Most would agree that imagination is powerful tool for scientists when used correctly because it allows them to visuals worlds that are beyond their ability to observe.

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 Schrödinger’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.

A Vision For the Science of Imagination

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 Schrödinger’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 Schrödinger’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 Schrödinger’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 Schrödinger’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 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 energy in terms of its spatial instead of it time components would allow one to derive the physicality of Schrödinger’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 Schrödinger’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 Schrödinger’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

 

Anthology of
The Imagineer’s Chronicles
Vol. 1 thru 5

2007 thru 2014


Ebook
$10.50

 

The Reality
of the Fourth
Spatial
Dimension

 
Paperback
$9.77
Ebook

$6.24

     

The Imagineer’s
Chronicles
Vol. 5 — 2014

 
Paperback
$13.36
Ebook
$9.97

 
 

The Imagineer’s
Chronicles
Vol. 4 — 2013


Paperback
$13.29
E-book
$7.99

The Imagineer’s
Chronicles
Vol. 3 — 2012



Paperback

$10.96
Ebook
$6.55

The Imagineer’s
Chronicles
Vol. 2 — 2011

 
Paperback
$8.32
Ebook
$6.57

 
 

 

The Imagineer’s
Chronicles
2007 thru 2010


Paperback
$14.97
Ebook
$7.82

   
         

 

MIT Lecture 1 Introduction to Superposition

Quantum mechanics defines a particle only in terms of the probabilistic values associated with Schrödinger wave equation and assumes that it exists or is superpositioned in all possible places before a measurement is made.

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 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 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 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 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

 

Anthology of
The Imagineer’s Chronicles
Vol. 1 thru 5

2007 thru 2014


Ebook
$10.50

 

The Reality
of the Fourth
Spatial
Dimension

 
Paperback
$9.77
Ebook

$6.24

     

The Imagineer’s
Chronicles
Vol. 5 — 2014

 
Paperback
$13.36
Ebook
$9.97

 
 

The Imagineer’s
Chronicles
Vol. 4 — 2013


Paperback
$13.29
E-book
$7.99

The Imagineer’s
Chronicles
Vol. 3 — 2012



Paperback

$10.96
Ebook
$6.55

The Imagineer’s
Chronicles
Vol. 2 — 2011

 
Paperback
$8.32
Ebook
$6.57

 
 

 

The Imagineer’s
Chronicles
2007 thru 2010


Paperback
$14.97
Ebook
$7.82

   
         

 

« Previous Articles    
The Imagineer's Chronicles is based on WordPress platform, RSS tech , RSS comments design by Gx3.