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

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

The "Invisible Reality" of Quantum Theory with Alan Alda, Brian Greene

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

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.

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.

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

 

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Quantum mechanics defines our observable environment only in terms of the probabilistic values associated with Schrödinger’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. 

 

Schrödinger Equation and Material Waves

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

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.

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 Einstein’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

 

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