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 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.

He tells us the reason may have been because it defines the charge around a solitary electron as being caused by spontaneous creation of virtual electron-positron pairs which then magically disappear.  However being virtual means that they are very close to being something without actually being it.  In others words according to QED the force between two charged particles is something that it is not.

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

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 particles.  Granted 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 he was unable to describe or define electromagnetism or charge separation in the same terms, as was documented by the American Institute of Physics.

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

However the symmetry of the mathematics he used to define his space-time environment may enable us to use his theories to bring them together and define the “reality” of charged particles without the existence of virtual ones.

For example the fact that he used the constant velocity of light and the geometric properties of space-time to define the energy provides a method of converting a unit of time he associated with it 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.

This change in perspective allows one to qualitatively and quantitatively redefine the curvature in space-time he associated with gravity in terms of four *spatial* dimensions and is bases for assuming, as was done in the article “Defining energy?” Nov 27, 2007 that all forms of energy including gravitational and electrical can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However this would have allowed Einstein to define and understand the forces associated with electromagnetic charge in terms of their spatial instead of time properties.

For example as was shown as was shown in the article “What is electromagnetism?“ Sept, 27 2007 one can derive the forces associated with the charge fluctuations in an electromagnetic wave in terms of the displacement caused by the “peaks” and “toughs” of a matter wave moving on the “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly it showed it is possible to derive the properties of electromagnetism by extrapolating the laws of Classical Wave Mechanics in a three-dimensional environment to a matter wave moving on it

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 the electrical component of electromagnetic radiation in terms of the energy associated with the “peaks” and “troughs” of a matter wave 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.

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 could not support the bi-directional movement required to support the electromagnetic component of a matter wave moving on its “surface”. 

However, as was shown above it also defines the forces associated charges and their separation in terms of the physical properties of the spatial dimensions without the need of assuming the existence of virtual or imaginary particles.

In other words it shows that change particles and their associated forces can be explained and predicted in terms of their relative position with respect to a fourth *spatial* dimension. 

Some would say that even if that were true it still cannot explain why those forces would be quantized.

However as was shown in the article in the article “Why is energy/mass quantized?” Oct. 4, 2007 can also derive the quantum mechanical properties of charges by extrapolating the physical properties 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.

In other words defining the quantum mechanical properties of energy/mass in terms of physical properties of four *spatial* dimensions eliminates the need to make irrational assumptions like the interaction of virtual with real particles is responsible for charges and their separation.

It should be remember Einsteinâ€s genius and the fact that he defined the geometry of space-time in terms of the constant velocity of light allows us to choose to define our universe as either a space-time environment or one consisting of four *spatial* dimension when. 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 giving us a new perspective on charges and their associated forces.

Latter Jeff

Copyright Jeffrey O’Callaghan 2015

The post Scientific irrationality: is it really necessary? 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.

For example as long as you are not actually observing an electron, its behavior is that of a wave of probability however moment you do it is becomes a particle.  But as soon as you are not looking at it it behaves like a wave again. That is rather weird, and no ordinary idea of classical objectivity can accommodate it.”

Bohr summarized this reality as follows:…”however far the [quantum physical] phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms. The argument is simply that by the word “experiment” we refer to a situation where we can tell others what we have done and what we have learned and that, therefore, the account of the experimental arrangements and of the results of the observations must be expressed in unambiguous language with suitable application of the terminology of classical physics.

This crucial point…implies the impossibility of any sharp separation between the behavior of atomic objects and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear…. Consequently, evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be regarded as complementary in the sense that only the totality of the phenomena exhausts the possible information about the objects.

In other words the choice one makes on how to observe a quantum object determines if it is a particle or wave.

This behavior is exposed by the double slit experiment in which a coherent source of light illuminates a screen after passing through a thin plate with two parallel slits cut in it. The wave reality of light causes the light waves passing through both slits to interfere, creating an interference pattern of bright and dark bands on the screen. However, when being observed, the light is always found to be absorbed as discrete particles, called photons.
However one of the reason it is so difficult to understand how observation effects a quantum system may be because too much attention has been focused on its  mathematical properties and not enough on its physical meaning in a space-time environment.  This is made even more difficult because they are defined in terms of the spatial properties of a quantum system instead of its space-time properties.

This suggest one may be able to obtain a better understanding of what happens when one observes it if one could view it in terms its spatial instead of its time or space-time properties.

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 it provided a method of converting a unit of time he associated with energy to unit of space associate with position. 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.

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 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.

However redefining the physical properties of quantum system in terms of its spatial instead of its time components would allow one to derive a single picture of its wave and particle characteristics thereby allowing one to understand how observation effects our perception of it.

For example the article “Why is energy/mass quantized?” Oct. 4, 2007 showed one can derive its physicality 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 a matter wave the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

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

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

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

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

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

Yet it also allowed one to derive the physical boundaries responsible for the creation 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 is what defines the spatial boundaries of the resonant system associated with the particle component of it’s wave properties in the article “Why is energy/mass quantized?“

However assuming its wave energy is result of a displacement in four *spatial* dimension instead of four dimensional space-time as was done in the article “Defining energy?” Nov 27, 2007 allows one to not only derive the physicality of its particle component as was just done but also the reason why when you are not actually observing it its behavior is that of a wave however moment you do it is becomes a particle with a physically defined position. 

For example Classical wave Mechanics tell us that because of the continuous properties of waves, the energy the article “Why is energy/mass quantized?” associated with a quantum system is free to move over the entire “surface” of three-dimensional space with respect to a fourth *spatial* dimension similar to how the wave generated by a vibrating ball on a surface of a rubber diaphragm are free to move or be distributed over its entire surface.  However to observer it one would have to touch its surface with a probe thereby restricting the wave motion of its surface.

Similar the wave reality of a quantum system that is not being observed is allow to freely move though space as is done in the double slit experiment when it moves though the slits undetected thereby allowing is wave reality become observable as demonstrated by a diffraction pattern on a screen placed behind the slits.

In other words similar to the rubber diaphragm there is a probability that its wave reality could be found anywhere on the “surface” of three dimensional space.

However if we decide to restrict or redirect some of its energy by probing or observing it becomes a particle that 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 was responsible for its particle reality to become reality.

In other words by assuming space it composed of four spatial dimensions instead of four dimensional space-time one can understand why the act of observation defines the reality of a quantum environment by extrapolating our experiences in a three-dimensional environment to a fourth *spatial* dimension.

It should be remember that Einsteinâ€s genius allows us to choose whether to define the reality of a quantum system in either a space-time environment or one consisting of four *spatial* dimension when he derived its physical geometry in terms of the constant velocity of light.

Later Jeff

Copyright Jeffrey O’Callaghan 2015

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Quantum theory defines the existence of particles in terms of a mathematically generated probability function created by Schrödinger’s wave equation and assumes that particles do not exist until a conscience observer looks at it.  In other words it assumes the act of observation or measurement creates their reality.

However because it is based on probabilities it also assumes that the predictability associated with the laws of causality that govern our macroscopic universe do not apply to a quantum world.

In other words in quantum theory, everything is unpredictable.

Einstein hated this uncertainty, famously dismissing it when he said “God does not play dice with the universe” even though he was unable to give a reason.

However he gave us a clue as to why God must play dice when he said “If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless”

In other words we may be able to understand why a quantum environment lacks causality if we can transform the abstract or non-physical aspects or the probabilities associated with Schrödinger’s wave equation to one that more closely resembles the physical properties of our classical world.

For example Einstein told us that our physical environment is made up of four dimensional space-time however no one has ever observed the physicality of time or a space-time dimension.

Therefore it is extremely difficult to form a physical image of the quantum world or any other based on the existence of time or a space-time dimension because it is not part of our sensory environment.

Granted Einstein’s theories give us a detailed and very accurate description of how an interaction of time with the three *spatial* dimensions is responsible for the “reality” of the sensory world we inhabit and he was able to give us a clear physical image how a curvature in space-time can be responsible for gravity.

For example the most common physical image use to explain gravity does not use time but instead extrapolates the image of an object moving on a curved two dimensional “surface” in a three dimensional environment to four dimensional space-time.  However this image only contains reference only to the sensory reality of the spatial dimensions and not a time or space-time dimension.

Yet, the fact that most humans define our physical “reality” in terms of the spatial dimensions instead of a time or space-time dimension suggests that one may be able to form a physical image of how and why the quantum world is what it is by viewing our universe in terms of its spatial instead of its time properties.

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 a 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 space-time 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 gravity in terms of four *spatial* dimensions allows one to form an image of its causality in terms of the physical properties of the spatial dimension instead of the non-physical ones most of us associate with time or a space-time dimension. 

As was mentioned earlier one of the advantage to redefining Einstein space-time concepts in terms of four *spatial* dimensions is that it not only allows one to understand gravitational energy in more direct terms but also allows on to form a physical image in terms of a classical environment for the unpredictability of the quantum world.

For example in the article “Why is energy/mass quantized?” Oct 4, 2007 it was shown one can derive the quantum mechanical properties of a particle by extrapolating the laws governing resonance in a classically three-dimensional environment to a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Additionally, it was showed why all energy exists in these resonant systems and therefore must be quantized.

Briefly it was 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 its natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would also be found in one consisting of four.

The existence of four *spatial* dimensions would give three-dimensional space (the substance with a natural frequency) 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, these oscillations in a “surface” of a three-dimensional space manifold, according to classical mechanics would generate a resonant system or “structure” in space.  These resonant systems are known as particles.

(In an earlier article “The geometry of quarks” Mar. 2009 it will be shown how and why they join together to form these resonant systems in terms of the geometry of four *spatial* dimensions.)

The energy in a classically resonating system is discontinuous and can only take on the discrete values associated with its fundamental or a harmonic of its fundamental frequency.

However, these properties of a classically resonating system are the same as those found in a particle in that they are made up of discreet or discontinuous packets of energy/mass.  This is the basis for assuming, as was done in the article “Why is energy/mass quantized?” that its quantum mechanical properties are a result of a resonant system in four *spatial* dimensions.

The reason why we do not observe energy in its extended wave form is that, as mentioned earlier all energy is propagated through space in discrete components associated with its resonant structure.  Therefore, its energy appears to originate from a specific point in space associated with where an observer samples or observes that that energy.

This is analogous to how the energy of water in a sink is release by allowing it to go down the drain.  If all we could observe is the water coming out of the drain we would have to assume that it was concentrated in the region of space defined by the diameter of the drain.  However, in reality the water occupies a much larger region.

However, treating the quantum mechanical properties of energy/mass in terms of a resonant system generated by a matter wave also allows one to form a physical image of its unpredictability by extrapolating the laws of our classical three-dimensional world to a fourth *spatial* dimension.

Classical wave mechanics tells us a waveâ€s energy is instantaneously constant at its peaks and valleys or the 90 and 270-degree points as its slope changes from positive to negative while it changes most rapidly at the 180 and 360-degree points.

Therefore, the precise position of a particle quantum mechanics associates Schrödinger’s wave equation with could be only be defined in terms of the peaks and valleys of the matter wave responsible for its resonant structure because those points are the only places where its energy or “position” is stationary with respect to a fourth *spatial* dimension.  Whereas it’s precise momentum would only be definable with respect to where its energy change or velocity is maximum at the 180 and 360-degree points of that wave.  All points in between would only be definable in terms of a combination of its momentum and position.

However, to measure the exact position of a particle one would have to divert or “drain” all of the energy at the 90 or 270-degree points to the observing instrument leaving no energy associated with its momentum to be observed by another instrument.  Therefore, if one was able to determine precise position of a particle he or she could not determine anything about its momentum.  Similarly, to measure its precise momentum one would have to divert all of the energy at the 180 or 360 point of the wave to the observing instrument leaving none of its position information left to for an instrument which was attempting to measure it.  Therefore, if one was able to determine a particles exact momentum one could not say anything about its position.

The reason we observe a particle as a point mass instead of an extended object is because, as mentioned earlier the article “Why is energy/mass quantized?” showed its energy/mass must be packaged in terms of a resonant system.  Therefore, when we observe or “drain” the energy continued in its wave function, whether it be related to its position or momentum it will appear to come from a specific point in space similar how the energy of water flowing down a sink drain appears to be coming from a “point” source with respect the extended volume of water in the sink.

However, this allows one to form a physical image of the unpredictability of a quantum environment because it give us a Classical reason why we cannot precisely measure the both the momentum or position of a quantum object because the measurement of one effects the measurement of the other. 

For example, if one wants to measure the position of a particle to within a certain predefined distance “m” its wave energy or momentum will have to pass through that opening.  However, Classical Wave Mechanics tells us that as we reduce the error in our measurement by decreasing that predefine distance interference will cause its energy or momentum to be smeared our over a wider area.  Similarly, to measure its momentum one must observe a portion the wavelength associated with its momentum.  However, Classical wave mechanics tell us we must observe a larger portion of its wavelength to increase the accuracy of the measurement of its energy or momentum.  But this means that the accuracy of its position will be reduced because the boundaries determining its position within the measurement field are greater.

However, because of the dynamic interaction between the position and moment component of the matter wave responsible for generating the resonant system associated with a particle defined in the article a ”Why is energy/mass quantized?” the change or uncertainty of one with respect to the other would be defined by the product of those factors.

Another way of looking at this would be to allow a particle to pass through a slit and observe where it struck a screen on the other side.  One could get a more precise measurement of its position by narrowing the slit however classical wave mechanics tell us this will increase the interference of the wave properties associated with its resonant structure.  However this will cause the interference pattern defining its momentum to become more spread out and therefore make it more difficult to accurately determine its value.

Therefore, Classical wave mechanics, when extrapolated to Schrödinger’s wave equation in an environment consisting a fourth *spatial* dimension tells us the more precisely the momentum of a particle is known, the less precisely its position can be known while the more precisely its position is known, the less precisely its momentum can be determined.  In other words it tells us in terms of a physical image based on a classical environment the reason why God must play dice is because the physicality of a quantum environment prevents us from precisely determining the initial condition of a particle through observation.

Later Jeff

Copyright Jeffrey Oâ€Callaghan 2014

The post The causality of quantum probabilities or why God must play dice. appeared first on Unifying Quantum and Relativistic Theories.

But some say what we see in it does not define “THE reality” because of the limitation of our senses.  For example humans can only see a very small portion of the electromagnetic spectrum therefore, because of those limitations they say that our senses should not be the only arbiters of “THE reality”.

In other words because our instruments tell us that reality extends far, far beyond what our senses see, many feel the only way to find it is through the window they provide instead the one provided by our senses.
However, our impression of “THE reality” is made up of a combination of what our senses see around us and what our instruments tell us about that world.

In other words each is an integral part of how we and science views “THE reality” and therefore the different realities they show us cannot be treated as separate.

For example the instruments we use to observe it tell us that a fundament component of a quantum environment is that all objects exist simultaneously as both particles and waves.

However, our senses tell us objects cannot be both a particle and wave at the same time.

But how can we merge or integrate these two realities and determine their fundamental component when what our instruments “tell” us about our world appears to conflict with what our senses see in it.

Einstein gave us a clue when he said “If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless.”

Yet how can we form a physical image of the quantum world when its fundamental component, the wave particle duality of objects is contradictory to the physicality of our sensory environment.

We can start by reexamining how we define our sensory environment.

For example Einstein told us that our physical environment is made up of four dimensional space-time however no one has ever observed the physicality of time or a space-time dimension.

Therefore it is extremely difficult to form a physical image of the quantum world or any other based on the existence of time or a space-time dimension because it is not part of our sensory environment.

Granted Einstein’s theories give us a detailed and very accurate description of how an interaction of time with the three *spatial* dimensions is responsible for the “reality” of the sensory world we inhabit and he was able to give us a clear physical image how a curvature in space-time can be responsible for gravity.

For example the most common physical image use to explain gravity does not use time but instead extrapolates the image of an object moving on a curved two dimensional “surface” in a three dimensional environment to four dimensional space-time.  However this image only contains reference only to our sensory reality of the spatial dimensions and not a time or space-time dimension.

However, the fact that most humans define our physical “reality” in terms of the spatial dimensions instead of a time or space-time dimension suggests that one may be able to form a physical image of how and why the quantum world is what it is by viewing our universe in terms of its spatial instead of its time properties.

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 a 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 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 and gave us the ability to redefine the curvature or displacement he associated with energy/mass in a space-time environment to a spatial displacement in a fourth *spatial* dimension.

On pages 17 thru 23 of Richard P Feynman book “QED The Strange Theory of Light and Matter” he address the conflict between our sensory world and the particle wave reality of a quantum environment by describing what happens when light when it is partially reflected by two surfaces,

On those pages he writes that by placing two glass surfaces exactly parallel to each other one can observe how the photons of light reflected from the bottom surface interact with those reflected from the top surface.  Depending on the distance between the glass surfaces he can determine, by using a photo detector, that four percent or 4 out of 100 photons reflected from the lower surface of the glass could add up to as many as 16 or none at all when they interact with the photons reflected from the upper surface of the glass because of the reinforcement of the reflected wave energy from the bottom and top surfaces of the glass.

In other words the 4 photons reflected from the surface of the bottom piece of glass would interact with the incident ones to that surface creating from 0 to 8 photons while the 4 photons reflected from the surface of the top piece of glass would interact with the incident ones to it creating 0 to 8 more photons for a total of 0 to 16 photons.

These observations by Mr. Feynman support a wave theory of electromagnetic radiation because according to it, the energy associated with the interference of the 4 photons reflected from the bottom surface with 4 from the top will result in energy variations that corresponds to the energy of 0 to 16 photons.

However, wave theory also predicts the energy variations should be continuous.

In other words, the energy of the reflected photons should be able to take on any value between 0 and the combined energies associated with 16 photons.

The fact that the energy of the reflected photons Richard Feynman observed in the above experiment only took on integral values equal to the energy of the photons that originally struck the surface of the glass indicates that their energy is not transmitted by a wave but by a particle.

This shows that in a quantum environment a photon can either be a particle or a wave. However, our senses tell us objects such as photons cannot be both a particle and wave at the same time.

Yet as mentioned earlier we may be able to merge or integrate these two realities and determine the fundamental component of “THE reality”  by viewing them, as mentioned earlier in terms four *spatial* dimension instead of four dimensions space-time.

For example in the article “Why is energy/mass quantized?” Oct. 10, 2007 it was shown one can derive both the wave and particle properties of objects and a photon by extrapolating the physical image of a wave 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.  Additionally it showed that all energy must be propagated in these resonant systems.

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 its natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

The existence of four *spatial* dimensions would give the “surface” of three-dimensional space (the substance) the ability to oscillate spatially with respect to a fourth *spatial* dimension thereby fulfilling one of the requirements for classical resonance to occur.

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

Therefore if one extrapolates the physical image of a wave in a three dimensional environment to a fourth *spatial* dimension one could understand how these oscillations in a “surface” of a three-dimensional space manifold would generate the wave properties of objects in a quantum environment.

However we know from observations that tell us resonant system can only have the incremental or discrete energy associated with its fundamental or a harmonic of its fundamental frequency. Similarly the incremental or discrete energies associated with individual photons in Richard Feynman’s experiment could be understood in terms of the physical image of the resonate properties of wave in four *spatial* dimensions. However, one can also describe the physical boundaries of a particle in terms of the wave properties of its resonant structure.

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

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

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

This would allow one to merge or integrate the wave particle duality of a quantum environment into our sensory world by extrapolating, as was show earlier the physical image of wave moving on water to a matter wave moving on the “surface” of a three dimension space manifold with respect to a fourth *spatial* dimension or four dimensional space-time environment because remember, as was also show earlier they are equivalent.  

For example, the wave like interference of photons Richard Feynman’s experiment observed in his experiment would be due to the wave properties of the resonant “system” defined in the article “Why is energy/mass quantized?“.

If the distance between the two glass surfaces was equal to half of the wavelength of the resonant “system” associated with a photon, classical wave mechanics tell us the interference of its wave properties would interfere and will, as mentioned earlier yield the energy associated with 0 photons.

 If the distance between two glass surfaces is equal to its wavelength of they will reinforce each other and yield the energy associated with 16 photons.

However, it also tells us the reason the energy variations caused by their interference are quantized and not continuous as wave theory predicts they should is because, as was shown in the article “Why is energy/mass quantized?” the resonant properties of four *spatial* dimensions means that their energy must be propagated through space in the discrete quantized values associated with the fundamental or harmonic of fundamental frequency of four *spatial* dimensions or space-time environment they are occupying.

Yet this also defines reason the wave properties of 8 reflected photons reinforce themselves to create the energy associated with16 photons is because in our sensory environment when two waves in phase interact they will reinforce each other.  Therefore if energy is propagated in discrete quantized values associated with the wavelength or frequency of a resonant system the reinforcement of the wave properties of 8 photons must be carried away in the integral or discreet energies associated with resonant systems of up to 16 photons of the same frequency as those original 8 photons.

This demonstrates how one can project the “structure” of “OUR reality” beyond our sensory environment to explain and understand the quantum world.   It also demonstrates why forming a physical image of a process is so valuable to science because it shows that one can integrate or merge the reality shown to us by our instruments into “OUR” sensory reality in terms of “THE reality” of four *spatial* dimension or four dimensional space-time.

It should be remember Einsteinâ€s genius allows us to choose if we want to resolve all paradoxes between the readily of microscopic world of quantum mechanics and  that of macroscopic world of Relativity 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 sensory spatial as well as the non-sensory time properties of our universe thereby giving us a new perspective on the physical relationship between them.

 Later Jeff

Copyright Jeffrey O’Callaghan 2014

The post The structure of “OUR reality” appeared first on Unifying Quantum and Relativistic Theories.

“However far the quantum physical phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms. The argument is simply that by the word “experiment” we refer to a situation where we can tell others what we have learned and that, therefore, the account of the experimental arrangements and of the results of the observations must be expressed in unambiguous language with suitable application of the terminology of classical physics.

This crucial point…implies the impossibility of any sharp separation between the behavior of atomic objects and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear…. Consequently, evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be regarded as complementary in the sense that only the totality of the phenomena exhausts the possible information about the object.”

In other words he did not think that it was possible to use classical concepts to integrate the wave and particle characteristics of a quantum particle into a single picture therefore he felt that there exits a physical division between the macroscopic world of classical objects and the microscopic world of quantum particles. 

However this may not be the true and one can understand why if one views the universe in terms of four *spatial* dimensions instead of four dimensional space-time.

(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 space-time universe to a unit of a *spatial* dimension identical to those in our three-dimensional universe .  Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

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

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

One of the advantage to doing is that allows one to understand the wave particle duality of energy/mass or its complementary property in terms of the concepts of classical physics.

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

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

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

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

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

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

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

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

This allows one to define the particle properties of energy/mass in terms of the classical concepts of a wave.

However, one can define its wave properties in terms of the classical concepts of a particle in terms of the boundaries of its resonant structure.

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 is what defines the spatial boundaries of the resonant system associated with a particle in the article “Why is energy/mass quantized?“

However it also provides the ability to understand the inseparability of the wave and particle properties of energy/mass because it clearly demonstrates how one is depend on the other.

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

Additionally it defines a classical reason why particles sometimes behave like wave and sometimes like particle and why it is impossible simultaneously observe them.

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

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

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

This demonstrates how one can integrate the wave and particle characteristics of a quantum particle into a single picture and why the  physical division between the macroscopic world of classical objects and the microscopic world of quantum particles as was assumed by Bohr many not exist. 

Later Jeff

Copyright Jeffrey O’Callaghan 2014

The post Mass from first principles appeared first on Unifying Quantum and Relativistic Theories.

He then compared his result with the mass evaluated from the light the galaxies shed. He realized that there was way more matter in the cluster than what was visible or baryonic matter. This matter of an unknown type generated a gravitational field without emitting light; hence its name, dark matter.
Further observations suggest the baryonic or visible forms of matter in the universe only comprise approximately 5 to 10% of the mass required to account for the total gravitational energy in the universe.

However, the fact that 90 to 95% of the mass of the universe is invisible or “Dark” even with the recent advancements in particle detection technology suggests that it may be made up some else.

Einstein’s may have given us a clue as to what this could be when he defined gravitational forces and the quantity of mass in a give volume of space-time in terms of its field properties and not in terms of the particle or physical properties of mass.

This means the additional gravitational forces over and above that associated with the visible matter Fritz Zwicky measured in 1933 may be related to geometric property of space-time and not to the particle properties of baryonic or visible mass.

One can understand why by use the example Einstein gave us of a rubber sheet to visualize how a curvature in a space-time results in a gravitational field.

For example if one places a heavy ball in the middle of a flexible rubber sheet and then pushes a smaller ball the general direction of the heavy ball, will follow a curved path, as if “attracted” by the mass.  In other words the small ball is attracted to the focal point of the depression caused in the surface of the sheet by the heaver one.

However this does not accurately describe the gravitational fields associated with spiral galaxies because their rotational energy causes then to occupy a spatially extended region around its center.

Again one can understand the effects of the flattening of space caused by their rotational energy has on their total gravitational potential by using the example of a marble on a rubber diaphragm. 

For example if one places a  heavy ball in the middle or a rubber sheet and then pushes several smaller balls in the general direction of the heavy ball, will follow a curved path, as if “attracted” by the mass.  However the curvature in the sheet associated with each individual marble will be greater than what it would if it was just resting on the rubber sheet because the kinetic energy of their rotation will flatten and therefore increase the overall the curvature in its surface.

The rotation energy of the individual stars in galaxies would have the same effect the curvature in space-time.

However Einstein told us that the magnitude of a curvature in space defines the magnitude of the gravitational forces and therefore the total mass of in a volume of space.

Therefore to be valid representation of the gravitational forces in a galaxy one would have to analyze what the flattening of the bottom of a displacement in space-time does to the magnitude of the slope of the curvature in its surface.

Einstein told us what the effects of this would be when he defined the equivalence between energy and mass in terms of the equation E=Mc^2 because that tells us that the kinetic energy of the stars motion also posses gravitational potential.

If one flattens the distribution of the marbles around their original focal point while keeping their overall depth the same as it was before that flattening it would make the curvature steeper than it would be if no flattening had occurred.

Similarly because of the *flattening* of space by the rotation energy of the individual stars in galaxies the magnitude of the slope of the displacement in space-time associated with gravitational forces would be greater than it would be if one only viewed the sum of that associated with the individual stars as if they were not in relative motion with respect to each other. In other words the gravitational potential Einstein with the Kinetic energy of individual stars in galaxies would increase the magnitude of the curvature in space time over and above that caused by their visible mass.

However, as mentioned earlier Einstein define gravitational force and the quantity of mass in a given volume of space in terms of the magnitude of a curvature in space.

Therefore, one would measure the total gravitational potential and mass of a galaxy or galactic cluster to greater than that associated with the individual stars or visible baryonic matter they contain.

Additionally because the gravitation potential due to spatial flattening of space-time would be cumulative and linear with respect to the distance from the galaxy’s center the gravitational forces experienced by each star orbiting it would increase as its distance from the center does.  This also means that there should be linear relationship between a stars distance from the center of a galaxy and its orbital velocity.

In other words Einstein predicted the existence of Dark Matter when he defined gravitational potential in terms of a geometric property of space-time.

However this means that some of the gravitation potential associated with Dark Matter in galaxies galactic clusters and supper clusters and the recently observed dark matter web may not be due to baryonic matter but to the distortion or flattening of in space-time caused by their rotational energy.

One could observational verify the above hypothesis by determining the ratio of Dark matter to the orbital dynamics of galaxies.  If it is found that spiral galaxy have a larger ratio of dark matter to visible matter than globular clusters it would suggest that flattening of space does contribute the total gravitational potential in of a given volume of space.  This is because the rotational velocity of stars in spiral galaxies would have a slightly greater flattening effect on space than globular ones.

Another way of observational verifying this hypothesis would be to determine where the gravitational nodes would be located in the space between galactic clusters and determine if they match the patterns associated with the dark matter web.  If it does it would go a long way in confirming it.

Later Jeff

Copyright Jeffrey O’Callaghan 2013

The post The Geometry of Dark Matter appeared first on Unifying Quantum and Relativistic Theories.

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

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

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

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

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

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

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

The fact that the equation E=mc^2 allows us to quantitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is one the bases of assuming as was done in the article “Defining energy” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

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

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

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

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

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

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

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

Later Jeff

Copyright Jeffrey O’Callaghan 2013

The post Dark Energy in four spatial dimensions appeared first on Unifying Quantum and Relativistic Theories.