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Unifying Quantum and Relativistic Theories

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  • Jeffrey O'Callaghan
  • January 15, 2020 05:43:57 PM
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The purpose of this blog is to show how changing ones perspective on the physical structure of the universe will allow one to unite the abstract concepts of Quantum Mechanics with the observable realities of both Einstein's Special and General Theories of Relativity.

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    Is our universe expanding in space or is it expanding through time?

    A few years after Albert Einstein unified space and time in his (and by now very well tested!) Theory of General Relativity he applied it to the entire universe and found something remarkable. The theory predicts that the whole universe is either expanding or contracting. Later in 1929 the astronomer Edwin Hubble measured the velocities […] The post Is our universe expanding in space or is it expanding through time? appeared first on Unifying Quantum and Relativistic...

    A few years after Albert Einstein unified space and time in his (and by now very well tested!) Theory of General Relativity he applied it to the entire universe and found something remarkable. The theory predicts that the whole universe is either expanding or contracting.

    Later in 1929 the astronomer Edwin Hubble measured the velocities of a large selection of galaxies and found that the majority of them were moving away from us.  In other words, the universe was expanding.

    However, is the universe expanding in space or is it expanding through time? 

    To answer this one must first define what time and space are.

    Some define time only in the abstract saying that is an invention of the human consciousness that gives us a sense of order, a before and after so to speak.  To physicist’s it is a measure of the relative interval between events which is measured in units of time such as seconds minutes or hours.

    However, space can be defined as the arena where events occur.  We use the measurements of inch or meter to define the position of those event in that arena.

    As was mentioned earlier, Einstein’s General Theory of Relativity mathematically define the universe in terms of a melding of time with space.  However, as was mention above they are they have vastly different properties.  For example, one is measure in terms of second while the other is in inches or meters.

    Therefore, it is very difficult to understand how time which is measured in seconds can have a dynamic effect on space measured in meters.

    To this end Marina Cortês, a cosmologist from the Royal Observatory, Edinburgh came up to what has come to be called the block universe.

    Basically, it asks us to imagine a regular chunk of cement. It has three dimensions but we live in four dimensions: the three spatial dimensions plus one time dimension. A block universe is a four-dimensional block, but instead of being made of cement, it is made of space-time. And all of the space and time of the Universe are there in that block."block universe

    We can’t see this block, we’re not aware of it, as we live inside the cement of space-time. And we don’t know how big the block universe we live in is: "We don’t know if space is infinite or not. Or time – we don’t know whether it has a beginning or if it will have an end in the future. So, we don’t know if it’s a finite chunk of space-time or an infinite chunk."

    However, picture this presents a problem for cosmologists because if the merging of space and time causes it to become as ridge as a block of cement how can its spatial component be expanding.

    It should be remembered only the spatial component of the universe is expanding not time. 

    Additionally, because Einstein defined the universe in terms of only four dimensions, one time and three spatial how can we understand its spatial expansion without adding an additional one because a spatial one cannot expand to one made up of time because, as mentioned earlier they have vastly different properties.

    Yet, Einstein gave us an alternative 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 four *spatial* dimensions.

    In other words, Einstein’s mathematics actually defined two mathematically equivalent physical models of the universe one consisting of four-dimensional space-time and one of only four spatial dimensions. 

    Yet, because both of these models are mathematically equivalent and since we cannot physically observe  either a time or a fourth *spatial* dimension, we must look to the effects they would have on the ones we can observe to determine which one of these physical models is correct.

    For example, if we were a two-dimensional creature living on the surface of a balloon that was inflating, we could explain its spatial expansion by assuming we were living in an environment consisting three spatial dimensions because they have the same properties as the two dimension surface of the balloon therefore, it could expand through it.  However, we could not explain it by assuming that we were living in an environment consisting of only time and the two-dimensional surface of the balloon because time as mentioned earlier it does not have the properties of space and therefore could not expand in it. 

    Similarly, we can explain why our three-dimensional world was undergoing a spatial expansion by assuming we were living in an environment or universe consisting four *spatial* dimensions because it would have the same spatial properties as the three dimension one we live in.  However, we could not if we assume our universe consisted of four-dimensional space-time because time does not have the properties of space and therefore similar to the surface of the balloon it could not expand in it.

    As was mentioned earlier  "A few years after Albert Einstein unified space and time (and by now very well tested! ) in his theory of General Relativity" and showed it can be "applied to the entire universe ." Therefore, he also showed that because of their mathematical equivalence, a physical model based on one unifying three-dimensional space with a fourth *spatial* dimension has also been very well tested and could also be applied it to the entire universe.

    However, as was shown above his physical model based on four *spatial* dimensions pass an additional test which his space-time model cannot, that of explaining the spatial expansion of our three-dimension environment. 

    Latter Jeff

    Copyright Jeffrey O’Callaghan 2020

    The post Is our universe expanding in space or is it expanding through time? appeared first on Unifying Quantum and Relativistic Theories.


    A Quantum mechanical Arrow of Time

    The arrow of time, is the name reason given to the "one-way direction" or "asymmetry" of time by British astrophysicist Arthur Eddington in the macroscopic universe.  Its direction, according to Eddington, is determined by studying the spatial organization of atoms, molecules, and bodies, and might be drawn upon a four-dimensional relativistic map of the world. […] The post A Quantum mechanical Arrow of Time appeared first on Unifying Quantum and Relativistic...

    The arrow of time, is the name reason given to the "one-way direction" or "asymmetry" of time by British astrophysicist Arthur Eddington in the macroscopic universe.  Its direction, according to Eddington, is determined by studying the spatial organization of atoms, molecules, and bodies, and might be drawn upon a four-dimensional relativistic map of the world.

    However physical processes at the microscopic level are believed to be either entirely or mostly time-symmetric: if the direction of time were to reverse, the theoretical statements that describe them would remain true. Yet as was just mentioned at the macroscopic level it appears that this is not the case. arrow of time[3]

    The question as to why things appear to different on the microscopic level is an unanswered question.

    Many explain the observed temporal asymmetry at the macroscopic level, the reason we see time as having a forward direction, ultimately comes down to thermodynamics, the science of heat and its relation with mechanical energy or work, and more specifically to the Second Law of Thermodynamics. That laws uses the states that the entropy of a system either remains the same or increases in every process. This phenomenon is due to the extraordinarily small probability of a decrease or that a system will return to its original configuration, based on the extraordinarily larger number of microstates in systems with greater entropy. In other Entropy  can decrease or a system can return to its original configuration, but for any macroscopic system, this outcome is so unlikely that it will never be observed in the future.

    However, entropy can decrease somewhere, provided it increases somewhere else by at least as much. The entropy of a system decreases only when it interacts with some other system whose entropy increases in the process.

    Yet, it is difficult to apply that definition to a quantum environment because Schrödinger wave equation that quantum mechanics uses to determine the position component of a particle when observed does so in terms of a probability distribution over the entire universe.  Therefore, to define an arrow of time for a quantum system in terms of entropy one must show there is a physical connection between the macroscopic space-time environments we live in and a particles position in that probability field when it is observed.

    Unfortunately, we define the spatial components of entropy in our macroscopic universe in terms of the space-time concepts defined by Einstein.  Therefore, to define the arrow of time in the probabilistic world associated quantum mechanics in terms of entropy we must show how it is physically connected to the spatial properties of the macroscopic universe defined by him.

    Einstein gave us the ability to do this when he used the equation E=mc^2 and the constant velocity of light to define the geometric properties of space-time because it provided a method of converting a unit of time he associated with energy to unit of space.   Additionally, because the velocity of light is constant, he also defined a one to one quantitative correspondence between the both the relativistic and physical properties of a space-time universe and one made up of only four *spatial* dimensions.

    Doing so allow will one to physically connect the probabilities associated with Schrödinger’s wave equation to the Thermodynamic laws that governor the entropy in our macroscopic universe.

    For example, the article “ Why is energy/mass quantized? ” Oct 4, 2007 showed one can derive the quantum mechanical wave/particle properties of matter in terms of an energy wave on a "surface" of a three-dimensional space manifold with respect to fourth spatial dimension by extrapolating our understanding of a resonant structure created by a wave in a three-dimensional environment.

    Briefly it showed the four conditions required for resonance to occur in a three-dimensional environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in one consisting of four spatial dimensions.

    The existence of four *spatial* dimensions would give an electromagnetic wave the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

    These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the "surface" of a three-dimensional space manifold to oscillate with the frequency associated with the energy of that event.

    The oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established space.

    Therefore, these oscillations in a "surface" of a three-dimensional space manifold would meet the requirements mentioned above for the formation of a resonant system or "structure" in four-dimensional space if one extrapolated them to that environment.

    In our three-dimensional environment the energy of a resonant system can only take on the discrete or quantized values associated with its fundamental or a harmonic of its fundamental frequency.

    Hence, these resonant systems in four *spatial* dimensions would be responsible for the discrete quantized energy quantum mechanical associates with the particle properties of matter.

    Yet one can also define its boundary conditions of its resonate structure in the terms of our perceptions of a three-dimensional environment.

    For example, in our three-dimensional world, a point on the two-dimensional surface of paper is confined to that surface. However, that surface can oscillate up or down with respect to three-dimensional space.

    Similarly, an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate “up” or “down” with respect to a fourth *spatial* dimension.

    It is the confinement of the “upward” and “downward” oscillations of an energy with respect to a fourth *spatial* dimension by an observation is what defines the spatial boundaries associated with a particle in the article “Why is energy/mass quantized? " Oct 4, 2007.

    This shows the reason Quantum Mechanics can define matter in terms of a particle/wave duality and why it only presents its particle or position properties when it is observed is because its wave component is only confined to three-dimensional space when an observation is made.

    However, as mentioned earlier it also provides a way to physical connect the probabilistic environment defined by Schrödinger wave equation to the physicality of Einstein’s relativistic universe.

    The physics of wave mechanics tell us that due to the continuous properties of the wave component associated with a quantum system it would be distributed throughout the entire "surface" a three-dimensional space manifold with respect to a fourth *spatial* dimension.

    For example, the energy of a vibrating or oscillating ball on a rubber diaphragm would be disturbed over its entire surface while the magnitude of those vibrations would decrease as one move away from the focal point of the oscillations.

    Similarly, if the assumption outlined above, that quantum properties of matter are a result of vibrations or oscillations in a "surface" of three-dimensional space is correct those oscillations would be distributed over the entire "surface" three-dimensional space while the magnitude of those vibrations would be greatest at the focal point of the oscillations and decreases as one moves away from it.

    lenth[4]

    (Some may question the fact that the energy wave associated with particle would be simultaneously distributed over the entire universe.  However, the relativistic properties of space-time tell us the distance perceived by objects or particles in relative motion is dependent on their velocity which become zero at the speed of light.  Therefore, from the perspective of an energy wave moving at the speed of light, the distance between all points in the universe along its velocity vector is zero.  In other words, because its electromagnetic wave component of a particle is moving at the speed of light as all electromagnetic0 energy must is it would be distributed or simultaneous exists at every point in the universe along its velocity vector.  There can be no other conclusion if one accepts the validity of Einstein’s theories.)

    As mentioned earlier the article “ Why is energy/mass quantized? ” shown a wave/particle duality of matter can be understood in terms of a resonant structure formed wave energy on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

    Yet the science of Wave Mechanics tells us resonance would most probably occur on the surface of the rubber sheet were the magnitude of the vibrations is greatest and would diminish as one move away from that point,

    Similarly, a particle would most probably be observed were the magnitude of the vibrations in a "surface" of a three-dimensional space manifold is greatest and would diminish as one move away from that point.

    This demonstrates that one can interconnect probabilities associated with Schrödinger’s wave equation to the physicality of the Einstein’s Relativistic universe.

    As was mentioned earlier the arrow of time is defined in classical system in terms of entropy or the level of randomness (or disorder) of a system and the Second law of thermodynamics which states that there is an the extraordinarily small probability that a system will return to its original configuration, based on the extraordinarily larger number of microstates in systems with greater entropy even though its. 

    Additionally, the above discussion also shows one can use the same definition for the arrow of time in a quantum universe as the one used in a macroscopic one because the position of a particle in a quantum can only be determine with respect to other particles in probability field Schrödinger’s equation.  Therefore, due to the fact that there are infinite number of possibilities in the probabilistic universe of quantum mechanics there an extraordinarily small chance of that universe retuning to is original configuration when an observation is made in the future.  

    Later Jeff

    Copyright Jeffrey O’Callaghan 2020

    The post A Quantum mechanical Arrow of Time appeared first on Unifying Quantum and Relativistic Theories.


    The illusion of Quantum Entanglement

    Presently, there is disconnect between our understanding of one of the most mysterious facets of quantum mechanics quantum, that of quantum entanglement and the classical one of separation. Entanglement occurs when two particles are linked together no matter their separation from one another. Quantum mechanics assumes even though these entangled particles are not physically connected, […] The post The illusion of Quantum Entanglement appeared first on Unifying Quantum and Relativistic...

    Presently, there is disconnect between our understanding of one of the most mysterious facets of quantum mechanics quantum, that of quantum entanglement and the classical one of separation.

    Entanglement occurs when two particles are linked together no matter their separation from one another. Quantum mechanics assumes even though these entangled particles are not physically connected, they still are able to share information with each other instantaneously seemingly breaking one of the most hard-and-fast rules of classical physics and Einstein theories: that no information can be transmitted faster than the speed of light.

    Even though it may be hard for some to accept the instantaneous sharing of information over what appears to be long distances has been proven time and time again over the years.

    For example, when researchers create two entangled particles, separate them and independently measure their properties, they find that the outcome of one measurement influences the observed properties of the other particle.

    This was made possible in 1964, when John Bell showed there is a theoretical limit beyond which correlations can only be explained by quantum entanglement, not classical physics.

    However, we must be careful not to jump to conclusions because Einstein gave us the definitive answer as to how and why particles are entangled in terms of the physical properties of space-time even though he was so upset to what he called this  “spooky action at a distance.” that in 1935 he along with Podolsky Rosen proposed the following thought experiment which came to be called the EPR Paradox.

    In 1935, Einstein co-authored a paper with Podolsky–Rosen highlighted a problem that they felt showed that Quantum Mechanics could not be a complete theory of nature.  This thought experiment came to be called the EPR Paradox. The first thing to notice is that Einstein was not trying to disprove Quantum Mechanics in any way.  In fact, he was well aware of its power to predict the outcomes of various experiments.  What he was trying to show was that there must be a “hidden variable” that would allow Quantum Mechanics to become a complete theory of nature.

    The argument begins by assuming that there are two systems, A and B (which might be two free particles), whose wave functions are known.  Then, if A and B interact for a short period of time, one can determine the wave function which results after this interaction via the Schrödinger equation or some other Quantum Mechanical equation of state.  Now, let us assume that A and B move far apart, so far apart that they can no longer interact in any fashion.  In other words, A and B have moved outside of each other’s light cones and Therefore, are spacelike separated.

    With this situation in mind, Einstein asked the question: what happens if one makes a measurement on system A?  Say, for example, one measures the momentum value for it.  Then, using the conservation of momentum and our knowledge of the system before the interaction, one can infer the momentum of system B.  Thus, by making a momentum measurement of A, one can also measure the momentum of B.  Recall now that A and B are spacelike separated, and thus they cannot communicate in any way.  This separation means that B must have had the inferred value of momentum not only in the instant after one makes a measurement at A, but also in the few moments before the measurement was made.  If, on the other hand, it were the case that the measurement at A had somehow caused B to enter into a particular momentum state, then there would need to be a way for A to signal B and tell it that a measurement took place.  However, the two systems cannot communicate in any way!

    If one examines the wave function at the moment just before the measurement at A is made, one finds that there is no certainty as to the momentum of B because the combined system is in a superposition of multiple momentum eigenstates of A and B.  So, even though system B must be in a definite state before the measurement at A takes place, the wave function description of this system cannot tell us what that momentum is!  Therefore, since system B has a definite momentum and since Quantum Mechanics cannot predict this momentum, Quantum Mechanics must be incomplete.

    As was mentioned earlier, in response to Einstein’s argument about incompleteness of Quantum Mechanics, John Bell derived a mathematical formula that quantified what you would get if you made measurements of the superposition of the multiple momentum eigenstates of two particles.  If local realism was correct, the correlation between measurements made on one of the pair and those made on its partner could not exceed a certain amount, because of each particle’s limited influence.

    In other words, he showed there must exist inequities in the measurements made on pairs of particles that cannot be violated in any world that included both their physical reality and their separability because of the limited influence they can have on each other when they are “spacelike” separated.

    When Bell published his theorem in1964 the technology to verify or reject it did not exist. However, in the early 1980s, Allen Aspect performed an experiment with polarized photons that showed that the inequities it contained were violated.

    Since then there have been many experiments using the properties of paired of photons and other particles that verify without any doubt that two photons and others particles that are spatially separated can be entangled.

    In quantum mechanics it is assumed that the act of measuring the state of one of a pair of entangled particles instantly affects the other no matter how far they are apart.

    However, Einstein in his Special Theory of Relativity gives us a classical explanation in terms his theory for the entanglement of two particles.

    For example, with regards to the polarized photons mentioned earlier that Allen Aspect used to verify the quantum mechanical interpretation of entanglement his theory tells us that because photons must always be moving at the speed of light they can never be separated with respect to an external observer no matter how far apart he or she perceives them to be.

    This is because he tells that that there are no preferred reference frames by which one can measure distance. Therefore, one must not only view the separation of a photon with respect to an observer who was external to them but must also look at that separation from a photon’s perspective.

    However, his theory tells the distance between the two photons A and B would be defined by their relative speed with respect to an observer.

    Specifically, he told us that it would be defined by

    Yet, this tell us that the separation between two photons moving at the speed of light from their perspective would be zero no matter how far apart they might be from the perspective of an observer in a laboratory because 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 with all other paired photons no matter how far apart or “spacelike” separated they may appear to be to ALL observers.

    In other words, the inequities in the measurements made on ALL REPEAT ALL pairs of photons should be violated in a world containing the physical reality of Einstein’s theories because they will influence each other no matter how far they may be separated when viewed from a reference frame other than a photon’s, such as a laboratory.

    Up until now we only have addressed the entanglement of photons that are moving at the speed of light.  However, the same the relativistic properties of motion can be applied to explain the entanglement of other particles that are not moving at that speed.

    This is because quantum mechanics defines the composition of matter in terms of its wave particle duality.  More specifically, as was shown in the previously article  “Quantum mechanics in a nutshell…Don’t look: waves. Look: particles Dec. 1, 2015 it assumes that before an observation is made matter is propagated though space in terms of its wave properties and only after being observed does it present its particle properties.

    In other words, in Quantum Mechanics matter has an extended volume while moving through space which is directly related to the wavelength associated with its particle properties.

    This means the wavelengths of two particles in motion will overlap and be entangled if the separation between the end points of an observation as measured from their perspective is less that the wavelength of those particles.

    However, as mentioned earlier Einstein tells us that we must use this theory to derive the separation of two moving particles from their perspective and not from the prospective of observers in a laboratory.

    Therefore, even though particles may appear to be separated from the view point of a laboratory observer they may not be separated from the view point of the particles that are moving with respect to those observers because of an overlap of their wave properties..

    In other words, one does not have to break one of the most hard-and-fast rules of classical physics and Einstein theories: that no information can be transmitted faster than the speed of light because one can use his classical theories to explain how and why particles that appear to be separated can communicate instantaneously. REVIEW BUTTON

    The illusion is not that entanglement of two spatial separated particles from the perspective of the observers in Allen Aspect experiment mentioned earlier does not exist.  The illusion is that entanglement is not the result of the quantum mechanical properties of matter but instead is the result of the physical reality of Einstein’s Theory of Relativity because it tells us that the separation of particles must be measured from their perspective and not from the perspective of an observer in a laboratory.

    Copyright Jeffrey O’Callaghan 2020

    The post The illusion of Quantum Entanglement appeared first on Unifying Quantum and Relativistic Theories.


    Einstein’s explanation of the Double Slit Experiment

    Richard Feynman the farther of Quantum Electrodynamics believed Thomson’s double slit experiment provided a mechanism for understanding the wave particle duality of energy/mass because it clearly demonstrates their inseparability and provides a mechanisms for understanding how it is propagated through space. The wave–particle duality postulates that all particles exhibit both wave and particle properties. A […] The post Einstein’s explanation of the Double Slit Experiment...

    Richard Feynman the farther of Quantum Electrodynamics believed Thomson’s double slit experiment provided a mechanism for understanding the wave particle duality of energy/mass because it clearly demonstrates their inseparability and provides a mechanisms for understanding how it is propagated through space.

    The wave–particle duality postulates that all particles exhibit both wave and particle properties. A central concept of quantum mechanics, this duality addresses the inability of classical concepts like "particle" and "wave" to fully describe the behavior of quantum-scale objects.  Standard interpretations of quantum mechanics explain this paradox as a fundamental property of the Universe, while alternative interpretations explain the duality as an emergent, second-order consequence of various limitations of the observer.

    The reason the above-mentioned experiment is so important is because it provides a mechanism for understanding how electromagnetic energy is propagated and why the particle wave dually exists purely in terms of Einstein’s Theory of Relativity.

    But before we begin, we must first understand how the electromagnetic wave component of a particle’s duality is propagated through space and time.

    One of the difficulties involved in doing so is that we define its movement though space in terms Maxwell’s equations which are based on the interaction between its electric and magnetic components with respect to time not space.  This presents a problem because the particle component of its duality must always be defined by its spatial position when observed. Therefore, to understand how they are related we should attempt to define its movement through space and time in term of its spatial properties.

    Einstein gave us the ability to do this purely in terms spatial properties of its electromagnetic wave components when he used the constant velocity of light to defined the geometric properties of space-time because it allows one to convert a unit of time in his space-time universe to an equivalent unit of space in an environment consisting of only four *spatial* dimensions.  Additionally, because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

    In other words, by mathematically defining the geometric properties of a space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

    This gives one the ability to derive the properties of an electromagnetic wave and understand its movement in terms of the spatial displacement that would be created by its observed transverse wave characteristics. 

    For example, a transverse wave on the two-dimensional surface of water moves through water because it causes a point on that surface to be become displaced or rise above or below the equilibrium point that existed before the wave was present.  A force is developed by the differential displacement of the surfaces, which will result in the elevated and depressed portions of the water moving towards or become "attracted" to each other and the surface of the water. This results in a wave to move on the surface of the water.

    Similarly, an energy wave on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would cause a point on that "surface" to become displaced or rise above and below the equilibrium point that existed before the wave was present.  This would result a wave moving on the "surface" of three-dimensional space.

    Therefore, classical wave mechanics, if extrapolated  to four *spatial* dimensions tells us a force will be developed by the differential displacements caused by an energy wave moving on a "surface" of three-dimensional space with respect to a fourth *spatial* dimension that will result in its elevated and depressed portions moving towards or become "attracted" to each other causing it to move through space.

    This defines the causality of the attractive forces of unlike charges associated with the electromagnetic wave component of a photon in terms of a force developed by a differential displacement of a point on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

    However, it also provides a classical mechanism for understanding why similar charges repel each other because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement.

    Similarly, the magnitude of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by two similar charges will be greater than that caused by a single one.  Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two charges than it would be for a single charge.

    One can also define the directionality of electrical component of electromagnetic energy in terms of the energy associated with its "peaks" and "troughs" that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement because classical Mechanics tells us a horizontal force will be developed by that displacement which will always be 90 degrees out of phase with it.  This force is called magnetism.

    This is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls matter horizontally towards the apex of that displacement.

    However, this means that one can define a physical model for the propagation of an electromagnetic field in terms of Einstein’s space-time theory because, as was shown above when he mathematically defined its geometric properties in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining his theory in terms of the geometry of four *spatial* dimensions.

    Yet, viewing it in terms of its spatial components also allows one to understand the mechanism responsible for the wave particle duality of a photon as observed in the Thomson’s double slit experiment and why electromagnetic energy always presents itself as a particle when it strikes the detector in the that experiment.

    For example, the article, "Why is energy/mass quantized?" Oct. 4, 2007 showed that one can use the Einstein’s theories to explain the quantum mechanical properties of an electromagnetic wave by extrapolating the rules of classical resonance in a three-dimensional environment to an energy wave moving on “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

    Briefly it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in an energy wave moving in four *spatial* dimensions.

    The existence of four *spatial* dimensions would give the energy wave associated with a photon the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

    These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

    However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in four *spatial* dimensions.

    As was shown in that article these resonant systems in four *spatial* dimensions are responsible for the particle called a photon.

    However, one can also use Einstein space-time theories when viewed in their spatial equivalent to explain how the boundaries of the standing wave responsible for creating the resonant system that article indicated was responsible of a particles formation are created.

    In classical physics a standing wave is created when the vibrational frequency of a source causes reflected waves from one end of a confined medium to interfere with incident waves from the source.  This interference of the wave energy causes their peaks troughs to be reinforce in the volume they are occupying thereby creating a standing wave.

    The confinement required to create a standing wave in space-time or its equivalent in four *spatial* dimensions can be understood by comparing it to the confinement a point on the two-dimensional surface of paper experiences when oscillating with respect to three-dimensional space.  The energy associated with the wave motion of that point would be confined to its two-dimensional surface and would be reflected and interfere with the incident wave when reaches three-dimensional space at its edge. Therefore, a standing would be created by its interaction with three-dimensional space.

    In other words, when a wave on the surface of a piece of paper encounters the third *spatial* dimension at its edge it is reflected back allowing a standing wave to be formed on its surface.

    Similarly, an electromagnetic wave moving on the surface of three-dimensional space would be confined to it and reflected back to that volume, similar to the surface of the paper if it was prevented from oscillating with respect to a four *spatial* dimensions or four-dimensional space-time.

    In other words, the interference caused by the confinement of an electromagnetic wave to three-dimensional space, which is caused by it striking the detection screen in the Thomson’s double slit experiment results in the resonant standing wave to be formed in space called a photon.

    That experiment is made up of "A coherent source of photons illuminating a screen after passing through a thin plate with two parallel slits cut in it.  The wave nature of light causes it wave component to interfere after passing through both slits, creating an interference pattern of bright and dark bands on the screen.  However, at the screen, the light "is always found to be absorbed as discrete particles, called photons".

    When only one slit is open, the pattern on the screen is a diffraction pattern however, when both slits are open, the pattern is similar but with much more detail.  These facts were elucidated by Thomas Young in a paper entitled "Experiments and Calculations Relative to Physical Optics," published in 1803.  To a very high degree of success, these results could be explained by the method of Huygens–Fresnel principle that is based on the hypothesis that light consists of waves propagated through some medium.  However, discovery of the photoelectric effect made it necessary to go beyond classical physics and take the quantum nature of light into account.

    However, the most baffling part of this experiment comes when only one photon at a time impacts a barrier with two opened slits because an interference pattern forms which is similar to what it was when multiple photons were impacting the barrier.   This is a clear implication the particle called a photon has a wave component, which simultaneously passes through both slits and interferes with itself.  (The experiment works with electrons, atoms, and even some molecules too.)"

    Even more puzzling is why any attempts to measure which slit that electron passed through cause the interference pattern to disappear.

    Yet, as mentioned earlier one can derive the outcome of this experiment by assuming that electromagnetic energy is propagated by a wave on the "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension instead of four-dimensional space-time

    For example, the reason why the interference patterns remain when only one photon at a time is fired at the barrier with both slits open or "the most baffling part of this experiment" is because, as was just shown it has an extended spatial volume which is directly related to the wavelength.

    This means a portion of its energy can simultaneously pass both slits, if the diameter of its volume exceeds the separation of the slits and recombine on the other side to generate an interference pattern.

    Additionally, one can also explain why the interference pattern disappears when a detector is added to determine which slit a photon has passed through.  The energy required to measure which slit it passes through interacts with it causing the wavelength of that portion to change so that it will not have the same resonant characteristics as one that passed through the other slit   Therefore, the energy passing thought that slit will not be able to interact, with the energy passing through the other one to form an interference pattern on the screen.

    However, as was shown earlier one can also show the reason the interference pattern appears as a particle when electromagnetic wave contacts a detection screen is because striking it results in it being confined to three-dimensional space instead of four-dimensional space-time or four spatial dimensions, thereby creating a standing wave in either four spatial dimensions or four dimensional space-time to be created.

    In other words, it clearly shows the reason all forms of energy exhibit both wave and particle properties are because they are physically made up of waves in terms of Einstein’s Theory of Relativity.

    The above discussion shows that Richard Feynman was right in assuming that Thomson’s double slit experiment provided a mechanism for understanding the  wave particle duality of energy/mass because it clearly demonstrates their inseparability.

    Additionally, it also provides an explanation how and why energy  is propagated through space because it shows the quantum mechanical and wave properties of energy displayed in the double slit experiment can be understood if one assumes they are made up of a resonant system in a moving in a four dimensional space-time manifold or on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension in terms Einstein theories.  REVIEW BUTTON

    It should be remembered that Einstein’s genius allows us to choose whether to define an electromagnetic wave either a space-time environment or one consisting of four *spatial* dimension when he defined its geometry in terms of the constant velocity of light.

    Later Jeff

    Copyright Jeffrey O’Callaghan 2020

    The post Einstein’s explanation of the Double Slit Experiment appeared first on Unifying Quantum and Relativistic Theories.


    Plato’s lesson on Quantum Mechanics

    We are reposting this article, first published in 2012 because we do not want its message to become lost in time. Many think the quantum mechanical world of probabilities define our reality.  However, the Greek philosopher, Plato around 375 BC would disagree. In Plato’s allegory "The cave" he describes how people who have been chained […] The post Plato’s lesson on Quantum Mechanics appeared first on Unifying Quantum and Relativistic...

    We are reposting this article, first published in 2012 because we do not want its message to become lost in time.

    Many think the quantum mechanical world of probabilities define our reality.  However, the Greek philosopher, Plato around 375 BC would disagree.

    In Plato’s allegory "The cave" he describes how people who have been chained to a cave wall view the world outside of it.  "The people watch shadows projected on the wall by things passing in front of a fire behind them, and begin to ascribe forms to these shadows. According to Plato’s Socrates, the shadows are as close as the prisoners get to viewing reality. He then explains how the philosopher is like a prisoner who is freed from the cave and comes to understand that the shadows on the wall do not make up reality at all, as he can perceive the true form of reality rather than the mere shadows seen by the prisoners.

    However, he could have been talking about today’s scientists who are locked into a worldview that projects shadows that cannot be made to agree with the reality of the world they are living in.

    For example, Quantum theory defines the existence of particles in terms of a mathematically generated probability function and that they do not exist until a conscience observer looks at it.  In other words, it assumes the act of observation or measurement creates the physical reality of our particle world.  However, because only conscience beings can be observers it implies that it cannot exist without them being there to observe it.

    However, if one assumes reality exist only after someone observes it one must also assume that we humans evolved out of something that did not exist.

    This seems to contradict the most common definition of reality: that it is an environment with a set of physical properties that exists even when there are no observers present.  In other words, most believe the world exist in even when no one is there to observe it.

    Plato’s in his allegory "The Cave" he tells us that one should base his or her interpretation of reality on direct physical observations of the "shadows" they cast on the cave walls because he feels it is the only way to connect their existence to the reality of the world outside of it.

    However, the  proponents of quantum mechanics face an even greater problem than those who reside in Plato’s cave because they assume that reality and existence is defined in terms of abstract mathematical probabilities which by definition do not have physical properties; Therefore, they are unable to cast shadows on the reality of the non-abstract environment that exists all around us.

    In other words, the reality defined by quantum mechanics cannot create or define the physicality of the shadows projected on the walls of our world or cave as Plato calls it because they themselves do not have any.

    Some would argue the fact that quantum mechanics can accurately predict what we observe in the world in terms of the abstract nature of probability functions means that what we perceive as the reality does not exist.

    However, as Plato pointed out our only connection to reality is though the observation of the "shadows" it displays on our physical or material world.  Yet because of the abstract nature of probability functions of quantum mechanics they, by definition can never be part or interact with that world.  Therefore, because we can physicality observe of the "shadows" of the quantum mechanical world in our environment isn’t it more likely the abstract one defined by quantum mechanics does not exist while those of the world that we can see and touch do.

    Einstein was often quoted as saying "If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless."

    He realized as Plato did that reality can only be discovered by forming a physical image of what its shadows are telling us.

    For example, Newton in a letter to Bentley in 1693, talks about a conceptual problem he has with his gravity theory by rejecting the action at a distance that it requires.

    "It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact…That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it."

    Einstein looked at the shadows of reality cast by gravity and realized they could be created by a universe made up of four-dimensional space-time.  He extrapolated the physical image of how objects move on a curve surface in a three-dimensional environment to a curved four-dimensional space-time manifold to show that it can explain and predict how gravity "may act upon another at a distance through a vacuum" in terms of a curvature in space and time.  This allowed him to understand the reality behind the shadows we can see in our three-dimension world in terms of a physical image based on the existence of four-dimensional space-time.

    In other words, he was able to explain the gravitational shadows on the Newtonian cave walls in terms of a physical image cast by four-dimensional space-time on them.

    As Plato would say he perceived the true form of reality based on a physical image of the shadows seen by its prisoners.

    Unfortunately, many of today scientists seem to be ignoring the lessons taught to us by Plato and Einstein.  They chose to look for reality in terms of abstract mathematics instead of the physical imagery given to us by its shadows.

    The reason may be because it is easier to alter an abstract environment based on mathematics to conform to an observational inconsistency that it is to alter one based on physical imagery.

    For example, Quantum theory makes predictions based on the random properties of a probability function.  However, because its abstract properties are not connected to any physical images of our world all observations no matter how inconsistent they are with the physical world it is describing can be incorporate into it.

    This is in sharp contrast to the space-time environment defined by Einstein in that projecting the physical image of objects moving on a curve surface in a four-dimensional environment directly connects it to the physicality of the shadows it casts on our three-dimensional environment.

    For example, a mass that was repelled by gravity instead of begin attracted would contradict the physical model define by Einstein and would be extremely if not impossible to explain according to that model because that would mean that we should observe objects rolling up hill in our three-dimensional environment.  In other words, because he defined gravity in terms of a physical image based on how objects move on a curve surface in a three-dimensional environment it makes observations like two masses repelling gravitational each other impossible to incorporate into it.

    If However, if some observation happened to contradict complimentary principal of quantum mechanics such as simultaneously observing both the particle and wave properties mass it could easily explained in terms of the fact that its probability functions tell us that anything that can happen eventually will  This makes it impossible to find an observation that would contradict it because it tells us the even the impossible is possible if we wait long enough.  However, this can only happen in an abstract environment which is not bound by the physicality of our observational world because in that world we observe that some things just cannot happen.

    But why should science put in the effort to understand the physical reality behind the shadows of our world when both the abstract mathematical foundation of quantum mechanics and the physics imagery of Einstein’s theories make very accurate predictions of future events based on the past.  Review Unifying Quantum and Relativistic Theories at Blogging Fusion Blog Directory

    Because the mission of a science is to define reality in terms of what we perceive in the world around us which by definition is not abstract.

    Later Jeff

    Original Copyright Jeffrey O’Callaghan 2012

    The post Plato’s lesson on Quantum Mechanics appeared first on Unifying Quantum and Relativistic Theories.


    Electromagnetism and gravity as aspects of a broader mathematical structure.

    Untitled DocumentMaxwell defined the propagation of an electromagnetic wave in terms of a field consisting of both electric and magnetic components which continuously interact with each other, forming an electromagnetic wave. While Quantum Field Theory defines an electromagnetic field in terms of discrete parcels of energy while avoiding the question as to how it moves […] The post Electromagnetism and gravity as aspects of a broader mathematical structure. appeared first on Unifying...

    Untitled DocumentMaxwell defined the propagation of an electromagnetic wave in terms of a field consisting of both electric and magnetic components which continuously interact with each other, forming an electromagnetic wave.

    While Quantum Field Theory defines an electromagnetic field in terms of discrete parcels of energy while avoiding the question as to how it moves through space.

    Additionally, it cannot explain in terms of a physical model and why an electromagnetic wave always without exception becomes a particle when observed.

    Einstein also had a problem of deriving its electromagnetic properties and how they moved through space in terms of a physical model based on his gravitational theories as was documented by the American Institute of Physics .

    “From before 1920 until his death in 1955, Einstein struggled to find laws of physics far more general than any known before. In his theory of relativity, the force of gravity had become an expression of the geometry of space and time. The other forces in nature, above all the force of electromagnetism, had not been described in such terms. But it seemed likely to Einstein that electromagnetism and gravity could both be explained as aspects of some broader mathematical structure. The quest for such an explanation — for a “unified field” theory that would unite electromagnetism and gravity, space and time, all together — occupied more of Einstein’s years than any other activity.

    However, one of the difficulties in understanding the similarities between electromagnetic forces and gravity is that we define its movement though space in terms of an interaction between its electric and magnetic components with respect to time while we define the magnitude of gravitational forces in terms of the physical distance between two bodies.

    Therefore, to understand a physical connection between them we should define the interaction of the forces associated with an electromagnetic wave in in terms of distance as we do with gravity.

    Einstein gave us the ability to do this when he used the constant velocity of light and the equation E=mc^2 to define geometric properties of forces in a space-time environment because it allows one to convert a unit of time in his four-dimensional space-time universe to a unit of space in a universe consisting of only four *spatial* dimensions.   Additionally, because the velocity of light is constant it is possible to define a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

    In other words, by mathematically defining the geometric properties of time in his space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of define the time-based components of Maxwell’s equations in terms of their spatial counterparts. 

    The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with gravitational forces in terms of four *spatial* dimensions is one bases for assuming, as was done in the article “ Defining energy? ” Nov 27, 2007 that all forms of energy including gravitational and electromagnetism can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

    This allows one to form a physical image of electromagnetic force and why it moves through space as was done in the article " What is electromagnetism? " Sept, 27 2007 in terms of the differential force caused by the "peaks" and "toughs" of an energy wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

    Briefly it showed it is possible to derive the electrical and magnetic properties of an electromagnetic field by extrapolating the laws of Classical Wave Mechanics in a three-dimensional environment to a wave moving on a "surface" of three-dimensional space manifold with respect to a fourth *spatial* dimension.

    For example, a wave on the two-dimensional surface of water causes a point on that surface to become displaced or rise above or below the equilibrium point that existed before the wave was present.  A force is developed by that differential displacement of the surfaces, which will result in the elevated and depressed portions of the water moving towards or become "attracted" to each other and the surface of the water.

    Similarly, an energy wave on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would cause a point on that "surface" to become displaced or rise above and below the equilibrium point that existed before the wave was present.

    Therefore, classical wave mechanics, if extrapolated to four *spatial* dimensions tells us a force will be developed by the differential displacements caused by an energy wave moving on a "surface" of three-dimensional space with respect to a fourth *spatial* dimension that will result in its elevated and depressed portions moving towards or become "attracted" to each other resulting as the wave moves through space.

    This defines the causality of the attractive forces of unlike charges associated with the electromagnetic field component of a photon in terms of a force developed as the wave moves through four *spatial* dimensions by a differential displacement of a point on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

    However, it also provides a classical mechanism for understanding why similar charges repel each other because observations of water show that there is a direct relationship between the magnitude of a displacement in its surface to the magnitude of the force resisting that displacement.

    Similarly, the magnitude of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by two similar charges will be greater than that caused by a single one.  Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two charges than it would be for a single charge.

    One can also derive the magnetic component of an electromagnetic wave in terms of the horizontal force developed by the displacement caused by its peaks and troughs.  This would be analogous to how the perpendicular displacement of a mountain generates a horizontal force on the surface of the earth, which pulls matter horizontally towards the apex of that displacement.

    Additionally, one can derive the causality of electrical component of electromagnetic energy in terms of the energy associated with its "peaks" and "troughs" that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement because classical Mechanics tells us a horizontal force will be developed by that displacement which will always be 90 degrees out of phase with it.  This force is called magnetism.

    In other words, it allows one to define a physical model for the propagation of an electromagnetic field in terms of Einstein’s space-time theory.

    Additionally, the above conceptual model can be quantified, as was mentioned earlier by using the valid laws of mathematics to transform his space-time equations to their equivalent in four *spatial* dimensions. This equivalence also allows one to explain both electromagnetism and gravity "as aspects of some broader mathematical structure" in terms of the geometry of four *spatial* dimensions or four-dimensional space-time. 

    Yet, it also explains why electromagnetic energy when observed always presents itself as the particle called a photon in terms of Einstein’s space-time model.

    For example, the article, " Why is energy/mass quantized? " Oct. 4, 2007 showed that one can use the Einstein’s theories to explain the quantum mechanical properties of an electromagnetic wave by extrapolating the rules of classical resonance in a three-dimensional environment to an energy wave moving on “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

    Briefly it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in an energy wave moving in four *spatial* dimensions.

    The existence of four *spatial* dimensions would give the energy wave associated with a photon the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

    These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

    However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in four spatial dimensions.

    As was shown in that article these resonant systems in four *spatial* dimensions are responsible for the particle called a photon.

    However, one can also use Einstein space-time theories to explain how the boundaries of the standing wave responsible for creating the resonant system that article indicated was responsible of a particles formation.

    In classical physics a standing wave is created when the vibrational frequency of a source causes reflected waves from one end of a confined medium to interfere with incident waves from the source.  This interference of the wave energy causes their peaks troughs to be reinforce in the volume they are occupying thereby creating a standing wave.

    The confinement required to create a standing wave in space-time or its equivalent in four *spatial* dimensions can be understood by comparing it to the confinement a point on the two-dimensional surface of paper experiences when oscillating with respect to three-dimensional space.  The energy associated with the wave motion of that point would be confined to its two-dimensional surface and would be reflected and interfere with the incident wave when reaches three-dimensional space at its edge. Therefore, a standing would be created by its interaction with three-dimensional space.

    In other words when a wave on the surface of a piece of paper encounters the third spatial dimension at its edge it is reflected back allowing a standing wave to be formed on its surface.

    Similarly, an electromagnetic wave moving on the surface of three-dimensional space would be confined to it and reflected back to that volume, similar to the surface of the paper if it was prevented from oscillating with respect to a four spatial dimensions or four-dimensional space-time by an observation.

    In other words, when an electromagnetic wave is confined to three-dimensional space by an observation or an interaction with particle like a proton or electron the interference caused by that confinement sets up a resonant standing wave in space which is called a photon.

    Additionally, it tells us that the reason the energy of electromagnetic wave always without exception becomes a particle when observed is because of the fact that all observations or interactions with other particles will confine its motion to three-dimensional space thereby creating the resonate system that defined a particle that was shown to be responsible for a particle in the article " Why is energy/mass quantized? " Oct. 4, 2007

    As mentioned early, the above conceptual model can be quantified by using the valid laws of mathematics to transform his space-time equations to their equivalent in four *spatial* dimensions.  This equivalence as was shown above allows one to explain both particle and wave properties of electromagnetisms and gravity "as aspects of some broader mathematical structure" in terms of the geometry of four *spatial* dimensions or four-dimensional space-time. Review Unifying Quantum and Relativistic Theories at Blogging Fusion Blog Directory

    It should be remembered that Einstein’s genius allows us to choose whether to define an electromagnetic wave either a space-time environment or one consisting of four *spatial* dimension when he defined its geometry in terms of the constant velocity of light.

    Later Jeff 

    Copyright Jeffrey O’Callaghan 2020

    The post Electromagnetism and gravity as aspects of a broader mathematical structure. appeared first on Unifying Quantum and Relativistic Theories.


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