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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.

Later Jeff

Copyright Jeffrey O’Callaghan 2014

One of the most fundamental questions science can ask is "How did our unversed begin?"

For example The Big Bang theory, the prevailing cosmological model for the early development of the Universe assumes that in the beginning it was in an extremely hot and dense state which began expanding and after cooling sufficiently, energy was converted into subatomic particles, including protons, neutrons, and electrons.

It offers a one of the most comprehensive explanations we have for most observed phenomena, including the abundance of light elements, the cosmic microwave background, large scale structure, and the Hubble expansion with two notable exceptions which have been given the name the Flatness and Horizon problem.

The first or the Flatness problem addresses the apparent fine-tuning of the density of matter and energy in the universe. The problem is that the current density of the universe is observed to be very close to the critical value required to make it flat. Since the total density departs rapidly from this critical value over cosmic time, the early universe must have had a density even closer to the critical density, departing from it by one part in 1062 or less. This leads cosmologists to question how the initial density came to be so closely fine-tuned to this "special" value

The other or the Horizon problem is address the fact that different regions of the universe which have not been able to interact with each other have the same temperature and other physical properties.

To resolve these issues physicist Alan Guth proposed the universe underwent a very rapid period of expansion (called inflation) increasing its size by more than a trillion in the first few nano-seconds after its birth. This resolves the Flatness problem because its size is magnified so much by the inflation factor that locally it appears flat.

The reason for this can be understood by imagining what a two-dimensional creature who was living on a surface of a balloon would observe regarding the curvature of its surface. If the size of the balloon were small compared to his field of vision he would notice that it surface was curved while if its size was very large, again compared to his field of vision it would appear to her or him to be flat.

Similarly if the universe underwent a very rapid exponential expansion early in its history it would have become so large that it would appear to be flat with respect to our field of vision.

However adding an inflationary period to the big bang models also solves the Horizon problem because prior to the inflationary period the entire universe would have been extremely small and therefore each point could be causally connected. It was during this period, according to its proponents the physical properties of the universe evened out. Inflation then caused its volume to increase to the point where different parts were too far apart to allow their properties to interact. This essentially froze any irregularities and prevented them from being “smoothed out” which according to this theoretical model explains why the universe appears to be almost**, but not** perfectly homogeneous. In other words they assume the solution to the Horizon problem is the fact that in the modern era distant areas in the sky which appear to be unconnected causally were in the past because they were much closer together.

*However the science of physics is devoted to answering questions regarding the outcome of experiments based on observing the environment in which they occur. Unfortunately we cannot nor will we ever able to directly observe the origins of our universe. *

Even so most scientist would agree that a valid theoretical model of the beginnings of our universe must consist of two parts. The first part must allow one to accurately predict its properties based on the outcome of experiments or observations that we can perform in today’s environment while the second is to provide a logically consistent explanation for their origins in terms of the currently accepted laws of physics that govern that environment.

However the inflationary model fails to satisfy those requirement because it cannot logically explain where the energy to power the inflationary period originated from in terms of any observable processes even though some cleaver physicists have convinced themselves that they have in terms of a mathematical model which says it originated in what is call vacuum energy. Unfortunately there is very little or no observational evidence to support its existence.

*Yet what is even more damaging to the inflationary model is that it is possible to develop a theoretical model of our beginnings using only our ability to observe our present environment and the laws that govern it if one views it in terms of four *spatial* dimensions instead of four dimensional space time.*

*(The reason will become obvious latter.) *

Einstein provided a way of doing this when he defined the geometric properties of space-time in terms energy/mass, the constant velocity of light and equation E=mc^2 because that provided a method of converting a unit of space-time he associated with energy to unit of space we think he would have associated with mass. Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between the time related properties of a space-time universe with the spatial properties of one made up of four *spatial* dimensions.

In other words it allow one to define energy/mass in terms of a curvature or displacement in a "surface" of a three dimensional space manifold with respect to a fourth *spatial* dimension as well as a curvature in a space-time manifold.

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 differs from Einstein’s theory in that it defines only gravitational energy in terms of a displacement in a surface of a space-time manifold while using the above concepts one can define both it and kinetic energy in terms of *oppositely directed displacements* in a "surface" of a three-dimension space manifold with respect to a fourth *spatial* dimension.

Yet having the ability to define both gravity and kinetic energy in terms of a common geometry can add significantly to our understanding of the shape of our universe because its geometry is related to the ratio of total gravitational potential of its energy/mass to the total kinetic energy associated with its expansion. This would allow one to theoretically derive the energy density of the universe’s kinetic energy in terms of an oppositely directed displacement in a "surface" of a three-dimensional space manifold with respect to the energy density of its matter component. This means that the "flatness" of our universe would be an intrinsic property of its existence and would not require the fine-tuning of any of its components to explain it.

This is because the universe, by definition is a closed system the law of conservation of energy/mass tells us there must a dynamic balance between the curvature created by the gravitational potential of the its energy/mass and the oppositely directed kinetic energy associated with its expansion.

However, as was shown in the article "Defining potential and kinetic energy?" this means the "downward" directed displacement in a "surface" of three-dimension space with respect to a fourth "spatial* dimension it associates with the total gravitational potential of the universe would be offset by the "upwardly" directed one associated with its Kinetic energy.

For example observations of the three-dimension environment occupied by a piece of paper shows us that if one crumples a piece that was original flat and views its entire surface the overall magnitude of the displacement caused by that crumpling would be zero because the height of it above its surface would be offset by an oppositely directed one below its surface. Therefore, if one views its overall surface only with respect to its height, its curvature would appear to be flat. In other words flatness is an intrinsic property of a piece of paper that has been crumpled.

Similarly, if the energy density associated with the momentum of the universe’s expansion is a result of oppositely directed displacements in a "surface" of a three-dimensional space manifold with respect to that associated with its matter component their overall density would appear to be flat because, similar to a crumpled piece of paper the "depth" of the displacement below its "surface" caused by matter would offset by the "height" of the displacement above it caused by its Kinetic energy.

However this would be true only if only if the matter and energy in our universe was "flat" or equally disturbed in the beginning.

Many proponents of the Big Bang Model assume it began from the expansion of mass and energy around a one-dimensional point. However, if we are correct in assuming that density of the mass and energy components of our universe are a result of oppositely directed curvatures in a "surface" of a three-dimensional space manifold, the universe must have been "flat" with respect to their density at the time of the Big Bang. This is because a one-dimensional point would have no "vertical" component with respect to a fourth *spatial* dimension and therefore the "surface" of three-dimensional space originating from it would be "flat" with respect to that dimension.

However, if the universe was flat with respect to the density of its energy/mass in the beginning it would remain flat throughout its entire expansive history because as was shown above its expansion would result in a proportional reduction in the displacements above and below its three-dimensional "surface" as it expanded.

This unlike, Alan Guth‘s inflationary model, which does not have any observational support provides a logically consistent and verifiably explanation of why our universe appears flat and remains flat throughout its evolution in terms of its observable properties and the currently accepted laws of physics that govern that it.

The other reason physicists have for proposing the inflationary model was to solve the other inconsistency with the big bang theory or the Horizon problem which is related to the fact that different regions of the universe which have not been able to interact with each other have the same temperature and other physical properties. This should not be possible, given that the transfer of information (or energy, heat, etc.) can occur, at most, at the speed of light.

As mentioned earlier Alan Guth Inflationary model also solves the Horizon problem because it assume that the early universe was extremely small and therefore each point was causally connected Unfortunate as mentioned earlier there is not observational evidence to support this hypothesis.

However similar to the solution of the Flatness problem, defined earlier it is possible to develop a theoretical model of our beginnings that solves the Horizon problem in a manner that is consistent with observable properties of our universe if one views it in terms of four *spatial* dimensions instead of four dimensional space time.

We know from observations the equation E=mc^2 defines the equivalence between mass and energy in an environment and since mass is associated with the attractive properties of gravity it also tells us, because of this equivalence, the kinetic energy associated with the universe’s expansion also possess those attractive properties. However the law of conservation of energy/mass tells us that in a closed system the creation of kinetic energy cannot exceed the gravitational energy associated with the total energy/mass in the universe and that a reduction in one must be compensated for by an increase in the other.

This means 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 it will enter a contractive phase because the total gravitational potential must eventually exceed the kinetic energy of its expansion. This is would be true even though the gravitational potential of its Kinetic energy components would be disturbed or "diluted" by a factor of c^2.

(Many physicists would disagree because recent observations suggest that a force called Dark energy is causing the expansion of the universe accelerate. Therefore they believe that its expansion will continue forever. However, as was shown in the article "Dark Energy and the evolution of the universe" Oct. 1, 2012 if one assumes the law of conservation of mass/energy is valid, as we have done here than the gravitational contractive properties of its mass equivalent will eventually have to exceed its expansive energy because as mentioned earlier kinetic energy also possess gravitational potential therefore there will be constant force opposing this accelerated expansion. Therefore the gravitational potential of Dark Energy must slow the rate of the acceleration and eventually allow gravity to take over and cause the universe to enter a contractive phase. There can be no other conclusion if one accepts the validity of the laws of thermodynamics and Einstein General Theory of Relativity.)

The rate of contraction will increase until the momentum of the galaxies, planets, components of the universe equals the radiation pressure generated by the heat of that contraction.

At some point in time the total kinetic energy of the universe would be equal to the total mass equivalent of that energy or E=mc^2. From this point on the velocity of the contraction will slow due to the radiation pressure generated by the heat of its contraction and be maintained by the momentum associated with the remaining mass component of the universe.

However after a certain point in time the radiation pressure generated by it will become great enough to *fully *ionize its mass component and to cause it to reexpand.

Yet at some point in future the contraction phase will begin again because as mentioned earlier its kinetic energy can never exceed the gravitational energy associated with its mass/energy equivalent.

Since the universe is a closed system, the amplitude of the expansions and contractions will remain constant because the law of conservation of mass/energy dictates that in a closed system energy/mass cannot be created or destroyed.

This results in the universe experiencing in a never-ending cycle of expansions and contractions.

*This would solve the Horizon problem because the repeated cycles would allow different regions of the universe to mix and equalize thereby explaining why their temperature and other physical properties are almost identical*.

This would be analogous to mixing the content of two cans of paint by pouring one into the other. The evenness of the mixture would increase in proportion to the number of times one pored one can into the other.

Similarly the evenness of the temperature distribution and physical properties of the universe would increase in proportion to the number of cycles it had gone through.

However it also explains why there are small temperature and other physical irregularities in the large-scale structure of the universe.

For example one cannot completely mix two different colors of paint no matter how many times they pour one can into another because the random motion of the different colored paint molecules means that some regions will have more of one color than the other.

Similarly the random condensation of baryonic matter in the universe during its expansive phase means that some regions will have more matter or be denser that others no matter how many cycles of expansion or contraction it has undergone.

This explains why the large-scale structures such as galactic clusters exist.

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/mass 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 the universe would have to enter an expansion phase. This will result the energy/mass of the universe will oscillate around a point in space because its momentum will carry it beyond the equilibrium point were the radiation pressure was equal to its gravitational contractive component.

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.

There can be no other interoperation if one assumes the validity of the first law of thermodynamics which states that the total energy of the universe is defined by the mass and the momentum of its components. Therefore, when one decreases the other must increase which means the universe must oscillate around a fixed point in four-dimensional space.

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.

*However this theoretical model provides, unlike the inflation model a logically consistent explanation based on the currently accepted laws of physics where the energy to power the current expansion of our universe came from because, as was shown above one can use the conservation laws to show that the kinetic energy of its expansion originated in the Gravitational energy of its mass.*

One could verify this scenario by observing our current universe and using Einstein General Theory of Relativity and the law of conservation of energy/mass to calculate the how long it would take for the radiation pressure generated by its gravitational collapse to become large enough to cause it to expand and determine if it would allow enough time for different regions to be causally connected to the point where it could explain Horizon Problem and why there are small variations homogeneous structure. Additionally one could determine if the heat generated by that collapse would be great enough to ionize its mass component enough to explain the properties of the cosmic background radiation.

*It should be noted that this derivation of the universe’s origin, its geometry and matter distribution does provide an observational method for verification or falsification because it relies exclusively on the interoperation of physical observations and the accepted laws of physics, not, as is the case with the inflation model on abstract creations of human intellect.*

Later Jeff

Copyright Jeffrey O’Callaghan 2014