One of the most fundamental questions in physics and cosmology is why the physical constants are what they are.
For example the fine structure constant is one of the about 22 empirical parameters in the Standard Model of particle physics, whose value is not determined within it.
In other words their values are not determined by theory but by experimentation.
An even more puzzling question is why a certain number of them lie within a very narrow range, so that if any were only slightly different, the Universe would be unable to develop matter, astronomical structures, elemental diversity, or life as we presently understand it.
However there are several theoretical models that attempt to explain why we live in a universe that is so fine tuned for life.
For example the Multiverse class of theories assumes the value of the fundamental constants vary randomly though out many different universes and that we happen to live in one that have the values that will support life.
In other words they all assume the existence of many universes, each with randomly chosen physical constants, some of which are hospitable to intelligent life and because we are intelligent beings, we are by definition in a hospitable one.
However all of then suffer from the same problem in that are not verifiable or falsifiable because by definition universes are closed systems and cannot interact with each other. Therefore because they cannot interact with ours there is no way to verify or falsify their existence.
This is why Critics of the Multiverse-related explanations argue that they are unscientific because there is no way to experimentally verify or falsify their existence.
Yet the reason why we live in a universe in which the values of fundamental constants are fine tuned to allow life to developed may not be due to a random property of their origins but may be because they are preordained to have those values by a dynamic resonant property of energy/mass defined by Einstein’s General Theory of Relativity and his equation E=mc^2.
In other words the fundamental constants are what they are because they correspond to the most stable configuration of energy/mass possible.
For example a guitar string has a frequency at which it will naturally resonant at due, in part to the tension it is experiencing, and will, if allowed to, drift towards and stabilize at that optimal value.
Similarly the values of the fundamental constants associated with the resonant structure of energy/mass defined by Einstein would have a tendency to drift towards and stabilize at their optimal value.
However if it is true that the fundament constants are due to a dynamic resonant property of energy/mass one should be able to determine their values, including that of fine structure and cosmological constant by measuring the components of the resonant system it creates.
The dynamic relationship between mass and energy defined by the equation E=mc^2 tell us that they are oppositely directed in the sense that if one increases the other must decrease. However this also tells that whenever they interact a resonant structure would be formed whose fundamental frequency would be determined in part by the "tension" created their oppositely directed components similar to how the frequency of a guitar string also depends on the tension it is under.
This suggest that the magnitude of the fine structure constant may be the result of a resonant structure formed by the "tension" created between the mass and the oppositely directed quantized electrical energy of its components defined by the equation E=mc^2. Additionally because of the dynamic properties of energy/mass discussed above its value will adjust and stabilize around one that defines the optimal resonant structure for those components.
In other words the value of fine structure constant may not be a random feature of our universe but is determine by a dynamic relationship between energy/mass and its quantized components.
However if it is true that the values of all of the fundamental constants are due to resonant property of energy/mass defined by Einstein then, as with the fine structure constant one should also be able to determine the value of the cosmological constant in terms of those resonant properties.
The dynamic relationship between mass and energy describe above tells us that the universe’s expansion would form a resonant structure whose fundamental frequency would be determined by the relative strengths of the "tension" associated with the kinetic energy of its expansion and the gravitational contractive forces associated with its mass. Again this would be similar to how the fundamental frequency at which a guitar string resonates depends upon the tension of its strings.
This means the value of the cosmology constant associated with the universe’s expansion may be related to the dynamic resonant properties of energy and mass and not to some random function as is assumed by most of Multiverse theories.
As mentioned earlier Einstein General Theory of Relativity tells us there is a dynamic balance between the universe’s gravitational potential energy and the kinetic energy associated with its expansion. However, not all of the energy associated with that 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 from us. Therefore, not all of the kinetic energy present at the time of its origin is directed towards its expansion.
Additionally the equation E=mc^2 which defines the equivalence between mass and energy tells us the kinetic energy of the universe’s expansion also posses gravitational potential.
However the law of conservation of energy/mass tells that energy/mass cannot be created or destroyed in a closed environment. This also tells us since, by definition the universe is closed system the kinetic energy of the universe’s energy/mass cannot exceed its gravitational contractive properties of its mass because Einstein tells us that its kinetic energy is made up of that mass.
Therefore 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. Which means 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.
(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" 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 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 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 and oppositely directed with respect to the radiation pressure associated with the heat of its collapse. From this point on the velocity of the contraction will slow due to the radiation pressure and be maintained by the momentum associated with the remaining mass component of the universe.
However, after a certain point in time the heat and radiation pressure generated by its contraction will become great enough to ionize the remaining mass and cause it to reexpand because the expansive forces associated with the radiation pressure will exceed the contractive forces associated with its mass.
This will result in the universe entering an expansive phase and going through another age of recombination when the comic background radiation was emitted. 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 drift and stabilize at a specific value corresponding to its resonant frequency similar to how a guitar string drift and stabilize at it’s resonant frequency
This results in the universe experiencing in a never-ending cycle of expansions and contractions whose frequency would be defined by its resonant properties.
Many cosmologists do not accept this 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 would be analogous to the how momentum of a mass on a spring causes it to stretch beyond its equilibrium point resulting it osculating around it.
There can be no other interpretation if one assumes the validity of the first law of thermodynamics which states that the total energy is a closed system is defined its mass and the momentum of its components. Therefore, when one decreases the other must increase and therefore it must oscillate around a point in space and time.
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.
If this theoretical model is valid the heat generated by the collapse of the universe must raise the temperature to a point where it energy/mass would become ionized into their component parts thereby making the universe opaque to radiation. It would remain that way until it entered the expansion phase and cooled enough to allow them become deionized. This Age of Recombination, as cosmologists like to call it is the causality of the Cosmic Background Radiation.
As mentioned earlier the frequency of the expansions and contractions of all resonant systems is defined by their resonant properties.
Similarly the resonant structure created by the contractive properties of universe’s gravitational potential and the kinetic energy of its expansion will also have a natural frequency which would be determine by resonant properties. Like all resonant structures any frequencies that do not correspond to that value will be attenuated.
Therefore the value of the cosmologic constant which would define the rate or frequency at which the universe is expanding or contracting would be determined by the resonant properties of energy/mass define by Einstein.
In other words the value of its cosmological constant may not be randomly chosen but would be defined by the physical relationship between mass and kinetic energy defined by Einstein.
This means one could experimentally quantify and this scenario by using Einstein equations to determine the value of the cosmology constant based on that relationship and see if it agrees with its observed value.
In other words it is not necessary to assume the existence of multiple universes to understand why fundamental physical constants lie within a very narrow range that allows life to develop because their values may not be random chosen but are preordained to have them by a physical property of energy and mass defines by Einstein.
As mentioned earlier many Critics of the Multiverse-related explanations argue that there is no evidence or any way of verifying or falsifying the existence of other universes.
However we can observe and verify the existence of the resonant properties of energy and mass and if want we have said above is true that values all of the fundamental constants in physics are related to those resonant properties them it would be falsified if it was found that the value of even one of them could not be derived using that concept.
Copyright Jeffrey O’Callaghan 2014
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