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 its reality we must rely solely on the mathematical predictions of the General Theory of Relativity regarding their formation.
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 observations means that we 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 his General Theory of Relativity.
Copyright Jeffrey O’Callaghan 2013
2007 thru 2010 Paperback
The Higgs Boson which was tentatively confirmed to exist on 14 March 2013 appears to confirm the existence of the Higgs field. Its discovery is pivotal to the Standard Model and other theories within particle physics because it explains why some fundamental particles have mass when the symmetries controlling their interactions should require them to be massless, It should allow physicists to finally validate the last untested area of the Standard Model’s approach to fundamental particles and forces, guide other theories and discoveries in particle physics, and potentially lead to developments in.
But what does the discovery of the Higgs Boson tell us about the reality of the Higgs field.
This is an import question because its existence is based on abstract mathematical constructs which may or may not describe its reality. In other words even though they may have predicted its existence it has not yet been connected it to the observable reality of what we can see and touch.
The importance of connecting a theoretical idea to the observable properties of our world was demonstrated by Einstein 200 years after Newton realized that his gravitational theory meant “one body may act upon another at a distance”.
“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 that one can understand how gravity “may act upon another at a distance through a vacuum” by extrapolating the physical image of how objects move on a curve surface in a three-dimensional environment to a curved four dimensional space-time manifold. This allowed him to conceptually understand gravity in terms of a physical image based on our three-dimension environment.
In other words the mathematics developed by Newton was only able to quantitatively predict gravitational forces while Einstein gave us the ability to conceptually understand why “one body may act upon another at a distance” by physically connecting it to the reality of what we can see and touch.
However he was unable to tell us what mass is, he was only able tell us how mass interacts with space-time.
As Steven Weinberg said “Mass tells space-time how to curve while space-time tells mass how to move”.
This is similar to Newton in that he was able to mathematically define how mass gravitational interacts with other masses but was unable to understand or define a physical mechanism that could account for that interaction.
Einstein was often quoted as saying “If a new theory (such as that associated with the Higgs boson) was not based on a physical image simple enough for a child to understand, it was probably worthless.”
In other words to fully understand the theoretical significance of the Higgs Field and why it is responsible for mass one should be able to describe how it interacts with mass in terms of a physical image based on what we can see and touch in our three-dimensional world much as Einstein was able describe how space and time interacted with each other to cause gravity.
However Einstein’s and modern scientist’s inability to define or derive the casualty of mass in terms of a physical image can be traced to the fact that they chose to define the universe in terms of energy instead of mass.
Einstein told us that a curvature in space-time is responsible for gravitational energy and because of the equivalence been energy and mass defined by his equation E=mc^2 one must also assume that it is responsible for mass.
This suggest that one should be able to learn what the Higgs Field is made up of if one converts or transposes the Einstein’s space-time universe which defines field properties of energy in terms of geometry of space-time to one that defines mass of in terms of its field properties.
He gave us the ability to do this when he defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy by the equation E=mc^2 and the constant velocity of light.
Observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein’s one must assume that energy must also have spatial properties.
As mentioned earlier Einstein equation E=mc^2 tells us there is a dynamic relationship between the geometric properties of our universe and the mass and energy it contains and when one coverts mass to energy in a closed three-dimensional environment it expands because it would reduce the magnitude of the curvature of three-dimensional space while if one coverts energy to mass, that environment contracts because that would increase its curvature.
However the fact that he defined the geometric relationship between energy and mass in terms of the constant velocity of light means that one can also quantitatively and qualitatively define a one to one correspondence between the properties of energy in a space-time universe and the properties of mass four *spatial* dimensions.
Therefore one could also say that when one coverts mass to energy in a closed three-dimensional environment that environment expands towards a fourth *spatial* dimension while if one coverts energy to mass their environment would contract with respect to it.
This was the bases for assuming as was done in the article “Defining energy” Nov 27, 2007 that all forms of energy including thermo and that associated with mass 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 instead of one in a space-time environment.
However changing ones perspective on the geometric structure of the universe form one of space-time to four *spatial* dimensions, as was just shown to be possible gives one the ability to define the physical mechanism by which the Higgs Field or the field properties of four *spatial* dimension creates mass and why it is quantized in the fundamental particles of the Standard Model in terms of a physical image formed by our three-dimensional environment.
For example one can form a physical image of why mass is quantized, as was done in the article “Why is energy/mass quantized?” Oct. 4, 2007″ by extrapolating the image of a wave and its resonant properties in three dimension environment to one made up of four *spatial* dimensions. This would be analogous to how Einstein, as mentioned earlier was able to explain gravity by extrapolating the physical image of how objects move in a three-dimension space to one consisting of four dimensional space-time.
(Louis de Broglie was the first to predict the existence of the wave properties of mass when he theorized that all particles have a wave component. His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer).
Briefly that article 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 be meet in one consisting of four.
The existence of four *spatial* dimensions would give a matter wave that Louis de Broglie associated with a particle 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 respect to a fourth *spatial* dimension at a frequency associated with the energy of that event.
However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established in four *spatial* dimensions.
Classical mechanics tells us that resonant systems can only take on the discrete or quantized energies associated with a fundamental or a harmonic of their fundamental frequency
Therefore, these resonant systems in a four *spatial* dimensions would define mass and its quantum mechanical properties because of the fact that the volumes of space containing them would have a higher concentration of energy and therefore the mass associated with those volumes would be greater.
This suggest that the Higgs field is made up of the field properties of four *spatial* dimensions and that the magnitude of a mass would be dependent on its geometrical configuration.
If true one should be able to use those field concepts to explain why the mass of corresponding particle types across the three fundamental families of particles in the Standard Model listed in the table below grows larger in each successive family.
|Family 1||Family 2||Family 3|
|Up Quark||.0047||Charm Quark||1.6||Top Quark||189|
|Down Quark||.0074||Strange Quark||.16||Bottom Quark||5.2|
As mentioned earlier the article “Why is energy/mass quantized?” showed that one can derive the mass of a particle in terms of the energy contained within a resonant system generated by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension while the article “Defining energy” showed that one can derive the energy or temperature of an environment in terms a displacement in the same three-dimensional space manifold with respect to a fourth *spatial* dimension.
Therefore using the concepts developed in those articles one could derive the total mass of a particle in terms of the sum of the energies associated with that resonant structure and the displacement in the “surface” of three-dimensional space associated with the energy of the environment it is occupying.
Yet Classical Mechanics tells us there will be specific points in space where the matter wave that Louis de Broglie associated with a particle can interact with the energy content or temperature of its environment to form a resonant system.
Therefore, the mass of each family member would not only be dependent on the energy associated with the resonant system that defined their quantum mechanical properties in the article “Why is energy/mass quantized?” but also on temperature or energy of the environment they are occupying.
Thus suggest the reason “The corresponding particle types across the three families have identical properties except for their mass, which grows larger in each successive family.” is because of an interaction between the resonant properties defined in the article “Why is energy/mass quantized?” and the mass content of the environment they are occupying.
This means the particles in the first family would be found in relativity low energy environments, are relatively stable, and for the most part can be observed in nature. However, the particles in the second and third families would be for the most part unstable and can be observed only in high-energy environments of particle accelerators. The exception is the Muon in the second family, which is only observed in the high-energy environment of cosmic radiation.
The relative masses of the fundamental particles increases in each successive family because the higher-energy environments where they occupy would result in the corresponding particles in each successive family to be formed with a greater relative “separation” in the “surfaces” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
Therefore, the corresponding particles in the second family will have a greater mass than the particles in the first family because the “separation”, with respect to a fourth *spatial* dimension of the three-dimensional space manifold associated with them is greater than the “separation” associated with the first family.
Similarly, the corresponding particles in the third family will have a greater mass than those in the second family because the “separation”, with respect to a fourth *spatial* dimension, of the three-dimensional space manifold associated with them is greater than the spatial “separation” associated with the second family.
Additionally the corresponding particle types across the three families have “identical properties” because as shown in the article “The geometry of quarks” Mar. 15, 2009 they are related to the orientation of the “W” axis of the fourth *spatial* dimension with the axis of three-dimensional space. Therefore, each corresponding particle across the three families will have similar properties because the orientation of the “W” axis of the fourth *spatial* dimension with respect to the axis of three-dimensional space is the same for the corresponding particles in all of the families.
This explains why “The corresponding particle types across the three families having identical properties except for their mass, which grows larger in each successive family” in terms of the properties of classical resonance and the field properties of four *spatial* dimensions.
This shows how one can use the field properties of four *spatial* dimension or the Higgs Field to understand the causality of the masses of the fundamental particles in the Standard model in terms of a physical image based on the reality of what we can see and touch in our three dimensional environment.
However assuming the Higgs Field is created by the geometry of four *spatial* dimensional allows one to understand the dynamics of the mass of the Higgs boson in same terms as the fundamental particles defined above.
As mentioned earlier the article “Why is energy/mass quantized?” showed that one can derive the total mass of all particles in terms of the sum of energy contained within a resonant system generated by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension and the energy associated with displacement in the “surface” of three-dimensional space associated the environment it is occupying.
However if one assumes as was done above the Higgs field is created by a spatial displacement in the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension one can conceptually understand how it interacts with space to create its potential energy in terms of the physical image formed by water in a dam. This is because the potential energy of water is defined by its spatial separation with respect to the bottom of a dam. Therefore according to the above theoretical model, the potential energy or mass contained in the Higgs boson would be defined by its spatial separation in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
In other words it gives one the ability to define the energy and therefore the mass of the Higgs bosom and where it should be located in an environment consisting of four *spatial* dimension in terms of the physical image of water in a dam. This is because as mentioned earlier the potential energy of water in a dam is solely dependent on the height of the dam while that of the Higgs Boson would be dependent on magnitude of the spatial separation of the three-dimension space manifold it is occupying with respect to a fourth *spatial* dimension.
This shows how it is possible to understand the reality of the Higgs Field in terms of a physical image by reformatting (as was done in the article “Reformulating space-time” Oct 1, 2013) Einstein General Theory of Relativity in terms of four *spatial* dimensions.
It should be remember that Einstein’s genius allows us to chose weather to view the reality of the Higgs Field,Dark matter (Oct. 15, 2013) or Dark Energy (Mar. 1, 2013) in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of energy/mass and the constant velocity of light.
Copyright Jeffrey O’Callaghan 2013
2007 thru 2010 Paperback