There can be no doubt the probabilistic interpretation of Schrödinger’s wave equation predicts with amazing precision the results of every experiment involving the quantum world that has ever been devised to test it.
However this interpretation is at odds with the reality of the classical or deterministic world most of us appear to live in because it assumes that for a given set of initial conditions there can only be one outcome while the probabilistic interpretations of quantum mechanics assumes there can be an infinite number.
However many of the standard interpretations of quantum mechanics assume that probability is the fundamental property of the universe, while alternative interpretations explain it as an emergent or a second-order consequence of various limitations of the observer or the environment he or she is occupying when making an observation.
Determining which is the correct way of interpreting it is difficult because due to the limitation imposed on observers by uncertainty principle we can never be sure what is happening on the quantum scale when an observation is made.
Yet that does not mean that we cannot extrapolate what we can learn from observing our four dimensional space-time environment to the quantum world to help us understand what happens when we make an observation.
However we will find it beneficial to redefine Einstein space-time model of the universe into its equivalent in four spatial dimensions.
(The reason for this will become obvious later on)
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 it he associated with energy to unit of space we feel he would have associated with mass. 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.
As mentioned earlier Quantum mechanics assumes one can only determine the future evolution of a particle in terms of the probabilistic values associated with its wave function which is in stark contrast to the Classical "Newtonian" assumption that one can assign precise values of future events based on the knowledge of their past.
In other words in a quantum system Schrödinger’s 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.
This accentuates the fundamental difference between quantum and classical mechanics because the latter defines the reality of future events in terms of pervious events whereas quantum mechanics defines them based on the "non-classical" reality of the sum total of all possible events that can occur.
However as mentioned earlier one may be able to understand the physical reason why these two theories define the reality of events differently if, as was done earlier one redefine Einstein’s space-time concepts in terms of four spatial dimensions.
In the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown one can understand the physicality of 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 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, if a quantum mechanical properties of particle is a result of a matter wave on a “surface” of three-dimensional space with respect to a fourth *spatial* dimension, as this suggests one should be able to show that it is responsible for the uncertainties and probabilistic predictions made by Schrödinger and his wave equation regarding the position and momentum of particles.
Classical wave mechanics tells us a wave’s energy is instantaneously constant at its peaks and valleys or the 90 and 270-degree points as its slope changes from positive to negative while it changes most rapidly at the 180 and 360-degree points.
Therefore, the precise position of a particle could be only be defined at the “peaks” and “valleys” of the matter wave responsible for its resonant structure because those points are the only place where its energy or “position” is stationary with respect to a fourth *spatial* dimension. Whereas it’s precise momentum would only be definable with respect to where the energy change or velocity is maximum at the 180 and 360-degree points of that wave. All points in between would only be definable in terms of a combination of its momentum and position.
However, to measure the exact position of a particle one would have to divert or “drain” all of the energy at the 90 or 270-degree points to the observing instrument leaving no energy associated with its momentum left to be observed by another instrument. Therefore, if one was able to precisely determine position of a particle he could not determine anything about its momentum. Similarly, to measure its precise momentum one would have to divert all of the energy at the 180 or 360 point of the wave to the observing instrument leaving none of its position energy left to for an instrument which was attempting to measure its position. Therefore, if one was able to determine a particles exact momentum one could not say anything about its position.
The reason we observe a particle as a point mass instead of an extended wave is because, as mentioned earlier the article ”Why is energy/mass quantized?“ showed energy must be packaged in terms of its discrete resonant properties. Therefore, when we observe or “drain” the energy continued in its wave function, whether it be related to its position or momentum it will appear to come from a specific point in space similar how the energy of water flowing down a sink drain appears to be coming from a “point” source with respect the extended volume of water in the sink.
As mentioned earlier, all points in-between are a dynamic combination of both position and momentum. Therefore, the degree of accuracy one chooses to measure one will affect the other.
For example, if one wants to measure the position of a particle to within a certain predefined distance “m” its wave energy or momentum will have to pass through that opening. However, Classical Wave Mechanics tells us that as we reduce the error in our measurement by decreasing that predefine distance interference will cause its energy or momentum to be smeared our over a wider area thereby making its momentum harder to determine. Summarily, to measure its momentum “m”kg / s one must observe a portion the wavelength associated with its momentum. However, Classical wave mechanics tell us we must observe a larger portion of its wavelength to increase the accuracy of the measurement of its energy or momentum. But this means that the accuracy of its position will be reduced because the boundaries determining its position within the measurement field are greater.
However, this dynamic interaction between the position and momentum component of the matter wave would be responsible for the uncertainty Heisenberg associated with their measurement because it shows the measurement of one would affect the other by the product of those factors or m^2 kg / s.
Yet because of the time varying nature of a matter wave one could only define its specific position or momentum of a particle based on the amplitude or more precisely the square of the amplitude of its matter wave component.
This defines the physical reason in terms of four *spatial* dimensions for why we are unable to measure the exact position and moment of a quantum system.
However it also defines the reason why the probably functions of quantum mechanics are an emergent or a second-order consequence of various limitations of the observer or the environment and not a fundamental property of our universe because as was just shown the physicality of four *spatial* dimension places limitations on our ability to define the initial conditions or momentum and position of a quantum system we are measuring.
In other words the reason quantum mechanics can only predict the probability of an event occurring is because of the limitations the physical properties of four *spatial* dimension places on an observer.
This shows why we should view the probabilistic properties of quantum mechanics as an emergent or a second-order consequence of the limitations of the four *spatial dimension or space-time environment he or she is occupying when making an observation and not a fundamental property of the universe.
Copyright Jeffrey O’Callaghan 2014
Vol. 3 — 2012
Before the discovery of Dark Energy cosmologists had two models of how the universe’s expansion would end.
In first scenario, there would be enough matter in the universe to slow the expansion to the point it would come to a halt and gravitational forces would cause it to begin contracting which eventually would result in a fiery death called the "Big Crunch.
In the other scenario, there would be too little matter to stop the expansion and everything would drift on forever, always slowing but never stopping. This would end in a vast, dark, and cold state: a "Big Chill," as the stars faded and died out.
However the discovery of a force causing the expansion of the universe to accelerate called Dark Energy opened up the possibility that the galaxies, solar system, stars, planets, and even molecules and atoms could be shredded by the ever-faster expansion. In other words the universe that was born in a violent expansion could end with an even more violent expansion called the Big Rip.
Most scientists would agree that the best way of determining which one these scenarios defines its ultimate fate would be to understand the forces involved based on the most successful theories we have regarding the macroscopic properties of the universe.
However modern theories only address two of them. For example the laws of thermodynamics which defines the forces associated with heat early in the universe and Einstein’s General Theory of Relativity which defines the gravitational forces which effect its evolution are two of the most success theories we have. Unfortunately neither of them, in their present form addresses the expansive force called Dark Energy.
This is true even though Einstein foresaw the existence of Dark Energy when he added a cosmological constant to his General Theory of Relativity to make it conform to his belief in a static universe.
Granted he added it in an "adhoc" manner to force it, in keeping with physicists thinking at the time to predict a stationary universe. However when it became clear that the universe wasn’t static, but was expanding Einstein abandoned the constant, calling it the “biggest blunder" of his life.
But lately scientists have revived Einstein’s cosmological constant (denoted by the Greek capital letter lambda) to explain this mysterious force which as mentioned earlier is causing the expansion of our universe to accelerate even though they have been unable to Einstein integrate it into the theoretical structure of his General Theory of Relativity.
However we may find clue as to why by observing how our universe is expanding.
For example observations of the universe’s expansion tell us that three-dimensional space is expanding towards a higher spatial dimension not a time or space-time dimension.
Therefore, to explain the how the expansive force called dark energy is accelerating the spatial expansion of the universe one would have to assume the existence of a another *spatial* or fourth *spatial* dimension in addition to the three spatial dimensions and one time dimension that Einstein’s theories contain to account for that observation.
This would be true if Einstein had not given us a means of qualitatively and quantitatively converting the geometric properties of his space-time universe to one consisting of only four *spatial* dimensions.
He did this when he defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2 and the constant velocity of light because that provided a method of converting the displacement in space-time manifold he associated with energy to its equivalent displacement in four *spatial* dimensions. Additionally because the velocity of light is constant he also defined a one to one qualitative and quantitative 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 it in terms of the geometry of four *spatial* dimensions.
The fact that the equation E=mc^2 allows us to quantitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is the 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 displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of one in a space time manifold.
As mentioned earlier one reason why it is difficult to integrate the accelerated special expansion of three-dimensional space towards a higher space dimension into Einstein space-time universe because it does not define one.
However it is easy to do if one redefined it, as was done above in terms of four *spatial* dimension because that higher spatial dimension would become an integral part of its theoretical structure.
Yet it also allows one to understand how and why Dark Energy is causing the accelerated spatial expansion of the universe and what its ultimate fate will be in terms the laws of thermodynamics and the concepts of Einstein’s theories.
We know from the study of thermodynamics that energy flows from areas of high density to one of low density very similar to how water flows form an elevated or "high density" point to a lower one.
For example, if the walls of an above ground pool filled with water collapse the molecules on the elevated two-dimensional surface of the water will flow or expand and accelerate outward towards the three-dimensional environment surrounding it while the force associated with that expansion decreases as it expands.
Additionally we know from observations of the cosmic background radiation that presently our three-dimensional universe has an average energy component equal to about 3.7 degrees Kelvin.
However this means that according to concepts developed in the article “Defining energy" (mentioned earlier) the three-dimensional "surface" of our universe which has an average energy component of 3.7 degree Kelvin would be elevated with respect to a fourth *spatial* dimension.
Yet this means similar to the two dimensional surface of the water in the pool the particles that occupy that elevated region of three-dimensional space and the space they occupy will accelerate and flow or expand outward in the four dimensional environment surrounding it and that the force associated with that expansion will decline as it expands.
This shows how reformulating Einstein’s theories in terms of four *spatial* dimensions allows one to use the laws of thermodynamics to explain what the force called Dark Energy is and why it is causing the accelerated expansion of the universe in terms of those theories.
Many feel that because space is everywhere, the force called Dark Energy is everywhere, and its effects increase as space expands. In contrast, gravity’s force is stronger when things are close together and weaker when they are far apart.
However if the above theoretical model is correct than the magnitude of Dark Energy relative to gravitational energy will not continue to increase as the universe expands but will decrease because similar to the water in a collapsed pool the accelerative forces associated with it will decline as it expands. et because the mass of the universe remains constant throughout its history the gravitational potential associated with it will also.
Therefore the gravitational contractive forces associated with it will exceed the expansive forces associated with Dark Energy even though its components may be separated by extremely large distances because as just mentioned the force associated with dark energy will decease relative to gravity as time goes by.
However the equivalence between mass and energy defined by Einstein tells us that energy also possess gravitational potential.
Therefore, just after the big bang when the concentration of energy and mass was high, gravitational force would predominate over Dark Energy because the distance between both its energy and mass components was relatively small.
However as the universe expands the gravitational attractive forces will decrease more rapidly than the expansive force associated with Dark Energy because they are related to the square of the distance between them while those of the expansive forces of Dark Energy are more closely related to a linear function of the total energy of content of the universe.
Therefore after a given period of time the expansive forces associated with Dark Energy will become predominate and the expansion of the universe will accelerate.
However as the universe expands and cools that force will decrease because as mentioned earlier similar to the two-dimensional surface of the water in a collapsed pool, the forces associated with that expansion will decrease as it expands.
This means that eventually gravitational forces will overcome those of Dark energy because, as mentioned earlier the laws of thermodynamics tells us the total accelerative forces associated with it will decease and therefore will eventually approach zero, while the total mass content and the gravitational attractive forces associated with it will remain constant as the universe expands even though they may be separated by a greater distant.
However this is not the end of the story for our universe because after a certain point in time the heat generated by its gravitational collapse will raise its temperature to the point where its expansive properties will exceed gravitational forces causing it to reexpand.
Yet many cosmologists do not accept the cyclical scenario of expansion and contractions because they believe a collapsing universe would end in the formation of a singularity similar to the ones found in a black hole and therefore, it could not re-expand.
However, according to the first law of thermodynamic the universe would have to begin expanding before it reached a singularity because that law states that energy in an isolated system can neither be created nor destroyed
Therefore because the universe is by definition an isolated system; the energy generated by its gravitational collapse cannot be radiated to another volume but must remain within it. This means the radiation pressure exerted by its collapse must eventually exceed momentum of its contraction and therefore it would have to enter an expansion phase because its momentum will carry it beyond the equilibrium point were the radiation pressure is greater that the momentum of its mass. This will cause the mass/energy of our three-dimensional universe to oscillate around a point in the fourth *spatial* dimension.
This would be analogous to the how momentum of a mass on a spring causes it spring to stretch beyond its equilibrium point resulting it osculating around it.
The reason a singularity can form in black hole is because it is not an isolate system therefore the thermal radiation associated with its collapse can be radiated into the surrounding space. Therefore, its collapse can continue because momentum of its mass can exceed the radiation pressure cause by its collapse in the volume surrounding a black hole.
In other words if this theoretical model is correct our universe has never ending future which exists between an icy death caused by Dark Energy and a fiery rebirth created by gravity.
There can be no other conclusion if one accepts the validity of Einstein’s theories and the laws of thermodynamics because the theoretical arguments presented are a base solely on their validity.
Copyright Jeffrey O’Callaghan 2014
Vol. 3 — 2012