Quantum mechanics defines our observable environment only in terms of the probabilistic values associated with Schrödingerâ€s wave equation.

However it is extremely difficult to define a set of statements which explains how those probabilities are physically connected to it even though it has held up to rigorous and thorough experimental testing.

This may be the reason most physicists consider quantum mechanics only in terms of its mathematical formalization instead trying to understand the meaning of it in terms of the space-time environment we occupy. 
For example in 1924 Louis de Broglie was the first to realize all particles are physically composed of a matter wave as the discovery of electron diffraction by crystals in 1927 by Davisson and Germer) verified.  However in his paper, “Theory of the double solution“ he unsuccessfully attempted to define a physical interpretation of Schrödinger equation in classical terms of space and time.

As is pointed at his biography on the nobleprize.org web site in “1951, he together with some of his younger colleagues made another attempt, one which he abandoned in the face of the almost universal adherence of physicists to the purely probabilistic mathematical interpretation of, Bohr, and Heisenberg.”

However the fact that no has been able to physically connect those probabilities to our environment does not change the fact that there must be one because if there wasn’t they could not interact with it to create the physicality of observable world upon which those probabilities are based.

As mentioned earlier Louis de Broglie and his colleagues tried unsuccessfully to find a physical interpretation of Schrödinger equation in classical terms of space and time.

However the reason for their failure may be due to the fact that it is related to the spatial not time dependent properties of the wave function.

If so one may be able to establish the connection by looking at it in terms of its spatial properties instead of the space-time one Louis de Broglie and his colleagues used.

Einstein gave us the ability to do this defined the geometric properties of space-time in terms of the constant velocity of light and a dynamic balance between mass and energy because that  provided a method of converting a unit of time in a space-time environment of unit of space in four *spatial* dimensions.  Additionally because the velocity of light is constant he also defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

The fact that one can use Einsteinâ€s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with 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.

This would have allowed Louis de Broglie to physically connect the probabilities associated Schrödinger equation to the quantum properties of a matter wave in terms of a physical or spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension as was done in the article  “Why is energy/mass quantized?” Oct. 4, 2007. 

Briefly that article showed that one can do this by assuming they are caused by the formation of a resonant system on a “surface” of a three-dimensional space manifold with respect to fourth “spatial” dimension.  This is because it showed the four conditions required for resonance to occur in a three-dimensional environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in one made up of four.

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* 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.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established on a surface of a three-dimensional space manifold.

Yet the classical laws of three-dimensional space tell us the energy of resonant systems can only take on the discontinuous or discreet energies associated with their fundamental or harmonic of their fundamental frequency.

Additionally it also tells us why in terms of the physical properties four dimensional space-time or four *spatial* dimensions 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.

However, these are the similar to the quantum mechanical properties of energy/mass in that they can only take on the discontinuous or discreet energies associated with the formula E=hv where “E” equals the energy of a particle “h” equal Planck’s constant “v” equals the frequency of its wave component.

In other words Louis de Broglie would have been able to physicality connect the the quantum mechanical properties of his particle waves to Schrödinger equation in terms of the discrete incremental energies associated with a resonant system in four *spatial* dimensions if he had assume space was composed of it instead of four dimensional space-time.

Yet it also would have allowed him to define the physical boundaries of a quantum system in terms of the geometric properties of four *spatial* dimensions.

For example in classical physics, a point on the two-dimensional surface of a piece 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?” Oct. 4, 2007

As mentioned earlier in the article “Defining energy?” Nov 27, 2007 showed all forms of energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However assuming the energy associated with Louis de Broglie particle wave is result of a displacement in four *spatial* dimension instead of four dimensional space-time as was done earlier would allows one to connect the probabilities associated with Schrödinger equation to the physicality of our observable environment we all live in.

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

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

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

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

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

Similarly a particle 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.

This shows how one can physically connect the probabilities associated Schrödinger wave equation to our observable environment by redefining it in terms of four *spatial* dimensions.

It should be remember Einsteinâ€s genius allows us to choose to define a quantum system in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories thereby giving us a new perspective on the probabilistic properties of a quantum environment and how they physically connected to our observable universe.

Later Jeff

Copyright Jeffrey O’Callaghan 2015

The post The physical meaning of Schrödinger wave equation appeared first on Unifying Quantum and Relativistic Theories.

In other words in a quantum system Schrödinger wave equation plays the role of Newtonian laws in that it predicts the future position or momentum of a particle in terms of a probability distribution by assuming that it simultaneously exists everywhere in three-dimensional space. 

This accentuates difference between quantum and classical mechanics because it derives the evolution of a particle in terms of it being in one place both before and after a measurement was taken whereas quantum mechanics derives its finial resting place in terms of an infinite number of possible starting points.

However one may be able to reconcile these two conflicting concepts by observing how matter and energy interact in terms of the classical properties of space-time.

But it will be easier if we first transpose or covert Einstein’s space-time universe to one consisting of only four *spatial* dimensions.

This is because it will allow us to define the mechanism responsible for the superpositioning of particles it in terms of a geometry which is directly related their position or spatial properties instead of its non-positional or temporal components.

Einstein gave us the ability to do this when he use the equation E=mc^2 and the constant velocity of light to define the geometric properties of space-time because that provided a method of converting a unit of space-time associated with energy to unit of space associated 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.

However 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.

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

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

The existence of four *spatial* dimensions would give 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 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.

Yet it also allows one to define the boundary of a quantum system 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 associated with a particle in the article “Why is energy/mass quantized?“

As mentioned earlier in the article “Defining energy?” Nov 27, 2007 showed all forms of energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

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

Classical mechanics tell us that due to the continuous properties of waves the energy 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.

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

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

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

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

Similarly a particle 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.

In other words a particle appears to be superpositioned because its wave energy is distributed in probabilistic manner throughout the entire universe.

This suggests the reason why particles appear to be superpositioned is not due to the mathematical probabilities associated with Schrödinger wave equation but due to a classical interaction of the wave properties of a quantum system with the  geometry of a universe of a consisting either four dimensional space-time or four *spatial* or time dimension.

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

Later Jeff

Copyright Jeffrey O’Callaghan  2015

The post A classical explanation of Quantum Superposition appeared first on Unifying Quantum and Relativistic Theories.

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.

Most scientist would agree the best way of accomplishing this would be to determine if one can be explained in terms of the other.

For example can one explain why many proponents of quantum mechanics assume that a particle simultaneously exists everywhere in space until it is observed or measured in terms of the classical laws that govern our macroscopic environment.  

In Brian Greene book “The Fabric of the Cosmos: Space, Time, and the Texture of Reality” (Kindle Locations 1825-1836) he explains the difference between the probabilistic world of quantum mechanics and the deterministic world of Newtonian mechanics.

“According to Newton, if we knew in complete detail the state of the environment (the positions and velocities of every one of its particulate ingredients), we would be able to predict (given sufficient calculation prowess) with certainty whether it will rain at 4:07 p.m. tomorrow; if we knew all the physical details of relevance to a craps game (the precise shape and composition of the dice, their speed and orientation as they left your hand, the composition of the table and its surface, and so on), we would be able to predict with certainty how the dice will land. Since, in practice, we canâ€t gather all this information (and, even if we could, we do not yet have sufficiently powerful computers to perform the calculations required to make such predictions), we set our sights lower and predict only the probability of a given outcome in the weather or at the casino, making reasonable guesses about the data we donâ€t have.

However one of the most fundamental laws of classical mechanics is that each cause has a specific effect and that identical causes will have identical effects.  However it also states that random causes will have random outcomes and that one can determine the probability of a certain event occurring based on the randomness of its cause.

Yet many feel that one cannot apply the concepts of Classical Newton physics to the quantum world because as Brian Greene points out in his book The Fabric of the Cosmos: Space, Time, and the Texture of Reality (Kindle Locations 1833-1836), “The probability introduced by quantum mechanics is of a different, more fundamental character (than classical Newton probabilities) Regardless of improvements in data collection or in computer power, the best we can ever do, according to quantum mechanics, is predict the probability of this or that outcome. The best we can ever do is predict the probability that an electron, or a proton, or a neutron, or any other of natureâ€s constituents, will be found here or there. Probability reigns supreme in the microcosmos.”
However if someone strikes a pool ball on a pool table in a dark room and cannot measure or determine initial conditions there is an extremely high probability that he will find it on the table when he turns on the light.  However, he or she does not assume that the balls simultaneously exist on every point on its surface until the light is turned. Additionally one can apply Newton’s laws and the probability of the different initial conditions associated with that event to determine the final resting place of the pool balls on the table after the light is turn on.  I think most would consider someone mentally deficient if he tried to convince us that the pool balls simultaneous existed every at every point on the surface of the pool table when the light off and only materialize when it was turn on just because he could not see how they got there.

Similarly why do some make the outlandish claim that a particle simultaneously exists in at every point in space and only materializes when it is observed based on the fact that they cannot “see” or measure the initial conditions and how they traveled to a specific point in space.

The reason is because quantum mechanics does not deal with evolution of a measurement but only with its outcomes. Therefore, because we in the macroscopic world and cannot “see” the initial condition responsible the evolution of a quantum system many assume that its entire history must be probabilistic. 

However, as with the balls on a pool table the finial resting place of them and all quantum systems would be definable only in terms of the random probabilities of their initial conditions if one cannot “see” or determine them even if its evolutionary history conforms to Newton’s laws.

This shows how one can explain probabilistic outcomes of experiments in the quantum world in terms of the classical laws of the macroscopic world by assuming randomness of their outcomes is due to a lack of knowledge of their initial condition and not due the the probabilistic properties of their evolution. 

Granted as Brian green pointed out nature may prevent us from ever develop the technology to precisely measure the initial conditions of a quantum system.  However, as was shown above that does not means we cannot find an explanation of what we cannot see in the microcosmos in terms of what we can see in the macro cosmos.

In other words it is a fallacy to assume that the quantum mechanical probabilities of the micro cosmos lack or cannot be explained by the determinism of the macro cosmos.

Later Jeff

Copyright Jeffrey O’Callaghan 2013

The post The quantum fallacy appeared first on Unifying Quantum and Relativistic Theories.

In other words even though one can find equations to accurately quantify or define an environment does not mean that they have found an valid explanation as to how and why it is what it is.

For example both Quantum Mechanics and the Standard Model of Particle Physics define and quantify the environment of particles in terms of what could be considered the mystical properties of a non-dimensional mathematical point.

Mystical in the sense that the definition of mysticism as being or having vague speculation: a belief without sound basis could be applied to it.  This is because by definition no one has or ever will be able to observe the non-dimensional mathematical point they use to define a particle therefore we do not have an observational and therefore a sound basis for assuming its existence.

Most who have study the history of science are aware of the fact that many medieval and Renaissance astronomers assumed the planets were imbedded in rigid celestial spheres whose movement was guided celestial intelligences, souls or impressed forces.

Today many would classify that concept as being mystical because there is no observation evidence to support the assumption that the motion of the planets is control by some form of intelligence.

However many modern scientists would disagree with the assertion that a non-dimensional particle has similarities to the mystical ones we now associate with the Renaissance astronomer’s celestial intelligences by pointing to the fact that it permits them to accurately quantify its environment within the limit of our modern observational capabilities.

Yet the same argument could and most probably was used by them to justify their belief in idea that a celestial intelligence were guiding the planet because it also permitted them to accurately define and quantify the orbital environment of the planets within the limits of their observational capabilities.

The Standard Model of particle physics uses the concept of point particle only because it makes its mathematical description of their properties possible.   However it assumes that a point is appropriate representation of any object whose size, shape, and structure are irrelevant in a given context. For example, from far enough away, an object of any shape will look and behave as a point-like object.

While Quantum Mechanics derives the world of the very small in terms of the probability function based on mathematical representation of particle as a non dimension point for reason similar to why the standard model does.  In other words the only way to define the position of a particle in terms of a probably function is buy assuming that it does not have any spatial properties.  Therefore it also assumes that it size, shape, and structure are irrelevant in a given context.

Unfortunately for the proponents of Quantum Mechanics the concept of a point particle is complicated by the Heisenberg uncertainty principle, which tells us even in the domain of quantum mechanics an elementary particle, with no internal structure, occupies a nonzero volume because of the uncertainty involved in determine the exact point where it is located in space.

As mentioned earlier both of these theoretical models assume that non-dimensional point is an appropriate representation of a particle because its size, shape, and structure are irrelevant in a given context.

But what if it is relevant?

For example what if the Heisenberg’s Uncertainty Principle which asserts there is a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position x and momentum p, can be simultaneously known is related to the spatial extension of a particle and not to its point properties as quantum theory assumes.

As was shown in the article “Why is energy/mass quantized?” Oct. 4, 2007 it is possible to understand the quantum mechanical properties of energy/mass in terms of an extended object by extrapolating the laws of classical resonance in a three-dimensional environment to a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

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

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

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

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

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

Therefore the discrete or quantized energy of resonant systems in a continuous form of energy/mass would be responsible for the discrete quantized quantum mechanical properties of particles.

However, it did not explain how the spatial boundaries or volume of these resonant structures is defined.

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

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

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

The mathematics of Quantum mechanics support the assumption that a particle occupies a finite volume berceuse it 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. 

As mentioned earlier both the standard model of particle physics and quantum mechanics assume that a point particle is an appropriate representation of any object whose size, shape, and structure is irrelevant in a given context.

However, even though the size and shape of a particle may be irrelevant to someone looking at it from the macroscopic perspective of a human observer it may be very relevant to the process and mechanisms reasonable for what a human observes.

For example if one assumes, as quantum mechanics does that a particle is a non-dimensional point then according to the above concepts there would be an uncertainty in determining its position because that non-dimensional point could be found any with the volume of the three-dimensional “box” mentioned above.

Yet one could come to the same conclusion if one assumes that the quantum properties of a particle are a result of resonate system in four spatial dimensions because according to the above concepts there would be an uncertainty in determining its position because that non dimensional point could be found anywhere within the volume of the “box” mentioned above.

Planckâ€s length is one of fundamental components of Quantum Physics and along with Heisenbergâ€s Uncertainty Principle it defines the uncertainty in the ability to measure more than one quantum variable at a time.  For example attempting to measure an elementary particleâ€s position (â–²x) to the highest degree of accuracy leads to an increasing uncertainty in being able to measure the particleâ€s momentum (â–²p) to an equally high degree of accuracy.  Heisenbergâ€s Principle is typically written mathematically as â–²xâ–²p  Â³ h / 2  where h represents Planck constant

As mentioned earlier the resonant wave that corresponds to the quantum mechanical wave function defined in the article “Why is energy/mass quantized?” predicts that a particle will most likely be found in the quantum mechanical “box” whose dimensions would be defined by that resonant wave.  However quantum mechanics treats particles as a one dimensional points and because it could be anywhere in it there would be an inherent uncertainty involved in determining the exact position of a particle in that “box”.

For examine the formula give above ( â–²xâ–²p  Â³ h / 2 ) tells us that uncertainty of measuring the exact position of the point in that “box” defined by its wavefunction would be equal to â–²xâ–²p  Â³ h / 2.   However because we are only interested in determining its exact position we can eliminate all references to its momentum.

However if we eliminate the momentum component from the uncertainty in a particle position become 6.626068 × 10^-34 meters or Planckâ€s constant.

As mentioned earlier the uncertainty involved in determining the exact position of a particle is because it is impossible to determine were in the “box” defined earlier the quantum mechanical point representing that particle is located.  However as mentioned earlier Planckâ€s constant tells us that one cannot determine the position of a particle to an accuracy greater that 6.626068 × 10^-34.  This suggest that Planck constant 6.626068 × 10^-34 defines the physical parameters or dimensions of that “box” because it defines the parameters of where in a given volume of space a quantum particle can be found.

Classical mechanics uses also uses the existence of a point at the center of mass to calculate the position of an extended object and to predict how it would interact with other objects in a gravitational field.  Similar to quantum mechanics it assumes that the object position can be determined by measuring it from a point defining its center because from a distance they feel it gives them an appropriate representation of the size, shape, and structure of the object. 

Therefore they can define the position of an irregular shaped object such as an asteroid by determining the distance from that point to whatever reference point they chose.

However Classical mechanics accepts the fact that there are limitation to the concept of using the center of an object to predict its position and how it will interact with other objects because as the resolution of the measurements increase or distance between decreases between it and the measure device it accepts the fact that the object shape has an effect on those measurements.

Similarly fact that Quantum mechanics tells us the individual quanta of energy/mass have a spatial extension defined by the equation E = h c / L means that there would always be an uncertainty in determining its position related to its shape because as mentioned earlier the resonant structure defining its particle properties is made up of the dynamic components of a matter wave and therefore there would be a predictable randomness when interacting with a measurement device.

Therefore on a quantum scale the size, shape, and structure of a particle would be relevant in determining a particle reality

This shows how one can not only mathematical describe the quantitative “reality” of a particles environment but also define how and why we observe them to interact the way we do based on the observable and therefore the verifiably properties of a three-dimensional environment instead speculating on the existence of a mystical non-dimensional particle.

As mentioned earlier assuming non-dimensional point particle can describe the quantum world is mystical in the same sense as the assumption made in the middle ages that celestial intelligences, souls or impressed forces were guiding the planets because there is no sound observational basis for their existence.

However history has shown that the greatest advances in science are made when one eliminates mysticism from the description of reality

As mentioned earlier Scientist especially physicists should always remember that describing reality is different from defining it.

Later Jeff

Copyright Jeffrey O’Callaghan 2013 

The post The Mysticism of a non-dimensional particle appeared first on Unifying Quantum and Relativistic Theories.

Einstein told us that energy and mass are interchangeable however he did not define what mass is.  He only told us how mass interacts with space-time.

As Steven Weinberg said “Mass tells space-time how to curve while space-time tells mass how to move”.

However Einstein’s inability to define or derive the casualty of mass is can be traced to the fact that he chose to define the energy associated with it in terms of four dimension space-time instead of defining the mass associated with energy in terms four *spatial* dimensions.

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

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

This was the bases for assuming as was done in the article “Defining energy” Nov 27, 2007 that all forms of energy including thermo and inertia or momentum of mass 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 instead of one in a space-time environment.
However changing ones perspective on the geometric structure of the universe form one of space-time to four *spatial* dimensions not only gives one the ability to understand the causality of mass but also give one the ability derive its quantum mechanical properties as was done in the article “Why is energy/mass quantized?” Oct. 4, 2007″ in terms of its wave component and the resonant properties of four *spatial* dimensions.

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

Briefly that article 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 four.

The existence of four *spatial* dimensions would give a matter wave that Louis de Broglie associated with a particle 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 respect to a fourth *spatial* dimension at a 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.

Classical mechanics tells us that resonant systems can only take on the discrete or quantized energies associated with a fundamental or a harmonic of their fundamental frequency.

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

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

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

The confinement of the “upward” and “downward” oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the geometric boundaries of the resonant system associated with a particle.

Therefore, these resonant systems in a four *spatial* dimensions would define mass and its quantum mechanical properties because of the fact that the volumes of space containing them would have a higher concentration of energy and therefore the mass associated with those volumes would be greater.

This would allow one to, not only understand the causality of the absolute properties of mass such as inertia but it would allow us to derive all of its relativistic ones.

For example one can use these concepts to explain why the corresponding particle types across the three fundamental families of particles in the Standard Model listed in the table below have identical properties except for their mass, which grows larger in each successive family.

As mentioned earlier the article “Why is energy/mass quantized?” showed that one can derive the mass of a particle in terms of the energy contained within a resonant system generated by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension while the article “Defining energy” showed that one can derive the energy of its environment in terms a displacement in the same three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore using the concepts developed in those articles one could derive the total mass of a particle in terms of the sum of the energies associated with that resonant structure and the displacement in the “surface” of three-dimensional space associated with the energy of the environment it is occupying.

Yet Classical Mechanics tells us there will be specific points in space where the matter wave that Louis de Broglie associated with a particle can interact with the energy content or temperature of its environment to form a resonant system.

Therefore, the mass of each family member would not only be dependent on the energy associated with the resonant system that defined their quantum mechanical properties in the article “Why is energy/mass quantized?” but also on temperature of the environment they are occupying.

Thus suggest the reason “The corresponding particle types across the three families have identical properties except for their mass, which grows larger in each successive family.” is because of an interaction between the resonant properties defined in the article “Why is energy/mass quantized?” and the energy content of the environment they are occupying.

This means the particles in the first family would be found in relativity low energy environments, are relatively stable, and for the most part can be observed in nature.  However, the particles in the second and third families would be for the most part unstable and can be observed only in high-energy environments of particle accelerators.  The exception is the Muon in the second family, which is only observed in the high-energy environment of cosmic radiation.

The relative masses of the fundamental particles increases in each successive family because the higher-energy environments where they occupy would result in the corresponding particles in each successive family to be formed with a greater relative “separation” in the “surfaces” of a three-dimensional space manifold with respect to a fourth *spatial* dimension..

Therefore, the corresponding particles in the second family will have a greater mass than the particles in the first family because the “separation”, with respect to a fourth *spatial* dimension of the three-dimensional space manifold associated with them is greater than the “separation” associated with the first family.

Similarly, the corresponding particles in the third family will have a greater mass than those in the second family because the “separation”, with respect to a fourth *spatial* dimension, of the three-dimensional space manifold associated with them is greater than the spatial “separation” associated with the second family.

Additionally the corresponding particle types across the three families have “identical properties” because as shown in the article “The geometry of quarks” Mar. 15, 2009 they are related to the orientation of the “W” axis of the fourth *spatial* dimension with the axis of three-dimensional space.  Therefore, each corresponding particle across the three families will have similar properties because the orientation of the “W” axis of the fourth *spatial* dimension with respect to the axis of three-dimensional space is the same for the corresponding particles in all of the families.

This explains why “The corresponding particle types across the three families having identical properties except for their mass, which grows larger in each successive family” in terms of the properties of classical resonance and the existence of four *spatial* dimensions.

However it also allows one to derive the absolute properties of mass associated with Newton’s first and second laws of motion because as was shown in the article “The Equivalence Principal: an alternative to space-time” July 15, 2008 all accelerations or forces (including gravitational) can be derive in terms of a curvature in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

(This curvature is analogous to the curvature in space-time Einstein assumed was responsible for gravitational forces.)

Newton’s first law of motion which defines the inertial properties of the mass of an object or particle states that “Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it”

However this is what one would expect if one assumes, as mentioned earlier the momentum of an object is caused by a displacement of a “surface” of a three-dimension space manifold with respect to a fourth *spatial* dimension because according those concepts it would tent to stay rest or once in motion would tend to stay in motion because its displacement would remain constant unless it interacted with an external force or as was shown in the article “The Equivalence Principal: an alternative to space-time” a three dimensional “surface” that was curved with respect to a fourth *spatial* dimension.

However it also allows on to understand the causality of Newton’s second law which defines the relationship between an object’s mass “m”, its acceleration “a”, and why the change in velocity of an object or particle is define by the equation is F = ma because as mentioned earlier, the rest mass of an object is directly proportional to a displacement a “surface” of three-dimensional space manifold with respect to fourth *spatial* dimension.  Therefore, as was shown in the article “Defining energy” there will be a 1 to 1 correspondence between it and the curvature in space associated with the energy required to make a unit change in its displacement with respect to a fourth *spatial* dimension.  Therefore the inertia of an object or its resistance to change in velocity would be directly related to its mass. 

In other words using Einstein’s field equations to redefine his space-time universe in terms of four *spatial* dimension allows one to not only understand and derive the causality of the relativistic properties of mass but also the absolute properties associated with its inertia without the need of assuming the existence of the Higgs Boson.

Later Jeff

Copyright Jeffrey O’Callaghan 2013

The post Deriving mass without the Higgs Boson appeared first on Unifying Quantum and Relativistic Theories.

For example the Copenhagen interpretation tells us that a particle is spread out as a wave over the entire universe and only appears in a specific place when a conscience observer looks at it.  Therefore it assumes the act of measurement or observation creates its physical reality and that of the universe.  However because only conscience human beings can be observers it implies that nothing can exist without them being there to observe them.

Not only is it a bit self centered for humans to assume that they (humans) are the sole arbiters of the physicality of the universe but it is also shows how out of touch with reality those who believe in it are for the simple fact that the is overwhelming scientific evidence that humans physically evolved over a finite period of time.  However, if one assumes that atoms exist only after being observed by a human one must also assume that humans evolved out of something that did not exist.

However one of the reasons many scientist believe this is because they feel it is the only way to resolve the physical conflicts they find between the experimental observations of the microscopic realm of the atom and the “reality” we see in our macroscopic universe.
For example quantum mechanics assumes that all energy/mass is encapsulated in what is called a wave function which collapses into the reality most of us associate with our particle world only when it is observed. 

However as Greene, Brian points out in his book “The Fabric of the Cosmos: Space, Time, and the Texture of Reality” (Kindle Locations 3750-3752).

“No one has been able to explain how an experimenter making a measurement (observation) cause a wavefunction to collapse? In fact, does wavefunction collapse really happen, and if it does, what really goes on at the microscopic level? Do any and all measurements cause collapse?

The name give to the inability to define what happens to the wave properties of energy/mass when a measurement or observation is made is called the measurement problem and has given rise to different interpretations of quantum mechanics.  Many of these interoperations assume that Schrödinger wave function defines an atom in terms of the linear superposition of its particle and wave states even though actual measurements always find the physical system in a definite state.   Additionally experiments tell us that any future evolution must be based on the state the system was discovered to be in when the measurement was made and not on its history, meaning that the measurement “did something” to the process under examination.   Many believe whatever that “something” may be does cannot be explained in terms of classical theories.

However, it can be shown that one can explain and understand the “something” that happens when a measurement of the wave function is made by extrapolating the theoretical concepts of classical mechanics in a three-dimensional environment to a fourth *spatial* dimension.

In the article “A classical Schrödingerâ€s wave equation” Mar. 15, 2010 it was shown one can derive the physical reality of the quantum mechanical properties of energy/mass associated with Schrödinger’s wavefunction by extrapolating observations of classical three-dimensional space to a fourth *spatial* dimension.

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

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* 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.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established on a “surface” of a three-dimensional space manifold.

Yet classical theories of three-dimensional space tell us the energy of resonant systems can only take on the discontinuous or discreet energies associated with the fundamental or harmonic of their fundamental frequency.

However, these are the similar to the quantum mechanical properties associated with the wavefunction in that it only takes on the discontinuous or discreet energies associated with the formula E=hv where “E” equals the energy of a particle, “h” or Planckâ€s constant would correspond to the energy associated with the fundamental frequency of four *spatial* dimensions and “v” equals the frequency of its wave component.

This shows how one can not only define the physicality of the quantum mechanical properties of Schrödinger wavefunction but also of Planck’s constant by extrapolating the classical laws governing resonant system in a three-dimensional environment to a resonant system formed by a matter wave moving in four *spatial* dimensions. 

However it also gives one the ability to understand why evolution of a quantum system is effected by observation or measurement.

Classical mechanics tells us that one should be able predict the future evolution of a system based on its history.  In other words if one knew every detail of a systems history one could measure its future evolution with complete certainty.  However it also tells us that one must interact with a system and therefore change its history to make a measurement.  Therefore, the laws of classical mechanics tell us that one must base the future evolution of a system on new history created by a measurement. 

Yet this is precisely what we observed in a quantum environment in that the act of measurement creates a new history for a system.  The only difference between a classical and a quantum environment is that in the latter the act of measurement always makes significant change which cannot be ignored in determining the future of the environment. 

However this does not mean that one cannot use the conceptual “reality” defined by classical mechanics to understand the physicality of the quantum world because as mentioned earlier classical mechanics also tells us the act of measurement must affect the future evolution of a system.

The other as of yet unanswered question that Brian Breen brought up in his book involving what happens to the quantum mechanical wave function when a measurement is made can also be found in classical mechanics.

As mentioned the earlier article “A classical Schrödingerâ€s wave equation” showed that one can derive the quantum mechanical properties of energy/mass in terms of a resonant structure by physically extrapolating the laws of classical mechanics to wave in a quantum environment.

This tells us that because of the continuous properties of waves, the energy associated with a quantum system would be distributed throughout an extended volume of space similar to how the wave generated by a vibrating ball on a surface of a rubber diaphragm are disturbed over its entire surface while the magnitude of the displacement it causes will decrease as one moves away from the point of contact.

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 must be disturbed throughout the entire universe while the displacement created by its wave energy would decrease as one moves away from its position.  This means there would be a non-zero probability they could be found anywhere in our three-dimensional environment because as was shown earlier a quantum mechanical system is a result of a resonant structure formed by wave oscillations which are disturbed throughout space.

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

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

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

Yet this also means the wave function does not collapse but its evolution is redirected towards the observer.

In other words it answers the question “how an experimenter making a measurement (observation) causes a wave function to collapse” Greene, Brian asked in his book “The Fabric of the Cosmos: Space, Time, and the Texture of Reality” by using the laws of classical mechanics to define the quantum environment and “explain ”  show that the act of observation does not cause the collapse of the wavefunction but only redirects its evolution towards the observer.

It should be remember that we are not trying to quantify our quantum experiences but only to explain how and why we experience it the way we do in terms of the “realty” most of us associate with our classical world.

Later Jeff

Copyright 2012 Jeffrey O’Callaghan

The post A Classical Quantum environment appeared first on Unifying Quantum and Relativistic Theories.

To this point physicists have identified six types of quarks, called the UP/Down, Charm/Strange and Top/Bottom. The Up, Charm and Top have a fractional charge of 2/3 while the Down, Strange and Bottom have a fractional charge of -1/3.

They assume each quark carries a charge called “color” which like electric charge is always conserved. However, unlike electric charge, the color charge (the chromo in Chromodynamics) comes in three varieties or red, green, and blue and that each quark comprising a particle must have a different color, red, green, or blue.

The reason is because Pauliâ€s exclusion principle says no particle can be made up of components with identical quantum states.  They incorporate this principal into Quantum Chromodynamics theoretical structure by assigning a color to individual quarks and adopting a rule that says for a stable particle to exist the colors of their components must combine to make a colorless particle.  This requires particles to conform to Pauliâ€s exclusion principle because colorless or white light only exist if it is made up of one part red, blue, and green light.  Therefore a stable particle can only exist it is made up of three different types of quarks with colors of red blue and green.

However as of yet no one has been able to define the reason for their fractional charge or their color component in terms of the physicality of the environment they occupy.

Yet as was show in the article “The geometry of quarks” Mar. 15, 2009 one can derive a physical reason for their fractional charge and color properties if one assumes as was done in the article “Why is energy/mass quantized?” Oct 4, 2007 that the quantum mechanical properties of energy/mass can be derived in terms of a resonant structure formed by a matter wave on “surface” a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly that article 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 four spatial dimensions.

The existence of four *spatial* dimensions would give space (the substance) 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.

Therefore, these oscillations in 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.

The only way to dampen the frequency of a classically resonating system is to add or remove energy from it, which results in changing the characteristics of that system.

Additionally the energy in a classically resonating system is, as mentioned earlier is discontinuous and can only take on the discrete values associated with its fundamental or 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 and when energy is either added or removed from it, its characteristics changed.

But if space was made up of four *spatial* dimensions one should also be able to explain why quarks have a fractional charge and how their color properties interact to form stable particles in terms of the geometry four *spatial* dimension.

The article Defining energy Nov. 26, 2007 showed it is possible to define all forms of energy including electrical in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, we as three-dimensional beings can only observe three of the four *spatial* dimensions.  Therefore, the energy associated with a displacement in its “surface” with respect to a fourth *spatial* dimension will be observed by us as being directed along that “surface”.  However, because two of the three-dimensions we can observe are parallel to that surface we will observe it to have 2/3 of the total energy associated with that displacement and we will observe the other 1/3 as being directed along the signal dimension that is perpendicular to that surface.

This means the 2/3 fractional charge of the Up, Charm and Top may be related to the energy directed along a “surface” of a displaced three-dimensional space manifold with respect to a four *spatial* dimension while the -1/3 charge of The Down, Strange and Bottom may be associated with the energy that is directed perpendicular to that “surface”.

The reason why quarks come in three configurations or colors with a fractional charge of 1/3 or 2/3 may be because, as was shown in the article Embedded Dimensions Nov. 22, 2007 there are three ways the individual axis of three-dimensional space can be oriented with respect to a fourth *spatial* dimension.  Therefore, the geometric configuration or “colors” of individual quarks may be related to how its energy is distributed in three-dimensional space with respect to a fourth *spatial* dimension.

However, it may also explain why it takes three quarks of different “colors” to form a stable particle because, as mentioned earlier one can define a particle in terms of a resonant system on a “surface” a three-dimensional space manifold with respect to a fourth *spatial* dimension.  If the colors of each quark represent the central axis associated with its charge then to form a stable resonate system would require three quarks that have different central axis to balance its energy with respect to the axes of three-dimensional space.  A particle could not exist if two quarks have the same central axis or color because it would cause an energy imbalance along that axis.  Therefore, a particle consisting of anything but quarks of three different colors would not stable.

This shows how one can put the color and therefore the Chromo in Quantum Chromodynamics by assuming that space is composed of four *spatial* dimensions instead of four dimensional space-time.

Later Jeff

Copyright 2012 Jeffrey O’Callaghan

The post Putting the Chromo in Quantum Chromodynamics 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.

Therefore the gravitational forces associated with that component of Dark Matter would be “dark” or invisible to our scientific instruments.

However, if Dark Matter or a continuous non-quantized field of energy/mass did make up a significant percentage of the universe’s mass, as observations suggest it does it would have an effect on our understanding of the evolution of the universe for two reasons?  The first is because its attractive properties would affect the evolution of the large scale structures of the universe such as galaxies and galactic clusters.  The second is because of the effect it would have on the propagation of light.

Most scientists are aware that light is shifted towards the red end of the spectrum when it passes though interstellar dust clouds like those found in the Orion Nebula.  However they do not share the same awareness of the effects the existence of a continuous field of energy/mass would have on it.

Yet before we begin to address the reason for those effects it would be beneficial to discuss some other observations that support its existence.

For example in 1927 by Davisson and Germer confirmed Louis de Broglie theory that all particles have a wave component. This is observational proof of the existence of a continuous field of energy/mass because waves are by definition a continuous form of energy and therefore the existence of a continuous field of energy/mass is necessary to support the internal wave component of particles.

However one of the strongest arguments that can be made for its existence when combined with four *spatial* dimensions instead of four dimensional space-time is that it allows one to theoretically derive the quantum mechanical properties of energy/mass and electromagnetic waves by extrapolating classical observations of a three-dimensional environment to a fourth *spatial* dimension.

In the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown that one can derived the quantum mechanical properties of energy/mass and a photon in terms of a resonant “system” formed in the continuous field properties of energy/mass in four *spatial* dimensions by extrapolating the laws of classical resonance in a three-dimensional environment to a fourth *spatial* dimension.

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

The existence of four *spatial* dimensions would give the continuous field of energy/mass (the substance) the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the continuous field of energy/mass to oscillate with respect to a fourth *spatial* dimension at the frequency associated with the energy of that event.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established in a continuous field of energy/mass.

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

As the article “Why is energy/mass quantized?” showed these resonant systems in a continuous field of energy/mass are responsible for the quantum mechanical properties of a photon and energy/mass.

However, it is also possible to use the existence of a continuous non-quantized form of energy/mass as is required by the wave properties of the resonant system defined in that article to explain the internal electromagnetic wave properties of a photon in terms of the matter wave that is responsible for its quantum mechanical properties.

Briefly 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 would 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 which will result in its elevated and depressed portions moving towards or become “attracted” to each other.

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

The reason electromagnetic energy is observed to be made up of discrete quantized units called photons and not a continuous wave is because, as mentioned earlier article “Why is energy/mass quantized?“ showed the energy of a matter wave forms resonant “system” formed in four dimensional space.  Therefore, its energy will propagated in the quantized resonant systems called photons.

Yet if it is true that electromagnetic waves are propagated in a continuous field of energy/mass it would affect our present understanding of the evolution of the universe because most of them are based on the fact that light does not interact with space.

In 1929 Edwin Hubble observed the characteristic colors, or spectral lines emitted by the stars in the galaxies do not have exactly the same wavelengths observed in the laboratory; rather they are systematically shifted to longer wavelengths, toward the red end of the spectrum.

He correctly assumed this change in the observed frequency of light occurs in part because its source i.e. galaxies and observer are in motion relative to each other, with the frequency increasing when the source and observer approach each other and decreasing when they move apart.  Therefore, he assumed the red shift he observed in the spectrum of galaxies meant that they were moving way.

However, he also found the further a galaxy is away from the Earth the larger its redshift and therefore its recessional velocity form the Earth is proportional to their distance from it.  Astronomers still use the formula called Hubble law he derived from these observations to predict the rate at which the universe is expanding.  It states that it is directly related to distance times a constant known as the Hubble Constant.  

Yet, as mentioned earlier the existence of Dark Matter or a continuous non-quantized field of energy/mass would affect our understanding of the evolution of the universe because it would interact with the wave properties of a photon causing them to be red shifted thereby reducing the magnitude of the distance predicted by that law.

This “Tired Light” concept of the energy loss associated with the red shifting of photons by its interaction with space has been dismissed by many because no Compton scattering is observed in them.

Compton scattering is a type of scattering that X-rays and gamma rays undergo in matter.  The inelastic scattering of photons in matter results in a decrease in energy (increase in wavelength) of an X-ray or gamma ray photon, called the Compton Effect.  Part of the energy of the X/gamma ray is transferred to a scattering electron, which recoils and is ejected from its atom (which becomes ionized), and the rest of the energy is taken by the scattered, “degraded” photon.

Many feel it demonstrates that light cannot be explained purely as a wave phenomenon.  Thomson scattering, the classical theory of an electromagnetic wave scattered by charged particles, cannot explain low intensity shifts in wavelength (Classically, light of sufficient intensity for the electric field to accelerate a charged particle to a relativistic speed will cause radiation-pressure recoil and an associated Doppler shift of the scattered light, but the effect would become arbitrarily small at sufficiently low light intensities regardless of wavelength.)  Light must behave as if it consists of particles to explain the low-intensity Compton scattering.  Compton’s experiment convinced physicists that light can behave as a stream of particle-like objects (quanta) whose energy is proportional to the frequency.

The reason why many astronomers believe the entire redshift of a star is the result of its movement away from an observer is, as just mentioned classical theory of charged particles interacting with an electromagnetic wave, cannot explain any shift in wavelength.

Therefore, if the red shift was caused by a particle interaction one should observed Compton scattering in red shifted light.  Since no Compton scattering is observed in light coming from a star it is assumed by many astronomers it can only be caused by the movement of an object away from an observer because as mentioned earlier it is the only way they can explain it.

Yet one can show why low intensity shifts in wavelength of photons can occur when they interacted with a continuous non-quantized form of energy/mass in terms of Classical wave mechanics if one assumes as was done in the article “Why is energy/mass quantized?” that their quantum mechanical properties are a result of a matter wave in a continuous non-quantized field of energy/mass.  This is because the velocity of electromagnetic energy is constant while that of an electron is not. Therefore, the only way to alter the energy, direction or momentum of light is by “degrading” or changing its wavelength. Yet, if the electromagnetic and particle properties of both a photon and electron are a result of a matter wave is as suggested by that article then classical wave mechanics could define their interaction in terms of the interference of their electromagnetic wave properties. However this also tells us their scattering at very low light intensities could take on any arbitrarily small value for both an electron and a photon regardless of wavelength.

In other words if it is true that photons do interact with Dark Matter them we will have to reevaluate the distances calculated by Hubble’s law and our understanding of the evolution the universe which is based on it.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

The post Dark Matter and its affect on Hubble’s law appeared first on Unifying Quantum and Relativistic Theories.