When the Copenhagen interpretation was first introduced Neils Bohr found it was necessary to assume the collapse of wave function to distinguish the quantum from the classical world.  This allowed it to develop without distractions from interpretational worries.  Nevertheless since then that it meaning has be hotly debated because if it is a fundamental properties of nature as many have assumed it would contradict the classical or Newton assumption that the world is deterministic.
However 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.

One of the reason it has been so difficult to understand what happens to the position component of a quantum system when it is observed may be because too much attention has been focused on the mathematical aspects of the wave function and not enough on its physical meaning in a space-time environment.  This is made even more difficult because the concept of superposition is defined in terms of the spatial properties of a quantum system instead of its space-time properties.

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

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

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

However defining the dimensional properties of quantum system in terms of its spatial instead of its time components would allow one to derive the physicality of the wave functioned associated with 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 derive its physicality by extrapolating the laws of classical wave mechanics in a three-dimensional environment to a matter wave on a “surface” of a three-dimensional space manifold with respect to  a fourth *spatial* dimension.

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

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

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

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

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

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

Hence, these resonant systems in four *spatial* dimensions would be responsible for the discrete quantized energy associated with 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 similar resonant interaction between three and four dimensional space.)

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 Schrödingerâ€s equation as was just done but also the physical reason why its particle components would be in superpositioned state 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 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 three-dimensional space one must assume the oscillations associated with each individual quantum system must be disturbed thought the entire universe while the spatial displacement associated with its energy defined in the in the article “Defining energy?” Nov 27, 2007 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 mentioned earlier the article “Why is energy/mass quantized?” shows that a quantum mechanical system is a result of a resonant structure formed by the oscillations on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

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

Additionally this tells us that the wave function does not collapse but its energy is redirected towards the observer and as was shown in the article Why is energy/mass quantized? he would record its redirected energy in term of discrete quantized properties associated with a particle.

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.

Yet even though we may never be able to directly observe the fourth *spatial* dimension we can verify its existence by observing the effects it has on our observable three-dimensional environment similar to how Einstein was able to conclude that gravity was a result of a curvature in a space time environment.

Later Jeff

Copyright Jeffrey O’Callaghan 2015

The post A classical interpretation of the wave function collapse appeared first on Unifying Quantum and Relativistic Theories.

Unfortunately many physicists attempt to define reality based solely on what they measure and do not attempt to conceptually integrate those measurements into the realty we see around us.

One example can be found in Brian Clegg book Before the Big Bang: The Prehistory of Our Universe (p. 137) where he describes how Neils Bohr reacted when Heisenberg proposed his uncertainty principal.
“When Heisenberg first told his boss, Neils Bohr, about the uncertainty principle, he put it across in the form of an imaginary microscope. He described a particle as an electron passing through a make-believe ultra powerful microscope. We use light to examine the object, so a beam of photons (quantum particles just as the electron is) is constantly crashing into the electron. The result is that the electronâ€s path is changed. You canâ€t look at a quantum particle without changing things. Heisenberg is said to have been reduced to tears when Bohr ripped his idea to pieces. Heisenberg had assumed that until the microscope scanned the electron, the electron had an exact position and momentum. He thought it was the process of observing it that messed things up. But actually, Bohr pointed out, the uncertainty was more fundamental than that. There was no need to observe the electron for uncertainty to apply: it was inherent to the nature of a quantum particle.”

In other words Neils Bohr said that because we will never be able to observe an electron without changing it or its environment one must simply accept the fact that we will never be able to understand why it behaves the way it does in terms of the “reality” we see around us.

However the science of physics is defined as “the asking fundamental questions regarding how and why matter and energy interact while demanding the answers be validated by observations.

Yet this definition appears to conflict with Neils Bohr assertion that the uncertainty principal is inherent to the nature of a quantum particle because that immunizes it from such questions.

Additionally he said since it is true that uncertainty principal is inherent to the nature of the unseen world of a quantum particle “Everything we call real is made of things that cannot be regarded as real”.

Yet if one uses his philosophy that “reality” does not exist then the observations used to define that principal also cannot be real or exist because one cannot observe something that does not exist.  In other words the very arguments Neils Bohr uses to support his concept of the uncertainty principal leads to it invalidation.

However history has shown us that one of the advantages to defining the universe that we cannot and will never be able to see in terms of the “reality” of our observable environment is that it limits the ability of our imagination to create nonexistent or fantasy worlds to support them.

For example Einstein mathematically derived the force of gravity in terms of a curvature in a four dimensional space-time universe.  However even though he knew that he would never be able to physically observe how a time dimension interacts with the three spatial dimensions he attempted and succeeded in explaining how a curvature in a space-time environment can result in the force gravity by watching how a marble moved on a curved surface in our observable three dimensional universe.

In other words Einstein not only mathematically quantified the measurements of the force of gravity but he also provided a qualitative explanation of how it could act at distance by anchoring it to the observable properties of an object moving on a curved surface in three-dimensional environment.

This methodology is in sharp contrast to how Newton defined gravity in that he simply accepted the fact that he was able to accurately quantify it using the concept of action at a distance even though he was aware that it disagreed, as the following excerpt from a letter he wrote to Bentley with the “reality” he saw around him.

“It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact…That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.

However Einstein’s unwillingness to accept action at a distance gave him the ability more accurately quantify gravity while providing an understanding of how it could act at a distance by aqs mentioned earlier anchoring it to the “reality” of our three-dimensional environment.  Additional it showed that Newton’s concept of absolute space and time only existed in the fantasy world of his imagination because according to Einstein gravity is caused by their variability.

This shows the power of attempting to understand the unobservable in terms of the observable by anchoring it to the “reality” of what we see around us and why we should be skeptical about accepting the validity of the uncertain principal based on Neils Bohr assertion that it is inherent to the nature of a quantum particle

However what is even more damaging to his ideology of blindly accepting a mathematical interpretation of the uncertainty principle, is that it is possible (much as Einstein did) to extrapolate the observable properties of our three dimensional environment to a quantum one as was done in the article “A classical interpretation of Heisenbergâ€s Uncertainty Principal” Dec. 1 2012 to explain and predict how and why it behaves the way it does.

However before we begin we must first reformulate Einstein space-time concept to their spatial equivalent.

(The reason will become obvious latter)

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

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

On advantage to doing this is that it gives one a different perspective on the “reality” of the quantum environment and the uncertainty principal in terms of the observable properties of our three dimensional universe.

For example the article “Why is energy/mass quantized?” Oct. 4, 2007 demonstrated it is possible to understand the quantum mechanical properties of energy/mass 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 a matter wave the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

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

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

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

Therefore the discrete or quantized energy of resonant systems in a continuous field of four spatial dimensions could explain the discrete quantized quantum mechanical properties of particles.

However, it 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 “box” containing the resonant system the article “Why is energy/mass quantized?” associated with a particle and why quantum systems behave the way they do.

However not only using the properties of a fourth *spatial* dimension allow one to understand why energy/mass in our three-dimensional world in terms of our experiences but it can also be used to explain the uncertainty principle

For example in quantum mechanics, the uncertainty principle asserts that there 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.

As mentioned earlier one can define a mechanism responsible of the uncertainty principal in terms the geometry of the four *spatial* dimensions because Quantum Mechanics mathematically defines the position and momentum of a particle in terms of non dimensional point.  This means there would be an uncertainty in determining its position because that point could be found anywhere within the volume of the “box” mentioned above.

Similarly there would be an uncertainty in measuring its momentum, again because quantum mechanics defines it in terms of a non dimensional point.  Therefore before one could determine a particle’s momentum one would have to know the exact position of the “end” points one uses to measure its velocity.  However, as mentioned above that non dimension point representing a particle could be found anywhere in the box containing the resonant structure that defined a particle in the article “Why is energy/mass quantized?“  Therefore one could not determine its exact velocity and momentum because there will always be an uncertainty as to where the non dimensional point representing a particle is in the box when the measurement was taken

The reason why one cannot simultaneously measure both with complete accuracy is because the act of measure its momentum or position requires one to access different segments the “box” containing particle.

For example if one wants to make the most accurate measurement possible of its momentum internal to the box one would have to measure the time it took for it to transverse a given segment of it.  However this means that one could not determine its position because it would be changing throughout the entire time that it took it to transverse that portion of the box.

However if one wanted to make the most accurate measurement possible of its position internal to the box it would have to be stationary with respect to the box’s geometry meaning that one could not determine its monument because it would not be moving.  Since these two measurements required one to access different segments of a particles geometry they are mutually exclusive. 

Therefore one cannot simultaneously measure a particle position x and momentum p with complete accuracy.

This defines why, in terms of the reality we see around us there is a 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.

However it also tells us we should always attempt to conceptually integrate our theoretical models into the “reality” of what we “see” around us because it allows one to physically connect the abstract properties of a theoretical environment created by our imagination to the reality of the worlds they are describing thereby limiting its ability to create fantasy worlds such as the one Neils Bohr believed in to explain their theoretical models.

Later Jeff

Copyright Jeffrey O’Callaghan 2014

The post Should we let our imaginations define reality? appeared first on Unifying Quantum and Relativistic Theories.