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.

However the reason may be because gravity is not propagated by a particle such as a photon but by field properties of space.

The currently accepted view among most cosmologist and physicist is that all forces mediated by particles.  This viewpoint is support the success the Standard Model of Particle Physics has had in explaining and predicting the observed properties of electromagnetic energy, weak, and strong nuclear forces in terms of particles.  It makes very accurate and verifiable predictions of the nature and causality of those forces in terms of particle interactions.

However it falls short of being a complete theory of fundamental interactions because it cannot or does not incorporate the full theory of gravitation as described by General Relativity.  This is because Einstein’s General Theory of Relativity derives gravity in terms of a continuous curvature in the field properties of four-dimensional space-time and not in terms of the discontinuous properties of the quantum.

This fact makes it extremely difficult to conceptually integrate them because something that is discontinuous cannot be by definition continuous.
However it may be possible to integrate gravity with the particle properties of the forces defined in the Standard Model if instead of assuming they are propagated by particles one assumes that the particle properties of all forces are propagated by the fields.

It is easier to explain the mechanism responsible for creating the gravity or quantum of gravitational force by redefine Einstein’s space-time universe into one consisting of only four *spatial* dimensions.

(The reason will become obvious latter in the article)

Einstein gave us the ability to do this when he used he used equation of E=mc^2 and the constant velocity of light to defined gravity in terms geometric properties of space-time because it allows one to convert a unit of time in his space-time universe to a unit of 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 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 his space-time universe in terms of the geometry of four *spatial* dimensions.

However it allows one to define a physical mechanism that would responsible creating a particle or quanta of space-time in terms of the field properties of four *spatial* dimensions.

For example the article “Why is energy/mass quantized?” Oct. 4, 2007 showed it is possible to explain the discontinuous properties of space by extrapolating the laws classical resonance in a three-dimensional environment to a matter wave on a continuous “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

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

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

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

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

Therefore these discrete or quantized energy of resonant systems in a field consisting of four *spatial* dimensions would be responsible for the particle characteristics the standard model associates with the propagation of gravity electromagnetic energy, weak, and strong nuclear forces.

However, it does not explain how or why we observed them in terms of discontinuous properties of a particle instead of the continuous properties of a field as the above theoretical model and Einstein Theories predicts we should.

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 defines the mechanism responsible for the quantization of the field properties of space associated with energy/mass in the article “Why is energy/mass quantized?“.

Quantum mechanics defines the smallest possible unit of space and increment of energy in terms of Planck’s length “h” while defining the size of an individual quantum of force in terms of the equation E = h c / L. 

In other words the physical size of the fundamental quanta of all forces is not the same as is suggest by the Standard Model of Particle Physics and quantum mechanics but varies with their energy and the higher energy there is the smaller its volume.

However this means the length and therefore the volume of a Graviton would be considerably larger when compared to the volume associated with a quantum unit of the electromagnetic weak or strong forces because of its relatively low energy content with respect to theirs.

The theoretical evidence to support this conclusion is provided by the fact that the energy of a quantum of force is mathematically defined by its frequency and wavelength.  This means a higher energy particle with a shorter wavelength would occupy a smaller volume than lower energy ones.

Observational evidence can be found in the fact that quanta of the strong and weak forces can only be observe in particle accelerators capable of generating the energy required to magnify their environment enough to allow for us to observe them.

In other words the reason why we can observe quanta of the strong and weak forces is because we can create experimental apparatus that can magnify the environment to the point where they become visible.

While a quantum of a less energetic electromagnetic force associated with visible light is observable because it size is comparable to the size to the sensing apparatus in the cones and rods in the eyes use to detect it.

However electromagnetic forced is about a million billion billion billion billion (10^42) times stronger than gravitational.

Using the same logic one reason why we have been unable to observe a Graviton may be because we have been unable to construct an observing platform a million billion billion billion billion (10^42) larger than the one need to observe quanta of electromagnetic force of the same strength. 

However the relatively large size of a Graviton or an individual quanta of gravity predicted by quantum mechanics suggests another reason why we have been unable to observe it.

We know from observations that gravitational forces act on much smaller scales than the physical size of an individual Graviton predicted by quantum mechanics. However this means that we should observe that the orbital energy of objects should also be quantized.

Some may disagree by saying that the size of the quantum unit of gravitational force is too small relative to the mass of objects that the effect of its quantization would be unobservable.

However the equation that defines the size of a Gravitron ( E = h c / L ) tells us that it would relatively large with respect to the orbits of many of the observable planets.  Additionally the force of gravity is always attractive or only acts in one direction therefore the effects of its quantization would be cumulative

In other words if gravity is propagated by the graviton the cumulative effects over the life of the universe should be observable with the increased sensitivity and high resolution of modern instrumentation.

Therefore one must assume that Einstein was correct we he defined gravity in terms of its field and not the quantum properties of space-time because if it was propagated by the Graviton then quantum mechanics tells us due to its relative large size that we should have observed discrete regions of space where orbits of stars planets and moons are not found.

This strongly suggest the reason why we have been unable to observe a Graviton is because gravity is not propagated it but by the field properties of space.

Later Jeff

Copyright Jeffrey O’Callaghan 2013 

The post Finding the graviton appeared first on Unifying Quantum and Relativistic Theories.

However, for the past 50 years brightest minds in the scientist community have been unable to observe the Gravitron or the particle it assumes it responsible for the force of gravity.

Some say this is because it interacts so weakly with matter that modern instruments are not sensitive enough to detect it even with, as mentioned earlier the recent exponential increase in their sensitivity. 
However the reason may be because we have been looking in the wrong direction.

For example in the article ” Linking Gravity with electromagnetism in four *spatial* dimensions”  Dec. 15, 2007 it was shown that one can derive quantum properties of gravitational and electrical forces in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension in a manner that makes prediction identical to those of General Relativity.

Einstein gave us the ability to derive gravity in terms of a displacement a “surface” of a three dimensional space manifold with respect to a fourth spatial dimension when he defined the geometric properties of a space-time universe in terms of the equation E=mc^2 and the constant velocity of light because that provided a method of converting the displacement in space-time he associated with gravity to its equivalent displacement 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.

However as that article one also can derive electromagnetism in terms of spatial displacement of a “surface” of a three dimensional space manifold with respect to fourth *spatial* dimension

For example a wave on the two-dimensional surface of water causes a point on that surface to be become displaced or rise above or below the equilibrium point that existed before the wave was present.  A force will be developed by the differential displacement of the surfaces, which will result in the elevated and depressed portions of the water moving towards or become “attracted” to each other and the surface of the water.

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

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

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 similar charges than it would be for a single charge. 

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

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

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

This cannot be done in terms of four-dimensional space time because a time or a space-time dimension is only observed to move in one direction forward and therefore could not support the bidirectional movement required to create a differential displacement.

However it also provides a method of linking electromagnetic and gravitational forces to their quantum mechanical properties the Standard Model associated with the Gravitron because as the article ” Why is energy/mass quantized? ” Oct. 4, 2007 showed one can derive them by extrapolating the laws of classical 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 environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet by a matter wave in an environment 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 (the substance) to oscillate with respect to a fourth *spatial* dimension at the frequency associated with the energy of that event.

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

Observations of a three-dimensional environment tell us that the energy of a resonant system can only take on the discrete or quantized values associated with the fundamental or a harmonic of its fundamental resonant

Similarly the energy of a resonant system in an environment consisting of four *spatial* dimensional environment could only take on the discrete or quantized values associated with the fundamental or a harmonic of a resonant system in that environment. 

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

However the above theoretical model shows that the quantum unit of both gravity or the Gravitron and electromagnetism; the photon share a common origin in a resonant system and therefore would interact with each other. This suggests that instead of looking for gravitons effect on matter one would be more likely to find it by observe the random effects it would have on the movement of extremely light particles such as low frequency photons.

This random effect would be amplified by the distance traveled so with our advanced technologies if it exists we should be able to observe a difference between photons with nearby verse ones with far away origins.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

The post Finally, someone found a physical link between the graviton and the photon appeared first on Unifying Quantum and Relativistic Theories.

The evidence for the existence of Dark matter comes from the detained analysis of the orbital motions of galaxies in galactic clusters.

In 1933 a Swiss astrophysicist Fritz Zwicky, of the California Institute of Technology applied Newtonâ€s law of gravity to the Coma cluster of galaxies and obtained evidence of unseen mass.  He estimated the clusterâ€s total mass based on the motions of galaxies near its edge and compared that estimate to one based on the number of galaxies and total brightness of the cluster. He found that there was about 400 times more estimated mass than was visually observable. The gravity of the visible galaxies in the cluster would be far too small for such fast orbits, so something extra was required.  This is known as the “missing mass problem”. Based on these conclusions, Zwicky inferred that there must be some non-visible or dark form of matter which would provide enough of the mass and gravity to hold the cluster together.”

The fact that 70% of the universes energy is “dark” is determined by analyzing its spatial geometry.

(For those who are interested the video on the right gives a detail description of how its geometry determines the quantity of dark energy and matter it contains.)

At the present time we have some very good theories about the normal matter in the universe.  The standard model of particle physical tells us what the particles are and how they interact in a manner that is consistent with all experimental observations.   However the same cannot be said for dark matter because as of yet no one has observe any particles that could explain its properties.

However science has developed some theoretical models explaining its properties in terms of the existence of a non-baryonic form of particles such as neutrinos, and entities such as axions, supersymmetric particles, or WIMPs.

Yet, as Lee Smolin points out in his book “The Trouble with Physics” none of them are supported by observations.

Neutrinos because of their mass would be characterized by high random speeds in the early universe. However, observations of the early universe indicate the matter that condensed to form galaxies was not hot enough to support the energy that would be associated with those high speeds.

The other particles, which could provide the missing mass fall into two classes: those which have been proposed for other reasons but happen to solve the dark matter problem, and those which have been proposed specifically to provide the missing dark matter.
Examples of objects in the first class are axions and the supersymmetric particles. Their properties are defined by the theory, which predicts them, and by virtue of their mass; they can solve the dark matter problem only if they exist in the correct abundance.

The second class of particles contains entities such as the WIMP or “Weakly Interacting Mass Particle” whose properties are not specified. However, they are assumed to have properties that would allow them to explain the missing mass associated with dark matter along with other “ad hoc” ones that would explain why they have not yet been observed experimentally.

However, the existence of them along with axions and the supersymmetric particles is not based on observations so therefore there is no way to either confirm their existence or that they are responsible for the gravitational force associated with dark matter.

Yet it may be possible to understand what Dark Matter is if one assumes it is made up of a continuous field of mass because it will allow one to derive both its gravitational and quantum properties by extrapolating the laws of classical mechanics to the wave properties associated with particles.

Louis de Broglie was the first to theorize that all particles have the properties of waves.  His theory was confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer. .

However this observation allows one to explain as was done in the article Why is energy/mass quantized?” Oct. 4, 2007 how the continuous field properties of mass or dark matter become quantized and why we cannot directly observe it by extrapolating the laws of classical wave mechanics in to the properties of a continuous field.

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 in a a space-time environment

The existence of four dimensional space-time would give a wave in a continuous field of mass the ability to oscillate spatially on a “surface” of three dimensional space 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 spatially 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 its fundamental or a harmonic of its fundamental frequency.

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

However if dark matter and the gravitational forces it posses in made up of a continuous field of mass why is it that we cannot directly observe it.

There are at least two reasons for this. The first is because all observations require an exchange of energy between what is being observed and the observer.  However as was shown above the most effective and efficient way for nature to transfer information to our instruments is, as was shown in the article “Why is energy/mass quantized?“ in a resonate system made up of the field properties of mass.  Therefore in all measurements the particle properties associated with its resonant system will always be predominant over its field ones.

The second is that to directly measure a quantity there must be a physical difference between what is being measured and what is doing the measuring.  For example one cannot measure the changing level of water in a ship lock from a ship in it by measure how high it is above the surface of the water ship is floating in because it is changing at the same rate.

Similarly one cannot measure the field properties of the mass component of space because the field properties in the measuring instrument are changing at the same rate.

However we can indirectly measure how the field properties of mass interact with particles as was shown by in 1927 by Davisson and Germer observation of electron diffraction by crystals.

In other words assuming Dark Matter is made up of a continuous field of mass not only explains why we cannot observe 25%.percent of the universe mass but also the Davisson and Germer discovery of  electron diffraction by crystals in 1927 while at the same time deriving the quantum mechanical properties of particles in terms of the classical filed properties of space and time.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

The post Why we cannot see 25% percent of the universe mass appeared first on Unifying Quantum and Relativistic Theories.

For example an electron in certain atoms will spontaneously decay after being excited by emitting pairs of polarized photons such that one is aligned horizontally the other vertically.  According to quantum mechanics these photons are entangled and act of observing one instantly affects the other no matter how far they are apart.
This instantaneous communication between the entangled photons is at the heart of quantum entanglement.  This is the “spooky action at a distance” Einstein believed was theoretically implausible because according to Relativistic theories information cannot be propagated instantaneously but only at the speed of light.

To demonstrate this 1935, Einstein co-authored a paper with Podolsky and Rosen which was intended to show that Quantum Mechanics could not be a complete theory of nature.  The first thing to notice is that Einstein was not trying to disprove Quantum Mechanics in any way.  In fact, he was well aware of its power to predict the outcomes of various experiments.  What he was trying to show was that there must be a “hidden variable” that would allow Quantum Mechanics to become a complete theory of nature

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

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

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

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

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

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

Many believed this provided experimental verification of the concept of Quantum entanglement.  Additionally it meant that science has to accept that either the reality of our physical world or the concept of separability does not exist.

However this may not be true because in the article “The *reality* of quantum probabilities” Mar. 31 2011 it was shown the probability functions quantum mechanics associates the wave function can be understood by assuming it is physically a result of a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Very briefly the article “Why is energy/mass quantized?” Oct. 4, 2007 showed that one can derive the quantum mechanical properties energy/mass by extrapolating the laws of classical resonance to a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

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

It showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet in one consisting of a continuous non-quantized field of energy/mass and four *spatial* dimensions.

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

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force space (the substance) to oscillate with the frequency associated with the energy of that event.

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

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 this defines a physical mechanism responsible for why energy/mass is quantized in terms of a matter wave move on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

In an earlier article “Embedded dimensions” Oct. 4, 2007 it was shown that one can derive all forms of energy including that of quantum systems in terms of displacement in a *surface*that manifold

However assuming its energy is result of a displacement in four *spatial* dimension allows one to derive, the probability distribution associated with the wave function of individual particles by extrapolating the laws of a three-dimensional environments to a fourth *spatial* dimension.

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

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

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

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

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

Similarly a quantum system would most probably be found were the magnitude of the vibrations in a “surface” of a three-dimensional space manifold is greatest and would diminish as one move away from that point,

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

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

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

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

However, this may not be true.

According to quantum mechanics act of measuring the state of one of pair of entangled photons instantly affects the measurement of the other no matter how far they are apart.  Yet if it is true as mentioned earlier that each particle shares an identical wave or probably function as it move through space the measurement of the state of one particle would be reflected in the measurement of the other because those measured states will have the same probability of occurring in each particle.

In other words the reason why Bell’s inequity is violated in quantum system is not because they are physically entangled or connected at the time of measurement but because their individual wave or probability functions were “entangled” or identical at the time of their separations and remained that way as they moved apart.  Therefore even though they are not physical connected measurements based on their quantum mechanical probability function would be.

Additionally quantum entanglement is defined in terms probability. Therefore, there would be a non-zero probably that bellâ€s inequity will be violated when measuring the influence of one particle on another because those measurement are based on probabilities. Therefore, one could mathematical quantify the scenario proposed above because the probability of this occurring should mirror the individual quantum mechanical probability function of each individual particle.

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

This shows how one can by extrapolating the classical laws governing a three-dimensional environment to a fourth *spatial* dimension define a mechanism responsible for the correlation of the quantum mechanical measurements of particles that exist in non-local environments while maintaining the classical concepts of reality and separability.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

The post Quantum entanglement: A Classical non-locality appeared first on Unifying Quantum and Relativistic Theories.