Should we let imagination define our reality? If so how much should we allow science to dependent on it?
Most if not all explanatory models of reality rely to some extent on ones imagination because they use unobservable quantities to support them.
For example Einstein used the concept of a space-time dimension to define gravity. However no one has ever directly observed a space-time dimension.
Similarly quantum mechanics describes the interactions of particles in terms of the mathematical probabilities associated with a wavefunction which like a space-time dimension is also unobservable.
In other words both of these theories have imagination as a core component of their explanatory structure.
However there is distinct difference in how they apply it to the environment they are attempting to explain.
For example Einstein in his the "General Theory of Relativity" uses imagination and mathematics to expand a curvature in our observable three-dimension environment to define a four-dimensional space-time universe.
In other words even though its explanatory mechanism is based the existence of a space-time dimension that can only exist in our imagination he was able by using Riemannian geometry mathematically connect to our observable environment.
Similarly Quantum mechanics also uses imagination and mathematics to very accurately describe the particle interaction based on probabilities.
But unlike Relativity it uses a mathematical construct know as the wavefunction to describe the mechanism responsible for the future position of a particle which has no counterpart in our observable environment.
As Steven Weinberg mentioned in his book "Dreams of a Final Theory" the reason this difference in methodology is important is because mathematics in itself is never the explanation of anything because it is only the means by which we use one set of facts to explain another. This is true even though it may be the only the language in which we express them. In other words mathematics should not be used to justify the mathematics of an explanatory model.
However as was just mentioned quantum mechanics uses the mathematics associated with a wavefunction to explain the mathematical mechanism it assumes is responsible for particle interaction.
Why then when mathematics in itself is never the explanation of anything do so many tell us that the mathematical properties of a wavefunction explain the quantum environment.
They do so because to this date it is the only way available to explain and predict how, among many other things chemical process occur and why the particles that were present in the Big Bang, evolved to create the universe we live in even though its entire theoretical structure is based purely on the imagination of those who developed it.
Some may question using the term imagination to describe the mathematical properties of the wavefunction. However its definition of "being the faculty or action of forming new ideas, or images or concepts of external objects not present to the senses" is applicable to them.
This is true even though science can use its abstract mathematical properties to accurately predict the evolution of particle system.
However as we have shown throughout the Imagineer’s Chronicles there may be more to the wavefunction than just mathematics. In other words by using the imagination one may be able to explain or expand the abstract mathematical properties of the wavefunction to the observable properties of our environment similar to how Einstein was able to expand a curvature in our observable three-dimension environment using Riemannian geometry to define a four-dimensional space-time universe.
For example in the article "Why is energy/mass quantized?" Oct. 4, 2007 it was shown one can understand how and why energy/mass is quantized in terms of the observable properties of resonant systems in our three dimensional environment.
Other articles like "Quantum entanglement: a classical explanation" July 15, 2015 clearly shows that the "spooky action at a distance, as Einstein called it can be explained in terms of the laws of classical causality. In other words it is merely an illusion resulting from a lack of understanding of a classic physicality of a quantum environment
Many of the 250 articles published in the Imagineer’s Chronicles over the past nine years show that one can apply the classical laws of our observable environment to a quantum one to explain hoe the mathematical properties of the wavefunction physically describe how particles interact.
Imagination as was mentioned earlier is a critical component of all modern theoretical models of physics. But we must not allow it to be only the only one because it can result in defining an environment that does not describe the reality we are attempting to define.
In other words similar to how Einstein was able to expand a curvature in our observable three-dimension environment to define a four-dimensional space-time universe one must, as we have tried to do make an effort to expand the physical properties of our observable environment to explain the world of quantum mechanics and the wavefunction that defines its environment.
Copyright Jeffrey O’Callaghan 2016
The universe’s most powerful enabling tool is not
knowledge or understanding but imagination
because it extends the reality of one’s environment.
However its scientific effectiveness is closely
related to how strongly it is
anchored in the reality it defines.
Vol. 5 — 2014
Is the quantization of energy/mass a fundamental or an emergent characteristic of reality.
Quantum mechanics assumes that it is fundamental because it defines all interactions within it in terms of its quantized properties while one could say that Einstein’s General Theory of Relativity defines it in terms of an emergent property of continuous space-time manifold because that’s how it defines reality.
Most would agree the best way of which to determine which one is fundamental would be to see if one can be explain in terms of the other.
For example it is impossible to explain the apparent continuous properties of space-time in terms of the discrete properties quantum mechanics associates with energy/mass because by definition something that is discrete cannot by definition be continuous. However it is possible to explain how the continuous properties of space-time can be broken up into the discrete components of energy/mass that allows quantum mechanics to define it in those terms.
Quantum mechanics assumes that energy/mass is quantized based, in part on Schrödinger wave equation which is used to predict and define the quantized energy distribution of electrons in an atom in terms of the Principal number (n), the Angular Momentum "ℓ" (l), Magnetic (m) and Spin Quantum Number(+1/2 and -1/2).
However as mentioned earlier it may be possible to define an emergent mechanism based on the reality of four dimensional space-time that can explain why the energy distribution in a atom is quantized.Yet because quantum mechanics defines its operational environment in terms of the spatial properties of position or momentum and not in terms of temporal properties of time or a space-time environment it would be easier to understand how by redefining that environment in terms of its spatial equivalent
Einstein gave us the ability to qualitatively and quantitatively convert the geometric properties of his space-time environment to an equivalent one consisting of only four *spatial* dimensions when he defined the geometric properties of a space-time universe and the dynamic balance between mass and energy in terms of the equation E=mc^2 and the constant velocity of light. This is because it allows one to redefine a unit of time he associated with energy in his space-time universe to unit of space we believe he would have associated with mass in a universe consisting of only four *spatial* dimensions.
In other words by defining the geometric properties of a space-time universe in terms of the equation E=mc^2 and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.
However this would allow explain how the spatial characteristics of the energy distribution quantum mechanics associated with the four quantum numbers can emerge from reality of environment consisting of four dimensional space-time or its four *spatial* dimension equivalent.
For example in the article "Why is energy/mass quantized?" Oct. 4, 2007 it was shown one can explain the quantum mechanical properties of energy/mass by extrapolating the "reality" of a three-dimensional environment to a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
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 one consisting of four spatial dimensions
The existence of four *spatial* dimensions would give the "surface" of a three-dimensional space manifold (the substance) the ability to oscillate spatially with respect to it 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.
Therefore, these oscillations on a "surface" of three-dimensional space, would meet the requirements mentioned above for the formation of a resonant system or "structure" in space.
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 discreet or incremental values associated a fundamental or a harmonic of the fundamental frequency of its environment.
In other words this defines the quantization or the particle properties of energy/mass in terms of an emergent property of four *spatial* dimensions.
However the fact that one can derive the quantum mechanical properties of energy/mass by extrapolating the resonant properties of a wave in three-dimensional environment to a fourth *spatial* dimension means that one should also be able to derive the quantum numbers that define the properties of the atomic orbitals in those same terms.
As mentioned earlier there are four quantum numbers. The first the Principal Quantum number is designated by the letter "n", the second or Angular Momentum by the letter " ℓ" the third or Magnetic by the letter "m" and the last is the Spin or "s" Quantum Number.
In three-dimensional space the frequency or energy of a resonant system is defined by the vibrating medium and the boundaries of its environment.
For example the energy of a standing wave generated when a violin string plucked is determined in part by the length and tension of its strings.
Similarly the energy of the resonant system the article " Why is energy/mass quantized?" associated with atom orbitals would be defined by the "length" or circumference of the three-dimensional volume it is occupying and the tension on the space it is occupying.
Therefore the physicality of "n" or the principal quantum number would be defined by the fundamental vibrational energy of three-dimensional space that article associated with the quantum mechanical properties of energy/mass.
The circumference of its orbital would correspond to length of the individual strings on a violin while the tension on its spatial components would be created by the electrical attraction of the positive charge of the proton.
Therefore the integer representing the first quantum number would correspond to the physical length associated with the wavelength of its fundamental resonant frequency.
However, classical mechanics tells us that each environment has a unique fundamental resonant frequency which is not shared by others.
Additionally it also tells us why in terms of the physical properties four dimensional space-time or four *spatial* dimensions an electron cannot fall into the nucleus is because, as was shown in that article all energy is contained in four dimensional resonant systems. In other words the energy released by an electron "falling" into it would have to manifest itself in terms of a resonate system. Since the fundamental or lowest frequency available for a stable resonate system in either four dimensional space-time or four spatial dimension corresponds to the energy of an electron it becomes one of the fundamental energy unit of the universe.
This defines physicality of the environment associated with the first quantum number in terms of an emergent property of four *spatial* dimensions and why it is unique for each subdivision of electron orbitals. Additionally observations tell us that resonance can only occur in an environment that contains an integral or half multiples of the wavelength associated with its resonant frequency and that the energy content of its harmonics are always greater than those of its fundamental resonate energy.
This allows one to derive the physicality of the second "ℓ" or azimuth quantum number in terms of how many harmonics of the fundament frequency a given orbital can support.
In the case of a violin the number of harmonics a given string can support is in part determined by its length. As the length increase so does the number of harmonics because its greater length can support a wider verity of frequencies and wavelengths. However, as mentioned earlier each additional harmonic requires more energy than the one before it. Therefore there is a limit to the number of harmonics that a violin string can support which is determined in part by its length.
Similarly each quantum orbital can only support harmonics of their fundamental frequency that will "fit" with the circumference of the volume it occupies.
For example the first harmonic of the 1s orbital would have energy that would be greater than that of the first because as mentioned earlier the energy associated with a harmonic of a resonant system is always greater than that of its fundamental frequency. Therefore it would not "fit" into the volume of space enclosed by the 1s orbital because of its relatively high energy content. Therefore second quantum number of the first orbital will be is 0.
However it also defines why in terms of classical wave mechanics the number of suborbital associated with the second quantum number increases as one move outward from the nucleus because a larger number of harmonics will be able to "fit" with the circumference of the orbitals as they increase is size.
This also shows that the reason the orbitals are filled in the order 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, 5s is because the energy of the 3d or second harmonic of the third orbital is higher in energy than the energy of the fundamental resonant frequency of the 4th orbital. In other words classical wave mechanics tells us the energy of the harmonics of the higher quantum orbitals may be less than that of the energy of the fundamental frequency of preceding one so their harmonics would "fit" into circumference of the lower orbitals
The third or Magnetic (m) quantum number physical defines how the energy associated with each harmonic in each quantum orbital is physically oriented with respect to axis of three-dimensional space.
For example it tells us that the individual energies of 3 "p" orbitals are physically distributed along each of the three axis of three-dimensional space.
The physicality of the fourth quantum or spin number has nothing to do with the resonant properties of space however as was shown in the article "Pauli’s Exclusion Principal: a classical interpretation" Feb. 15, 2012 one can derive its physicality by extrapolating the laws of a three-dimensional environment to a fourth *spatial* dimension.
Briefly the article "Defining potential and kinetic energy?" Nov. 26, 2007 showed all forms of energy including the angular momentum of particles can be defined in terms of a displacement in a "surface* of three-dimensional space manifold with respect to a fourth *spatial* dimension. In three-dimensional space one can use the right hand rule to define the direction of the angular momentum of charged particles. Similarly the direction of that displacement with respect to a fourth *spatial* dimension can be understood in term of the right hand rule. In other words the angular momentum or energy of an electron with a positive spin would be directed "upward" with respect to a fourth *spatial* dimension while one with a negative spin would be associated with a "downwardly" directed one.
Therefore one can define the physically of the fourth or spin quantum number in terms of the direction a "surface" of three-dimensional space is displaced with respect to a fourth *spatial* dimension. For example if one defines energy of an electron with a spin of -1/2 in terms of a downward directed displacement one would define a +1/2 spin as an upwardly directed one.
The physical reason why only two electrons can occupy a quantum orbital and why they have slightly different energies can also be derived by extrapolating the laws of a classical three-dimensional environment to a fourth *spatial* dimension.
There a two ways to fill a bucket. One is by pushing it down and allowing the water to flow over its edge or by using a cup to raise it to the level of the buckets rim.
Similarly there would be two ways fill an atomic orbital according to the concepts presented in the article "Defining potential and kinetic energy?”. One would be by creating a downward displacement on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* to the level associated with the electron in that orbital while the other would be raise it up to that energy level .
However the energy required by each method will not be identical for the same reason that it requires slightly less energy to fill a bucket of water by pushing it down below its surface than using a cup to fill it.
However it also explains why no two quantum particles can have the same quantum number because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement.
Similarly the magnitude of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by two quantum particles with similar quantum numbers would greater than that caused by a single one. Therefore, they will repel each other and seek the lower energy state associated with a different quantum number because the magnitude of the force resisting the displacement will be less for them if they had the same number.
This shows how one can derive the physicality of the four quantum numbers of an emergent property of four *spatial* dimension or its space-time equivalent.
Copyright Jeffrey O’Callaghan 2016
Vol. 5 — 2014