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.
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.
Copyright Jeffrey O’Callaghan 2015
Vol. 3 — 2012
Astrophysicists have identified three possible fates for the universe, one is called the Big Crunch, where gravity takes over and begins to pull the cosmos back, compressing to one point. Another is the Big Rip, where the accelerative forces associated with Dark Energy causes it to expand at an every increasing rate until the galaxies, stars, planets, atoms and space itself is ripped apart. Another popular scenario is called the Big Freeze in which the universe’s expansion is not great enough for it to be ripped apart. Instead it will continue to expand, carrying everything we see today over the cosmic horizon where they will be so far away, that their light cannot reach us. The sky will be dark and as all of the stars begin to go out, the universe will grow, cold and lifeless.
However as was shown in the article "Why the Big Rip cannot happen" June 15. 2015 there are several inconsistencies in that theoretical model which makes it extremely unlikely.
The most obvious is that it violates one of most treasured laws of science that of the law of conservation of mass/energy.
That law tells us that the kinetic energy of the universe’s energy/mass cannot exceed its.combined total. However that is exactly what would have to happen for the Big Rip to occur.
For example for a rocket to escape or be "Rip" from the earth’s gravitational influence one must provide it with more kinetic energy than the gravitational potential of its energy/mass.
Similarly for the universe to be "Rip" apart one would have to provide its components with enough kinetic energy to overcome the total gravitational potential of its energy/mass.
However as was just mentioned the law of conservation energy/mass tells us that since by definition the universe is a closed system the kinetic energy of the its components cannot exceed the total energy of its gravitational components.
In other words if we are to assume that the universe will be Rip apart by Dark Energy we must also assume that energy/mass can be created and that the law of conservation or energy/mass is invalid.
Yet there is also an inconsistency with the assumption that universe would continue to expand indefinitely resulting in what has come to be called the Big Freeze.
This inconsistency revolves around the fact that the equation E=mc^2 which defines the equivalence between mass and energy in an environment tells us that, because of it, the kinetic energy associated with the universe’s expansion also possess the gravitational potential associated with mass while the law of conservation of energy/mass tells us that at as the universe expands and cools the gravitational potential of the kinetic energy loss associated with that cooling must be returned to the universe. Granted it would be disturbed or deluded by a factor of c^2 however it would still increase the total gravitational potential of the universe’s energy/mass.
Yet this means as the universe cools the total gravitational potential of its energy/mass must increase. Therefore at some point in time its gravitation potential will increase to the point where it will be greater than the kinetic energy associated with its expansion resulting in it entering a contraction phase because it is decrease while the other is increasing.
There can be no other conclusion if one accepts the validity of Einstein’s General Theory of Relativity and the law of conservation energy/mass.
As was mentioned earlier the article "Why the Big Rip cannot happen" June 15. 2015 showed why the assumption that Dark Energy would "rip" apart the universe is untenable if one assumes the validity of the law of conservation of energy/mass while the other possible end to our universe or the big freeze is also ruled out for the reasons stated above.
However that means the only viable option for the end our universe is the big crunch if the currently accepted laws of physics eliminates the Big Freeze and the Big Rip because those same laws tell us as was just shown the total gravitation potential of the universe must increase as it expands and cools approaching a maximum value at absolute "0" while at the same time the kinetic energy of its expansive components must decrease. Therefore, at some point in time, the universe will enter a contractive phase because the total gravitational potential will eventually exceed the kinetic energy of its expansion. This is would be true as mentioned earlier even though the gravitational potential of its Kinetic energy components would be disturbed or diluted by a factor of c^2.
Therefore at that point, in time the universe will have to enter a contractive phase.
In other words the only one of the three options our universe has to end it life that is supported by today’s scientific understanding of its evolutionary mechanism is the Big Crunch
Copyright 2015 Jeffrey O’Callaghan
Vol. 3 — 2012