The standard interpretation of his mathematics suggests that gravity is cause by a displacement in a three-dimensional space manifold with respect to time.

However an equally valid one defines gravity in terms of an environment consisting of only four *spatial* dimensions because by defining its geometric properties in terms of the equation E=mc^2 and the constant velocity of light gives one the ability to redefine a unit of time he associated with gravity in his space-time universe to unit of space in one consisting of only four *spatial* dimensions.
In other words it gives us mathematical way to convert a universe composed of four dimensional space-time to one made up of four *spatial* dimensions because one can define distance in it in terms of time times the constant velocity of light.

Even though these two interpretations yield the exactly the same numerical results describing our universe there is a very significant qualitative difference in that we observe we can only move in one direction forward with respect to a time dimension while in the spatial dimensions we can move in two direction upward or downwards backwards or forward.

This is significant because if gravity is caused by displacement in a three-dimensional space manifold with respect to spatial not a time dimension it may be possible to create a negative or antigravity potential in space.

In other words if gravity is cause by a displacement in a three dimensional space manifold with respect to a spatial instead of a time dimension it, at least in theory should possible to create an oppositely directed displacement which for all practical purposes would repel the gravitational field of normal matter and cause it to be propelled thought space.

It should be remember the existence of a time or space time dimension is the based exclusively on Einstein’s mathematics because no one has or will ever be able to directly observe it.

However the same could be said about a fourth *spatial* dimension in that it cannot be directly observed. But there is an experiment that could without ambiguity determine if our universe is physically made up of four *spatial* dimensions or four dimensional space-time.

As describe in the NewScientist article “Antimatter mysteries 3: Does antimatter fall up?” Apr 29, 2009, it is possible use uncharged particles to prevent electromagnetic forces from drowning out gravitational effects of antimatter. First we will be required to build highly unstable pairings of electrons and positrons, known as positronium, then excite them with lasers to prevent them annihilating too quickly. Clouds of antiprotons will rip these pairs apart, stealing their positrons to create neutral antihydrogen atoms.

Pulses of these anti-atoms shot horizontally through two grids of slits will create a fine pattern of impact and shadow on a detector screen. By measuring how the position of this pattern is displaced, the strength – and direction – of the gravitational force on antimatter can be measured

However if it is found the gravitational field of antiparticles opposes that of particles then we will be required to rethink our understanding gravity because Einstein’s Theory of General Relativity tells that objects that create gravitational field cause time to “move” slower with respect to a region of space that does not contain mass. In other words Einstein theory tells if antiparticle posses a negative gravitational potential time should be accelerated or move in the “opposite direction” were they exist with respect to the slowing he associated with gravity; something which would be observable in particle accelerators if it were to happen. The fact that this has not been observed tells us if antiparticles do have a negative gravitational potential it cannot be related to the physical property of a time dimension.

However as was mentioned earlier the fact that one can use Einsteinâ€s equations to qualitatively and quantitatively redefine the energy he associated with gravity in a space time environment in terms of four *spatial* dimensions would give us a viable explanation for the negative gravitational potential antimatter that would be consistent with his theories.

Later Jeff

Copyright Jeffrey O’Callaghan 2018

The post Antigravity propulsion; a real possibility. appeared first on Unifying Quantum and Relativistic Theories.

For example in his General Theory of Relativity he derived the causality of gravity in terms of a curvature in the geometry of space and time.

One can understand how in terms of the physical image of a marble on a curved surface of a rubber diaphragm.  The marble follows a circular pattern around the deformity in its surface. Similarly planets revolve around the sun because they follow a curved path in the deformed “surface” of space-time.

In other words he was able to integrate the physicality of gravity into our consciousness in terms of a physical image based on observing a marble moving on a curved surface.

However he was unable to do the same for electrical forces as was documented by the American Institute of Physics.

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

In other words because time is only observed to move in one direction forward, a space-time universe can only support a force that cause movement in one direction towards an object such as gravity. 

However, it would be easier to form a physical image of electrical forces if one converts or transposes Einstein’s space-time universe to one of only four *spatial* dimensions the because of the bidirectional symmetry of the spatial dimension.

In other words because time is only observed to move in one direction forward, a space-time universe can only support a force that cause movement in one direction towards an object such as gravity while one made up four *spatial* dimensions could support the towards and away or bi-directional movement associated with electromagnetism. Therefore because of the bidirectional symmetry of a spatial dimension it would be easier to form a physical image of electrical forces if one converts or transposes Einstein’s space-time universe to one of only four *spatial* dimensions.

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

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

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

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

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

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

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

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

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

This shows how one can define a physician image for the causality electromagnetic forces in terms of the existence of four spatial dimensions.

Einstein was unable to accomplish this in terms of four-dimensional space-time because as mentioned earlier time is only observe to move in one direction forwards and therefore could not support the bi-directional component of electromagnetic forces.

However this also shows that Einstein was right, as was mentioned above in the  American Institute of Physics article that electromagnetism and gravity can both be explained as aspects of some broader mathematical structure because as was shown above using only valid mathematical rules one can transform his space-time equations to four *spatial* dimensions thereby allowing one to form a clear physical image explaining the causality electromagnetic forces.

It should be remember that Einstein’s genius allows us to choose whether to create physical images of an unseen “reality” in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in choose terms of energy/mass and the constant velocity of light.

Later Jeff

Copyright 2018 Jeffrey O’Callaghan

The post Electromagnetism: a new perspective Einstein would have like. appeared first on Unifying Quantum and Relativistic Theories.

For example both Einstein’s General Theory of Relativity define existence in terms of a space-time geometry.  However it only defines the forces it encompasses and not how they come together to create space or as John Wheeler put it “Matter tells space how to curve. Space tells matter how to move.”

But this does not tell us what space is made of it only tells us how matter interacts with it to cause it to move in the space-time environment defined by him.

Granted it is possible in the abstract mathematical world of Einstein’s theories to fully define an environment without addressing the question as to why it is there as he seems to have done.  However his theories are based on a universe where cause and effect rule. Therefore if they are valid one should be able to define why it exists in terms of those parameters.

However Einstein also told us that in a space-time environment there is a causal link between mass and energy defined by E=mc^2 and space.  For example converting energy to mass causes the curvature in space-time to increase while changing mass to energy causes it to decrease.

This suggest that their maybe a causal link between mass and the existence of space.

However it is difficult to form a clear picture of how mass can interact with time to create space because as was shown in the article “Defining what time is” Sept. 20, 2007 most view time not in terms of the physical properties of space but as an irreversible physical, chemical, and biological change in it. Therefore it is difficult to understand how these abstract properties of change can interact with mass to create the physicality of the world we live in.

However Einstein gave us the ability to solve this dilemma and develop more direct understanding of how and why mass can interact with the physical geometry of our universe to form space when he used the equation E=mc^2 and the constant velocity of light to define the geometric properties of mass in a space-time universe.  This is because that provided a method of converting a unit of time in a space-time to unit of space in four *spatial* dimensions.  Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

This makes it possible as was shown in the article “Defining energy” Nov 27, 2007 to derive all forms of motion caused by mass, in terms of a physical displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

In other words one can use Einsteinâ€s theories to redefine how and why mass can tell space how to curve and how space tells matter how to move based exclusively on the physicality most associate with space instead of non-physical properties of time.

However this also provides a way of understanding why space is here in terms of an interaction between matter and energy defined by Einstein.

For example when the air in a balloon is cooled it becomes more concentrated the magnitude of the curvature in its surface increases and its volume decreases while heating it causes it to expand resulting in decreasing its curvature and increasing its size.

In other words the balloon owes its existence and structure to the dynamic forces of the air pushing its two dimensional “surface” towards a third dimension because if they were not there it could not maintain in physical structure.

Similarly Einstein theories tell us if mass is converted to energy the magnitude of the curvature in space-time and the strength of the gravitational field associated with it decreases while converting energy to mass causes an increase in the curvature of space-time and the gravitational field associated with it.

Yet as mentioned earlier it is difficult to form a clear picture of how three-dimensional space can interact with time to form the structural boundary by which the dynamic forces of energy and mass can push against to causes its curvature to change because of its abstract properties.

However one can develop a much clearer understanding of how the dynamic properties of mass and energy can interact to create the physical structure of space if one redefines Einstein space-time universe as was done earlier to its equivalent in four spatial dimensions.

For example as mentioned earlier the structure of a balloon is the result of its two-dimensional membrane or manifold restricting or preventing the air in the balloon from moving freely in the third spatial dimension.

Similarly the “surface” of a three-dimensional manifold would present a barrier for all things made up of mass from moving freely in to the fourth *spatial* dimension because they are three dimensional objects.

However it also gives one the ability to form a physical image of why space is there in terms of the energy contain space pushing on the “surface” of a three-dimensional manifold causing it to expand towards a fourth *spatial* dimension.

In other words similar to a balloon when energy becomes more concentrated in the form of mass the curvature in the surface of space increases and its volume to decreases while making it less concentrated by changing mass to energy causes it to expand resulting in decreasing its curvature and increasing its physical size.

Thus suggests that space exists because of a interaction of mass and energy with the physical geometry of our universe.

It should be remember these same concepts can applied to universe consisting four dimensional space-time because as was shown earlier Einstein gave us the ability to define the physical  relationship be energy, mass and the geometry properties of space in terms of either its spatial or time properties.

In other words the existence of three-dimensional space depends on the energy pushing the “surface” of a three-dimensional space manifold towards a higher fourth dimension which can ether be made up of time or another spatial dimension.

It should also be remember that the reason for this article was not to define the what space is made or what its geometry is only why it is here. Those questions will be answered in future articles.

Later Jeff

Copyright Jeffrey O’Callaghan 2015

The post Why does space exist? appeared first on Unifying Quantum and Relativistic Theories.

For example, if a pair of particles is generated in such a way that their total spin is known to be zero, and one particle is found to have clockwise spin on a certain axis, then the spin of the other particle, measured on the same axis, will be found to be counterclockwise. Because of the nature of quantum measurement, however, this behavior gives rise to effects that can appear paradoxical. For example any measurement of a property of a particle can be seen as acting on that particle (e.g. by collapsing a number of superimposed states); and in the case of entangled particles, such action must also act on the entangled system as a whole. It thus appears that one particle of an entangled pair “knows” what measurement has been performed on the other, and with what outcome, even though there is no known means for such information to be communicated between the particles, which at the time of measurement may be separated by arbitrarily large distances.”

Einstein referred to this as “spooky action at a distance” because it assumed that objects or particle can interact instantaneously, regardless of distance separating them which according to his perception of reality this was not possible.

To demonstrate this he co-authored a paper with Podolsky–Rosen which came to be called the EPR Paradox whose intent was to show that Quantum Mechanics could not be a complete theory of nature because it does not agree with his perception of reality.  The first thing to notice is that Einstein was not trying to disprove Quantum Mechanics in any way.  In fact, he was well aware of its power to predict the outcomes of various experiments.  What he was trying to show was that there must be a “hidden variable” that would allow Quantum Mechanics to become a complete theory of nature

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

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

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

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

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

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

This meant that science has to accept that either the reality of our physical world or the concept entanglement does not exist because they are mutually excessive.

However there are two reasons to side with reality our world over the mathematical one that sides with entanglement.  The first is based on the core principals of Einstein’s theories while the second involves the physical properties of the wave function that quantum mechanics uses to define the probability of a particle’s state.

Einstein’s Theory of Relativity tells us the length of an object or particle contracts; approaching zero as it nears the speed of light.  Additionally he told us that it becomes zero when observed from all other reference frames because at the speed of light its length in the direction of motion becomes zero. 

But his theory also tells us from the perspective of the photon moving at the speed of light, the physical distance between observers and their observations must also be zero because from the photons perspective the observers are moving at the velocity of light with respect to them.

This is true even though the two photons may be traveling in opposite directions because length contraction is based on the absolute value of velocity and therefore is independent of direction. Therefore form their perspective the length of the reference frame containing the observer must be zero.

In other words according to the core principals of Einstein Theory of Relativity two photons will interact instantaneously or appear entangled regardless of the distance separating observers  because from the vantage point of photons because they are moving at the speed of light.

There can be no other interpretation if one accepts the validity of Einstein theories.

However as mentioned earlier one can also understand not only the “reality” behind quantum entanglement of particles that are not moving at the speed of light by deriving the probability functions quantum mechanics associates with Schrödinger wave equation in terms of Einstein theories but the mechanism responsible for its quantization.

However we must first redefine Einstein’s four dimensional space-time universe to four *spatial* dimensions.

(The reason will become obvious later.)

Einstein gave us the ability to do this when he used the velocity of light to define the geometric properties of space-time because it allows one to convert a unit of time in his four dimensional space-time universe to a unit of space identical to those of our three-dimensional space. Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

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

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

This makes it possible as was shown in the article “Why is energy/mass quantized?” Oct. 4, 2007 to understand mechanism responsible for the quantum properties energy/mass by extrapolating the laws of classical wave mechanics in a three-dimensional environment to a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Very briefly that article showed that one can derive the quantum mechanical properties energy/mass by extrapolating the laws of classical resonance to a matter wave in a continuous non-quantized field of energy/mass moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

(Louis de Broglie was the first to predict the existence of a continuous form of energy/mass when he theorized all particles have a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.)

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 in one consisting of a continuous non-quantized field of energy/mass and 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 continuous non-quantized field of energy/mass to oscillate with the frequency associated with the energy of that event.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established in it.

These resonant systems are responsible for the quantum mechanical properties energy/mass.

However assuming energy is result of a displacement in four *spatial* dimension also allows one to define the physicality of the probability distribution associated with the wave function of individual particles by extrapolating the laws of a three-dimensional environment to a fourth *spatial* dimension and how it is physical for the entanglement of particle

As was shown earlier redefining Einstein space-time in terms of four *spatial* dimension tells us that the energy of a photon moving at the speed of light is distributed throughout the universe in a two-dimensional plane that is perpendicular to its velocity vector therefore as the article “The *reality* of quantum probabilities” Mar 31, 2011 showed the probability’s associated with a quantum particle’s wave function would be distributed throughout the entire two-dimensional “surface’ of the three-dimensional space manifold it is occupying with respect to a fourth *spatial* dimension.

The effect of this would be analogous to what happens when one vibrates a ball on a continuous rubber diaphragm.  The oscillations caused by the vibrations would be felt over its entire surface while their magnitudes would be greatest at the point of contact and decreases as one move away from it.

However, this means if one extrapolates the mechanics of the rubber diaphragm to a “surface” of a three-dimensional space manifold one must assume the physical oscillations in the surface of three-dimensional space that associated with the wave function must exist everywhere in three-dimensional space.  This also means there would be a non-zero probability they could be found anywhere in our three-dimensional environment.

This is because Classical Wave Mechanics tells us that 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 quantum system 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,

However this means each individual particle in a quantum system has its own wave and probably function and therefore the total probability of a quantum system being in a given configuration when observed would be equal to the sum of the individual probability functions of each particle in that system.

As mentioned earlier Allen Aspect verified that Bell inequities were violated by the quantum mechanical measurements made on pairs of polarized photons that were space like separated or in different local realities.

Yet, as just mentioned the wave or probability function of a quantum system is a summation of the probably function of all of the particles it contains.  Therefore, two particles which originated in the same quantum system and were moving in opposite directions would have identical wave or probability functions even if they were not physically connect.

The measurements Allen Aspect made on the polarized photon verified that Bells inequity was violated because a correlation was found between the probabilities of each particle being in a given configuration based on the concepts of quantum mechanics.  When this correlation was found many assumed that somehow they must be entangled or physical connected even though they were in different local realities.  In other words the Newtonian concept separability does not apply to quantum environment. 

However, this may not be true.

According to quantum mechanics act of measuring the state of a pair of entangled photons instantly affects the other no matter how far they are apart.  Yet if it is true as mentioned earlier that each entangled particle has an identical wave or probably function as it moves through space the measurement of the state of one particle would be reflected in the measurement of the other.  This is because the probability of them being in a specific state would be determined at the point of origin or where they were entangled and that common probably would be “carried” by each particle until a measurement was made. Therefore when making a measurement on one particle in a close system containing two entangled particles the rules of quantum mechanics tell us that the inequities found in Bellâ€s Theorem should be violated not because they are physically connected in space but because they are connected through their common probability function.

In other words the reason why Bell’s inequity is violated in a quantum system that are not moving at the speed of light with respect to observers is not because the particles are physically entangled or connected in space at the time of measurement but because their individual wave or probability functions were “entangled” or identical at the time of their separation and remained that way until a measurement was made on them.

But to say the correlation of the quantum characteristics of two particles are identical because they are entangle or are physically connected is like saying the correlation between the color characteristics of the hair of identical twins is because they have been physically connect throughout their entire life.

This shows that Quantum Mechanics is a “complete theory of nature” contrary to what Einstein believed because based on the core principals of relativity one can define a mechanism responsible for the correlation of the quantum characteristics of particles that exist in non-local environments by extrapolating the “reality” of a environment governed by the physical laws laid down by him or the rules governing quantum mechanics.

Later Jeff

Copyright Jeffrey O’Callaghan 2014

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However there is a conceptual discontinuity between QFT and its relativistic component because it is based on the abstract properties mathematics while the Einstein’s Theory of Relativity is based on the physical properties of space-time environment.

For example the Schrödinger wave equation that is used to mathematically define a particle in QFT does so in terms of a non-dimensional harmonic oscillator at each point in space but does not define what is physically oscillating while Einstein defines the relativistic properties of space and time in terms of a physical interaction of time with three-dimensional space.  Additionally it is difficult to understand how non-dimensional point oscillation can be responsible for dimensional properties of a particle because by definition it cannot have those properties.

Yet one may be able resolve this issue if one views the relativistic properties of our universe in terms of four *spatial* dimensions instead of four dimensional space-time and define what physically happens to continuous properties of space and time when a particle is created.

(The reason will become obvious later.)

Einstein gave us the ability to do this when he used the velocity of light to define the geometric properties of space-time because it allows one to convert a unit of time in his four dimensional space-time universe to a unit of space identical to those of our three-dimensional space.  Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by mathematically defining the geometric properties of time in his space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry 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 the field properties of four *spatial* dimensions is one bases for assuming, as was done in the article “Defining energy?” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space field with respect to a fourth *spatial* dimension. 

However it also allows one to define the physicality of the harmonic oscillator QFT associates with a particle in terms of physical interaction of the field properties of three-dimensional space with a fourth spatial dimensional similar to how Einstein define gravity in terms of a physical interaction of time with three-dimensional space.

For example the article, “Why is energy/mass quantized?” Oct. 4, 2007 showed that one can explain and understand the physicality of the harmonic oscillator QFT associates with particles terms of the classical field properties of a wave by extrapolating the laws of resonance in a three-dimensional environment to a matter wave moving on “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension.  It also explained why all energy must be quantized or exist in these discrete resonant oscillators when observed.

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 a matter wave moving in 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 with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

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

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.

Therefore these resonant systems in would be responsible incremental or discreet energy associated with quantum mechanical systems.

This allows one to define the physicality of the harmonic oscillators QFT associates with particles in terms field properties of either four dimensional space-time or four spatial dimensions because as was shown earlier they are equivalent.

However, one can also define its field properties of a particle in terms of the boundaries of its harmonic oscillator.

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 a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries of the harmonic resonator associated with a particle in the article “Why is energy/mass quantized?“

However as mentioned earlier it also defines the physical boundaries of the harmonic oscillator QFT associates with a particle in terms of the properties of a wave moving on a continuous field consisting of four *spatial* dimensions or four dimensional space-time because remember as was show earlier they are equivalent

This also provides the ability to understand the inseparability of the concepts of a field and particles in QFT because it clearly defines how one is depend on the other.

However it also explains why a field can display either the properties of a particle or the wave properties of a harmonic oscillator when measured because if one wants to measure the total energy contained in a given volume of space one will observe it as a particle while if one want to measure how it is propagated through space one must observe its wave properties.

Additionally it defines a classical reason why particles sometimes behave like oscillators and sometimes like particle and why it is impossible simultaneously observe these two different properties.

As shown earlier the energy contained in a quanta of space associated with a particle would be defined by the wavelength of its harmonic oscillator.  In other words to observe or measure the particle properties of a given volume of space one has to sample all of its energy leaving nothing of its wave component to measure.  Similarly if one wants to observe or measure fully the wave energy of a quantum of space one would have to sample all of its energy leaving none of its particle properties behind. 

(If one does not want to observe all of the energy in a given volume of space then one would expect that the difference would be made up by the emission of the harmonic oscillator QFT associates with photon or other particle.)

The reason why one cannot simultaneously measure both its wave and particle of the harmonic oscillator it is because as mentioned the energy of a particle is defined by its wave properties. Since the energy that defines a particle is the smallest unit of its harmonic oscillator if one measures its particle properties there would be no wave energy left for measuring its wave proprieties while if someone measure its wave energy there would be no energy left to support its particle properties. Therefore making one of these measurements precludes the other.

This shows that one can integrate the abstract mathematical properties of Schrödinger wave equation or the foundation of Quantum field theory with the continuous physical of space and time In Einstein’s theory of relativity.

It should be remember Einsteinâ€s genius allows us to chose whether to solve all problems in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of energy/mass and the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the spatial as well as the time properties of our universe and gives us a new perspective on the integration of QFT with the relativistic properties of space and time.

Later Jeff

Copyright Jeffrey O’Callaghan 2014

The post Solving the conceptual problems with quantum fields appeared first on Unifying Quantum and Relativistic Theories.

Unfortunately many physicists attempt to define reality based solely on what they measure and do not attempt to conceptually integrate those measurements into the realty we see around us.

One example can be found in Brian Clegg book Before the Big Bang: The Prehistory of Our Universe (p. 137) where he describes how Neils Bohr reacted when Heisenberg proposed his uncertainty principal.
“When Heisenberg first told his boss, Neils Bohr, about the uncertainty principle, he put it across in the form of an imaginary microscope. He described a particle as an electron passing through a make-believe ultra powerful microscope. We use light to examine the object, so a beam of photons (quantum particles just as the electron is) is constantly crashing into the electron. The result is that the electronâ€s path is changed. You canâ€t look at a quantum particle without changing things. Heisenberg is said to have been reduced to tears when Bohr ripped his idea to pieces. Heisenberg had assumed that until the microscope scanned the electron, the electron had an exact position and momentum. He thought it was the process of observing it that messed things up. But actually, Bohr pointed out, the uncertainty was more fundamental than that. There was no need to observe the electron for uncertainty to apply: it was inherent to the nature of a quantum particle.”

In other words Neils Bohr said that because we will never be able to observe an electron without changing it or its environment one must simply accept the fact that we will never be able to understand why it behaves the way it does in terms of the “reality” we see around us.

However the science of physics is defined as “the asking fundamental questions regarding how and why matter and energy interact while demanding the answers be validated by observations.

Yet this definition appears to conflict with Neils Bohr assertion that the uncertainty principal is inherent to the nature of a quantum particle because that immunizes it from such questions.

Additionally he said since it is true that uncertainty principal is inherent to the nature of the unseen world of a quantum particle “Everything we call real is made of things that cannot be regarded as real”.

Yet if one uses his philosophy that “reality” does not exist then the observations used to define that principal also cannot be real or exist because one cannot observe something that does not exist.  In other words the very arguments Neils Bohr uses to support his concept of the uncertainty principal leads to it invalidation.

However history has shown us that one of the advantages to defining the universe that we cannot and will never be able to see in terms of the “reality” of our observable environment is that it limits the ability of our imagination to create nonexistent or fantasy worlds to support them.

For example Einstein mathematically derived the force of gravity in terms of a curvature in a four dimensional space-time universe.  However even though he knew that he would never be able to physically observe how a time dimension interacts with the three spatial dimensions he attempted and succeeded in explaining how a curvature in a space-time environment can result in the force gravity by watching how a marble moved on a curved surface in our observable three dimensional universe.

In other words Einstein not only mathematically quantified the measurements of the force of gravity but he also provided a qualitative explanation of how it could act at distance by anchoring it to the observable properties of an object moving on a curved surface in three-dimensional environment.

This methodology is in sharp contrast to how Newton defined gravity in that he simply accepted the fact that he was able to accurately quantify it using the concept of action at a distance even though he was aware that it disagreed, as the following excerpt from a letter he wrote to Bentley with the “reality” he saw around him.

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

However Einstein’s unwillingness to accept action at a distance gave him the ability more accurately quantify gravity while providing an understanding of how it could act at a distance by aqs mentioned earlier anchoring it to the “reality” of our three-dimensional environment.  Additional it showed that Newton’s concept of absolute space and time only existed in the fantasy world of his imagination because according to Einstein gravity is caused by their variability.

This shows the power of attempting to understand the unobservable in terms of the observable by anchoring it to the “reality” of what we see around us and why we should be skeptical about accepting the validity of the uncertain principal based on Neils Bohr assertion that it is inherent to the nature of a quantum particle

However what is even more damaging to his ideology of blindly accepting a mathematical interpretation of the uncertainty principle, is that it is possible (much as Einstein did) to extrapolate the observable properties of our three dimensional environment to a quantum one as was done in the article “A classical interpretation of Heisenbergâ€s Uncertainty Principal” Dec. 1 2012 to explain and predict how and why it behaves the way it does.

However before we begin we must first reformulate Einstein space-time concept to their spatial equivalent.

(The reason will become obvious latter)

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

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe as was done in the article “The “Relativity” of four spatial dimensions” in terms of geometry of only four *spatial* dimensions.

On advantage to doing this is that it gives one a different perspective on the “reality” of the quantum environment and the uncertainty principal in terms of the observable properties of our three dimensional universe.

For example the article “Why is energy/mass quantized?” Oct. 4, 2007 demonstrated it is possible to understand the quantum mechanical properties of energy/mass by extrapolating the laws of classical resonance in a three-dimensional environment to a matter 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 be meet by a matter wave in 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 with respect to a fourth *spatial* dimension 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 in four *spatial* dimensions.

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

Therefore the discrete or quantized energy of resonant systems in a continuous field of four spatial dimensions could explain the discrete quantized quantum mechanical properties of particles.

However, it does not explain how the boundaries of a particleâ€s resonant structure are defined.

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 a three-dimension volume with respect to a fourth *spatial* dimension is what defines the geometric boundaries of the “box” containing the resonant system the article “Why is energy/mass quantized?” associated with a particle and why quantum systems behave the way they do.

However not only using the properties of a fourth *spatial* dimension allow one to understand why energy/mass in our three-dimensional world in terms of our experiences but it can also be used to explain the uncertainty principle

For example in quantum mechanics, the uncertainty principle asserts that there a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position x and momentum p, can be simultaneously known.

As mentioned earlier one can define a mechanism responsible of the uncertainty principal in terms the geometry of the four *spatial* dimensions because Quantum Mechanics mathematically defines the position and momentum of a particle in terms of non dimensional point.  This means there would be an uncertainty in determining its position because that point could be found anywhere within the volume of the “box” mentioned above.

Similarly there would be an uncertainty in measuring its momentum, again because quantum mechanics defines it in terms of a non dimensional point.  Therefore before one could determine a particle’s momentum one would have to know the exact position of the “end” points one uses to measure its velocity.  However, as mentioned above that non dimension point representing a particle could be found anywhere in the box containing the resonant structure that defined a particle in the article “Why is energy/mass quantized?“  Therefore one could not determine its exact velocity and momentum because there will always be an uncertainty as to where the non dimensional point representing a particle is in the box when the measurement was taken

The reason why one cannot simultaneously measure both with complete accuracy is because the act of measure its momentum or position requires one to access different segments the “box” containing particle.

For example if one wants to make the most accurate measurement possible of its momentum internal to the box one would have to measure the time it took for it to transverse a given segment of it.  However this means that one could not determine its position because it would be changing throughout the entire time that it took it to transverse that portion of the box.

However if one wanted to make the most accurate measurement possible of its position internal to the box it would have to be stationary with respect to the box’s geometry meaning that one could not determine its monument because it would not be moving.  Since these two measurements required one to access different segments of a particles geometry they are mutually exclusive. 

Therefore one cannot simultaneously measure a particle position x and momentum p with complete accuracy.

This defines why, in terms of the reality we see around us there is a limit to the precision with which certain pairs of physical properties of a particle, such as position x and momentum p, can be simultaneously known.

However it also tells us we should always attempt to conceptually integrate our theoretical models into the “reality” of what we “see” around us because it allows one to physically connect the abstract properties of a theoretical environment created by our imagination to the reality of the worlds they are describing thereby limiting its ability to create fantasy worlds such as the one Neils Bohr believed in to explain their theoretical models.

Later Jeff

Copyright Jeffrey O’Callaghan 2014

The post Should we let our imaginations define reality? appeared first on Unifying Quantum and Relativistic Theories.

However finding a way of conceptually integrating them has proven to be extremely difficult for two reasons

The first is that it is impossible to derive a mechanism to explain and predict the continuous properties of four dimensional space-time in terms of quantum mechanics because something that is discontinuous cannot by definition be continuous. 

However one can derive the them in terms of the continuous properties of space-time because something that is continuous by definition can be divided into smaller units. 

Yet the other reason why it is so difficult is because Quantum mechanics defines its domain in terms of the spatial properties of probabilities while Einstein theories define it in terms of the continuous geometric properties of time.

This suggest we may be able to integrate them if we could find a way defining them in the same terms.   In other words redefining the space-time environment of Relativity in terms of the spatial properties of quantum mechanics or redefine the continuous properties of space-time in terms of the quantum properties of quantum mechanics.

However the only realistic option is to redefine the space-time environment of Relativity in terms of the spatial properties of quantum mechanics because as was mentioned earlier it is impossible to derive a mechanism to explain and predict the continuous properties of four dimensional space-time in terms of quantum mechanics because something that is discontinuous cannot by definition be continuous. 

Fortunately Einstein gave us the ability to do this when he used he used the velocity of light to define its geometric properties of space time because it allows one to convert a unit of time in his space-time universe to an equivalent unit of space in four *spatial* dimensions.  Additionally because the velocity of light is constant means it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

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

However as mentioned earlier doing so would also allow one to define a physical mechanism responsible for creating a quantum of space-time in terms of the existence of four *spatial* dimensions.

For example the article “Why is energy/mass quantized?” Oct. 4, 2007 showed it is possible to explain the quantum properties of energy/mass by extrapolating the laws of classical resonance in a three-dimensional environment to a matter wave on the continuous “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 be meet by a matter wave in four spatial dimensions.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a continuous “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 with respect to a fourth *spatial* dimension 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 in four *spatial* dimensions.

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

Therefore the discrete or quantized energy of resonant systems in a continuous four dimensional environment would be responsible for the discrete quantized energy quantum mechanics associated with energy/mass.

However, it does not explain the mechanism responsible for quantizing the space containing energy/mass

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 a three-dimension volume with respect to a fourth *spatial* dimension is responsible for the quantization of four-dimensional space because it would result in the formation of discrete or quantized volumes associated with the observed quantum properties of energy/mass.

In other words defining space in terms of four *spatial* dimensions allows one to conceptually the integrate the discontinuous quantum mechanical properties of energy/mass into the continuous field properties four-dimensional space in terms of a resonant system created by its wave properties.

Physicists should remember it is impossible to derive a mechanism to explain and predict the continuous properties of four dimensional space-time in terms of quantum mechanics because something that is discontinuous cannot by definition be continuous.  However one can understand as was shown above the quantum mechanical properties of space in terms of the continuous properties of space-time because something that is continuous by definition can be divided  into smaller units.

Later Jeff

Copyright Jeffrey O’Callaghan 2013

The post A quantum of space-time appeared first on Unifying Quantum and Relativistic Theories.

According to Newtonâ€s view, force does not the cause motion but only a change in it and because a freely moving object continues to move inertia and motion in itself needs no causal explanation.

However as Gao, Shan points out in on page 29 of his book “God Does Play Dice with the Universe” there is a problem with that concept of motion because:

“According to Newton, neither external force nor internal force is the cause of constant motion. So there is only one possibility left , i.e., that motion has no cause.  In other words the change in position or state of an object due to a constant velocity does not have cause.
However modern science is based on the assumption that all changes in the state of a system require a cause.  In other words one cannot integrate the Newtonian concept of motion or the change in position associated with it into our current scientific paradigms which are based almost entirely on causality”.

Granted Einstein was able to define the causality of the energy associated  with gravity and accelerated motion in terms of curvature in four dimensional space-time and the relativistic properties of motion in terms of that same four dimensional model however he was unable or did not chose to address what causality of the energy of constant motion.

One reason may have been that constant motion by definition does not change with time even though it is undergoing a change in spatial properties.

Therefore to understand its casualty one should define it with respect those properties and not those of time or a space-time dimension.

Fortunately Einstein gave us the ability to do this when used the equation E=mc^2 and the velocity of light to define the properties of energy in of space-time environment because it allows one to convert a unit of displacement he associated with it in a four dimensional space-time universe to an equivalent unit of spatial displacement in four *spatial* dimensions.  Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words because he defined the geometric relationship between energy, mass, space and time in terms of the constant velocity of light means that one can quantitatively and qualitatively define a one to one between the properties of energy in a space-time universe to the physical properties of space four *spatial* dimensions.

The fact that one can use the Einstein’s equations to qualitatively and qualitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is one bases for assuming, as was done in the article “Defining energy?” Nov 27, 2007 that all forms of energy 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. 

One of the theoretical advantages to transposing Einstein space-time concepts to four *spatial* dimensions is that it allows one define a common mechanism for the causality of gravity, acceleration, inertia and constant motion.

For example the article “Why Space-time?” Sept. 27, 2007 showed the energy associated with rest mass is directly proportional to the magnitude of a curvature or “depression” in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Additionally it was shown that one can derive the causality of all accelerations including gravitational in terms of an interaction of rest mass with the slope of a curvature in the “surface” of three-dimensional space with respect to a fourth 8spatial* dimension caused by that displacement.

(This curvature is analogous to a curvature in a four-dimensional space-time manifold Einstein theorized was the causality of all accelerations.)

However as was shown in the article “Defining energy” there will be a 1 to 1 correspondence between an objects rest mass and the curvature in space associated with the energy required to make a unit change in its displacement with respect to a fourth *spatial* dimension.  Therefore the inertia of an object, as is confirmed by observations would be directly proportional to its rest mass if one assumes as was done in that article that causality of both is related to a displacement caused by a curvature in “surface” of a three-dimensional space manifold with respect to fourth *spatial* dimension.  This allows one to define the causality of inertia in terms of an interaction of the rest mass of an object with a curvature in a three-dimensional space manifold with respect to a four *spatial* dimensions.

This also to defines the causality of constant motion because according to the theoretical concepts presented in that article the energy associated with its momentum would be defined by a constant linear displacement of the depression associated with its rest mass in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore motion will continue unchanged unless it interacts with the curved “surface” of three-dimensional space that article associated with accelerations. This allows one to define the casualty constant motion in terms of a linear or constant displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However it also enables one to define causality of the relative properties of constant motion because according to the concepts develop in that article the momentum of an object in motion would be determined by the relative separation its three-dimensional “surface” has with respect to the three-dimensional “surface” of the object or measuring device used to determine its velocity.  In other words all motion is relative because its causality is directly related to the relative separation of its three-dimensional “surface” with respect to the three-dimension “surface” of another object or measuring device.

This defines a causal link between constant motion inertia, rest mass gravity and all accelerations in terms of an interaction of the “surfaces” of a three-dimensional space manifold and a fourth *spatial* dimension.

This shows how one can integrate the causality of a change in position associated with constant motion into our current scientific paradigms which are based almost entirely on causality and conceptually link it with Einstein’s concept of gravity and accelerate motion in terms of four *spatial* dimensions.

Later Jeff

Copyright Jeffrey O’Callaghan 2013

The post The causality of motion appeared first on Unifying Quantum and Relativistic Theories.

We think so.

Many including Albert Einstein and Erin Schrödinger, had difficulty accepting the “reality” of quantum mechanics because many of its concepts appear to contradict those of our observable universe.

For example in a quantum system Schrödinger’s wave equation defines the field properties of its environment and predicts the future distribution of a particle’s position only in terms of the abstract properties of probabilities.

However many including Einstein and Schrödinger define reality in terms of what they see or touch.

For example, Einstein used the observable “reality” of the interactions of electromagnetic energy with a photoelectric material to derive the quantum mechanical properties of energy/mass while using the observable properties of light in our three-dimensional environment to define his space-time universe.

In other words his conclusion that electromagnetic energy is quantized was based on the physical “reality” of the environment sounding the photoelectric material and how electromagnetic energy interacted with it, not on the abstract probabilities associated with quantum fields.

However the abstract properties of probabilities do share a common characteristic with Einstein’s space-time universe in that time or a space-time dimension have never be seen or touched and therefore they like the probability functions of quantum field theory are, by definition abstract quantities.

Fortunately they also have a common element, as mentioned earlier in the physically observable non-abstract properties of the *spatial* dimensions because the probabilities associated with Schrödinger’s wave equation are expressed in terms of the spatial properties of position.

Therefore because they share a common connection to the observable “reality” of our three-dimensional spatial environment one should be able to define the physical “reality” of both Einstein space-time dimension and the field properties of quantum mechanics in terms of their non-abstract spatial components.
Einstein gave us the ability to do this when he used the constant velocity of light in the equation E=mc^2 to define geometric properties of energy/mass because it allows one to convert a unit of time in his four dimensional space-time universe to a unit of space in a one consisting of only four *spatial* dimensions.  Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

The fact that one can use the Einsteinâ€s equations to qualitatively and qualitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is one bases for assuming, as was done in the article “Defining energy?” Nov 27, 2007 that all forms of energy 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. 

One of the theoretical advantages of modeling the existence of energy/mass on four *spatial* dimensions instead of four dimension space-time is it allows one to derive the “reality” of a quantum fields in terms of the observable non-abstract properties of our three-dimensional environment.

The physical “reality” of the field properties energy/mass in four *spatial* dimension was developed in the article “Electromagnetism in four *spatial* dimensions” Sept 27, 2007 where it was shown the forces associated with an electromagnetic field can be explained and predicted in terms of matter wave on field consisting of four *spatial* dimensions.

Briefly it showed that one can derive its field properties by extrapolating the observable non-abstract properties of a three-dimensional environment to a fourth *spatial* dimension.

For example 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 observations  of our three dimensional “reality”, if extrapolated  to four *spatial* dimensions tells us the force 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 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 non-abstract mechanism for understanding why similar charges repel each other because observations of wave on the surface of water tell us 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, observations of our three dimensional environment tell 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 how one can explain and predict the continuous field properties of electromagnetism by extrapolating the observable non-abstract properties of our three dimensional environment to a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, as was shown in the article “The Photon: a matter wave?” Oct. 1, 2007 the quantum field properties of four *spatial* dimension can also be derived by extrapolating the observable non-abstract resonant properties of a three-dimensional environment to one consisting of four *spatial* dimension.

There are four conditions required for resonance to occur in a three-dimensional environment an object or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial.

The existence of four *spatial* dimensions would give the continuous surface or field of three-dimensional space manifold (the substance) the ability to oscillate spatially with respect to a fourth *spatial* dimension 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 with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

Therefore, these oscillations in four *spatial* dimensions, would meet 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 four *spatial* dimensions are responsible for the incremental or discreet field energies associated quantum and electromagnetic field theories.

However if true one must also show how the probabilities associated with Schrödingerâ€s equation could have evolved out of those field properties.

Classical mechanics tell us that because of the continuous properties of waves, the energy the article “The Photon: a matter wave?” Oct. 1, 2007 associated with all quantum systems such as a photon would be distributed throughout the entire “surface” a three-dimensional space manifold with respect to a fourth *spatial* dimension similar to how the wave generated by a vibrating ball on a surface of a rubber diaphragm are disturbed over its entire surface while the magnitude of the displacement it causes will decrease as one moves away from the focal point of the balls oscillations.

However, this means if one extrapolates the mechanics of the rubber diaphragm to a “surface” of three-dimensional space one must assume the oscillations associated with each individual quantum system must be disturbed thought the entire universe while the spatial displacement associated with its energy; defined in the in the article “Defining energy?” Nov 27, 2007 would decrease as one moves away from its focal point.  Therefore their is a non-zero probability they could be found anywhere in our three-dimensional environment. 

Classical Wave Mechanics also tells us a 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 an observer would most probably find a quantum system 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.

However this is exactly what is predicted by Quantum mechanics in that one can only define a particle’s position or momentum in terms of the probabilistic values associated with vibrations of its wave function.

This shows how one can define the “reality” of the continuous field associated with Schrödinger’s wave equation and its associated probabilities in terms of a physical mechanism based on the observable non-abstract “reality” of our three-dimensional environment.

Latter Jeff

Copyright 2013 Jeffrey O’Callaghan

The post The reality of Quantum Fields appeared first on Unifying Quantum and Relativistic Theories.

Since then several different explanations have been proposed.  Maybe it was a result of a discarded version of Einstein’s theory of gravity, one that contained what was called a “cosmological constant.” Maybe there was some strange kind of energy-fluid that filled space. Maybe there is something wrong with Einstein’s theory of gravity and a new theory could include some kind of field that creates this cosmic acceleration.
However most cosmologists would agree the best way to understand why dark energy is causing universe’s expansion to accelerate would be to observe how it interacts with its environment and then try to incorporate it into a theoretical model.

For example we know form observations that it is not causing three-dimensional space to expand towards a time but a spatial dimension.

Unfortunately Einstein theories only contain three spatial dimension and one time dimension.

Therefore, to explain the observed spatial expansion of the universe one would have to assume the existence of a another *spatial* or fourth *spatial* dimension in addition to the three spatial and one time dimension that Einstein’s theories contain to account for that observation.

This would be true if Einstein had not given us a means of converting the geometric properties of his space-time universe to one consisting of only four *spatial* dimensions.

Einstein defined the geometric properties of a space-time in terms of a dynamic balance between mass and energy defined by the equation E=mc^2.  However when he used the constant velocity of light in that equation to define that balance he provided a method of converting a unit of time in a space-time environment with unit of space in four *spatial* dimensions.   Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

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

The fact that the equation E=mc^2 allows us to quantitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is one the bases of assuming as was done in the article “Defining energy” Nov 27, 2007 that all forms of 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.

In other words one can use Einstein’s equations to quantitatively define energy in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimensions instead of one in a space-time environment.

We know from the study of thermodynamics that energy flows from areas of high to ones with low density very similar to how water flows form an elevated or “high density” point to a lower one.

For example if the walls of an above ground pool filled with water collapse the elevated two-dimensional surface of the water will flow or expand and accelerate outward towards the three-dimensional environment sounding it.

Yet we know from observations of the cosmic background radiation that presently our three-dimensional universe has an average energy component equal to about 3.7 degrees Kelvin. 

However this means that according to concepts developed in the article “Defining energy” (mentioned earlier) the three-dimensional “surface” of our universe which has an average energy component of 3.7 degree Kelvin would be elevated with respect to a fourth *spatial* dimension.

Yet this means similar to the two dimensional surface of the water in the pool three-dimensional space will accelerate and flow or expand outward in the four dimensional environment surround it.

This shows that one can explain how and why the force called Dark Energy is causing the accelerated expansion of the universe in terms Einstein’s theory of gravity by converting or transposing his space-time geometry to its equivalent in four *spatial* dimensions.

Later Jeff

Copyright Jeffrey O’Callaghan 2013

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