Deriving the fundamental constants of nature

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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 them 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 value of all of the fundamental constants are due to resonant property of energy/mass defined by Einstein then one should be able to determine there values in terms of those resonant structures.

Einstein gave us the ability to do this when he not only defining the resonant properties energy/mass in his General Theory of Relativity but also the those of the entire universe because they  tells us that its present expansion must come to an end!!

Einstein’s 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 some 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.

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 that 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.

Some 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 know from observations that heat is generated when we compress a gas and that the 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 its 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 gravitational potential and 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 fundamental constants would define the rate or frequencies 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 those 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.

Later Jeff

Copyright Jeffrey O’Callaghan 2014

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