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

Albert Einstein and Leopold Infeld also addressed this issue in their book The Evolution of Physics, when they asked “what is light really? Is it a wave or a shower of photons? There seems no likelihood for forming a consistent description of the phenomena of light by a choice of only one of the two languages. It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do.”

In other words the quantum world has duel non overlapping realities: one consisting of waves; the other particles and which one we observe depends on how we observe it.

This is in stark contrast to the classical one we all live in which defines only one reality based on cause and effect.

However one of the reasons it has been it is so difficult to understand why these dual realties exist may be because too much attention has been focused on the mathematics that describe it and not enough on their physical meaning in our classical environment. 

Another reason may be because most have tried to integrate them into a space-time environment even though they are primarily defined in terms of the spatial properties of probabilities.

This suggest we may be able to better understand why the quantum world possess two distinct realties based on the single reality of a classical world of cause and effect if we view them in terms of spatial properties instead of their space-time ones.

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

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

However defining the dimensional properties of quantum system in terms of its spatial instead of its time components would allow one to understand why a quantum environment possess two distinct realities by extrapolating the laws governing cause and effect in the classical world to them.

For example the article “Why is energy/mass quantized?” Oct. 4, 2007 showed one can derive quantum properties of 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 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.

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.

Yet it also allowed one to derive the physical boundaries of a particle in terms of the geometric properties of four *spatial* dimensions.

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

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

The confinement of the “upward” and “downward” oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries of the resonant system associated with the particle component of its wave properties in the article “Why is energy/mass quantized?” Oct. 4, 2007.

In other words one can use classical wave mechanics to explain why a quantum system can possess both wave and particle properties.

However it does not help us to understand why they define two non-overlapping realties. 

In other words it does not help us to understand why if one devises and experiment to observe its particle properties one cannot at the same time observe its wave reality while if one observes its particle reality one cannot observe it wave properties.

However one can use the properties of classical reality to understand the causality of the complementary or dual real of quantum mechanics.

For example Classical Mechanics tell us that because of the continuous properties of waves, the energy the article “Why is energy/mass quantized?” Oct. 4, 2007 associated with a quantum system would be free to move over the entire “surface” of three-dimensional space with respect to a fourth *spatial* dimension similar to how the wave generated by a vibrating ball on a surface of a rubber diaphragm would be free to move over its entire surface.  However to observe the movement of the rubber diaphragm one must physically touch it with a probe thereby restricting its movement

Similarly to observe the movement of a quantum system one must use a probe which would restrict its movement.

However this also allows one to understand why observing a quantum system effects its reality as is demonstrate in the double slit experiment.

In this experiment the wave reality of a quantum system is demonstrated by the bright and dark interference bands produced on the screen after being allowed to freely pass through between two slits on a screen, However, it is always found to be absorbed at the screen at discrete points, as individual particles (not waves), while the interference pattern appears as varying density of these particle hits on the screen. Furthermore, its particle reality is demonstrated when someone puts detectors at the slits he finds that each detected photon passes through one slit (as would a classical particle), and not through both slits (as would a wave).

These results demonstrate the principle of wave–particle duality.

In the first part of this experiment the wave properties of a quantum system defines its reality because it is allowed to move freely through space. This would be analogous to classical reality of sound waves created by a random source in that they show no properties of quantization. 

However classical wave mechanics tells us that if one if one restrict the movement of a wave as is done in a pipe organ it will form a quantized resonant system.

For example if one restricts sound waves as is done in an organ pipe its output becomes quantized because it amplifies one of its wave components while diminishing all others.

As the article “Why is energy/mass quantized?” Oct. 4, 2007 showed the particle “reality” of a quantum system is the result of the restricting its wave “reality” which must always happen when an observation is made.

In other words as the reason why the particle reality of a quantum environment only occurs when an observation is made is because that act restricts the movement of its wave reality thereby creating the resonant structure associated with its particle properties defined in the article “Why is energy/mass quantized?” Oct. 4, 2007.

In other words the reason the interference pattern appears as varying density of these particle hits on the screen in the double slit experiment is because as was mentioned earlier observing a quantum system requires one to restrict its wave prosperities thereby causing the resonant system the article “Why is energy/mass quantized?” Oct. 4, 2007 associated with its particle really.

Additionally their varying density occurs because these resonant systems will most likely occur where the magnitude of the wave component is maximum and drop off as it decreases.  Therefore their position on the screen will form a wave interference pattern .

The reason why the two realties are complimentary or cannot be simultaneous observed is similar to why one cannot observe ice and water at the same time.  For example in an environment consisting of water that is well below freezing the reality is frozen water while its reality when it is above freezing is water.  Additionally our classical experiences tell us that these two states are complementary because they cannot be both at the same time but have to one or the other.

Similarly in an unobserved quantum environment the wave reality exists because is it allows to move freely through space while as was shown above the restrictions caused by observation makes its particle properties or reality become predominate.

This shows even though a quantum environment consists of two non-overlapping contradictory pictures of reality one can fully understand their existence by applying the cause and effect relationship of a classical reality to it.

Later Jeff

^{Copyright Jeffrey O’Callaghan 2015}

The post The dual realities of quantum mechanics: a classical explanation appeared first on Unifying Quantum and Relativistic Theories.

However their are some who wrongly believe that they can build successful theoretical models of our world based imagination or concepts that only exist in their minds.

For example Quantum theory defines existence by extrapolating the probabilities associated with Schrödingerâ€s wave equation and its collapse to define a reality in which particles do not exist until an observation is made.  In other words it assumes the act of observation or measurement causes the wave function to collapse and particles to mysteriously appear as if by magic at a specific point is space.
They justify this assumption because, using that concept of one can predict with amazing precision the results of every experiment involving the quantum world that has ever been devised to test it.

However it does create a problem for most of us who believe that “reality” is something that can be seen and touched because if Schrödingerâ€s wave equation does does not collapse and continues on even after it is observed one must assume that all of the other possible “realities” it defines must also  continue to exist after that observation.  In other word if taken literally all other possible outcome of an observation must have a reality of their own. 

However because physicists have been unable to define mechanism that would cause the Schrödingerâ€s wave equation to collapse some like Hugh Everett imagined a world in which its does not collapse and all of the other possible “realities” are realized in separate universe.  He argues that observing it creates a split in the universe.  In other words, in his world the universe makes copies of itself to account for all possibilities and these duplicates proceed independently in separate universes.  

The most troubling implication of this concept is that your perception of the world as a whole is never real.  In other words he believes we cannot extrapolate the perception of “reality” most of us believe to his world because in his “reality” there are many copies of you in other worlds reading this article at the same time.

However the science of physics is devoted to understanding the physical process responsible for creating the “reality” of our environment based on observing the physical interaction of its real not imagined components.  Real in the sense that they can be physically observed and measured.

As mentioned earlier most of us believe that reality is made up of something we can see and touch. However the existence of the multi universe is not based on that but how the mind interprets the abstract probabilities associated with Schrödingerâ€s wave equation.  Because of this the fundamental component of the Everett’s multi world theory does not have a presents in the physical reality most of us believe in.

But because as mentioned earlier physics is based on observations one would assume the proper way to proceed would be to define the probabilities associated with Schrödingerâ€s equation in terms of the observable properties of our space-time environment instead of using their abstract non-physical mathematical properties to define their reality.

However one of the difficulties faced by scientist in defining the “reality” of a quantum environment is that most look for in terms of it in terms of the properties of space-time.  Unfortunately of time is not something can be seen or touched while that of space is.  Therefore it should be easier to develop a theoretical model if we redefine Einstein space-time model of the universe into its equivalent in four *spatial* dimensions.

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

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

However defining the dimensional properties of energy in terms of its spatial instead of it time components would allow one to derive the physicality of Schrödingerâ€s equation by extrapolating the observable properties of our reality to the quantum world it describes.

For example the article “Why is energy/mass quantized?” Oct. 4, 2007 showed one can physical derive the quantized wave properties of 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 with the frequency associated with the energy of that event.

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

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

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

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

(In the article “The geometry of quarks” Mar. 15, 2009  the internal structure of quarks, a fundament component of particles was derived in terms of a resonant interaction between a continuous energy/mass component of space and the geometry of four *spatial* dimensions)

However assuming its energy is result of a displacement in four *spatial* dimension instead of four dimensional space-time as was done in the article “Defining energy?” Nov 27, 2007 allows one to not only derive the physicality of the wave properties Schrödingerâ€s equation and what happens when it is observed but also the physical reason why one can only determine the probability of where it will be found before an observation is made

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

For example putting a vibrating or oscillating ball on rubber diaphragm will create a displacement which will be  disturbed over its entire surface while the magnitude of that displacement will decrease as one moves away from the point of contact.

However, this means if one extrapolates the “reality’ of a 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 thought the entire universe while spatial displacement associated with its energy defined in the in the article “Defining energy?” Nov 27, 2007 would decrease as one move 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 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 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.

As mentioned earlier the foundation of Hugh Everett multi universe theoretical model is the assumption that observations do not cause the wave function collapse and therefore all the all of possible realties it define exist in other universe.

Yet as was shown above the energy associated with the wave function will be redirected towards the observer at the point of observation and would continue on that path until another observation is made.

In other words one can as was done above extrapolate observations of classical environment to the wave function to show that the act of observation makes the unique reality it defines visible to an observer.

However this means even if one assumes the wave function defines multiple realities as Hugh Everett believes the act of an observing it would result in all of them being combined into one directed towards the observer and NOT towards other worlds.

In others words it is not necessary to assume that universe splits when an observation is made to explain why the wave function behaves the way it does because as was shown above one can understand it based on the existence of a single universe.

As mentioned earlier the science of physics is devoted to understanding  the physical process responsible for creating the “reality” of our observable environment based on observing the physical interaction of its real not imagined components.

It is true the existence of a fourth “spatial” dimension along with the many worlds of Hugh Everett can only exist in our minds or imaginations because we cannot see or touch them.  However as was shown above the explanation provided by existence of four *spatial* dimension is based on the observable properties of our environment while that of the many world in only supported by the unobservable or imagined properties of Schrödingerâ€s wave equation.

As was mentioned earlier imagination is powerful tool for scientists because it allows them to visuals worlds that are beyond their ability to observe.  However to conform to the definition of physics given earler the existence of those worlds cannot be not based entirely on  their imagined properties but must have a foundation in the observable properties of our environment because that is the only way they can be connected to it.

Later Jeff

Copyright Jeffrey O’Callaghan 2015

The post The abuse of imagination in Physics appeared first on Unifying Quantum and Relativistic Theories.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(The reason will become obvious later.)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

However, this may not be true.

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

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

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

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

Later Jeff

Copyright Jeffrey O’Callaghan 2014

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

One of them is that it would allow for a logical explanation of the superposition principal associated with quantum mechanics based on extrapolating our experiences in a three-dimensional environment to a fourth *spatial* dimension.
Quantum mechanics assumes that one can only define the exact position or momentum of a particle in terms of the probabilistic values associated with its wave function.  Therefore, according to it one cannot predict future events based on their history.  This is in stark contrast to the classical assumption that one can assign precise values of future events based on the knowledge of their past. 

For example in a quantum system Schrödinger wave equation plays the role of Newtonian laws in that it predicts the future probability distribution of a particles position or momentum by assuming that it simultaneously exists or is superpositioned everywhere in three-dimensional space.  On the other hand classical physics derives the future based on the assumption that objects move through time in a unique trajectory based on the forces they experience.

Yet even though these two concepts appear to contradict each other one can as mentioned earlier define the “reality” of quantum superposition by extrapolating the laws of a three-dimension environment to one consisting of four *spatial* dimensions.

The superposition principal states that if a quantum system can be found in one of two state A and B with different properties it may also be found in aA and bB where “a” and “b” are any number.  Each such combination is called a superposition and each is, according to quantum mechanics is physically different. 

In the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown one can derive the quantum mechanical properties of energy/mass by extrapolating the laws of classical wave mechanics in a three-dimensional environment to a matter wave on a continuous “surface” of a three-dimensional space manifold with respect to  a fourth *spatial* dimension.

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 will 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 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 space.

These resonant structures are responsible for dividing the continuous wave properties of energy/mass and four *spatial* dimensions into their quantum mechanical components.

(In the article “The geometry of quarks” Mar. 15, 2009  the internal structure of quarks, a fundament component of particles was derived in terms of a resonant interaction between a continuous energy/mass component of space and the geometry of four *spatial* dimensions.)

However assuming the energy contained in quantum mechanical systems are a result a resonant structure formed by the continuous properties of a wave as was done above allows one to derive the fact that they simultaneously exists or are superpositioned everywhere in three-dimensional space

Earlier it was mentioned the energy/mass of a quantum system is made up of the resonant properties of a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  However, classic mechanics tell us that because of the continuous properties of a wave its energy would distributed throughout the entire volume of three-dimensional space.

In other words the sinusoidal displacements caused by the matter wave on a “surface” of a three-dimensional space manifold which the article Why is energy/mass quantized? showed was responsible for creating the resonant structures it associates with quantum mechanical systems would, similar to Schrödingerâ€s wave equation be disturbed throughout entire the universe.

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

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

As mentioned earlier the article “Why is energy/mass quantized?” 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 the resonance associated with a quantum system would most probably be found were the magnitude of the vibrations in a “surface” of a three-dimensional space manifold is greatest and would diminish as one move away from that point,

However, it also tells us the point in space associated with a quantum system would be superposed over of every other one because the displacement associated with each individual one is distributed throughout the universe.

Similarly Classical wave mechanics also tell us the distribution of the energy of multiple quantum systems, such as baseballs starts or planets would become more concentrated in a specific point in space as their numbers increased because the interference associated with their multiple wave identities would reduce the dispersion of their energy components.

This tells us the energy distribution of multiple quantum systems, such as baseballs starts or planets would distributed or superpositioned throughout the entire volume of three-dimensional space until someone observes the point in space the waves functions of its individual component reinforce to produce the greatest displacement.  When that happens the object or particle will “materialize” or emerge in a specific region of space where that observation was made.

This shows how one can explain the” reality” of quantum superposition by extrapolating the laws of classical wave mechanics to four *spatial* dimensions.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

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