Have you ever wondered why so many seeming rational scientists make irrational or groundless assumptions to explain why our universe is what it is?

For example many proponents of the Big Bang theory assume the universe expanded from a singularity which is by definition a region of space in which mass is concentrated in a volume whose gravitational field is so great that neither energy or mass can escape from it.

However how can something emerge or expand form something that it cannot emerge from.

Many would call someone irrational or maybe even mental deficient he or she tells us the rabbit a magician pulls out of his hat materialized out of thin air when we know or should know that it could not.

Similarly shouldn’t we hold scientists to that same rationality or mental standard when they tell us that the gravitational field of a singularity is so great that nothing can escape from it and then tell us that all of the matter and energy in the universe materialized out of it?

However an even more pertinent question is why do some of the most highly educated people in the scientific community believe and expect others to believe in the irrationality of a universe which began in a singularity.

*The answer may be because they rely to much on the quantitative and not enough on the qualitative properties of their theoretical models to explain or justify their mathematics to themselves and others. *

For example there are an infinite number of ways one can mathematically describe how four apples in a bag can find themselves on a table. One could mathematical quantify it by saying that the two of the four apples were taken out of the bag and later two more were removed and placed on the table. This gives you both the correct quantitative and qualitative or physical description of how those apples came to be on the table. However an equally valid mathematical quantification would be to assume that five apples were taken out of the bag and then one was put back. However if there only four apples to begin with the mathematical description using five apples even though it make an accurate mathematical prediction of why there are four apples on the table does not describe their environment because it never contained five apples.

A theoretical model of our universe consists of two parts. The first part allows one to accurate predict the quantitative outcome of experiments while the second is to provide a logically consistent explanation based on its qualitative or physical properties.

As mentioned earlier many proponents of the Big Bang Theory assume the universe began when the mass and energy contained in a singularity began to expand and defines the environment in which that expansion take place in terms of the concept presented in the General theory of Relativity.

*However if one took the time to analyze the physicality of environment that it defines one would realize that not only does it not predict the existence of a singularity it tells us that they cannot exist.*

Granted some cleaver scientists have come up with a mathematical model of what could be responsible for the universe originating from one such as an inflation field but it has no basis in either observations or theory.

*As mentioned earlier the existence of a singularity is based primarily on the quantitative mathematical properties of Einstein General Theory of Relativity. However just because one gets a mathematically correct answer to a question does not mean as was shown above that it defines the reality of the environment that it encompasses. *

Einstein in his General Theory of Relativity predicted time is dilated or moves slower when exposed to gravitational field than when it is not. Therefore, according to Einstein’s theory a gravitational field, if strong enough it would stop time.

In 1915, Karl Schwarzschild discovered that according to it the gravitational field of a star greater than approximately 2.0 times a solar mass would stop the movement of time if it collapsed to a singularity. He also defined the critical circumference or boundary in space around a singularity where the strength of a gravitational field will result in time being infinitely dilated or slowing to a stop.

In other words as a star contacts and its circumference decreases, the time dilation on its surface will increase. At a certain point the contraction of that star will produce a gravitational field strong enough to stop the movement of time. Therefore, the critical circumference defined by Karl Schwarzschild is a boundary in space where time stops relative to the space outside of that boundary.

This critical circumference is called the **event horizon** because an event that occurs on the inside of it cannot have any effect on the environment outside of it.

Many physicists believe the existence of a singularity is an inevitable outcome of Einstein’s General Theory of Relativity.

However, it can be shown using the concepts developed by Einstein; this is not true.

In Kip S. Thorne book "Black Holes and Time Warps", he describes how in the winter of 1938-39 Robert Oppenheimer and Hartland Snyder computed the details of a stars collapse into a black hole using the concepts of General Relativity. On page 217 he describes what the collapse of a star would look like, from the viewpoint of an external observer who remains at a fixed circumference instead of riding inward with the collapsing stars matter. They realized the collapse of a star as seen from that reference frame would begin just the way every one would expect. "Like a rock dropped from a rooftop the stars surface falls downward slowly at first then more and more rapidly. However, according to the relativistic formulas developed by Oppenheimer and Snyder as the star nears its critical circumference the shrinkage would slow to a crawl to an external observer because of the time dilatation associated with the relative velocity of the star’s surface. The smaller the circumference of a star gets the more slowly it appears to collapse because the time dilation predicted by Einstein increases as the speed of the contraction increases until it becomes frozen at the critical circumference. In other words from the perspective of an external observer Einstein theory tells us that a star cannot contract beyond it event horizon.

However, the time measured by the observer who is riding on the surface of a collapsing star will not be dilated because he or she is moving at the same velocity as its surface.

Therefore, the proponents of singularities say the contraction of a star can continue until it becomes a singularity because time has not stopped on its surface even though it has stopped to an observer who remains at fixed circumference to that star.

But one would have to draw a different conclusion if one viewed time dilation in terms of the gravitational field of a collapsing star.

Einstein showed that time is dilated by a gravitational field. Therefore, the time dilation on the surface of a star will increase relative to an external observer as it collapses because, as mentioned earlier gravitational forces at its surface increase as its circumference decrease.

This means as it nears its critical circumference its shrinkage slows with respect to an external observer who is outside of the gravitation field because its increasing strength causes a slowing of time on its surface. The smaller the star gets the more slowly it appears to collapse because the gravitational field at its surface increase until time becomes frozen for the external observer at the critical circumference.

Therefore, the observations of an external observer would make using conceptual concepts of Einstein’s theory regarding time dilation caused by the gravitational field of a collapsing star would be identical to those predicted by Robert Oppenheimer and Hartland Snyder in terms of the velocity of its contraction.

However, Einstein developed his Special Theory of Relativity based on the equivalence of all inertial reframes which he defined as frames that move freely under their own inertia neither "pushed not pulled by any force and therefore continue to move always onward in the same uniform motion as they began".

This means that one can view the contraction of a star with respect to the inertial reference frame that, according to Einstein exists in the exact center of the gravitational field of a collapsing star.

(Einstein would consider this point an inertial reference frame with respect to the gravitational field of a collapsing star because at that point the gravitational field on one side will be offset by the one on the other side. Therefore, a reference frame that existed at that point would not be pushed or pulled relative to the gravitational field and would move onward with the same motion as that gravitational field.)

The surface of collapsing star from this viewpoint would look according to the field equations developed by Einstein as if the shrinkage slowed to a crawl as the star neared its critical circumference because of the increasing strength of the gravitation field at the star’s surface relative to its center. The smaller it gets the more slowly it appears to collapse because the gravitational field at its surface increases until time becomes frozen at the critical circumference.

Therefore, because time stops or becomes frozen at the critical circumference for both an observer who is at the center of the clasping mass and one who is at a fixed distance from its surface the contraction cannot continue from either of their perspectives.

However, Einstein in his general theory showed that a reference frame that was free falling in a gravitational field could also be considered an inertial reference frame.

As mentioned earlier many physicists assume that the mass of a star implodes when it reach the critical circumference. Therefore, the surface of a star and an observer on that surface will be in free fall with respect to the gravitational field of that star when as it passes through its critical circumference.

This indicates that point on the surface of an imploding star, according to Einstein’s theories could also be considered an inertial reference frame because an observer who is on the riding on it will not experience the gravitational forces of the collapsing star.

However, according to the Einstein theory, as a star nears its critical circumference an observer who is on its surface will perceive the differential magnitude of the gravitational field relative to an observer who is in an external reference frame or, as mentioned earlier is at its center to be increasing. Therefore, he or she will perceive time in those reference frames that are not on its surface slowing to a crawl as it approaches the critical circumference. The smaller it gets the more slowly time appears to move with respect to an external reference frame until it becomes frozen at the critical circumference.

Therefore, time would be infinitely dilated or stop in all reference that are not on the surface of a collapsing star from the perspective of someone who was on that surface.

However, the contraction of a stars surface must be measured with respect to the external reference frames in which it is contracting. But as mentioned earlier Einstein’s theories indicate time on its surface would become infinitely dilated or stop in with respect to reference frames that were not on it when it reaches its critical circumference.

This means, as was just shown according to Einstein’s concepts time stops on the surface of a collapsing star from the perspective of all observers when viewed in terms of the gravitational forces. Therefore it cannot move beyond the critical circumference because motion cannot occur in an environment where time has stopped.

This contradicts the assumption made by many that the implosion would continue for an observer who was riding on its surface.

Therefore, based on the conceptual principles of Einstein’s theories relating to time dilation caused by a gravitational field of a collapsing star it cannot implode to a singularity as many physicists believe and must maintain a quantifiable minimum volume which is equal to or greater than the critical circumference defined by Karl Schwarzschild because as was show above time must stop for all observers at the event horizon.

This is true even though some have shown mathematically that mass can continue to collapse beyond the event horizon if it is not symmetrically distributed around its center

In other words because parts of it that are moving faster towards the center they could break through the event horizon and drag the rest of it in.

However as was shown above the increasing strength of the gravitational field causes time to slow and stop at the event horizon from the perspective of all observers.

Therefore no matter how asymmetrical the collapse of a mass is none of it can ever pass through the event horizon to form singularity according to the conceptual arguments presented in Einstein’s General Theory of Relativity.

This means either the conceptual ideas developed by Einstein are incorrect or there must be an alternative solution to the field equations based on the General Theory of Relativity that physicists used to predict the existence of a singularity because as has just been shown the theoretical predications made by them regarding its existence are contradictory to the concepts contained in it.

It should be remember we are not saying that black holes do not exist however we are saying that according to the concepts of Relativity a singularity is **NOT **an inevitable outcome of Einstein’s General Theory of Relativity. In other words the mass of a star greater than approximately 2.0 times a solar mass cannot collapse to a singularity but only to a finite volume equal to its event horizon.

As was mentioned earlier a valid theoretical model must seamlessly integrate both a quantitative and qualitative explanation of environment it encompasses because not doing so leaves it opened to criticism.

*In other words we must hold scientist’s accountable for both the mathematical as well as the qualitative properties of their theoretical models to minimize the possibility of them pulling a theoretical "rabbit" out of their hats.*

Later Jeff

Copyright Jeffrey O’Callaghan 2015

Quantum mechanics assumes that a particle is in a superposition of several states or positions based on the mathematical properties of Schrödinger’s wave equation before an observation is made. It also assumes that when it is observed it collapses resulting the particle it represents having a single or unique position.

When the Copenhagen interpretation was first introduced Neils Bohr found it was necessary to assume the collapse of wave function to distinguish the quantum from the classical world. This allowed it to develop without distractions from interpretational worries. Nevertheless since then that it meaning has be hotly debated because if it is a fundamental properties of nature as many have assumed it would contradict the classical or Newton assumption that the world is deterministic.

However the science of physics is devoted to understanding the physical process responsible for creating the "reality" of our observable environment based on observing the physical interaction of its real not imagined components.

One of the reason it has been so difficult to understand what happens to the position component of a quantum system when it is observed may be because too much attention has been focused on the mathematical aspects of the wave function and not enough on its physical meaning in a space-time environment. This is made even more difficult because the concept of superposition is defined in terms of the spatial properties of a quantum system instead of its space-time properties.

This suggest one be able to obtain a better understanding of what happens to it if one could view it in terms its spatial instead of it time or space-time properties.

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 time he associated with energy to unit of space associate with position. 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.

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.

However defining the dimensional properties of quantum system in terms of its spatial instead of its time components would allow one to derive the physicality of the wave functioned associated with Schrödinger’s equation by extrapolating the observable properties of our reality to the quantum world it describes.

For example the article “Why is energy/mass quantized?” Oct. 4, 2007 showed one can derive its physicality 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 similar resonant interaction between three and four dimensional space.)

However assuming its energy is result of a displacement in four *spatial* dimension instead of four dimensional space-time as was done in the article “Defining energy?” Nov 27, 2007 allows one to not only derive the physicality of Schrödinger’s equation as was just done but also the physical reason why its particle components would be in superpositioned state before an observation is made.

Classical mechanics tell us that because of the continuous properties of waves, the energy the article “Why is energy/mass quantized?” associated with a quantum system would be distributed throughout the entire "surface" a three-dimensional space manifold with respect to a fourth *spatial* dimension similar to how the wave generated by a vibrating ball on a surface of a rubber diaphragm are disturbed over its entire surface while the magnitude of the displacement it causes will decrease as one moves away from the point of contact.

However, this means if one extrapolates the mechanics of the rubber diaphragm to a "surface" of three-dimensional space one must assume the oscillations associated with each individual quantum system must be disturbed thought the entire universe while the spatial displacement associated with its energy defined in the in the article “Defining energy?” Nov 27, 2007 would decrease as one moves away from its position. This means there would be a non-zero probability they could be found anywhere in our three-dimensional environment because, as mentioned earlier the article “Why is energy/mass quantized?” shows that a quantum mechanical system is a result of a resonant structure formed by the oscillations on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Classical Wave Mechanics tells us a resonance would most probably occur on the surface of the rubber sheet were the magnitude of the vibrations is greatest and would diminish as one move away from that point,

Similarly an observer would most probably find a quantum system were the magnitude of the vibrations in a "surface" of a three-dimensional space manifold is greatest and would diminish as one move away from that point.

However as mentioned earlier this is exactly what is predicted by Quantum mechanics in that one can define a particle’s exact position or momentum only in terms of the probabilistic values associated with vibrations of its wave function

*Additionally this tells us that the wave function does not collapse but its energy is redirected towards the observer and as was shown in the article Why is energy/mass quantized? he would record its redirected energy in term of discrete quantized properties associated with a particle. *

As mentioned earlier the science of physics is devoted to understanding the physical process responsible for creating the "reality" of our observable environment based on observing the physical interaction of its real not imagined components.

Yet even though we may never be able to directly observe the fourth *spatial* dimension we can verify its existence by observing the effects it has on our observable three-dimensional environment similar to how Einstein was able to conclude that gravity was a result of a curvature in a space time environment.

Later Jeff

Copyright Jeffrey O’Callaghan 2015