Paul Adrien Maurice Dirac addressed this issue in a lecture he delivered on February 6, 1939 regarding “The Relation between Mathematics and Physics“.

“The physicist, in his study of natural phenomena, has two methods of making progress: (1) the method of experiment and observation, and (2) the method of mathematical reasoning. The former is just the collection of selected data; the latter enables one to infer results about experiments that have not been performed (or cannot be performed). There is no logical reason why the second method should be possible at all, but one has found in practice that it does work and meets with reasonable success. This must be ascribed to some mathematical quality in Nature, a quality which the casual observer of Nature would not suspect, but which nevertheless plays an important role in Nature’s scheme.

One might describe the mathematical quality in Nature by saying that the universe is so constituted that mathematics is a useful tool in its description. However, recent advances in physical science show that this statement of the case is too trivial. The connection between mathematics and the description of the universe goes far deeper than this, and one can get an appreciation of it only from a thorough examination of the various facts that make it up.”

But exactly how deep is the connection between the mathematical reasoning we use to predict nature to its reality.  In other words how can be sure the equations we use to “infer the results of experiments that have not been performed” (or cannot be performed) actually defines the reality of the environment that encompasses them
Unfortunately we cannot because, as was just mentioned we have not or may not ever be able to conduct them.

Therefore we must be very sure that the equations we use to predict a “quality of Nature” that is unobservable have a “factual” foundation in the theoretical models they are derived from because it is only way in which we can be connect them to true “Nature” of reality defined by that theoretical model.

This is especially true when we use the mathematics of an established paradigm such as the General Theory of Relativity to predict the existence of objects or things such as a singularity which, by definition can never be observed.

For example ESA, at its HubbleSite tells us using Newtonâ€s Laws in the late 1790s, John Michell of England and Pierre-Simon Laplace of France independently suggested the existence of an “invisible star.” Michell and Laplace calculated the mass and size – which is now called the “event horizon” – that an object needs in order to have an escape velocity greater than the speed of light. While n 1915, Einstein’s gave us a conceptual basis for their existence when he publish his General Theory Relativity was able to gives for their predicted the existence of black holes.

Later Karl Schwarzschild, when quantified their existence using mathematics based on Einstein General Theory of Relativity discovered that the gravitational field of a star greater than approximately 2.0 times a solar mass would collapse form a “invisible star” of black hole, as it is now called. Additionally he showed those same equation indicated that the mass would continue to collapse even after its formation to a singularity or one dimensional point. 

He was also able to mathematically quantify the critical circumference or boundary in space around it where the strength of a gravitational field will become strong enough to prevent light from escaping and 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.

However unlike a black hole which have been observationally confirmed through the gravitational effects they have on companion stars the singularity which Schwarzschild’s mathematics predicted is at its center has not been observed and never will be because, as mentioned earlier light cannot escape from a black hole.

Yet there are some who say that the mathematics used to predict the existence of a black hole also predicts, with equal certainty the existence of singularities.  In other words by verifying the existence of black holes though observation means that we have also verified the existence of singularities.

However that assumption is correct if and only if the formation of a singularity is consistent with the concepts of Einstein’s General Theory of Relativity because as mentioned earlier that is conceptual basis for the mathematics predicating their existence.

However, it can be shown there is an inconsistency between the mathematics Schwarzschild used to predict the existence of a singularity and the concepts developed by Einstein in his Theory of General Relativity. 

To understand why we must look at how it describes both the collapse of a star to a black hole and then what happens to its mass after its formation.

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, form 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.”

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 observer who is external to its 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 be identical to those predicted by Robert Oppenheimer and Hartland Snyder using conceptual concepts of Einstein’s theory regarding time dilation caused by the gravitational field of a collapsing star

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.

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 are 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 the theoretical model they are base on.

We agree with Dirac that the connection between mathematics and nature goes far deeper than just being a useful tool in its description.

However as was shown above one must make sure that facts upon which the mathematics is based reliably follow the theoretical model they were development from if we want to use them to understand the “quality of Nature” defined by that model.

Later Jeff

Copyright Jeffrey O’Callaghan 2014

The post The reliability of our mathematical universes appeared first on Unifying Quantum and Relativistic Theories.

Many physicists assume the General Theory of Relativity predicts that all the mass in a black hole is concentrated at its center in a singularity or a point which has zero volume and infinite density

However the idea it can be concentrated in a non-dimensional point of infinite density with zero volume is a bit hard to grasp even for Einstein whose theory is used to predict their existence.

What makes it even more bizarre is that scientists tell us the laws of physics which they use to predict its existence break down at a singularity.

Why then do many believe that they exist?

The reason is because many believe the mathematics of the General Theory of Relativity tells us that when star starts to collapse after burning up its nuclear fuel and forms a black hole the gravitational forces of its mass become large enough to cause matter to collapse to zero volume.

However even though there is observational evidence for the existence of black holes there never will be any for the singularity because according to the General Theory of Relativity nothing, including light can escape form one.

For example NASA’s Hubblesite tells us that "Astronomers have found convincing evidence for a black hole in the center of our own Milky Way galaxy, the galaxy NGC 4258, the giant elliptical galaxy M87, and several others. Scientists verified its existence by studying the speed of the clouds of gas orbiting those regions. In 1994, Hubble Space Telescope data measured the mass of an unseen object at the center of M87. Based on the motion of the material whirling about the center, the object is estimated to be about 3 billion times the mass of our Sun and appears to be concentrated into a space smaller than our solar system."

However as mentioned earlier we will never be able to observe a singularity because they only exist inside black hole.  Therefore to determine their reality we must rely solely on the mathematical predictions of the General Theory of Relativity regarding their formation.

There are some who say that the mathematics used to predict the existence of a black hole also predicts, with equal certainty the existence of singularities.  In other words by verifying the existence of black holes though mathematics means that they have also verified the existence of singularities.

However this would only be true if the mathematics used to predict both a black hole and a singularity conform to the conceptual arguments associated with Einstein General Theory of Relativity because the mathematics used to confirm its existence is based solely on them and not on observations as is the case of black holes.

In other words the fact that we can observe a black hole tells us the mathematics used to predict its existence has a valid basis in ideas of General Relativity.

However the same cannot be said about the existence of a singularity because the conceptual arguments found in that theory tells us that we cannot extrapolate the mathematics associated with it to the formation of a black hole.

To understand why we must look at how it describes both the collapse of a star to a black hole and then what happens to its mass after its formation.

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 as mentioned earlier 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 may 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, form 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.

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 but must maintain a quantifiable minimum volume which is equal to or greater than the critical circumference defined by Karl Schwarzschild.

Some claim that the irregularities in the velocity of contractions in the mass forming the black hole would allow it continue to collapse beyond its event horizon.  However Einstein’s theories tells us that time would move slower for the faster moving mass components of a forming black hole than the slower ones thereby allowing the them to catch up with their faster moving brothers.

In fact the conceptual arguments presented in Einstein’s theories tell us the entire mass of a forming black hole must reach the event horizon at exactly the same time because of time dilatation predicted by his theories.

Therefore assuming the irregularities in the velocity of contractions in the mass forming the black hole would allow it continue to collapse beyond its event horizon is not justified by the conceptual foundations in the General Theory Relativity

This means either the conceptual ideas developed by Einstein are incorrect or there must be an alternative solution to the field equations that many physicists used to predict the existence of singularities because as has just been shown the mathematical predications made by it regarding their existence is contradictory to its conceptual framework.

In other words just because we have observationally verified the existence black holes which were based on equations created from Einstein’s theory does not mean that a singularity at its center is an inevitable outcome of those equations. 

Later Jeff

Copyright Jeffrey O’Callaghan 2013

The post The demise of the singularity appeared first on Unifying Quantum and Relativistic Theories.

This question is very difficult to answer because current theories are only able to describe what happened after the beginning of our universe.  In other words how the universe came about and whether there is any meaning to a “before” or “after” is unknown and perhaps unknowable.  Therefore many believe it is not possible to determine if time began at the moment of its inception or if it had its beginnings in a previous epic.

The reason is because the most popular theories of its origin assume that it emerged from a singularity or one dimensional point and is expanding from the tremendously hot dense plasma environment associated with it.  This Big Bang theory, as this concept has come to be called assumes the momentum generated by the heat of that environment is sustaining the expansion.

Unfortunately for those looking for an answer to the question as to the eternity of time, the laws of physics cannot be applied to a singularity therefore it is impossible to use them to understand what may have happened in the period before the universe was formed.

However this may not be true because using the currently accepted laws of physics one can project observations made in our present time backwards to the show that it may not have had its beginning in a singularity.

For example observations in “our time” tell us when a star supernova explodes it expels hot gas.  However scientists know that a star existed before that event occurred because they can project the laws of physics governing the expanding hot gases backwards to define a period before it took place.  In other words they can determine what existed before an event occurred such as a supernova by projecting their understanding the process that happened after it backwards to the period before it took place.
Yet there are many observations like those associated with the expanding gases of supernova that suggest that our universes expansion did not begin form a one dimensional point or a singularity as the Big Bang models assumes but from an extended three-dimensional volume of space.

The difference between a theoretical model based on these “real time” observations and the mathematical model supporting the existence of a singularity is because, as mentioned earlier science cannot project the laws of physics beyond a mathematically predicted singularity but can through a three-dimensional volume.

Therefore using a theoretical model based on observations of a three-dimensional environment means that science could predict the existence of time before the beginning of our universe by projecting the currently accepted laws of physics beyond the three-dimensional volume that it suggests its expansion began from.

For example one of the most fundament and verifiable observations in science is that the total quantity of energy/mass in a closed system is conserved and that it cannot be created or destroyed.  Since, by definition our universe is a closed system according to its energy/mass cannot be created or destroyed in it.

Yet 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 the kinetic energy associated with the universe’s expansion also possess those attractive properties. Therefore 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.

However, not all of the energy of associated with the universeâ€s expansion is directed towards it because of the random motion of its energy/mass components.  For example, observations indicate that some stars and galaxies are moving towards not away us.  Therefore, not all of the energy present at the time of its origin is directed towards its expansion.

As mentioned earlier the law of conservation of energy/mass tells us that gravitational contractive properties of the universe’s energy/mass cannot exceed its kinetic energy equivalent at time the expansion of the universe began. However because some of the kinetic energy of its components is not directed towards its expansion the total gravitational contractive properties of its energy/mass must exceed the kinetic energy of its expansive components. Therefore, at some point in time the gravitation contractive potential of its energy/mass must exceed the kinetic energy of its expansion because as just mentioned not all of its kinetic energy is directed towards its expansion. Therefore at that point, in time the universe will have to enter a contractive phase.

Some may disagree by saying that as the universe expands its energy is spread out over a larger volume so after a while it just vanishes so to speak or as some like to say the universe experiences a heat death. However Einstein theories do not permit energy to just disappear or “die”. It unequivocally tells us that if the kinetic energy content in a closed environment decreases as it cools the mass content of that environment must increase irrespective of the volume of that environment. Therefore because by definition the universe is a closed system one must assume that any reduction in its overall energy content of the universe including its heat energy must be must be compensated for by an increase in its total attractive gravitational mass content.

Others 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” 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 exceed its expansive energy associated with dark energy and therefore the universe must at some time in the future enter a contractive phase.

We also know from observations that heat is generated when we compress a gas and that this heat creates pressure that opposes further contractions.

Similarly the contraction of the universe will create heat which will oppose its further contractions.

Therefore the velocity of contraction of our universe will increase until the momentum of the galaxies, planets, components of the universe equals the radiation pressure generated by the heat of its contraction.

At this point in time the total kinetic energy of the collapsing universe would be equal to the radiation pressure associated with the heat of its collapse. From this point on its contraction will 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 ionize its mass component and to cause it to reexpand.

This will result in the universe entering an expansive phase and going through another age of recombination when the comic background radiation was emitted and the recreation of the particle mass that latter is responsible for the development of stars and galaxies.  This is because the expansive forces associated with the radiation pressure caused by its collapse will exceed the contractive forces associated with the remaining mass of the universe.  The reason it will experience an age of recombination as it passes through each cycle is because the heat of its collapse would be great enough to completely ionize all forms of matter.

However, at some point in time the contraction phase will begin again because as mentioned earlier its kinetic energy cannot exceed the gravitational energy associated with the total mass/energy in the universe.

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 the total mass and energy in a closed system remains constant.

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

As mentioned earlier many cosmologists do not accept the cyclical scenario of expansion and contractions because they believe a collapsing universe would end in the formation of a singularity similar to the ones found in a black hole and therefore, it could not re-expand.

However, according to the first law of thermodynamic the universe would have to begin expanding before it reached a singularity because that law states that energy in an isolated system can neither be created nor destroyed

Therefore because the universe is by definition an isolated system; the energy generated by its gravitational collapse cannot be radiated to another volume but must remain within it.  This means the radiation pressure exerted by its collapse must eventually exceed momentum of its contraction and the universe would have to enter an expansion phase because its momentum will carry it beyond the equilibrium point were the radiation pressure is greater that the momentum of its mass.  This will cause the mass/energy of the universe to oscillate around a point in space. 

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 of mass and the momentum of its components.  Therefore, when one decreases the other must increase and the universe must oscillate around a point in space if it does enter a contraction phase.

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.

As mentioned earlier the heat generated by the collapse of the universe would raise the temperature to a point where electrons would be strip off all matter and it would become ionized, making it opaque to radiation.  It would remain that way until it entered the expansion phase and cooled enough to allow matter to recapture and hold on to them.  This Age of Recombination, as cosmologists like to call it is when the Cosmic Background Radiation was emitted.

One could quantify this scenario by using the first law of thermodynamics to calculate the temperature of the universe when the radiation pressure generated by the gravitational collapse of the universe exceeds the momentum of that collapse and see if it is great enough to cause another with the Age or Recombination as it must to account for the observed properties of the Cosmic back ground radiation.

As mentioned earlier using the above theoretical model scientists can predict the existence of time before the beginning and after the end of our present universe by projecting the currently accepted laws of physics beyond the three-dimensional volume that it suggests it began and will end in.

However this also tells us that the time we experienced is an integral part of our universe because one can trace its origins through the laws of physics to previous and future epics of universe creation. 

But it also tells us that that time does not exist eternally to our universe because the laws of physics we use to define how it progresses from the past to the future cannot be exported to an environment outside of it.

Therefore, one cannot ask when or at what time these cycles of expansions or contractions began or will end because, as just mentioned the time we experience only exists in our universe.

This means we must consider the time we experience as eternal because there is no meaning to asking when those cycles of expansion and contractions began or will end with respect to the existence of our universe because they are part of it.

Later Jeff

Copyright 2012 Jeffrey O’Callaghan

The post Is time eternal? appeared first on Unifying Quantum and Relativistic Theories.

However, they have had considerable difficulty explaining why different regions of the universe have nearly the same temperature and other physical properties. This is a problem because information can only be exchanged at the speed of light and the Big Bang model indicates the separation between different regions of space would have been too large to allow enough time for information to be exchanged between them.  Therefore, because they evolved independently from each other they should have different properties.  This inconsistency between theory and observations is what cosmologists call the Horizon Problem.
In 1980 Alan Guth, Andrei Linde, Paul Steinhardt, and Andy Albrecht proposed a modification to the big bang theory which appeared to provide a solution by postulating a short 10 ^{− 32} second period of exponential expansion (dubbed “inflation”) within the first minute or so of the universe’s existence.  During inflation, the universe would have increased in size by an enormous factor.

If correct, inflation solves the horizon problem by suggesting that prior to the inflationary period the entire universe was extremely small and therefore each point was 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 appear to be unconnected causally, but they were in the past because they were much closer together.

However, there is no observational basis for defining what caused this rapid inflation to begin or end.  Therefore, some say it is an “ADHOC” or contrived explanation of a flaw in original the Big Bang Theory.

Another problem with the inflationary concept is made evident by the fact that our universe is not homogenous because observations tell us it contains large-scale structures such as galactic clusters. 

This presents another problem for its proponents because, as mentioned earlier the reason Alan Guth proposed it was to explain why the universe was homogeneous.

This is why they had to add the passage “This essentially froze any irregularities and prevented them from being “smoothed out” ” to its description to “force” it to agree with the observation that it is not.

The only problem with this is that they have been unable to define what caused these initial irregularities to occur.

Some have theorized that quantum fluctuations or a temporary change in the amount of energy in space, arising from Werner Heisenberg’s uncertainty principle may be responsible.  But here again there is no observational evidence to support this claim.

In other words an “ADHOC” theory was created to explain why the universe is homogeneous must be modified by another “ADHOC” or abstract theoretical construct to explain why it is not.  (ADHOC in the sense that neither have a foundation in experimental or observational science.)

Physics as the name implies is the science that deals with physical properties matter, energy, motion, and force. Therefore the primary vehicle to guide our understanding of our universe should be the “reality” of the observable properties of matter energy, motion and force to develop theories of its origin and not the unobservable properties of an inflation field.

For example observations tell us our universe is expanding.

As mentioned earlier proponents of the Big bang explain this by assuming the energy driving its expansion was created in a tremendously hot dense environment.  Yet they are unable to tell us where the energy came from to create that environment.  Therefore they must assume that it was created out nothing which would be a violation of the law of conservation of energy/mass.

However, there is another explanation for the origin of our expanding universe which is not, as was shown in the article “The Return of the Big Bang” Jan. 15, 2008 based on the unobservable properties of an inflation field , does not violate any of the accepted physical laws of physics, and can be derived from direct observations of our environment.

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 universeâ€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

Therefore 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, where “E” equals the total Kinetic energy content of the universe and “m” equals the total mass content of the universe.  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 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 cannot 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 it remains constant.

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

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.

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 that the other.

Similarly the random motion of the baryonic matter in the universe 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 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.  The mass/energy 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 point in three-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.

As mentioned earlier the heat generated by the collapse of the universe would raise the temperature to a point where electrons would be strip off all matter and it would become ionized, making it opaque to radiation.  It would remain that way until it entered the expansion phase and cooled enough to allow matter to recapture and hold on to them.  This Age of Recombination, as cosmologists like to call it is when the Cosmic Background Radiation was emitted.

One could quantify this scenario by using the first law of thermodynamics to calculate the how long it would take for the radiation pressure generated by the gravitational collapse of the universe 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 generate 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 temperature and matter distribution does provide an observational method for verification or falsification because it relies exclusively the accepted laws of physics and on interoperation of physical observations and not as is the case with the inflation model on abstract creations of human intellect.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

The post A sensible solution to the Horizon Problem appeared first on Unifying Quantum and Relativistic Theories.

For example, the wind can blow a stack of papers off a desk into a disorganized pile on the floor but it can also pick up it up and organized them on a desk.

However, common sense tells most of us that we should not open a window and wait for a breeze to come in to pick up our report and reorganize for us even though it is mathematically possible to define such an event.

However, many physicists assume that if mathematics predicts an event can happen it will even if its occurrence does not agree with our common sense understanding of the process it is defining.

For example in Chapter 5 of Kip S. Thorne book Blacks Holes & Time Warps “Implosion is Compulsory” he describes how Oppenheimer and Snyder predicted that a star with a mass of 2.0 times greater that of our sun must implode at the end of their lives to a singularity or a dimensionless point in space based on a solution of Einstein’s field equations.

We do not disagree with the fact that based on Einstein’s field equations it is possible for the mass of a star to implode to form in a singularity however; we disagree with those that say that this must occur.

Common sense is based on humans ability observe the properties of their environment and to conceptually extrapolate them to new ones.

For example, observations of our environment tell most of us that it is highly unlikely that the wind will pick a report up off the floor and reorganize it on a desk for us even though it is mathematically possible.

Similarly, observations of our environment tell most of us that it is unlikely the mass of a star can be concentrated in a one-dimensional point in space even though it is mathematically possible.

Why then do some scientists tell us not only that it can but must happen?

The reason is that many physicists have a tendency to focus only on the mechanistic attributes of mathematical equations defining a theory and not on their conceptual implications.

As mentioned earlier, many physicists believe the implosion of a star into a black hole is possible based on a solution of Einstein’s field equations.  Additionally they tell us the gravitational forces inside of a black hole are so great that they compress its mass to a one dimensional point where the relativistic field equations that the define their creation cannot be apply.

Physicists have never made an observation in any environment that violates Einstein’s laws.  Yet, they use his field equations derived from his theories to predict an environment where his laws do not apply.  Even though Black holes may exist because they do not violate Einstein’s laws common sense should tell us that a singularity probably doesnâ€t in part because the equations that define its formation of cannot be applied to them.

(Please see the article “An alternative to a singularity?” Aug 15, 2008 for a common sense interpretation of what occurs at the center of a black hole based on Einstein’s theories.)

We are not saying that a star cannot collapse to form a black hole but we are saying is physicists should use some common sense and portion of their time looking at the conceptual aspects of a theory instead of only on the mechanistic attributes of its equations before using them to make predictions.

Physicists should remember “just because something can happen does not mean that it must”

Later Jeff

Copyright Jeffrey O’Callaghan 2008

The post Black holes and common sense. appeared first on Unifying Quantum and Relativistic Theories.

However, there is an alternative conclusion based on its concepts that suggest that a mass cannot, under any conditions form a singularity but must maintain a quantifiably finite volume which is greater than a one-dimensional point.

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, form 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.

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.

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 many 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.

We are not saying that black holes do not exist however we are saying that according to the concepts of Relativity a singularity is NOTan 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 may not collapse to a singularity but only to a finite volume equal to its event horizon.

Only observations can determine which one is correct because both are based on the validity of the concepts presented in Einstein’s theories and the mathematical equations he developed.

Later Jeff

Copyright Jeffrey O’Callaghan 2008

The post An alternative to a singularity? appeared first on Unifying Quantum and Relativistic Theories.