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 he tells one reason he may have felt this way is because it defines the charge around a solitary electron as being caused by the spontaneous creation and evaporation of virtual electron-positron pairs which then instantaneously disappear.  In other words when a virtual electron-positron pair is created near the (real) electron, the (imaginary) virtual positron will be attracted toward the real electron, while the virtual electron is repelled. Therefore there should be a resulting separation of charge

I think most rational people would consider someone irrational if they tried to convince l us the reason why they were late for work was because a swam of virtual or imaginary cars were blocking the road and disappeared after we showed up.

Shouldn’t we hold our scientists to the same degree of rationality?

Most who have studied the history of science are aware that Einstein was vehemently opposed to many of the fundamental components of quantum mechanics such as the existence of virtual particle’s to explain an isolated charge. 

This was true even though he was able, in his General Theory of Relativity to derive the force of gravity in terms of the geometry of space and time while being unable to do the same for electromagnetism and charge, as was documented by the American Institute of Physics.

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

One reason why it was difficult of him to visualize electromagnetic fields including those around a single charge may have been because he chose to define the universe in terms of four dimensional space-time instead of four *spatial* dimensions because, as will be shown below it easier to visualize the properties of electrometric waves and charge in terms of their spatial rather time or space-time properties.

However he did provide a method of understanding them in terms of their common properties when he chose to define gravity in a space-time environment in terms of the equation E=mc^2 and constant velocity of light because that give him the ability to redefined it terms of the spatial properties of four *spatial* dimensions.  Additionally because the velocity of light is constant he also defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

The fact that one can use Einsteinâ€s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with gravity in terms of four *spatial* dimensions is one bases for assuming as was done in the article “Defining energy?” Nov 27, 2007 that all forces 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 advantages to using this technique is that it allows one to define the physicality of gravitational and electrical forces including those around a single electron in the same terms.

For example In the article “Gravity in four spatial dimensions” Dec. 15, 2007 it was shown one can derive gravitational forces in terms of curvature or physical displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension as well as one in a four dimensional space-time environment.

However the article “What is electromagnetism?“ Sept, 27 2007 showed one can also derive the forces associated with electromagnetism in terms of a similar displacement in the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly that article showed it is possible to derive the forces associated with an electromagnetic wave by extrapolating the laws of Classical Wave Mechanics in a three-dimensional environment to a matter 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 matter wave on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension would cause a point on that “surface” to become displaced or rise above and below the equilibrium point that existed before the wave was present.

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

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

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

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

One can define the causality of electrical component of electromagnetic radiation in terms of the energy associated with its “peaks” and “troughs” that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement.

However, Classical Mechanics tells us a horizontal force will be developed by that perpendicular or vertical displacement which will always be 90 degrees out of phase with it.  This force is called magnetism.

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

However, as was mentioned earlier gravity can also be explain in terms of a differential force caused by a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This shows how one can define a common mechanism for the causality of both electromagnetism and gravity in terms of a “unified field” consisting of four *spatial* dimension by extrapolating the laws of classical mechanics in a three-dimensional environment to four *spatial* dimensions. 

In other words one can visualize the fact that unlike charge attract each other while like ones repel in terms of the asymmetrical properties of space-time or four spatial dimensions.

Einstein was unable to accomplish this in terms of four-dimensional space-time because time is only observe to move in one direction forwards and therefore making it difficult to visualize the bi-directional movement of the spatial component of a matter wave moving on its “surface” that is responsible for electromagnetism . 

However it also give a more rational explanation of the charge around a solitary electron than the spontaneous creation and evaporation of virtual electron-positron pairs because it shows that it can be understood in terms of a physical displacement in a “surface” of a three-dimension space manifold with respect to fourth spatial dimension.

In other words it shows that electric forces are related to a physical displacement in a surface of a three dimensional space manifold with respect to a either a higher spatial or time dimension thereby eliminating the need to evoke the existence of virtual electron-positron pairs to understand the behavior of a charge around a solitary electron.

It should be remember Einsteinâ€s genius allows us to choose to define charge in either a space-time environment or one consisting of four *spatial* dimension when he defined that environment in terms mass energy and the constant velocity of light. This interchangeability broadens the environment encompassed by his theories thereby giving us a new perspective on the physicality of charge.

Latter Jeff

Copyright Jeffrey Oâ€Callaghan 2016

The post Finally a logical explanation of the field around a solitary charge. appeared first on Unifying Quantum and Relativistic Theories.

For example the density of mass to energy in the early universe must have been very close to a specific value to explain how stars could have evolved because if their concentrations were not it would depart rapidly from the one that would allow them to form over cosmic time.  Calculations suggest that it could not have departed more than one part in 10⁶² from that value.   This leads cosmologists to question how the initial density came to be so closely fine-tuned to this ‘special’ value that would have allowed stars and therefore life to evolve.
This has come to be called the flatness problem because the density of matter and energy which affects the curvature of space-time must have very specific value to give it the flat geometry required for stars to form and life to evolve.  In other words if the energy of the universe expansion was much larger it would have overpowered gravity preventing the formation of stars while if gravity was to strong they would have formed to quickly thereby not give life as we know it time to evolve.  `

The problem was first mentioned by Robert Dicke in 1969. 

The most commonly accepted solution among cosmologists is cosmic inflation or the idea that the early universe underwent an extremely rapid exponential expansion by a factor of at least 10⁷⁸ in volume, driven by a negative-pressure vacuum energy density.

This solves the flatness problem because the act of inflation actually flattens the universe.  Picture a uninflated balloon, which can have all kinds of wrinkles and other abnormalities, however as the balloon expands the surface smoothes out.  According to inflation theory, this happens to the fabric of the universe as well.

However, many view the inflationary theory as a contrived or “adhoc” solution because the exact mechanism that would cause it to turn on and then off is not known.

Yet, if one defines energy/mass density of our universe in terms of its spatial properties instead of the temporal ones of four dimensional space-time one can explain and predict why it has the correct proportions to cause its geometry to be hospitable to life as we know it by extrapolating the laws of classical physics in a three-dimensional environment to one of four *spatial* dimensions.

Einstein gave us the ability to do this when he defined its geometry in terms of a dynamic balance between mass and energy defined by the equation E=mc^2 because when he used the constant velocity of light in that equation he 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 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 quantitative and qualitative means of redefining his temporal properties of a space-time universe in terms of the spatial ones of four *spatial* dimensions. 

However, doing so makes easier to understand the mechanisms responsible for creating a flat universe that would enable life to evolve because flatness is associated more with the properties of spatial environment than those of a temporal one.

For example it would allow one to derive the momentum and the gravitational potential of the universe mass components as was done in the in the article “Defining potential and kinetic energy?” Nov. 26, 2007 in terms of, oppositely directed curvatures in “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  In other words if one can define the gravitational potential of mass in terms of a depression in its “surface” one could derive momentum of its expansion in terms of elevation in it.

This differs from Einsteinâ€s theoretical definition of energy in that he only defines mass or its gravitational potential in terms of a temporal displacement in a four dimensional space-time manifold.

This difference is significant to our understanding of the shape or flatness of our universe because it allows one to define the geometry of its mass component in terms the spatial properties of a “downward” directed curvature in a “surface” of a three-dimensional space manifold with respect to a four *spatial* dimensions while defining its energy component in term an upwardly directed one.

Additionally Einstein’s equation E=mc^2 and Second Law of Thermodynamics tells us there would be a dynamic relationship between the curvature created by the gravitational potential of the universeâ€s mass and the oppositely directed momentum of its expansion.  In other words because that law tell us that energy flows from area of high density to low; if the energy density was too high in the early universe it would have been channeled into creating more matter while if the matter component was excessive it would have been converted to energy. 

Granted it also tells us the curvature caused by its energy component is c^2 greater than that caused by mass but it also tells the one caused by mass would be more concentrated and therefore deeper than the one caused by energy.  However the deeper curvature associated with mass would be offset by the shallower and more draw out curvature associated with energy thereby make the universe flat and therefore hospitable to life as we know it.

This process would be similar to what happens to interstellar gas as it collapses to form a star.  The gas heats due to its contraction which causes energy to be created by nuclear reactions in its core converting mass to energy which opposes further gravitational collapses.  If too much energy is created it will escape from the star allowing gravity to take over again. 

After a given about of time the creation of energy is exactly offsets gravity and the star enters a period where the curvature in space associated with its energy exactly matches the oppositely directed curvature associated with its gravity and no further change takes place making its spatial geometry be flat because the curvatures counteract each other.  Additional this geometry would be frozen in time until the star evolved to new stage in its life.

Similarly the equation E=mc^2 tells us in the early universe there was an interchange between energy and the creation of mass in the form of baryons and the components of dark matter.  Additional as was the case in the formation of a star the second law of thermodynamic tells us that energy flows from areas higher density to lower ones while E=mc^2 tells us if the energy density was too high in the early universe it would have been channeled into creating baryons and dark matter while if they were too abundant they would have been converted to energy.

In other words second law of thermodynamic and E=mc^2 tells us as the universe evolves it would move towards a flat geometry because as was just mentioned if its energy density was too high it would have been channeled into creating mass while if its mass were to abundant it would have been converted to energy.  This geometry would become frozen in time when the universe cooled enough for its mass and energy components to become stable.

This shows why one does not have to assume that a complicated change of events must have occurred such as inflation to give our universe the geometry needed to support beginnings of life because as was shown above that story is told by the Second Law of Thermodynamics and Einstein’s equation E=mc^2.

Later Jeff

Copyright Jeffrey O’Callaghan 2016

The post The story of life in four spatial dimensions. appeared first on Unifying Quantum and Relativistic Theories.

But it will be easier if we first transpose or covert Einsteinâ€s space-time universe to one consisting of only four *spatial* dimensions because it will enable us to define the mechanism responsible how this emergence takes place in terms of a geometry which is directly related the position or spatial properties associated with quantum probabilities instead of their non-positional or temporal components.

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

In other words the symmetry of the mathematics he use to define his space-time environment makes it possible to define the location of the quantum-classical boundary not only in terms of four dimensional space-time but also in four *spatial* dimensions thereby making it easier to understand how these two worlds interact.

For example the fact that one can use Einsteinâ€s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions allows one, as was done in the article “Defining energy?” Nov 27, 2007 to derive all forms of energy including those associated with quantum systems in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This will allow as was shown in the article “Why is energy/mass quantized?” Oct. 4, 2007 to understand of 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.

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

The existence of four *spatial* dimensions would give the wave properties of a quantum system 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.

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

As mentioned earlier in the article “Defining energy?” Nov 27, 2007 showed 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.

However assuming energy is result of a displacement in four *spatial* dimension allows one to derive the most probable position of a particle in terms of its wave function by extrapolating the observations and classical laws associated with a three-dimensional environment to a fourth *spatial* dimension.

Classical mechanics tell us, due to the continuous properties of waves the energy the article “Why is energy/mass quantized?” Oct. 4, 2007 associated with a quantum system would be distributed throughout the entire “surface” a three-dimensional space manifold with respect to a fourth *spatial* dimension.

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

Similarly if the assumption that quantum properties of energy/mass are a result of vibrations or oscillations in a “surface” of three-dimensional space is correct then classical mechanics tell us those oscillations would be distributed over the entire “surface” three-dimensional space while the magnitude of those vibrations would be greatest at the focal point of the oscillations and decrease as one moves away from it.

As mentioned earlier the article “Why is energy/mass quantized?” Oct. 4, 2007 showed a quantum mechanical system is a result of a resonant structure formed on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

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

Similarly if a particle as was shown earlier is a result of a resonant system formed in space it 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 also defines how quantum probabilities can emerge from an classical interaction of energy/mass with the geometry of four *spatial* dimensions or four dimensional space-time while the same time eliminating the need for Quantum Decoherence because it shows that the different elements in the quantum superposition of a wavefunction are the result of the relative spatial orientation or position of an observer with respect to the its most probable position.

In other words it justifies the framework and intuition of the probabilistic interpretation of quantum mechanics as an acceptable approximation of a classical environment without Quantum Decohernece.

It should be remember Einsteinâ€s genius allows us to choose to define a quantum system in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the spatial as well as the time properties of our universe thereby giving us a new perspective on the causality of the quantum mechanical interaction.

Later Jeff

Copyright 2015 Jeffrey O’Callaghan 

The post Do we really need Quantum Decoherence? appeared first on Unifying Quantum and Relativistic Theories.

For example one can easily understand how the curvature in space-time can be the causality of gravitational forces in terms of the physical image of a marble on a curved surface.  The marble follows a circular pattern around the deformity in the surface of the diaphragm. Similarly planets revolve around the sun because they follow a curved path in the deformed “surface” of space-time.

However the same cannot be said for the energy distribution within the atom because quantum mechanics defines it in terms of a non-deterministic probability function. This deeply trouble Einstein because he felt that the laws governing the entire universe must deterministic including those of the atom.  He spent the next few years attempt to define physical model of why energy levels of atoms behave the way they do. However by 1926 the problem of chance remained and Einstein became increasingly alienated from the developments in quantum theory; he insisted that “God does not play dice,” and thus there is no room for fundamental randomness in physical theory.

As mentioned earlier Einstein believed that a viable theory of nature should be base on determinism which should be describable by a physical image.

One reason for his inability to create a physical image of the quantum energy distribution in an atom may have been because he chose to define it in terms of time or space-time instead of its spatial properties.  In other words because the distribution of energy in an atom is related to its spatial not its time characteristics it may have been easier to do if he had define energy in terms of its spatial instead of time properties.

However he gave us the ability to do this when he defined the geometric properties of a space-time universe in terms of  the constant velocity of light because that allows one to redefine a unit of time he associated with energy in his space-time universe to unit of space in only four *spatial* dimensions. 

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

This would have allowed him to describe a physical image for why the energy levels of Principal Quantum number (n), the Angular Momentum “â„“” (l), Magnetic (m) and Spin Quantum Number (+1/2 and -1/2) are what they are. 

For example in the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown one can derive the quantum mechanical properties of energy/mass by extrapolating the physical image of resonance in a three-dimensional environment to a matter wave moving 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 Newtonian environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in one consisting of four spatial dimensions

The existence of four *spatial* dimensions would give the “surface” of a three-dimensional space manifold (the substance) the ability to oscillate spatially with respect to it 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 on a “surface” of three-dimensional space, 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 energy associated with quantum mechanical systems.

Additionally this also allows one to derive the physical boundaries of a particle in terms of the geometric properties of four *spatial* dimensions.

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

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

The confinement of the “upward” and “downward” oscillations of a three-dimension volume with respect to a fourth *spatial* dimension which always must occur, as was shown in the article “The observer effect in quantum mechanics a classical explanation” Sept. 1, 2015 when an observation is made is what defines the spatial boundaries of the resonant system associated with the particle component of its wave properties in the article “Why is energy/mass quantized?“

However the fact that one can derive the quantum mechanical properties of energy/mass by extrapolating the resonant properties of a wave in three-dimensional environment to a fourth *spatial* dimension means that one should be able to derive a physical image of the four quantum numbers that define the physical properties of the atomic orbitals in those same terms.

In other words one should be able to define a physical reasons in terms of the classical physics why the first the Principal Quantum number is designated by the letter “n”, the second or Angular Momentum by the letter “â„“” the third or Magnetic by the letter “m” and the last is the Spin or “s” Quantum Number are what they are.

In three-dimensional space the frequency or energy of a resonant system is defined by the vibrating medium and the boundaries of its environment.

For example the resonant energy of a standing wave generated when a violin string plucked is determined in part by the length and tension of its strings.

Similarly the energy of the resonant system the article “Why is energy/mass quantized?” Oct. 04 2007 associated with atom orbital would be defined by the “length” or circumference of the three-dimensional volume it is occupying and the tension on the space it is occupying.

Therefore the physicality of “n” or the principal quantum number would be defined by the fundamental vibrational energy of three-dimensional space that article associated with the quantum mechanical properties of energy/mass.

The circumference of its orbital would correspond to length of the individual strings on a violin while the tension on its spatial components would be created by the electrical attraction of the positive charge of the proton.

Therefore the integer representing the first quantum number would correspond to the physical length associated with the wavelength of its fundamental resonant frequency of the volume of electrons in orbit.

However, classical mechanics tells us that each environment has a unique fundamental resonant frequency which is not shared by others.

Additionally it also tells us why in terms of the physical properties of space-time an electron cannot fall into the nucleus is because, as was shown in that article all energy is contained in four dimensional resonant systems. In other words the energy released by an electron “falling” into it would have to manifest itself in terms of a resonate system. Since the fundamental or lowest frequency available for a stable resonate system in either four dimensional space-time or four spatial dimension corresponds to the energy of an electron it becomes one of the fundamental energy units of the universe.

This defines physicality of the environment associated with the first quantum number and why it is unique for each subdivision of electron orbitals. Additionally observations tell us that resonance can only occur in an environment that contains an integral or half multiples of the wavelength associated with its resonant frequency and that the energy content of its harmonics are always greater than those of its fundamental resonate energy.

This allows one to derive the physicality of the second “â„“” or azimuth quantum number in terms of how many harmonics of the fundament frequency a given orbital can support. 

In the case of a violin the number of harmonics a given string can support is in part determined by its length.   As the length increase so does the number of harmonics because its greater length can support a wider verity of frequencies and wavelengths.  However, as mentioned earlier each additional harmonic requires more energy than the one before it.  Therefore there is a limit to the number of harmonics that a violin string can support which is determined in part by its length.

Similarly each quantum orbital can only support harmonics of their fundamental frequency that will “fit” with the circumference of the volume it occupies.

For example the first harmonic of the 1s orbital would have energy that would be greater than that of the first because as mentioned earlier the energy associated with a harmonic of a resonant system is always greater than that of its fundamental frequency.  Therefore it would not “fit” into the volume of space enclosed by the 1s orbital because of its relatively high energy content.  Therefore second quantum number of the first orbital will be is 0. 

However it also defines why in terms of classical wave mechanics the number of suborbital associated with the second quantum number increases as one move outward from the nucleus because a larger number of harmonics will be able to “fit” with the circumference of the orbitals as they increase is size.

This also shows that the reason the orbitals are filled in the order 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, 5s is because the energy of the 3d or second harmonic of the third orbital is higher in energy than the energy of the fundamental resonant frequency of the 4th orbital.  In other words classical wave mechanics tells us the energy of the harmonics of the higher quantum orbitals may be less than that of the energy of the fundamental frequency of preceding one so their harmonics would “fit” into circumference of the lower orbitals

The third or Magnetic (m) quantum number physical defines how the energy associated with each harmonic in each quantum orbital is physically oriented with respect to axis of three-dimensional space.

For example it tells us that the individual energies of 3 “p” orbitals are physically distributed along each of the three axis of three-dimensional space.

The physicality of the fourth quantum or spin number has nothing to do with the resonant properties of space however as was shown in the article “Pauliâ€s Exclusion Principal: a classical interpretation” Feb. 15, 2012 one can derive its physicality by extrapolating the laws of a three-dimensional environment to a fourth *spatial* dimension.

That article it was shown all forms of energy including the angular momentum of particles can be defined in terms of a displacement in a “surface* of three-dimensional space manifold with respect to a fourth *spatial* dimension.

In three-dimensional space one can use the right hand rule to define the direction of the angular momentum of charged particles.  Similarly the direction of that displacement with respect to a fourth *spatial* dimension can be understood in term of the right hand rule.  In other words the angular momentum or energy of an electron with a positive spin would be directed “upward” with respect to a fourth *spatial* dimension while one with a negative spin would be associated with a “downwardly” directed one.
Therefore one can define the physically of the fourth or spin quantum number in terms of the direction a “surface” of three-dimensional space is displaced with respect to a fourth *spatial* dimension.  For example if one defines energy of an electron with a spin of -1/2 in terms of a downward directed displacement one would define a +1/2 spin as an upwardly directed one.

The physical reason for Pauli’s exclusion principal or why only two electrons can occupy a quantum orbital and why they must have slightly different energies can also be derived by extrapolating the observations of a classical three-dimensional environment to a fourth *spatial* dimension.

For example there a two ways to fill a bucket.  One is by pushing it down and allowing the water to flow over its edge or by using a cup to raise it to the level of the buckets rim.

Similarly there would be two ways fill an atomic orbital according to the concepts presented in that article.  One would be by creating a downward displacement on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* to the energy level associated with the electron while the other would create an upward displacement in that surface.

However the energy required by each method will not be identical because it requires slightly less energy to fill a bucket by pushing it down below the surface than it would be to fill one that was above it in part because the one above the surface would be at a higher gravitational potential.

Additionally it takes considerable more energy to push two buckets on on top of the other below the surface than it does just one.

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 quantum particles with similar quantum numbers would greater than that caused by a single one.  Therefore, they will repel each other and seek the lower energy state associated with a different quantum number because the magnitude of the force resisting the displacement will be less for them than if they had the same number.

This shows how one can define a physical model for the energy distribution with an atom by extrapolating the deterministic laws of a classical three-dimensional environment to a fourth *spatial* dimension.

However it also allows one to understand why in terms of a physical image the energy distribution within the atom MUST be defined in terms of a non-deterministic probability function.

As mentioned earlier the article “The observer effect in quantum mechanics: a classical explanation” Oct. 4, 2007 showed the particle component of a quantum system is the result of the restricting its wave motion through observation.

Briefly it showed that because of the continuous properties of waves, the energy the article “Why is energy/mass quantized?” Oct. 04 2007 associated with a quantum system it is free to move and therefore be distributed over the entire “surface” of three-dimensional space with respect to a fourth *spatial* dimension similar to how a wave generated by a vibrating ball on a surface of a rubber diaphragm would be disturbed over its entire surface.  However to observe it one would have to touch its surface with a probe thereby restricting the wave motion of that surface.

In other words there is a probability that a probe could observe the vibrations of the ball anywhere on that surface with a decreasing probably as one move away from the ball or center of the diaphragm.

Similarly an electron energy which is not being observed would be distributed throughout its entire orbit.

In other words similar to the rubber diaphragm the wave properties of an electron would be distributed throughout the entire volume of its atomic orbital.

However if we decide to restrict or redirect some of its energy by probing or observing it it appears to be at a specific place in space and time because as was shown in the article “Why is energy/mass quantized? the act of observation confines its wave component to specific volume thereby allowing the resonant system that article showed defines a particle’s position.

In other words in an atom an electron’s wave energy is allow freely move or exist within a specific volume however the act of observing where it is in its orbit restricts its movement thereby allowing the resonant system the article “Why is energy/mass quantized?“ associated with a particle to form and appear or be observed in a specific position within that orbital.

However similar to the vibrations in the rubber diaphragm there is a probability that a probe could observe them anywhere in their orbital with a decreasing probably as one move away from the center or focal point of its wave component.

In other words assuming space is composed of four spatial dimensions instead of four dimensional space-time in allows one to form a physical image of probabilistic interactions individual electrons in atoms have with observers and with electrons in other orbitals in terms of the classical laws of probabilities.

Later Jeff

Copyright Jeffrey Oâ€Callaghan 2015

The post Quantum energy distribution: a classical interpretation appeared first on Unifying Quantum and Relativistic Theories.

“More is unknown about it than is known. We know how much dark energy there is because we know how it affects the Universe’s expansion. Other than that, it is a complete mystery. But it is an important mystery. It turns out that roughly 68% of the Universe is dark energy. Dark matter makes up about 27%. The rest – everything on Earth, everything ever observed with all of our instruments, all normal matter – adds up to less than 5% of the Universe. Come to think of it, maybe it shouldn’t be called “normal” matter at all, since it is such a small fraction of the Universe.
One explanation for dark energy is that it is a property of space.  Albert Einstein was the first person to realize that empty space is not nothing. Space has amazing properties, many of which are just beginning to be understood. The first property that Einstein discovered is that it is possible for more space to come into existence. Then one version of Einstein’s gravity theory, the version that contains a cosmological constant, makes a second prediction: “empty space” can possess its own energy. Because this energy is a property of space itself, it would not be diluted as space expands. As more space comes into existence, more of this energy-of-space would appear. As a result, this form of energy would cause the Universe to expand faster and faster. Unfortunately, no one understands why the cosmological constant should even be there, much less why it would have exactly the right value to cause the observed acceleration of the Universe.” 

Most scientists would agree the best case scenario would be to understand the causality of dark energy and how it interacts with its environment in terms of observations and our currently accepted theoretical models.

However, presently there are only two scientific disciplines that address those interactions.  The first or the laws of thermodynamics defines the forces associated with heat early in the universe’s evolution and the second or Einstein’s General Theory of Relativity defines how gravity influences that evolution.

Unfortunately neither of them, in their present form address the expansive force of Dark Energy and how or why it interacts with its environment to cause it to accelerate.

Yet one of the most obvious difficulties in integrating it into Einsteinâ€s space-time universe is that observations tell us that three-dimensional space is expanding towards a higher spatial dimension not a time or space-time dimension.  

Therefore, in order 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 dimensions and one time dimension that Einsteinâ€s theories contain to account for that observation.

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

He did this when he defined the geometric properties of a space-time universe and the dynamic balance between mass and energy in terms of the equation E=mc^2 and the constant velocity of light because it allows one to redefine a unit of time he associated with energy in his space-time universe to unit of space in a universe consisting of only four *spatial* dimensions. 

In other words by defining the geometric properties of a space-time universe in terms of the equation E=mc^2 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 physical properties of energy in a space-time universe in terms of its spatial properties is the 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.

As mentioned earlier it is difficult to integrate the causality of three-dimensional space expanding towards a higher *spatial” dimension into Einstein space-time universe because it does not define a higher spatial dimension. 

However it is easy if one reformulates it, as was shown above to be possible in terms higher fourth *spatial* dimension.

Yet this also allows one to understand how and why the force called Dark Energy is causing an accelerated spatial expansion of our universe in terms of the laws of thermodynamics because it gives one the ability, as mentioned earlier to use his equations to qualitatively and 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.

We know from the study of thermodynamics that energy flows from areas of high density to one of 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 surrounding it while the force associated with that expansion decreases as it expands.

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 according to concepts developed in the article “Defining energy” that the three-dimensional “surface” occupied by the particles in 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 water molecules occupying the elevated two dimensional surface of the water in the pool, the particles occupying a region of three-dimensional space that is elevated because of its 3.7 degree temperature will flow and accelerate outward in the four dimensional environment surrounding it.

This shows how reformulating Einstein’s theories in terms of four *spatial* dimensions allows one to use the laws of thermodynamics to explain what the force called Dark Energy is and how it can be seamlessly integrated into his general theory of relativity.

Later Jeff

Copyright Jeffrey O’Callaghan 2014 

The post How Einstein may have explained Dark Energy 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

\

The post The reality behind quantum entanglement appeared first on Unifying Quantum and Relativistic Theories.

In first scenario, there would be enough matter in the universe to slow the expansion to the point where, like the baseball, it would come to a halt and the gravitational forces associated with it would result in it retracting causing it to crash together in a “Big Crunch.”

In the other scenario, there would be too little matter to stop the expansion and everything would drift on forever, always slowing and slowing but never stopping. This would end in a vast, dark, and cold state: a “Big Chill,” as the stars faded and died out.

However the discovery of Dark Energy or a force causing the accelerated expansion of the universe opened up the possibility that the galaxies, solar system, stars, planets, and even molecules and atoms could be shredded by the ever-faster expansion.  In other words the universe that was born in a violent expansion could end with an even more violent expansion called the Big Rip.
Most scientists would agree that the best way of determining which one these scenarios defines its ultimate fate would be to list all of the observations regarding the forces controlling its expansion and try to understand them based on the most successful theories we have regarding the macroscopic properties of energy/mass.

For example it is assumed by many that because space is everywhere, the force called Dark Energy is everywhere therefore its effects should increases as it expands.  In contrast, gravity’s force is stronger when things are close together and weaker when they are far apart.  Therefore many believe the expansion will continue at an ever increasing rate, eventually ripping space apart.

However if one views the observational evidence supporting the existence of Dark Energy in terms of the laws of thermodynamics and Einstein’s theories, it strongly suggests that it will weaken not increase as space expands and that eventually gravity will become the dominate force in our universe.

Observations of the expansive force called Dark Energy tell us that three-dimensional space is expanding towards a higher spatial dimension not a time or space-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 dimensions 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 qualitatively and quantitatively 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 universe 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 to define that balance he provided a method of converting a unit of space he associated with mass to a unit of space-time he associated with energy.   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  the 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.

As mentioned earlier it is difficult to integrate the causality of how three-dimensional space can be expanding towards a higher *spatial” dimension into Einstein space-time universe because it does not define a higher spatial dimension. 

However it is easy integrate it if one reformulates it, as was done above in terms higher fourth *spatial* dimension.

Yet it also allows one to understand how and why the expansive force called Dark Energy is causing the spatial expansion of our universe in terms of the laws of thermodynamics because it gives one the ability, as mentioned earlier to use his equations to qualitatively and 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 density to one of 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 surrounding it while the force associated with that expansion decreases as it expands.

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 surrounding it and that the force associated with that expansion will decline as it expands.

This shows how reformulating Einstein’s theories in terms of four spatial dimensions allows one to use the laws of thermodynamics to explain what the force called Dark Energy is and why it is causing the accelerated expansion of the universe in terms of the Einstein’s theories.

As mentioned earlier many feel that because space is everywhere, the force called Dark Energy is everywhere, and its effects increase as space expands. I n contrast, gravity’s force is stronger when things are close together and weaker when they are far apart.

However if the above theoretical model is correct than the magnitude of Dark Energy relative to gravitational energy will not continue to increase as the universe expands but will decrease because Einstein also told us that there is an equivalence between mass and energy and since mass is associated with the attractive properties of gravity it also tells us, because of that equivalence, the kinetic energy associated with the universeâ€s expansion also possess those attractive properties. However the law of conservation of energy/mass tells us that in a closed system the creation of kinetic energy cannot exceed the gravitational energy associated with the total energy/mass in the universe and that a reduction in one must be compensated for by an increase in the other.

This means the total gravitation potential of the universe must increase as it expands and cools approaching a maximum value at absolute “0” while at the same time the kinetic energy of its expansive components must decrease. Therefore, at some point in time, the universe MUST enter a contractive phase because the total gravitational potential must eventually exceed the kinetic energy of its expansion. This is would be true even though the gravitational potential of its kinetic energy components would be disturbed or “diluted” by a factor of c^2.

(Some may try to dismiss this by saying that as the universe expands its energy is spread out over a larger volume so after a while it just vanishes so to speak or as some like to say that the universe experiences a heat death.  However Einstein theories do not permit energy to just disappear or “die”.  It unequivocally tells us that if the kinetic energy content in a closed environment decreases as it cools the mass content of that environment must increase irrespective of the volume of that environment.  Therefore because by definition the universe is a closed system one must assume that any reduction in its overall energy content of the universe including its heat energy must be must be compensated for by an increase in its total attractive gravitational mass content.)

Therefore, just after the big bang when the concentration of energy and mass was high, gravitational force would predominate over Dark Energy because the distance between both its energy and mass components was relatively small.

However as the universe expands the its gravitational attractive forces will decrease more rapidly than the expansive force associated with Dark Energy because they are related to the square of the distance between them while those of the expansive forces of Dark Energy are more closely related to a linear function of the total energy of content of the universe. 

Therefore after a given period of time the expansive forces associated with Dark Energy will become predominate and the expansion of the universe will accelerate.

However as the universe expands and cools that force will decrease because as mentioned earlier similar to the two-dimensional surface of the water in a collapsed pool, the forces associated with that expansion will decrease as it expands.

This means that eventually gravitational forces will win because, as mentioned earlier thermodynamics tells us the total accelerative forces associated with Dark Energy will decease and therefore will eventually approach zero, while the total mass content and the gravitational attractive forces associated with it will remain constant as the universe expands even though they may be separated by a greater distant.

Therefore, gravity will eventually win the battle with dark Energy because as was just mentioned the forces associated with it approach zero as the expansion progress while those of gravity remain constant.

There can be no other conclusion if one accepts the validity of Einstein’s theories and the laws of thermodynamics because the theoretical arguments presented here are a base solely on their validity.

Later Jeff

Copyright Jeffrey O’Callaghan 2013

The post Gravity or dark energy: which one will win? appeared first on Unifying Quantum and Relativistic Theories.

The uncertainty principal of quantum mechanics tells us that we cannot know or observe the precise amount of energy contained in microscopic physical system over very short intervals of time. 

Some physicists feel that because they cannot know the precise “reality” of the amount of energy contained in microscopic physical system, it must fluctuate around a given point even though it is a vacuum which does not contain anything that can physically fluctuate.  They call the energy generated by the uncertainty principal quantum fluctuations or vacuum energy.

However, this means they are defining the “reality” of a vacuum in terms of their inability to know or define its reality.
However we have shown throughout this blog there are many theoretical advantages to defining the universe in terms of four *spatial* dimensions instead of four-dimensional space-time.

One is that it would allow us to understand the “reality” of a quantum vacuum by using our imagination to extrapolate the reality of a three-dimensional environment to a fourth *spatial* dimension.

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

This as mentioned earlier this would allow one to understand the reality of a quantum environment in terms of the classical laws physics.

For example in the article “Why is mass and energy quantized?‘“ Oct. 4, 2007 it was shown that one can understand the quantum properties of energy/mass by extrapolating the resonant properties of a three-dimension environment to a matter wave moving on a 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 could be meet by one 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 a continuous 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 fundamental or a harmonic of its fundamental frequency.

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

In other words one can understand the reality of a quantum environment in terms of the laws of classical physics if one views in terms of four *spatial* dimensions.

However, if true one may be able to define the “reality” of quantum vacuum by as mentioned earlier using one imagination to extrapolate observations of a three-dimensional environment to four *spatial* dimensions instead of relying, as many physicists seem to on their inability to observe them.

Casimir theorized that quantum fluctuations in a vacuum would cause a force to be developed between two uncharged metallic plates in a vacuum without an external electromagnetic field acting on them, if they were placed a few micrometers apart.  This contradicts classical reasoning because, the lack of an external field also means that there is no field between the plates, and therefore no force would be measured between them.  However if this field is instead studied using quantum electrodynamics, it is seen that the plates are affect the virtual photons which constitute the field, and generate a net force either an attraction or a repulsion depending on the specific arrangement of the two plates.

This force was first measured by Dutch physicists Hendrik B. G. Casimir and Dirk Polder in 1948 while participating in research at Philips Research Labs.  

They found its strength falls off rapidly with the distance between the plates and that it is only measurable when the distance between them is extremely small.  On a sub micrometer scale, this force becomes so strong that it becomes the dominant force between uncharged conductors.  In fact, at separations of 10 nm—about 100 times the typical size of an atom the Casimir effect produces the equivalent of 1 atmosphere of pressure, the precise value depending on surface geometry and other factors.

However, this is what one would expect if the quantum mechanical properties of vacuum were as was shown in the article “Why is mass and energy quantized?” a result of a resonant system form by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Observations of waves in a classical environment indicate the number of harmonic oscillators that can be established in a given environment is dependent on the distance or “gap” between the “end points” of their environments.

But the same concept can be applied to two uncharged metallic plates in a vacuum, because even without any external electromagnetic field the electromagnetic components of the atoms in each plate are vibrating because they are not at absolute zero they have thermal energy.  These random vibrations of their electromagnetic components will result in a random electromagnetic field to be generated between the plates.

However, classical wave mechanics tells us these random electromagnetic vibrations would be reinforced either constructively or destructively at certain points in space.  The number of harmonic oscillators or, as some physicist’s call them quantum fluctuations in the space between two plates would decrease as the gap between them decreases.  In other words, the smaller the gap between the plates the fewer number of quantum fluctuations that gap could support.

This means as was shown in the article ”Why is mass and energy quantized?“ there will be a greater number harmonic oscillators or quantum fields impacting the plates from outside of the gap than between it.  This will cause a force that will push the plates together because the energy density associated with harmonic oscillations outside of the gap would be greater than inside of it.

However, it also tells us there will be places where the distance between them will be equal to the wavelength associated with a fundamental or harmonic of the fundamental frequency of electromagnetic oscillations.  At those distances their energy will reinforce force each other and would push them apart.

Therefore, if one assumes as us done here that the quantum mechanical properties of energy/mass are a result of a resonant system in four *spatial* dimension one can understand why the specific arrangement of the two plates causes and attractive or repulsive force to be developed by extrapolating the reality of a three-dimensional environment to a fourth *spatial* dimension.

We know the reality of the wave properties of particles because in 1927 Davisson and Germer observed they are diffracted by crystals.  Additionally we can observe the reality and properties of a resonant system in three-dimensional space.

This suggests the Casimir effect may not be due to our inability to know the precise “reality” of the amount of energy contained in microscopic physical system but to the physical observable reality of the wave properties of a particle.

However, it also means the “reality” of a quantum vacuum could be defined, as was done in the article ”Why is mass and energy quantized?“ by extrapolating the laws of classical three-dimensional space to a fourth “spatial* dimensions instead of the non “reality” of quantum field theory.

Later Jeff

Copyright Jeffrey O’Callaghan 2010

The post Understanding the “reality” of a quantum environment appeared first on Unifying Quantum and Relativistic Theories.