Mathematics is the primary tool many of today’s science use to define the causality of the physical laws governing of our observable universe.
However it is by definition is an abstract creation of the mind and therefore is not physically connected to the observable real world, most of us believe we live in.
Therefore, we can never be sure the equations developed by science accurately define the physicality of those laws or the real world they are describing.
This is true even though they make accurate predictions because unless there is a way of physically connecting the mathematical worlds create by the intellect to the observable world we live in science cannot be sure that is has chosen the correct set of facts that defines its existence.
Granted the mind can systematical quantify the natural world as the mathematics of quantum mechanics does with great accuracy but that does not necessarily mean it tell us anything about the reality of how or why that quantification takes place.
For example there are an infinite number of ways one can mathematically describe the fact that there are two apples on a table. One can predict why based on the assumption that there were originally four apples and two were taken away or assume that originally there were six and four were taken away. However if there were only four apples to begin with the mathematical description using six apples even though accurately quantifies the existence of two apples it does not describe their world because in "reality’ that world did not contain six apples.
Similarly just because the mathematics of quantum mechanics can very accurately predict the quantitative observation of the particle world does not mean that it defines why it is that way.
Einstein was often quoted as saying "If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless."
He realized for science to make a claim that they have organized the natural world into a single set of patterns or laws that describe why we perceive its "reality" the way we do they must be able to conceptually connect the independent models developed by our minds to the reality of natural world that exists outside of it.
For example Newton in a letter to Bentley in 1693, talks about a conceptual problem he has with his gravity theory by rejecting the action at a distance that it requires.
"It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact…That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it."
However Einstein realized by extrapolating the physical image of how objects move on a curve surface in a three-dimensional environment to a four dimensional space-time manifold one could explain how gravity "may act upon another at a distance through a vacuum" in terms of a curvature in space and time. This enables one to understand gravity based on a physical image formed by the "reality" of what we can see and touch in our three-dimension world.
In other words he was able to connect the observable reality of our three dimensional world to the mathematical one he had created in his mind to explain gravity in terms of a physical imaged form in our three dimensional world.
Unfortunately many of today scientists seem to be ignoring the lessons taught to us by Einstein. They chose to look for reality only in terms of abstract mathematics instead of the physical imagery given to us by the "reality" of what we can see and touch.
The reason may be because it is easier to alter an abstract environment based on mathematics to conform to an observational inconsistency than it is to alter one based on physical imagery.
For example Quantum theory makes predictions based on the random properties of a probability function. However because the abstract properties of probabilities which are not physically connected to our world, all its predictions no matter how inconsistent they are with the world they are describing can be incorporate into it.
This is in sharp contrast to the space-time environment defined by Einstein in that projecting the physical image of objects moving on a curve surface in our three-dimensional environment physically connects it to a four-dimensional space time-environment
For example a single instance of a mass being gravitational repelled instead of attracted would contradict the physical imagery define by Einstein and would be extremely if not impossible to explain because no one has ever observe objects rolling up hill in our three-dimensional environment. In other words because he defined gravity in terms of a physical image based on how objects move on a curve surface in a three-dimensional environment it makes observations like two masses gravitational repelling each other virtually impossible to incorporate into it.
However because quantum mechanics is based on probabilities anything that can happen eventually will. Therefore it is virtually impossible to find any observation in the real world that contradicts it. However this can only happen in an abstract environment which is not bound by the physicality of our observational world.
As mentioned earlier unless science can conceptually connect the mathematical worlds created by the intellect to the observable world we live in we cannot say that we know or understand anything physical laws that we assume define its reality.
But why should science put in the effort to understanding our theoretical models in terms of the physical "reality" of our world when both the abstract mathematical foundation of quantum mechanics and the physical imagery of Einstein’s theories make very accurate predictions of future events.
Because the mission of a science is to define the real world in terms of what we perceive in our environment not to perceive an abstract mathematical environment to define what we want it to be.
Copyright 2014 Jeffrey O’Callaghan
Vol. 3 — 2012
"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