"Einstein once said, “What really interests me is whether God had any choice in the creation of the world. This is a fundamental question. Compared to this question, all others seem trivial. Yes, God would have had many choices if He had wanted to create a barren universe. However, in order to create a universe where life is possible, with the same set of natural laws as ours, it seems that He had only limited choices. According to recent findings, the values of physical constants should have been fine-tuned to make the emergence of life in the universe possible." Taeil Albert Bai Stanford University.
However one may be able to understand why they are what they by observing them in terms of the laws of causality that govern our present universe. In other words God may not have a choice in the creation of our world once those laws had been set.
For example one of the most puzzling questions facing cosmology today is why the density of matter and energy are so close to that required to create a flat universe.
The universe will be flat if and only if the attractive gravitational potential of its matter just equals the expansive energy of the big bang. This will result in the expansion slowing and only stopping after an infinite amount of time has passed.
This is important to life because the physical laws that govern our universe tell us if its expansion was much faster than its present value stars and galaxies would not have been able to form while the gravitational force of too much matter would have cause it to clump together more rapidly and thereby not giving enough time for life to evolve.
But why the universe appears to be flat even after 14 billion years of expansion is still a mystery because a flat universe is like the top of a hill. If you are a little away from it the expansion of the universe soon drives you far away from this value, just as a ball that is a short distance from a hilltop will roll down to the bottom. Therefore, when the Universe was one second old, it must have deviated from flatness by less than one part in ten-thousand-trillion. This is a problem because it is hard to understand how the amount of mass and the energy associated with the expansion could have been adjusted to such precision.
However as mentioned earlier one may be able to explain the reason by observing how matter and energy interact and apply the laws of causality that govern those interactions in our present universe to its formation.
For example recent observations tell us that space is not only expanding but accelerating towards a higher spatial dimension not a time or space-time dimension.
Therefore, to explain how the universe is expanding and accelerating towards higher spatial dimension one would have to assume the existence of another one 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 the 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 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 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.
However doing so can add significantly to our understanding how and why the forces of gravity and Dark Energy interact to cause the universe to be flat because it would allow one to derive them and the kinetic energy of its expansion in terms in terms of the common geometry of oppositely directed displacements in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
For example, one can understand why Dark Energy is causing the accelerated expansion of our universe by extrapolating that fact that 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.
Yet 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. Therefore similar to the water molecules occupying the elevated two dimensional surface of the water, the particles occupying an "elevated’ region of three-dimensional space will flow and accelerate outward in the four dimensional environment surrounding it and, as it was with the water molecules in pool their acceleration will decrease as they expand outward towards four dimensional space.
Yet deriving both gravity and the forces involved with the universes expansion in terms of a common geometry as was done above can not only explain why Dark Energy is causing it to accelerate but it can also add significantly, as mentioned earlier to our understanding of why it is flat in terms of the laws that govern our current universe.
This is because the fact that the universe is by definition is a closed system the law of conservation of energy/mass means 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.
This means as was shown in the article "Defining energy" 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.
This would allow one to understand why the universe is flat in terms of the observations of the three-dimensional environment occupied by a piece of paper. They show us that if one crumples one that was original flat and views its entire surface from its three dimensional center the overall magnitude of the displacement caused by that crumpling would be zero because the height above its surface would be offset by an oppositely directed one below its surface. (This would be true even if one folded it in half because there would be an equal amount of paper above and below its center.) 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 flat 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 with respect to its four dimensional center 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.
Another advantage to viewing our universe in terms of four *spatial* dimensions instead of four dimensional space-time is that it allows one to not only understand why it appears to be fine-tuned for flatness but also why the values of many of the other fundamental constants are what they are in terms of their evolution history.
We know from observations the equation E=mc^2 defines the equivalence between mass and energy and since mass is associated with the attractive properties of gravity it also tells us, because of that 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 MUST 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 as the universe cools there be an ever increasing force opposing its accelerated expansion. Therefore the increasing gravitational potential due to the cooling of the universe will 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 heat and radiation pressure generated by it collapse 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.
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 thermodynamics 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.
In other words if this theatrical model is correct our universe will osculate between a very dense hot dense environment and a cold dark one.
However the mechanism outlined above provides a negative feedback loop in terms of universe’s total mass because if it is to great the speed of its collapse will be faster due to its greater gravitational potential thereby causing the next cycle to begin at a higher temperature. This will result in a faster expansion rate and therefore less time for mass to clump together to form stars and galaxies. While if its mass component is too small it would expand to a larger volume resulting a slower contraction resulting in the next cycle beginning at a lower temperature which means its expansion will be slower allowing for the creation of more mass.
This would result in the universe’s fundamental constants that have a positive effect on the creation of mass to have a very specific values. This is because if they caused to much mass to form the feedback loop describe above would result in a new value that would reduce the total amount of mass created in the next cycle. Therefore after a few cycles they would approach an optimal value that is solely dependent on the ratio on the expansive and gravitational properties of the universe.
In other words after the laws that govern the expansion and contraction of our universe were established God may not have had a choice whether or not to create it with the fundamental constants required to sustain life because as was just shown their values would depend on those laws.
It should be noted that this conclusion is based solely on observing of how matter and energy interact and the laws of causality associated with the environment they are currently occupying
Copyright Jeffrey O’Callaghan 2014
Vol. 3 — 2012
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