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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 2021

“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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Articles posted in 2021 2020, 2019 , 2017 and 18 , 2016 , 2015 , 2014 , 2013 , 2012 , 2011 , 2010 , 2009 , 2008 , and 2007

 

Please click here for a brief summary of the ideas presented in this blog.

Some proponents of quantum mechanics have suggested that objective reality does not exist. However, if it does not how can any. For example, Planck defined his constant by observing the heat radiation given off by vibrating atoms. However, if that OBJECTIVE REALITY did not exist, how could he have observed it? One cannot say that objective reality does not exist based solely on a mathematical definition such as Quantum mechanics does if that math is based on that reality. This is because math allows for defining one in terms of what it is not.

For example, if you were asked to predict why we observed two apples on a table in a dark room you could say that there are four apples and two were taken away or there were 6 and four were removed. However, both give a correct prediction of what we observe however only one correctly defines its reality. One way to determine which one does would be to observe their environment. Granted we may not be able to so in the dark but we could determine the average weight of an apple by weighing and counting the number in a bushel of them and use that information to determine how many of them were present before two were removed.

There little doubt that quantum mechanics makes extremely accurate predictions and that the reality it defines is incomparable with the classical one we can observe.

As was mentioned earlier one way to distinguish which one is correct is to observe its environment which is what Planck did when he observed the heat radiation given off by vibrating atoms.

This suggests even though we may never be able to observe a quantum environment we can observe the mechanisms that interact to create the reality we can observe. This MAY repeat MAY to allow us to separate the reality of a prediction from a non-reality. For example, if we can define a mechanism based on observations of a classical environment for the quantum one or define a reason for the observable properties of classical environment in term of math of quantum mechanics, we MAY repeat MAY be able to determine which one defines reality. However, we should ALWAYS repeat ALWAYS remember that one cannot observe a reality based exclusively on math.

Quantum mechanics assumes the mathematical evolution of the wave function is responsible for quantization of ALL mass and energy.  Additionally, it assumes it exists in a superposition of several eigenstates and only reduces or COLLAPSES to a particle when it interacts with the external world.

While Einstein defined gravity in terms of how energy density of space effects the geometry of space-time.

THEREFORE ONE CAN PROVIDE A BRIDGE BETWEEN QUANTUM MECHANICS AND RELATIVITY  DEFINITION OF GRAVITY IF ONE CAN SHOW HOW AND WHY ENERGY DENSITY OF SPACE IS CONCENTRATED IN QUANTIZED UNITS OF SPACE TIME IN TERMS A GEOMETRY OF SPACE TIME.

But before we can understand how to do this we need to establish a connection between the mathematical evolution of the wave function, its collapse and the physical evolution of both electromagnetic and gravity waves. This can be accomplished because as was mentioned earlier in Relativity evolution of space-time is the result of an electromagnetic wave while, as was also mentioned earlier the wave function represents how a Quantum environment evolves to create a particle.

This commonality suggests the wave function MAY BE a mathematical representation of an electromagnetic wave in space-time. This means to derive the reason for its collapse in terms of space-time one must physically connect its evolution to it.

This can be done by using the science of wave mechanics and the fact that an electromagnetic wave moves continuously through space-time unless it is prevented from moving through time by its energy interacting with objects or an observer in three-dimensional space, resulting in its energy confined to it. The science of wave mechanics also tells us the three-dimensional “walls” of this confinement will result in its energy being reflected back on itself thereby creating a resonant or standing wave in three-dimensional space. This would cause the energy of an electromagnetic wave to be concentrated at the point in space were a particle would be found. Additionally, wave mechanics also tells us the energy of a resonant system such as a standing wave can only take on the discrete or quantized values associated with its fundamental or a harmonic of its fundamental frequency that the wave function associates with a particle. Putting it another way one can explain how and why the wave function reduces or COLLAPSES to a particle when it interacts with the external world if one assumes it is mathematical representation of an electromagnetic wave in space-time.

The boundaries or “walls” of its confinement would be defined by its wave properties. If an electromagnetic wave is prevented from moving through time it will be reflected back on itself. However, that reflected wave still cannot move through time therefore it will be reflected back creating a standing wave. The wave itself defines its boundaries because if it cannot move though time it MUST STAND in place in the form of a standing wave called a photon. Putting it another way a particle is a wave that is moving ONLY IN time and NOT THROUGH time and space.

In other words, if an electromagnetic or any energy wave is prevented from moving through space time either by being observed or encountering an object it is reduced or “Collapses” to a form a standing wave that would define the quantized energy quantum mechanics associates with a particle.

As was mentioned earlier Einstein defined gravity in terms of how energy density of space effects the geometry of space-time.

Therefore, one can define why gravity is quantized in terms of the how relativity defines the energy density of space in terms of the presence of a quantized unit of energy or a particle ofmatter.

This provides a bridge between quantum mechanics and relativity in terms of how it CAN define the quantization of the mass associated with a particle and therefore its gravitational potential

Please click here for a brief summary of the ideas presented in this blog.

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. However, as is shown below The General Theory of Relativity tells us the strength of the gravitational field at the event horizon of a black hole causes time to stop for all observers.. The question is how can matter move beyond the event horizon if time has stopped with respect to all reference frames. Since motion is define as the change in an objects position over time the General Theory of Relatively does not break down because it tells us the movement of all objects and matter must also stop at that point. Therefore it can not continue to collapse to the point called a singularity.

    In other words, based on the conceptual principles of Einstein’s theories relating to time dilation caused by the gravitational field of a black hole its laws do not break down because it tells us time freezes at its “surface” or event horizon with respect to all observers. This means it must maintain a quantifiable minimum volume which is equal to the one defined by the radius of it event horizon. Therefore, a singularity cannot form at its center because matter cannot continue to or collapse beyond that point.

    The question we need to answer is should we assume that quantum mechanics breaks down because it predicts the existence of a singularity in the center of a black hole

    Einstein told us 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 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.

Please click here for a brief summary of the ideas presented in this blog.

Quantum mechanics assumes the mathematical evolution of the wavefunction is responsible for quantization of ALL mass and energy.  Additionally, it assumes it exists in a superposition of several eigenstates and only reduces or COLLAPSES to a particle when it interacts with the external world.

Therefore, many feel detecting gravitons, the hypothetical quanta of gravity, would prove gravity is quantized. The problem is that gravity is extraordinarily weak and for that reason, detecting them is extremely difficult.

However, Einstein in his General Theory of relativity defined gravity in terms of the energy density of space. Therefore, one way of defining quantum gravity would be to define how and why it is quantized in terms in terms of his theory in a manner that is consistent with the mathematical foundations of Quantum mechanics.

The fact gravitational waves have been observed suggests it has properties similar to other energy waves, such as electromagnetic with one very important difference: it does NOT interact with matter or an observer in the same way as they do. This suggests the reason a graviton is so hard to detect while the photon or quantum electromagnetic energy is MAY NOT be related to its weakness but to how it interacts with its environment.

But before we can understand why we need to establish a connection between the evolution of the

wavefunction, its collapse and electromagnetic waves. This can be accomplished because in Relativity evolution of a space-time environment is defined by an electromagnetic wave while, as was also mentioned earlier the mathematics of the wave function defines how a Quantum environment evolves to create a particle.

This commonality suggests the wave function MAY BE a mathematical representation of an electromagnetic wave in space-time. However if this is true one should be able to derive the reason for its collapse in a manner that is consistent with the mathematical foundations of Quantum mechanics.

This can be done by using

the science of wave mechanics and the fact that Relativity tells us an electromagnetic wave moves continuously through space-time unless it is prevented from moving through space by someone or something interacting with it. This would result in it being confined to three-dimensional space. The science of wave mechanics also tells us the three-dimensional “walls” of this confinement will result in its energy being reflected back on itself thereby creating a resonant or standing wave in three-dimensional space. This would cause its to energy COLLAPSE or to be concentrated at the point in space were a particle would be found. Additionally, wave mechanics also tells us the energy of a resonant system such as a standing wave can only take on the discrete or quantized values associated with its fundamental or a harmonic of its fundamental frequency that the wave function associates with a particle.

(The boundaries or “walls” of its confinement would be defined by its wave properties. If an electromagnetic wave is prevented from moving through space it will be reflected back on itself. However, that reflected wave still cannot move through time Therefore, it will be reflected back creating a standing wave. The wave itself defines its boundaries because if it cannot move though time it MUST STAND in place in the form of a standing wave called a photon. Putting it another way a particle is a wave that is moving ONLY IN time and NOT THROUGH time and space.)

In other words, if an electromagnetic wave is prevented from moving through space-time either by being observed or encountering an object it is reduced or “Collapses” to a form a standing wave that would create a QUANTIZED repeat QUANTIZED increase the energy density of the space it occupies.

As was mentioned earlier Einstein in his General Theory of Relativity defined gravity in terms of the energy density in a space-time environment. Therefore, this provides an explanation which is consistent with foundational assumptions of quantum mechanics for the existence of a graviton as being the result of QUANTIZED increase in the energy density of space-time caused when an electromagnetic wave collapses due to an interaction with its space-time environment.

This also explains the reason the graviton has not been observed MAYBE because, as was mentioned earlier gravity waves do not interact or exchange energy with their environment and therefore, their energy will not be confined to three-dimensional space and quantized as is the case with electromagnetic waves.

For example, gravity waves have only been observed when they squeeze and stretch space. However, that observation does not result in an exchange of energy between it and the observer.

This is similar to how a wave on water does not exchange energy between water molecules it just “squeezes” and “stretches” the space between them returning them to their original position after it has passed.

However, quantum mechanics assumes the wave function reduces to a quantized unit of energy ONLY when it is observed or interacts with its environment.

This suggests the reason why a graviton is so hard to detect MAY NOT be because it is so weak but MAY be related to how we are trying to observe it. This is because gravity waves, as was just mentioned they do NOT interact with either the environment they are moving through or the equipment used to observe it. Therefore, according the rules of quantum mechanics the wave function SHOULD NOT and WILL NOT collapse to create a graviton unless we can find a way to get it to interact with its environment

Putting it another way just watching it pass by will not produce a graviton.

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