum mechanics that two particles or molecules share on a quantum level one or more properties such as spin, polarization, or momentum no matter how far they are separated. However, if it is found that entanglement does occur even if the separation was greater than their volume it would invalidate the core principals of relativity that no information can be transferred faster that the speed of light.
In other words, it gives us a doable experimental that will UNEQUIVOCALLY tell us if Quantum Mechanics or Einstein’s’ theories define why the universe is what it is
IT CANNOT GET MUCH SIMPLER THAN THAT.
Copyright Jeffrey O’Callaghan Apr. 2021