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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Additionally it also tells us why in terms of the physical properties four dimensional space-time or four *spatial* dimensions an electron cannot fall into the nucleus is because, as was shown in that article all energy is contained in four dimensional resonant systems. In other words the energy released by an electron “falling” into it would have to manifest itself in terms of a resonate system. Since the fundamental or lowest frequency available for a stable resonate system in either four dimensional space-time or four spatial dimension corresponds to the energy of an electron it becomes one of the fundamental energy units of the universe.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Later Jeff

Copyright Jeffrey O’Callaghan 2015

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

However it is by definition is an abstract creation of the mind and therefore is not physically connected to the observable real world, most of us believe we live in.

Therefore, we can never be sure the equations developed by science accurately define the physicality of those laws or the real world they are describing.

This is true even though they make accurate predictions because unless there is a way of physically connecting the mathematical worlds create by the intellect to the observable world we live in science cannot be sure that is has chosen the correct set of facts that defines its existence.
Granted the mind can systematical quantify the natural world as the mathematics of quantum mechanics does with great accuracy but that does not necessarily mean it tell us anything about the reality of how or why that quantification takes place.

For example there are an infinite number of ways one can mathematically describe the fact that there are two apples on a table. One can predict why based on the assumption that there were originally four apples and two were taken away or assume that originally there were six and four were taken away.  However if there were only four apples to begin with the mathematical description using six apples even though accurately quantifies the existence of two apples it does not describe their world because in “reality’ that world did not contain six apples.

Similarly just because the mathematics of quantum mechanics can very accurately predict the quantitative observation of the particle world does not mean that it defines why it is that way.

Einstein was often quoted as saying “If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless.”

He realized for science to make a claim that they have organized the natural world into a single set of patterns or laws that describe why we perceive its  “reality” the way we do they must be able to conceptually connect the independent models developed by our minds to the reality of natural world that exists outside of it.

For example Newton in a letter to Bentley in 1693, talks about a conceptual problem he has with his gravity theory by rejecting the action at a distance that it requires.

“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 realized by extrapolating the physical image of how objects move on a curve surface in a three-dimensional environment to a four dimensional space-time manifold one could explain how gravity “may act upon another at a distance through a vacuum” in terms of a curvature in space and time.   This enables one to understand gravity based on a physical image formed by the “reality” of what we can see and touch in our three-dimension world.

In other words he was able to connect the observable reality of our three dimensional world to the mathematical one he had created in his mind to explain gravity in terms of a physical imaged form in our three dimensional world.

Unfortunately many of today scientists seem to be ignoring the lessons taught to us by Einstein.  They chose to look for reality only in terms of abstract mathematics instead of the physical imagery given to us by the “reality” of what we can see and touch.

The reason may be because it is easier to alter an abstract environment based on mathematics to conform to an observational inconsistency than it is to alter one based on physical imagery.

For example Quantum theory makes predictions based on the random properties of a probability function.  However because the abstract properties of probabilities which are not physically connected to our world, all its predictions no matter how inconsistent they are with the world they are describing can be incorporate into it.

This is in sharp contrast to the space-time environment defined by Einstein in that projecting the physical image of objects moving on a curve surface in our three-dimensional environment physically connects it to a four-dimensional space time-environment

For example a single instance of a mass being gravitational repelled instead of attracted would contradict the physical imagery define by Einstein and would be extremely if not impossible to explain because no one has ever observe objects rolling up hill in our three-dimensional environment.  In other words because he defined gravity in terms of a physical image based on how objects move on a curve surface in a three-dimensional environment it makes observations like two masses gravitational repelling each other virtually impossible to incorporate into it.

However because quantum mechanics is based on probabilities anything that can happen eventually will.  Therefore it is virtually impossible to find any observation in the real world that contradicts it.  However this can only happen in an abstract environment which is not bound by the physicality of our observational world.

As mentioned earlier unless science can conceptually connect the mathematical worlds created by the intellect to the observable world we live in we cannot say that we know or understand anything physical laws that we assume define its reality.

But why should science put in the effort to understanding our theoretical models in terms of the physical “reality” of our world when both the abstract mathematical foundation of quantum mechanics and the physical imagery of Einstein’s theories make very accurate predictions of future events.

Because the mission of a science is to define the real world in terms of what we perceive in our environment not to perceive an abstract mathematical environment to define what we want it to be.

Later Jeff

Copyright 2014 Jeffrey O’Callaghan

The post The mathematics of the real world appeared first on Unifying Quantum and Relativistic Theories.