Niels Bohr, the founder of quantum mechanics summarized the complementary principal of quantum mechanics as follows:
"However far the quantum physical phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms. The argument is simply that by the word "experiment" we refer to a situation where we can tell others what we have learned and that, therefore, the account of the experimental arrangements and of the results of the observations must be expressed in unambiguous language with suitable application of the terminology of classical physics.
This crucial point…implies the impossibility of any sharp separation between the behavior of atomic objects and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear…. Consequently, evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be regarded as complementary in the sense that only the totality of the phenomena exhausts the possible information about the object."
In other words he did not think that it was possible to use classical concepts to integrate the wave and particle characteristics of a quantum particle into a single picture therefore he felt that there exits a physical division between the macroscopic world of classical objects and the microscopic world of quantum particles.
However this may not be the true and one can understand why if one views the universe in terms of four *spatial* dimensions instead of four dimensional space-time.
(The reason will become obvious later.)
Einstein gave us the ability to do this when he used the velocity of light to define the geometric properties of space-time because it allows one to convert a unit of time in his space-time universe to a unit of a *spatial* dimension identical to those in our three-dimensional universe . Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.
In other words by mathematically defining the geometric properties of a space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions.
The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions is one bases for assuming as was done in the article “Defining energy?” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
However it also allows one to understand the wave particle duality of energy/mass or its complementary property in terms of the concepts of classical physics.
For example the article, "Why is energy/mass quantized?" Oct. 4, 2007 showed that one can explain and understand the physicality of its particle properties in terms of the classical concept of waves by extrapolating the laws of resonance in a three-dimensional environment to a matter wave moving on “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension. It also explains why all energy must be quantized or exist in these discrete resonant systems when observed.
Briefly it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in a matter wave moving in four *spatial* dimensions.
The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.
These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the 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.
Observations of a three-dimensional environment show the energy associated with resonant system can only take on the incremental or discreet values associated with a fundamental or a harmonic of the fundamental frequency of its environment.
Similarly the energy associated with resonant systems in four *spatial* dimensions could only take on the incremental or discreet values associated a fundamental or a harmonic of the fundamental frequency of its environment.
Therefore these resonant systems in would be responsible incremental or discreet energy associated with quantum mechanical systems.
This allows one to define the particle properties of energy/mass in terms of the classical concepts of a wave.
However, one can define its wave properties in terms of the classical concepts of a particle in terms of the boundaries of its resonant structure.
In classical physics, a point on the two-dimensional surface of paper is confined to that surface. However, that surface can oscillate up or down with respect to three-dimensional space.
Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate "up" or "down" with respect to a fourth *spatial* dimension.
The confinement of the "upward" and "downward" oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries of the resonant system associated with a particle in the article "Why is energy/mass quantized?"
However it also defines the particle properties of waves in terms of the classical concept of resonant properties of a box because its physical properties define its frequency and energy.
This also provides the ability to understand the inseparability of the wave particle duality of energy/mass because it clearly demonstrates how one is depend on the other.
However it also explains why quantum systems either display the properties of a particle or a wave when measured because if one wants to measure the total energy contained in a given volume of space one will observe it as a particle while if one want to measure how it is propagated through space one must observe its wave properties.
Additionally it defines a classical reason why particles sometimes behave like wave and sometimes like particle and why it is impossible simultaneously observe these two different properties.
As shown earlier the energy contained in a quanta of space associated with a particle would be defined by the energy associated with the wavelength of its resonate structure. In other words to observe or measure the particle properties of a given volume of space one has to sample all of its energy leaving nothing of its wave component to measure. Similarly if one wants to observe or measure fully the wave energy of a quantum of space one would have to sample all of its energy leaving none of its particle properties.
(If one does not want to observe all of the energy in a given volume of space then one would expect that the difference would be made up by the emission of a photon or other particle whose energy would correspond to that difference.)
The reason why one cannot simultaneously measure both its wave and particle properties is because as mentioned the energy of a particle is defined by the wave properties of its resonant structure. Since the resonant system that defines a particle is the smallest unit of its resonate structure if one measures its particle properties there would be no wave energy left for measuring its wave proprieties while if someone measure its wave energy there would be no energy left to support its particle properties. Therefore making one of these measurements precludes the other.
This demonstrates how one can integrate the wave and particle characteristics of a quantum particle into a single picture and why the physical division between the macroscopic world of classical objects and the microscopic world of quantum particles as was assumed by Bohr many not exist.
Copyright Jeffrey O’Callaghan 2014
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