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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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    Do the laws of physics break down in a black hole?

    Absolutely not, because those laws as proposed by Einstein prevent that from happening. The existence of a singularity at the center of a black hole is often taken as proof that the theory of general relativity has broken down, which is perhaps not unexpected as it occurs in conditions where quantum effects should become important. […] The post Do the laws of physics break down in a black hole? appeared first on Unifying Quantum and Relativistic...

    Review Unifying Quantum and Relativistic Theories at Blogging Fusion Blog DirectoryAbsolutely not, because those laws as proposed by Einstein prevent that from happening.

    The existence of a singularity at the center of a black hole is often taken as proof that the theory of general relativity has broken down, which is perhaps not unexpected as it occurs in conditions where quantum effects should become important. time_dialiton2

    In the center of a black hole many believe a gravitational singularity occurs which contains a huge mass in an infinitely small space. In other words density and gravity become infinite while space-time curves infinitely. This would result in the laws of physics as we know them cease to operate. As the eminent American physicist Kip Thorne describes it, it is "the point where all laws of physics break down".

    Unfortunately, everyone including Kip Thorne is wrong because as was just mentioned the laws proposed by Einstein governing the existence of space-time tell us that a singularity can never repeat never exist in a black hole.

    The existence of a singularity is based on a mathematical solution developed in 1915, by Karl Schwarzschild who proposed based on Einstein theories the gravitational field of a star greater than approximately 2.0 times a solar mass would stop the movement of time.  Additionally, it is assumed that his solution identified a radius for any given mass, known as the Schwarzschild radius, where, if that mass could be compressed to fit within that radius, no known force or degeneracy pressure could stop it from continuing to collapse into a gravitational singularity or black hole. Thus, where the radius of the body is less than its Schwarzschild radius, everything, even photons of light, must inevitably fall into the central body called a singularity or a one-dimensional object in space-time.

    However, the according to the relativistic laws Einstein proposed for his space-time universe the time dilatation it associated with a gravitational field would prevent matter form collapsing beyond the event horizon of a black hole to form a singularity .

    In other words, the very theory is used to predict the existence of a black hole also prevents the formation of a singularity and the laws of physics, as defined by Einstein from breaking down in its space-time environment.

    To understand why one must analyze how he define the relativistic properties of space-time and how it interacts with matter in a gravitational field.

    For example, as a star contacts and its circumference decreases, the time dilation on its surface will increase.  At a certain point called the event horizon the contraction of that star will produce a gravitational field strong enough to stop the movement of time.  Therefore, the critical circumference defined by Karl Schwarzschild is a boundary in space where time stops relative to the space outside of that boundary.

    However, the existence of a singularity mentioned earlier is based on the assumption that time continues to move for matter even after it has past the event horizon of a black hole.

    However, this is a direct contraction of the relativistic properties of time as described in Einstein theories.

    In Kip S. Thorne book "Black Holes and Time Warps", he describes how in the winter of 1938-39 Robert Oppenheimer and Hartland Snyder computed the details of a stars collapse into a black hole using the concepts of General Relativity.  On page 217 he describes what the collapse of a star would look like, form the viewpoint of an external observer who remains at a fixed circumference instead of riding inward with the collapsing stars matter.  They realized the collapse of a star as seen from that reference frame would begin just the way every one would expect.  "Like a rock dropped from a rooftop the stars surface falls downward slowly at first then more and more rapidly.  However, according to the relativistic formulas developed by Oppenheimer and Snyder as the star nears its critical circumference the shrinkage would slow to a crawl to an external observer because of the time dilatation associated with the relative velocity of the star’s surface.  The smaller the circumference of a star gets the more slowly it appears to collapse because the time dilation predicted by Einstein increases as the speed of the contraction increases until it becomes frozen at the critical circumference.

    However, the time measured by the observer who is riding on the surface of a collapsing star will not be dilated because he or she is moving at the same velocity as its surface.

    Therefore, the proponents of singularities say the contraction of a star can continue until it becomes a singularity because time has not stopped on its surface even though it has stopped with respect to an observer who remains at fixed circumference to that star.

    But one would have to draw a different conclusion if one viewed time dilation in terms of the gravitational field of a collapsing star.

    Einstein showed that time is dilated by a gravitational field.  Therefore, the time dilation on the surface of a star will increase relative to an external observer as it collapses because, as mentioned earlier gravitational forces at its surface increase as its circumference decrease.

    This means, as it nears its critical circumference its shrinkage slows with respect to an external observer who is outside of the gravitation field because its increasing strength causes a slowing of time on its surface.  The smaller the star gets the more slowly it appears to collapse because the gravitational field at its surface increase until time becomes frozen for the external observer at the critical circumference.

    Therefore, the observations of an external observer would make using conceptual concepts of Einstein’s theory regarding time dilation caused by the gravitational field of a collapsing star would be identical to those predicted by Robert Oppenheimer and Hartland Snyder in terms of the velocity of its contraction.

    However, it also tells us, the laws of physics developed by Einstein for a space-time environment are not violated in black hole with respect to all external observers because the time dilation associated with its gravitational field would not allow the collapse of matter beyond its critical circumference to a singularity.

    However, Einstein developed his Special Theory of Relativity based on the equivalence of all inertial reframes which he defined as frames that move freely under their own inertia neither "pushed not pulled by any force and Therefore, continue to move always onward in the same uniform motion as they began".

    This means that one can view the contraction of a star with respect to the inertial reference frame that, according to Einstein exists in the exact center of the gravitational field of a collapsing star.

    (Einstein would consider this point an inertial reference frame with respect to the gravitational field of a collapsing star because at that point the gravitational field on one side will be offset by the one on the other side.  Therefore, a reference frame that existed at that point would not be pushed or pulled relative to the gravitational field and would move onward with the same motion as that gravitational field.)

    (However, some have suggested that a singularity would form in a black hole if the collapse of a star was not symmetrical with respect to its center.  In other words, if one portion of its surface moved at a higher velocity that another towards its center it could not be consider an inertial reference frame because it would be pushed or pulled due to the differential gravity force cause be its uneven collapse.  But the laws governing time dilation in Einstein’s theory tell us that time would move slower for those sections of the surface that are moving faster allowing the slower ones to catch up.  This also tells us that every point on the surface of star will be at the event horizon at the exact same time and therefore its center will not experience any pushing or pulling at the time of its formation and therefore could be considered an inertial reference frame.)

    The surface of collapsing star from this viewpoint would look according to the field equations developed by Einstein as if the shrinkage slowed to a crawl as the star neared its critical circumference because of the increasing strength of the gravitation field at the star’s surface relative to its center.  The smaller it gets the more slowly it appears to collapse because the gravitational field at its surface increases until it becomes frozen at the critical circumference.

    Therefore, because time stops or becomes frozen at the critical circumference for all observers who is at the center of the clasping mass and the contraction cannot continue from their perspectives.

    However, it also tells us, the laws of physics developed by Einstein for a space-time environment are not violated in black hole with respect to an observer who is  at the its center because the time dilation associated with its gravitational field would not allow the collapse of matter beyond its critical circumference to a singularity.

    Yet, Einstein in his general theory showed that a reference frame that was free falling in a gravitational field could also be considered an inertial reference frame.

    As mentioned earlier many physicists assume that the mass of a star implodes when it reaches the critical circumference.  Therefore, an observer on the surface of that star will be in free fall with respect to the gravitational field of that star when as it passes through its critical circumference.

    This indicates that point on the surface of an imploding star, according to Einstein’s theories could also be considered an inertial reference frame because an observer who is on the riding on it will not experience the gravitational forces of the collapsing star.

    However, according to the Einstein theory, as a star nears its critical circumference an observer who is on its surface will perceive the differential magnitude of the gravitational field relative to an observer who is in an external reference frame or, as mentioned earlier is at its center to be increasing.  Therefore, he or she will perceive time in those reference frames that are not on its surface slowing to a crawl as it approaches the critical circumference.  The smaller it gets the more slowly time appears to move with respect to an external reference frame until it becomes frozen at the critical circumference.

    Therefore, time would be infinitely dilated or stopped with respect to all reference frames that are not on the surface of a collapsing star from the perspective of someone who was on that surface.

    However, the contraction of a star’s surface must be measured with respect to the external reference frames in which it is contracting.  But as mentioned earlier Einstein’s theories indicate time in its external environment would become infinitely dilated or stop when the surface of a collapsing star reaches its critical circumference.

    Therefore, because time stops or becomes frozen at the critical circumference with respect to the external environment of an observer who riding on its surface the contraction cannot continue because motion cannot occur in an environment where time has stopped.

    However, it also tells us, the laws of physics are not violated in black hole with respect to all riding on the surface of a star because the time dilation associated with its gravitational field the collapse of matter beyond its critical circumference to a singularity.

    This means, as was just shown according to Einstein’s concepts time stops on the surface of a collapsing star from the perspective of all observers when viewed in terms of the gravitational forces the collapse of matter must stop at the critical circumference.

    This contradicts the assumption made by many that the implosion would continue for an observer who was riding on its surface.

    In other words, based on the conceptual principles of Einstein’s theories relating to time dilation caused by a gravitational field of a collapsing star it cannot implode to a singularity as many physicists believe because it causes time to freeze at its critical circumference with respect to all observers and therefore must maintain a quantifiable minimum volume which is equal to the one defined by Karl Schwarzschild.

    However, this means the laws of physics as defined by Einstein do not break done when a singularity forms at the  center of a black hole because as was shown above those laws tell us its formation is not supported by those laws.  Therefore it cannot be taken as proof that the laws as defined by General Theory Relativity has broken down, because those same laws prevent that from happening

    There can be no other conclusion if one accepts the validity laws as defined by Einstein Relativistic Theories and of the physical observations of the time dilation associated with a gravitational field.

    Copyright 2020 Jeffrey O’Callaghan

    The post Do the laws of physics break down in a black hole? appeared first on Unifying Quantum and Relativistic Theories.


    Particles as standing waves in space-time

    It is possible, as this article will show that a standing wave in space-time is responsible for a photon. A standing waves are created within a medium when the vibration frequency of the source causes reflected waves from one end of the medium to interfere with incident waves from the source. This interference occurs in […] The post Particles as standing waves in space-time appeared first on Unifying Quantum and Relativistic...

    It is possible, as this article will show that a standing wave in space-time is responsible for a photon.Review Unifying Quantum and Relativistic Theories at Blogging Fusion Blog Directory

    A standing waves are created within a medium when the vibration frequency of the source causes reflected waves from one end of the medium to interfere with incident waves from the source. This interference occurs in such a manner that specific points along the medium appear to be standing still. Because the observed wave pattern is characterized by points that appear to be standing still, the pattern is often called a standing wave pattern. Such patterns are only created within the medium at specific frequencies of vibration. These frequencies are known as harmonic frequencies, or merely harmonics. At any frequency other than a harmonic frequency, the interference of reflected and incident waves leads to a resulting disturbance of the medium that is irregular and non-repeating.

    In March 1905 Einstein published a paper on the photoelectric effect entitled "On a Heuristic Viewpoint Concerning the Production and Transformation of Light" in which he proposed the idea of energy quanta and postulated light exists as tiny packets, or particles, called photons.

    In that paper he stated Energy, in the propagation of a ray of light, is not continuously distributed over steadily increasing spaces, but it consists of a finite number of energy quanta but he did not say why.

    Even so many fell the idea of light quanta contradicts the wave theory of light that follows naturally from James Clerk Maxwell’s equations for electromagnetic behavior and, more generally, the assumption of infinite divisibility of energy in physical systems.

    Additionally he did not address the issue of how these "tiny packets" of energy called photons can move through space at the speed of light. This present a problem because he showed that energy and mass are equivalent and that the mass of any object or particle moving at the speed of is infinite. 
    Therefore, if energy is equivalent to mass one would assume that energy required to move a photon at the speed of light would be infinite.

    However, Einstein gave us a way to define electromagnetic energy in a manner which is not only consistent with his theories but also with our classical understanding of nature when, in his General Theory of Relativity he showed that matter can be converted into energy or energy into matter according to the equation E=mc2.

    For example Einstein defined the origin of the mass component of particles and all other objects, such as the sun in terms of curvature or distortion in the continuous field properties of space-time not in terms of their particle properties.

    QED defines the fundamental unit (quanta) of light as "bundles of pure energy traveling at the speed of light with the unique property of being both particle and wave. However this means that as light moves through space-time the peaks and troughs of its wave properties would cause positive and negative spatial displacements in the "surface’ of space time.

    Yet, it is difficult to understand how a spatial displacement can be responsible for of electromagnetism and how and why its wave properties morph to the particle QED defines as the photon when it is observed or interacts with matter because he CHOSE to use time or a displacement in space-time dimension to define mass and energy and not its spatial properties.

    Yet he gave us the ability to form a physical image of this how the spatial properties of a photon’s wave packet are responsible for its movement through space when he defined its geometric properties in terms of the constant velocity of light and a dynamic balance between mass and energy because that provided a method of converting a unit of time in a space-time environment to a 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.

    The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy 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 matter and energy 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.

    However, this change in perspective gives one the ability to understand how the energy of a photon can move through space at the speed of light why it becomes a particle when interacting with matter in terms of the concepts of his theories.

    For example as waves travel through water; they do not take the water with them because as wave arrives it lifts the water particles, they then travel forward, down and back so that each particle completes a circle. Circling movements of particles near the surface set off smaller circling movements below them therefore the waves don’t actually move the water forward. In other words the particles in a wave do not move with respect to space but exchange their potential energy of the water for kinetic energy associated with the wave’s movement.

    Similar to wave on water the trough of a light wave would create a point with a positive curvature on a "surface" of the three-dimensional space manifold with respect to a fourth *spatial dimension which would present itself as the potential energy Einstein associated with mass. That point in space would then travel forward and up and back so that each one completed a circle without moving with respect to background of space. As the wave passed this point the potential energy of positive curvature in four "spatial" dimensions Einstein associated with mass would be converted to kinetic energy associated with a moving mass. In other words the wave packet of a photon can move though space at the speed of light because similar to a wave on water light waves do not cause a point in space to move with respect to the background of space-time.

    This suggest that light is not electromagnetic wave but an energy wave in space-time which is the result of the potential energy created by the trough of a wave on its "surface" being converted to the kinetic energy associated with its peak thereby causing what is called light to move through space.

    However, this also tell us when viewed in terms of their spatial properties that the electromagnetic properties of a light wave are the result of its propagation and not the casualty as is suggested by Maxwell’s equations.

    (Later it will be shown in terms of those spatial properties the reason why this wave becomes a particle when interacting with matter but for now we would like to focus our attention on electromagnetic properties of light or a photon’s wave packet)

    As was mention earlier a wave on the two-dimensional surface of water 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 will be 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.

    Similarly a matter 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 a matter 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.

    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 define the causality of electrical component of electromagnetic radiation 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.

    However, Classical Mechanics tells us a horizontal force will be developed by that perpendicular or vertical 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.

    This shows that one can use the spatial properties of Einstein’s theories to derive causality of the electromagnetic forces of light and how the wave packet Quantum Electrodynamics associates with a photon is propagated through space by extrapolating the laws of classical mechanics in a three-dimensional environment to one consisting of four dimensional space-time or four *spatial* dimensions.

    However viewing a light in terms of the spatial instead of the time properties of his theories allows one to understand how why it always appears as a particle when measured or observed.

    For example in the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown one can physical derive photonic properties of light by extrapolating the laws of classical wave mechanics in a three-dimensional environment to a matter energy wave on a "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 one consisting of four spatial dimensions.

    The existence of four *spatial* dimensions would give a matter 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.

    Classical mechanics tells us the energy of a resonant system can only take on the discrete or quantized values associated with it fundamental or a harmonic of its fundamental frequency.

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

    Yet one can also define the boundary conditions required to establish the standing wave component of a resonant system mentioned earlier that is responsible for it its particle properties as defined by QED.

    For example in classical physics, 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.

    The confinement of the “upward” and “downward” oscillations of the field properties of mass with respect to a fourth *spatial* dimension is what defines the spatial boundaries that enables the formation of a resonant system which the article “Why is energy/mass quantized?” defined as being responsible for a particle.

    When a wave on water comes ashore the energy associated with its wave properties is confined to a specific region of the shoreline.

    Similarly when a photon’s wave packet is measured or observed a portion of its wave energy is transmitted to the measuring instrument while some of it may be redirected or reflected similar to a wave striking the shoreline. In other word the energy wave which earlier was define as being responsible for the transmission of light interacts with measuring equipment for the same reason a water wave interacts with the shoreline.

    However it also explains why light is always observed as a particle when it encounters encounters a measuring instrument or is observed.

    In the quantum mechanical system described above such as light interacting with a particle, resonance only occurs when the frequency at which the force applied is equal or nearly equal to one or a multiple of the natural frequencies of the system on which it acts. In other words light when confined to three-dimensional space by interaction with a particle it will always present itself as the resonant structure that has the energy equal to one or a multiple of the natural frequency of space time. The remaining energy will be radiated through space as light with a lower frequency.

    In other words the particle component of light or an electromagnetic wave is not the cause of its interaction with particles but a result of it.

    However one can use the above model to explain why photons do not interact with each other because similar to waves on water if their is no obstruction to hinder their movement a wave will not interact with each other.  In other words, photon do not interfere with each other for the same reason that all energy waves do not.

    Summing up, Einstein genius allows us to view his theory in either four dimensional space-time or four spatial dimensions. As was shown above changing ones perspective on his theory from time to its spatial equivalent allows one to define light as an energy wave in space and shows the electromagnetic properties are the result NOT the casualty of its propagation but a result of it. Similarly it shows the particle component of light is not the cause of its interaction with a particle but a result of it.

    It is important to note the validity these conclusions cannot be falsified if one accepts the validity of his theories.

    Later Jeff

    Copyright Jeffrey O’Callaghan 2019

    The post Particles as standing waves in space-time appeared first on Unifying Quantum and Relativistic Theories.


    Article Published in 2020

    Articles posted in 2019, 2017 and 18, 2016, 2015, 2014, 2013, 2012, 2011, 2010, 2009, 2008, and 2007 Preface The purpose of this blog is to elaborate on the theoretical ideas contained in its companion book “The Reality of Four Spatial Dimensions“.   In Thomas S. Kuhn’s book “The Structure of Scientific Revolution” he documents the […] The post Article Published in 2020 appeared first on Unifying Quantum and Relativistic...

    Articles posted in 2019, 2017 and 18, 2016, 2015, 2014, 2013, 2012, 2011, 2010, 2009, 2008, and 2007

    Preface

    The purpose of this blog is to elaborate on the theoretical ideas contained in its companion book “The Reality of Four Spatial Dimensions“.  

    In Thomas S. Kuhn’s book “The Structure of Scientific Revolution” he documents the doubts that precipitate a paradigm change in scientific thought.

    For example, even though one could still make accurate predictions of planetary motions using the 15 century geocentric models it became increasing more difficult to integrate that concept with the more accurate observational data provided by the new technologies of that day. This resulted in some scientists questioning their validity.

    He suggests the doubt generated by its persistent inability of to explain new data lead many scientists of that period to adopt the simpler rules of the revolutionary heliocentric model.

    Modern physics appears to be on the verge of a similar revolution because the discoveries of dark matter and dark energy are extremely difficult to integrate into its current theoretical models.

    As Thomas S. Kuhn points out failure of an existing paradigm is a prelude to the search for a new one.

    It continues the search, began in its companion book the “The Reality of Four Spatial Dimensions” to not only explain how one can seamlessly integrate the observations of dark matter and dark energy into a theoretical model based on the existence of four *spatial* dimensions but to provide a unifying mechanism responsible for the four forces of nature (gravity, electromagnetism, the weak, and strong) governing the interactions of matter, energy, space, and time.

    Each article covers one aspect of a search for the “reality” it defines. For example, the article “What is dark energy” defines its casually in terms of an interaction of three-dimensional space with a fourth while others derive the quantum mechanical properties of energy/mass in terms of a resonant system formed by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

    It is not meant to verify the many answers found in the book “The Reality of Four Spatial Dimensions”. Instead it is meant to give the scientific community the specific information and experiment techniques required to either verify or falsify it contents. It relies less on mathematics and more on conceptual logic and thought experiments (much like Albert Einstein did) to show how one can explain and predict all modern observations by extrapolating the rules defining classical three-dimensional space to a fourth *spatial* dimension.

    Copyright Jeffrey O’Callaghan 2011

    “The universe’s most powerful enabling tool is not
    knowledge or understanding but imagination
    because it extends the reality of
    one’s environment.”

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    Particles as standing waves in space-time

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    Einstein questions the existence of a quantum singularity

     A Quantum Singularity is a misnomer because it owes it existence to classical one created by a black hole not to its quantum mechanical properties.  Even so many physicists assume it is the key to unifying Quantum mechanics with Einstein’s General and Special Theories of Relativity because they believe the gravitational collapse of matter in […] The post Einstein questions the existence of a quantum singularity appeared first on Unifying Quantum and Relativistic...

     A Quantum Singularity is a misnomer because it owes it existence to classical one created by a black hole not to its quantum mechanical properties.black_hole_singularigy  Review Unifying Quantum and Relativistic Theories at Blogging Fusion Blog Directory

    Even so many physicists assume it is the key to unifying Quantum mechanics with Einstein’s General and Special Theories of Relativity because they believe the gravitational collapse of matter in a black hole, predicted by his theories also predicts, with equal certainty the existence of a singularity, which by definition is infinitely small and quantum mechanical in nature. Therefore, due to the fact that they are caused by gravitational forces a theory of quantum gravity would be required to define its formation.

    Its existence is based on a mathematical interpretation of General Theory of Relativity which tells us that when star starts to collapse after burning up its nuclear fuel and forms a black hole the gravitational forces of its mass become large enough to cause matter to collapse to zero volume or one that is governed by quantum mechanics.

    However, even though there is observational evidence for the existence of black holes there never will be any for a singularity because according to the General Theory of Relativity nothing, including light can escape form one.

    For example NASA’s Hubblesite tells us that "Astronomers have found convincing evidence for a black hole in the center of our own Milky Way galaxy, the galaxy NGC 4258, the giant elliptical galaxy M87, and several others. Scientists verified its existence by studying the speed of the clouds of gas orbiting those regions. In 1994, Hubble Space Telescope data measured the mass of an unseen object at the center of M87. Based on the motion of the material whirling about the center, the object is estimated to be about 3 billion times the mass of our Sun and appears to be concentrated into a space smaller than our solar system."

    However, as mentioned earlier we will never be able to observe a singularity because they only exist inside black hole.  Therefore to determine their reality we must rely solely on the predictions of the General Theory of Relativity regarding their formation.

    Yet, as mentioned earlier there are some who say the mathematics used to predict the existence of a black hole also predicts, with equal certainty the existence of singularities.  In other words by verifying the existence of black holes though mathematics means that they have also verified the existence of singularities.

    However this would only be true if the mathematics used to predict both a black hole and its singularity conform to the conceptual arguments associated with Einstein General Theory of Relativity because its existence is based solely on that mathematics of that theory and not on observations, as is the case of black holes.

    In other words the fact that we can observe a black hole tells us the mathematics used to predict its existence has a valid basis in ideas of General Relativity. 

    However the same cannot be said about the existence of a singularity because the conceptual arguments found in that theory tells us that we cannot extrapolate the mathematics associated with it to the formation of a black hole.

    To understand why we must look at how it describes both the collapse of a star to a black hole and then what happens to its mass after its formation.

    Einstein in his General Theory of Relativity predicted time is dilated or moves slower when exposed to gravitational field than when it is not.  Therefore, according to Einstein’s theory a gravitational field, if strong enough it would stop time.

    In 1915 Karl Schwarzschild discovered that according to it the gravitational field of a star greater than approximately 2.0 times a solar mass would stop the movement of time if it collapsed to a singularity.  He also defined the critical circumference or boundary in space around a singularity where the strength of a gravitational field will result in time being infinitely dilated or slowing to a stop.

    In other words as a star contacts and its circumference decreases, the time dilation on its surface will increase.  At a certain point the contraction of that star will produce a gravitational field strong enough to stop the movement of time.  Therefore, the critical circumference defined by Karl Schwarzschild is a boundary in space where time stops relative to the space outside of that boundary.

    This critical circumference is called the event horizon because an event that occurs on the inside of it cannot have any effect on the environment outside of it.

    Yet many physicists, as mentioned earlier believe the existence of a singularity is an inevitable outcome of Einstein’s General Theory of Relativity.

    However, it can be shown using the concepts developed by Einstein; this is not true.

    In Kip S. Thorne book "Black Holes and Time Warps", he describes how in the winter of 1938-39 Robert Oppenheimer and Hartland Snyder computed the details of a stars collapse into a black hole using the concepts of General Relativity. On page 217 he describes what the collapse of a star would look like, form the viewpoint of an external observer who remains at a fixed circumference instead of riding inward with the collapsing stars matter. They realized the collapse of a star as seen from that reference frame would begin just the way every one would expect. "Like a rock dropped from a rooftop the stars surface falls downward slowly at first then more and more rapidly. However, according to the relativistic formulas developed by Oppenheimer and Snyder as the star nears its critical circumference the shrinkage would slow to a crawl to an external observer because of the time dilatation associated with the relative velocity of the star’s surface. The smaller the circumference of a star gets the more slowly it appears to collapse because the time dilation predicted by Einstein increases as the speed of the contraction increases until it becomes frozen at the critical circumference.

    However, the time measured by the observer who is riding on the surface of a collapsing star will not be dilated because he or she is moving at the same velocity as its surface.

    Therefore, the proponents of singularities say the contraction of a star can continue until it becomes a singularity because time has not stopped on its surface even though it has stopped to an observer who remains at fixed circumference to that star.

    But one would have to draw a different conclusion if one viewed time dilation in terms of the gravitational field of a collapsing star from the reference frames of all observers as Einstein tells we must because they are all equivalence.

    Einstein showed that time is dilated by a gravitational field. Therefore, the time dilation on the surface of a star will increase relative to an external observer as it collapses because, as mentioned earlier those forces at its surface increase as its circumference decrease.

    This means, as it nears its critical circumference its shrinkage slows with respect to an external observer who is outside of the gravitation field because its increasing strength causes a slowing of time on its surface. The smaller the star gets the more slowly it appears to collapse because the gravitational field at its surface increase until time becomes frozen for the external observer at the critical circumference.

    Therefore, the observations of an external observer would make using conceptual concepts of Einstein’s theory regarding time dilation caused by the gravitational field of a collapsing star would be identical to those predicted by Robert Oppenheimer and Hartland Snyder in terms of the velocity of its contraction.

    However, as was mentioned earlier Einstein developed his Special Theory of Relativity based on the equivalence of all inertial reframes which he defined as frames that move freely under their own inertia neither "pushed not pulled by any force and therefore continue to move always onward in the same uniform motion as they began".

    This means that one can view the contraction of a star with respect to the inertial reference frame that, according to Einstein exists in the exact center of the gravitational field of a collapsing star.

    (Einstein would consider this point an inertial reference frame with respect to the gravitational field of a collapsing star because at that point the gravitational field on one side will be offset by the one on the other side. Therefore, a reference frame that existed at that point would not be pushed or pulled relative to the gravitational field and would move onward with the same motion as that gravitational field.)

    The surface of collapsing star from this viewpoint would look according to the field equations developed by Einstein as if the shrinkage slowed to a crawl as the star neared its critical circumference because of the increasing strength of the gravitation field at the star’s surface relative to its center. The smaller it gets the more slowly it appears to collapse because the gravitational field at its surface increases until time becomes frozen at the critical circumference.

    Therefore, because time stops or becomes frozen at the critical circumference for both an observer who is at the center of the clasping mass and one who is at a fixed distance from its surface the contraction cannot continue from either of their perspectives.

    However, Einstein in his general theory showed that a reference frame that was free falling in a gravitational field could also be considered an inertial reference frame.

    As mentioned earlier many physicists assume that the mass of a star implodes when it reach the critical circumference. Therefore, the surface of a star and an observer on that surface will be in free fall with respect to the gravitational field of that star when as it passes through its critical circumference.

    This indicates that point on the surface of an imploding star, according to Einstein’s theories could also be considered an inertial reference frame because an observer who is on the riding on it will not experience the gravitational forces of the collapsing star.

    However, according to the Einstein theory, as a star nears its critical circumference an observer who is on its surface will perceive the differential magnitude of the gravitational field relative to an observer who is in an external reference frame or, as mentioned earlier is at its center to be increasing. Therefore, he or she will perceive time in those reference frames that are not on its surface slowing to a crawl as it approaches the critical circumference. The smaller it gets the more slowly time appears to move with respect to an external reference frame until it becomes frozen at the critical circumference.Therefore, time would be infinitely dilated or stop in all reference that are not on the surface of a collapsing star from the perspective of someone who was on that surface.

    However, the contraction of a stars surface must be measured with respect to the external reference frames in which it is contracting. But as mentioned earlier Einstein’s theories indicate time on its surface would become infinitely dilated or stop in with respect to reference frames that were not on it when it reaches its critical circumference.

    There are some who claim that irregularities in the velocity of contractions in the mass forming the black hole would allow it continue to collapse beyond its event horizon. However Einstein’s theories tells us that time would move slower for the faster moving mass components than the slower ones thereby allowing the them to catch up with their faster moving onew so they will be moving at the same speed when they reach the event horizon.

    This means, as was just shown according to Einstein’s concepts time stops on the surface of a collapsing star from the perspective of all observers when viewed in terms of the gravitational forces. Therefore it cannot move beyond the critical circumference because motion cannot occur in an environment where time has stopped.

    This contradicts the assumption made by many that the implosion would continue for an observer who was riding on its surface.

    Therefore, based on the conceptual principles of Einstein’s theories relating to time dilation caused by a gravitational field of a collapsing star it cannot implode to a singularity as many physicists believe and must maintain a quantifiable minimum volume which is equal to or greater than the critical circumference defined by Karl Schwarzschild.

    This means either the conceptual ideas developed by Einstein are incorrect or there must be an alternative solution to the field equations that many physicists used to predict the existence of singularities because, as has just been shown the mathematical predications made by it regarding their existence is contradictory to conceptual framework of his theories.

    As was mentioned earlier many physicists think the key to unifying Quantum mechanics with Einstein’s General and Special Theories of Relativity is the singularity that some of the mathematical models say exists in black holes.   However, as was show above their existence is not supported by his theories.

    Later Jeff

    Copyright Jeffrey O’Callaghan 2019

    The post Einstein questions the existence of a quantum singularity appeared first on Unifying Quantum and Relativistic Theories.


    Planck’s Constant as a function of space-time

    In the late 1800’s, physics was facing a crisis. Physicists were trying to model the energy of an atomic orbital.  All the physics they knew at that point said it should look a certain way, but reality looked completely different and no one knew why.  The solution was found by Max Planck.  Previously physicists had […] The post Planck’s Constant as a function of space-time appeared first on Unifying Quantum and Relativistic...

    Review Unifying Quantum and Relativistic Theories at Blogging Fusion Blog DirectoryIn the late 1800’s, physics was facing a crisis. Physicists were trying to model the energy of an atomic orbital.  All the physics they knew at that point said it should look a certain way, but reality looked completely different and no one knew why. 

    The solution was found by Max Planck.  Previously physicists had assumed the microscopic world of an atom’s energy was continuous; that is, the energy of each electron orbital should be able to take on any value.  However, Planck correctly assumed that they could only have the energies that were whole number multiples of some base frequency, which he called "h". In other words, in the microscopic world of atoms energy appears to be quantized in a manner that corresponded to a whole number of the frequency "h" or Plank’s constant.

    However, Einstein, in his General Theory of Relativity defined energy in the macroscopic environment of stars and planets in terms of the continuous field properties of space-time. T

    he problem now became how can one integrate the continuous field properties of energy as described by Einstein with the discontinuous properties of an atomic orbital associated with Planck’s constant.

    In the past most researchers have attempted to do this without success by attempting to define its continuous field properties in terms of the discontinuous quantum properties associated with Planck’s constant.

    However, one may be able to if, instead of attempting to the define those properties in terms of discontinuous properties associated with an atomic orbital, we attempt to derive the discontinuous or quantum properties of an atomic orbital in terms of the continuous field properties of space-time.

    One of the difficulties in visualizing and understanding how this would be possible may be because Planck’s constant is defined in terms of the spatial not the time components of a system while Einstein’s theories define energy in terms of time or a space-time dimension.

    However, Einstein gave us a way to make it easier when he qualitatively and quantitatively derived the geometric properties of his space-time environment in terms of the constant velocity of light and the velocity of objects that do not move at that speed because it allows one to redefine a unit of time he associated with energy in his space-time universe to its equivalent unit of space in a universe consisting of only four *spatial* dimensions.

    In other words, by 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 the geometry pf his space-time universe in terms of its equivalent in four *spatial* dimensions.

    The fact that one can use Einstein’s equations to qualitatively and quantitatively to redefine the displacement in space-time he associated with energy in terms of its equivalent in four *spatial* dimensions is one bases for assuming as was done in the article “Defining energy?” Nov 27, 2007 that all forms of energy in including that of an electron orbiting the nucleus 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 as well as on in four dimensional space-time.

    For example as the article "Why is energy/mass quantized?" Oct. 4 2007 showed one could derive a model for an atomic orbital by extrapolating the laws of a resonance in our three-dimensional spatial environment to one made up of four.

    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 be meet by a matter wave in four *spatial* dimensions.

    The existence of four *spatial* dimensions would give space (the substance) 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 to oscillate with the frequency associated with the energy of that event.

    However, these oscillations in a continuous non-quantized field of energy caused by such an event would result in a resonant system or "structure" to be formed in space.

    Classical mechanics tells us the energy of a stable resonant system can only take on the discreet quantized values associated with its resonant or a harmonic of its resonant frequency.

    In other words, value of Planck’s constant can be understood by assuming that it defines the energy of the fundamental resonate frequency of field properties of space-time as defined by Einstein and therefore, the energies all orbits must be multiples of that fundamental frequency.

    However, one can also use the above theoretical model to explain the why quantum properties of Planck’s constant must be applied to all stable particles including photons.

    In classical physics, 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.

    Therefore, an energy wave, occupying a volume of three-dimensional space would be confined to it. similar to the surface of the paper when it is forced to oscillate “up” or “down” with respect to a fourth *spatial* dimension.

    The confinement of the “upward” and “downward” oscillations of a three-dimension volume with respect to a fourth *spatial* dimension by an observation is what defines the spatial boundaries associated with all particles including photons in the article “Why is energy/mass quantized?“.

    Not only that but it can be shown these resonant systems in a continuous field properties of space-time that are responsible for the incremental energies associated with an atomic orbital and Planck’s constant are also responsible for the energy profiles of black body radiation.

    The ultraviolet catastrophe is the error at short wavelengths in the Rayleigh–Jeans law (depicted as "classical theory" in the graph) for the energy emitted by an ideal black-body. The error, much more pronounced for short wavelengths, is the difference between the black curve (the wrong curve predicted by the Rayleigh–Jeans law) and the blue curve (the correct curve predicted by Planck’s law).

    At room temperature, black bodies emit mostly infrared wavelengths, but as the temperature increases past a few hundred degrees Celsius, black bodies start to emit visible wavelengths, appearing red, orange, yellow, white, and blue with increasing temperature.  By the time an object is white, it is emitting substantial ultraviolet radiation.

    The problem is the laws of classical mechanics, specifically the equipartition theorem, states that black-bodies which have achieved thermodynamic equilibrium are mathematically obligated (by classical, pre-quantum, laws) to radiate energy in the form of ultraviolet light, gamma rays and x-rays at a certain level, depending on the frequency of emitted light.

    However, observations of black body radiation indicate that there was less and less energy given off at high end of the spectrum.

    Einstein pointed out this difficulty could be avoided by making use of a hypothesis put forward five years earlier by Max Planck.  He had hypothesized that electromagnetic energy did not follow classical laws, but could only oscillate or be emitted only in discrete packets of energy proportional to the frequency, as given by Planck’s constant.  In other words, the light waves of each frequency in a black body could not have any energy but are limited to a few discrete values.

    However, as mentioned earlier the article "Why is energy/mass quantized?" showed energy of a photon at each frequency could be understood by extrapolating a physical image of a resonant system in three-dimensional space to a fourth *spatial* dimension similar to how Einstein was able to from a physical image of gravity.

    For example, as the above theoretical model shows using only the concepts of classical physics and field properties of Einstein’s Theory of Relativity a photon could only have the discrete energies or frequencies that are a fundamental or harmonic of the energy of an environment which would be determined by the temperature of the one it was occupying. Therefore, according to the above theoretical model any frequency other than that would be irregular and non-repeating and would be absorbed into the fundamental or harmonic frequency of that environment.

    In other words, it explains in terms of a physical image based on our classical reality why black-bodies which have achieved thermodynamic equilibrium are mathematically obligated by to radiate energy in the form of ultraviolet light, gamma rays and x-rays at  certain discrete levels, depending on the frequency of emitted light because of the field properties of Einstein space-time universe.

    As was shown above one can use the resonate field properties of a space-time environment to explain why the energy of a black body is what it is and why all particles AND the electrons orbiting in atoms can only have the energies that are a whole number multiples of the energy associated with Planck’s constant "h".

    It should be remembered; Einstein’s genius allows us to choose if we want to view the physical properties of Planck’s constant in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the particle and wave properties microscopic quantum world as well as microscopic one of Einstein thereby giving us a new perspective on the physical relationship between particles and waves.

    Later Jeff

    Copyright Jeffrey O’Callaghan 2019

    The post Planck’s Constant as a function of space-time appeared first on Unifying Quantum and Relativistic Theories.


    4 spatial dimensions and A Theory of Everything

    One cannot deny that Quantum mechanics, the theory that defines the tiny world of particles and Einstein’s theories, the one that defines what we see through a telescope have been the most successful scientific theories of modern times However, attempts to bring these two theories together and define "A Theory of Everything" have been unsuccessful. […] The post 4 spatial dimensions and A Theory of Everything appeared first on Unifying Quantum and Relativistic...

    One cannot deny that Quantum mechanics, the theory that defines the tiny world of particles and Einstein’s theories, the one that defines what we see through a telescope have been the most successful scientific theories of modern times However, attempts to bring these two theories together and define "A Theory of Everything" have been unsuccessful.

    However, the fact that we have been unable to do so suggests that one or both of these theoretical models does not describe the true nature of reality because the world we see through a telescope must have its foundations in the world of the very small therefore they must be connected.

    There can be many reasons for this.  One is that foundational assumptions of either or both of them is incorrect.  In other words, the world of the tiny may not be governed by probabilities as quantum theory suggests or the world, we see though a telescope may not be ruled by relativistic properties of four dimensional space-time.

    However, there is another possibility that many have over looked is that even though their mathematics makes very accurate perditions of experimental observations they do not accurately define reality of their operating environments.

    For example, Einstein mathematically defined the physical structure of the universe in terms of the geometry four dimensional space-time.

    However, when using the constant velocity of light and the velocity of objects that do not move at that speed to define its geometric properties he provided a way of mathematical converting a unit of time in a space-time universe to unit of space in one physically consisting of only four *spatial* dimensions.

    In other words, their is an equally valid interpretation of his mathematics in terms of only four spatial dimensions.

    Since both of these solutions that of four dimensional space-time and four spatial dimensions would yield the same numerical results it gives one a different way of connecting his theories to those of Quantum mechanics based on the physical properties of four spatial dimensions instead of four dimensional space-time.

    Quantum Theory on the other hand defines tiny world of particles in terms of the non physical probabilities associated with Schrödinger wave equation which as mentioned earlier no one has been able to physical connect to the space-time universe define by Einstein.

    However, the fact that Einstein provided an alternative solution to his mathematics in terms of four spatial dimensions suggests it may be possible to make that connection and therefore define a Theory of Everything by using the alternative solution of four spatial dimension that his theory provides instead of one based on four dimensional space-time.

    For example the article "Why is mass quantized?" Oct. 4, 2007 showed one could derive the quantum mechanical properties of energy in terms of a resonant "system" or structure formed by a energy wave on the surface of a three-dimensional spatial manifold with respect to a fourth *spatial* dimension.

    Briefly that article 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 can be meet in one consisting of terms of four spatial dimension.

    Its continuous properties would allow an energy wave on a "surface’ of a three-dimensional space manifold to oscillate with respect to a fourth *spatial* dimension thereby fulfilling one of the requirements for 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 with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

    Therefore, these oscillations in a continuous non-quantized field of energy would meet one of the requirements mentioned above for the formation of a resonant system or "structure" in space.

    Observations of a three-dimensional environment show the energy associated with resonant system can only take on the incremental or discreet values associated with a fundamental or a harmonic of the fundamental frequency of its environment.

    Similarly the energy associated with resonant systems in four *spatial* dimensions could only take on the incremental or discreet values associated a fundamental or a harmonic of the fundamental frequency of its environment.

    These resonant systems in a space-time environment would be responsible for the incremental or discreet energy associated with quantum mechanical systems.

    Another requirement for a resonate system to be formed is that the wave must be confined to specific volume of space.

    However, one can also define the confinement of the resonant component of a particle and therefore establish a physical connection to the wave particle duality quantum mechanics associates with energy in terms of the relativistic properties of four *spatial* dimensions.

    In physics, 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.

    The confinement of the "upward" and "downward" oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries associated with a particle in the article "Why is energy/mass quantized?".

    In other words, an energy wave in four *spatial* dimensions will maintain its wave properties unless it is confined to three by an observation, therefore it it always be view as a particle when an observation is made and any energy left over from the formation of its resonate structure will be radiating from the point of observation in the form of light or an energy wave.

    The physics of wave mechanics also tells us that due to their continuous properties the energy waves the article "Why is energy/mass quantized?" Oct. 4, 2007 associated with a quantum system 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 that quantum properties of energy 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.

    (Some may question the fact that the energy wave associated with particle would be distributed over the entire universe.  However, the relativistic properties of space-time and four spatial dimensions tell that 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 it velocity vector is zero.  In other words, it’s energy is distributed or simultaneous exists at every point in the universe along its velocity vector.  There can be not other conclusion if one accept the validity of Einstein’s theories.)

    As mentioned earlier the article “Why is energy/mass quantized?” shown a quantum particle is a result of a resonant structure formed by an energy wave 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 found 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 shows how, by interpreting Einstein space-time theories in their equivalent four spatial dimension one can connect the non physical probabilities associated with Schrödinger wave equation to the reality of the world defined by him.

    Additional it shows, by changing our interpretation of Einstein’s theories from four dimensional space-time to it equivalent in four spatial dimensions allows one to clearly understand the physical connection between the probabilistic world of quantum theory and the relativistic world of his theories, thereby allowing one to form a Theory of Everything.

    Later Jeff

    Copyright Jeffrey O’Callaghan 2019

    The post 4 spatial dimensions and A Theory of Everything appeared first on Unifying Quantum and Relativistic Theories.


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