3. Quantum Theory – Unifying Quantum and Relativistic Theories

Should we allow imagination to define physics?

jeffocal — Thu, 15 Dec 2016 08:51:34 +0000

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 The Road to Unification 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 The Road to Unification 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.

Later Jeff

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.

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Quantum mechanics as an emergent property of space-time.

jeffocal — Tue, 15 Nov 2016 09:33:06 +0000

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 SchrÃ¶dinger 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 “â„“” (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 relativistic properties of a space-time environment to an equivalent one consisting of only four *spatial* dimensions when he defined its geometric properties 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 in one consisting of only four *spatial* dimensions.

In other words by 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 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 ” â„“” 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 “â„“” 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?â€. 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.

Later Jeff

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Did Einstein predict Quantum Entanglement in 1905?

jeffocal — Mon, 15 Aug 2016 09:47:27 +0000

Quantum entanglement is defined “as a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot be described independently instead, a quantum state may be given for the system as a wholeâ€.

Einstein referred to this as “spooky action at a distance” because it assumed that particles can interact instantaneously, regardless of distance separating them which according to his perception of reality this was not possible.
However if one accepts the reality of the space-time universe defined by Einstein one would realize that according the core principals of his theories there is nothing spooky about action at distance relative to an observers velocity.Â

Even so he was so convince that he co-authored a paper with Podolskyâ€“Rosen whose intent was to show that if Quantum Mechanics was a valid theory it could not be complete because it does not agree with most people’s perception of reality. The first thing to notice is that Einstein was not trying to disprove Quantum Mechanics in any way. In fact, he was well aware of its power to predict the outcomes of various experiments. What he was trying to show was that there must be a “hidden variable” that would allow Quantum Mechanics to become a complete theory of nature

The argument begins by assuming that there are two systems, A and B (which might be two free particles), whose wave functions are known. Then, if A and B interact for a short period of time, one can determine the wave function which results after this interaction via the SchrÃ¶dinger equation or some other Quantum Mechanical equation of state. Now, let us assume that A and B move far apart, so far apart that they can no longer interact in any fashion. In other words, A and B have moved outside of each other’s light cones and therefore are spacelike separated.

With this situation in mind, Einstein asked the question: what happens if one makes a measurement on system A? Say, for example, one measures the momentum value for it. Then, using the conservation of momentum and our knowledge of the system before the interaction, one can infer the momentum of system B. Thus, by making a momentum measurement of A, one can also measure the momentum of B. Recall now that A and B are spacelike separated, and thus they cannot communicate in any way. This separation means that B must have had the inferred value of momentum not only in the instant after one makes a measurement at A, but also in the few moments before the measurement was made. If, on the other hand, it were the case that the measurement at A had somehow caused B to enter into a particular momentum state, then there would need to be a way for A to signal B and tell it that a measurement took place. However, the two systems cannot communicate in any way!

If one examines the wave function at the moment just before the measurement at A is made, one finds that there is no certainty as to the momentum of B because the combined system is in a superposition of multiple momentum eigenstates of A and B. So, even though system B must be in a definite state before the measurement at A takes place, the wave function description of this system cannot tell us what that momentum is! Therefore, since system B has a definite momentum and since Quantum Mechanics cannot predict this momentum, Quantum Mechanics must be incomplete.

In response to Einstein’s argument about incompleteness of Quantum Mechanics, John Bell derived a mathematical formula that quantified what you would get if you made measurements of the superposition of the multiple momentum eigenstates of two particles. If local realism was correct, the correlation between measurements made on one of the pair and those made on its partner could not exceed a certain amount, because of each particle’s limited influence on the other.

In other words he showed there must exist inequities in the measurements made on pairs of particles that cannot be violated in any world that included both their physical reality and their separability because of the limited influence they can have on each other when they are “spacelike” separated.

When Bell published his theorem in1964 the technology to verify or reject it did not exist. However in the early 1980s, Allen Aspect performed an experiment with polarized photons that showed that the inequities it contained were violated.

This meant that science has to accept that either the reality of our physical world or the concept of entanglement does not exist because they are mutually excessive.

However Einstein himself predicted the entanglement of particles that are moving at the velocity of light no matter how far apart they are in his Special Theory of Relativity because he showed us thatÂ the separability or the distance between two points is dependent on the velocity of the observer with respect to what is being observed.

For example his theory tells the distance between the two objects A and B would be defined by their relative speed with respect to an observer.

Specifically he told us that it would be defined by

However this tell us the distance or length between observations measured between two photons or any particle moving at the speed of light from the perspective a photon would be zero no matter how far those observation might from the perspective of the observers making them because according to the concepts of relativity one could view the photons as being stationary and the observers as moving at the velocity of light.Â This is true even if they are moving in opposite directions.

Therefore according to Einstein’s theory all photons which are traveling at the speed of light are physical entangled with all other photons that originated within a common system no matter how far apart or “spacelike” separated they may appear to be to all observers who are not traveling at the speed of light.

In other words inequities in the measurements made on pairs of photons should be violated in a world containing the physical reality of Einstein’s theory and separability because they are not “spacelike” separated when viewed from all reference frames which is not traveling at the speed of light.

This tells us that the hidden variable that would allow Quantum Mechanics to become a complete theory of nature is Einstein Theory of Relativity or the Relativistic properties of motion.

Additionally if quantum entanglement did not occur for photons that were space like separated then the physical reality of Einstein space-time universe as defined by his theory of Relativity must be discarded

One method for determining if this is the reason why Allen Aspect observed polarized photons violated Bells inequities would be to see if they are also violated by particles that were traveling slower that the speed of light because they would according to the Theory of Relativity could be “spacelike” separated.

In others words if it was observed that particles which were not traveling at the speed of light did not violate Bell’s inequity then it would support Einstein perception of reality and provide a physical verification for the causality in terms of the existence of space-time for one of the most puzzling aspects of quantum mechanics; that of quantum entanglement.

However if it is found that bell’s inequity is violated by particles moving slower than the speed of light then Einstein’s perception of reality would be invalidated because it demands that things which are “spacelike” separated can only have a limited influence one each other.

Yet one must be careful when performing the calculations because the distance separating the particles would not be determined by the distance between the end points as viewed by the experimenter but by relativistic distance as viewed from the particles,

Later Jeff

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The relevance of classical mechanics to a quantum environment.

jeffocal — Mon, 01 Aug 2016 12:24:57 +0000

Presently there is disconnect between our understanding of the probabilistic world of quantum mechanics and the classical one of causality because it can predict with precision the future position of an object while the other cannot.

However this may just be an illusion resulting from a lack of understanding of the quantum environment.

One of the fundament areas where this disconnect appears is in the probabilistic interpretation SchrÃ¶dinger wave equation

However one could eliminate this disconnect if one could explain the causality of those probabilities in terms of a physical image based on the laws of classical physics similar to how we explain the causality of the movement of the planets around the sun in terms of a physical image of a curvature in space-time.

Granted this will not change the fact that one cannot use quantum mechanics to make precise predictions of future events but it would give us a physical reason why we cannot in terms of our classical understanding of causality.

One way of accomplishing this would be look at the physically observable properties of all quantum systems and determine if by applying the laws of causality in a classical environment one can explain the reason for the probabilities associated with SchrÃ¶dinger’s equation.

For example in 1924 Louis de Broglie theorized that all quantum objects are physically composed of a wave as was verified by 1927 by Davisson and Germer) when he observed electrons diffracted by crystals.

However, the fact that no one has been able to physically connect the causality of those observable properties to the probabilities of all quantum systems does not change the fact that there must be one because if there wasn’t they could not interact with our environment to create the physically observable properties of the world upon which those probabilities are determined.
One reason for this failure may be due to the fact that those probability are related to the spatial not time dependent properties of the wave function.

If so one may be able to establish the connection by looking at it in terms of its spatial properties instead of the space-time ones associated with Einstein’s theories.

Einstein gave us the ability to do this when defined the geometric properties of space-time in terms of the constant velocity of light because that provided a method of converting a unit of time in a space-time environment of unit of space in four *spatial* dimensions. Additionally because the velocity of light is constant he also defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

The fact that one can use Einsteinâ€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 â€œDefining energy?â€ 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 doing so would have allowed Louis de Broglie to physically define the casualty of the quantum properties associated with SchrÃ¶dinger equation in terms of a physical or spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension as was done in the article “Why is energy/mass quantized?” Oct. 4, 2007.

Briefly, that article showed the quantized properties of energy/mass are the result of a resonant system formed by a matter “wave” on a “surface” of a three-dimensional space manifold with respect to fourth “spatial” dimension. This is because it showed the four conditions required for resonance to occur in a three-dimensional 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 made up of four.

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* dimension thereby fulfilling one of the requirements for classical resonance to occur.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established on a surface of a three-dimensional space manifold.

Yet the classical laws of three-dimensional space tell us the energy of resonant systems can only take on the discontinuous or discreet energies associated with their fundamental or harmonic of their fundamental frequency.

However, these are the similar to the quantum mechanical properties of energy/mass in that they can only take on the discontinuous or discreet energies associated with the formula E=hv where “E” equals the energy of a particle “h” equal Planck’s constant “v” equals the frequency of its wave component.

In other words Louis de Broglie would have been able to physicality connect the properties of his particle waves to the quantum mechanical properties of SchrÃ¶dinger equation in terms of the discrete incremental energies associated with a resonant system in four *spatial* dimensions if he had assume space was composed of it instead of four dimensional space-time.

Yet it also would have allowed him to define the physical boundaries of a quantum system in terms of the geometric properties of four *spatial* dimensions.

For example in classical physics, a point on the two-dimensional surface of a piece 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 â€œupâ€ or â€œdownâ€ with respect to a fourth *spatial* dimension.

The confinement of the â€œupwardâ€ and â€œdownwardâ€ oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries associated with a particle in the article “Why is energy/mass quantized?” Oct. 4, 2007.

As mentioned earlier in the article â€œDefining energy?â€ Nov 27, 2007 showed 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 assuming the energy associated with Louis de Broglie particle wave is result of a displacement in four *spatial* dimension instead of four dimensional space-time as was done earlier would allow one to define a classical causality for quantum probabilities in terms the observable environment we inhabit.

Classical mechanics tell us that due to the continuous properties of waves the energy the article “Why is energy/mass quantized?” Oct. 4, 2007 associated with a quantum system would be distributed throughout the entire “surface” a three-dimensional space manifold with respect to a fourth *spatial* dimension.

For example Classical mechanics tells us the energy of a vibrating or oscillating ball on a rubber diaphragm would be disturbed over its entire surface while the magnitude of those vibrations would decrease as one move away from the focal point of the oscillations.

Similarly if the assumption that quantum properties of energy/mass are a result of vibrations or oscillations in a “surface” of three-dimensional space is correct then classical mechanics tell us that those oscillations would be distributed over the entire “surface” three-dimensional space while the magnitude of those vibrations would be greatest at the focal point of the oscillations and decreases as one moves away from it.

As mentioned earlier the article â€œWhy is energy/mass quantized?â€ shown a quantum particle is a result of a resonant structure formed on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Yet Classical Wave Mechanics tells us resonance would most probably occur on the surface of the rubber sheet were the magnitude of the vibrations is greatest and would diminish as one move away from that point,

Similarly a particle would most probably be found were the magnitude of the vibrations in a “surface” of a three-dimensional space manifold is greatest and would diminish as one move away from that point.

This shows that one can define the causality of the probabilities associated SchrÃ¶dinger wave equation in terms of the laws of causality associated with our observable environment by redefining them in terms of four *spatial* dimensions.

In other words one can eliminate the disconnect between the probabilities associated his equation and a classical environment by defining their causality in terms of the laws of classical physics.

It should be remember Einsteinâ€s genius allows us to choose to define a quantum system in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories thereby giving us a new perspective on the probabilistic properties of a quantum environment and how they physically connected to our observable universe.

Later Jeff

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Infinities: what do they mean for Quantum theory.

jeffocal — Tue, 01 Mar 2016 09:20:41 +0000

Something that is infinite or the quality of having no limits or end cannot exist or be a part of the physically observable environment we live in primarily because it is finite.

Some might disagree by pointing out that we cannot know the full extent of our universe because the speed of light puts limits on our ability to observe parts beyond a specific point. However some could also argue that anything beyond that point is not in our observable universe and because of that it cannot be a part of it.

Yet even though Einstein’s theories does not mathematical rule out the possibility of an infinite universe it does not predict that one exists.

However the same cannot be said of Quantum Mechanics which mathematical defines mass, energy and forces in terms of a one dimensional point. Infinities arise because the forces and energies associated with the integrals which define them become larger as they approach each other reaching infinity when they come in contact.

The difference between these quantum mechanical infinites and relativistic ones is that they occur with the limits of our observable universe. In other words it predicts existence of masses, forces, and energies that are infinite within its finite boundaries.

Some might think this indicates the basic concepts of quantum mechanics that define our in terms of the mathematical properties of a one dimensional point is incorrect because most physicists and mathematicians would agree that the infinite entity cannot exist in a finite environment.

However its proponents disagree and have devised a clever method called renormalization which alters the mathematical relationships between the parameters in the theory to make these infinites disappear.

Granted even though one may be able to use renormalization to alter the mathematical relationships between point particles to eliminate infinites they cannot change the fact the point particle responsible for those infinities still exists before those alterations take place. In other words it assumes they exist before renormalization takes place because if they did not there would be no need for renormalization. Therefore even though the process of renormalization solves the mathematical problem of infinities it does nothing to solve the conceptual one that exist within the framework of quantum mechanics because it relies on the existence of point particles which as mentioned earlier are responsible for the infinites. `

Why then are we still using it to explain or predict that reality?

The most probable answer is because it predicts with amazing precision the results of every experiment involving the quantum world that has ever been devised to test it: so much so that many are willing to overlook the obvious fact that as was just mentioned the conceptual arguments use to make those predictions have a fatal flaw.

However we are not going to concern ourselves with resurrecting the conceptual content of quantum mechanics as has been the focus of the past three quarters of a century but instead will define another theory that can explain the behavior of energy/mass in terms of the properties of our observable environment in a way that eliminates the need for any “adhco” procedures such as renormalization to make it consistent with that behavior.

To do this one must be able to, in a logical and consistent manner using only the physical laws of our observable environment explain the existence of the four basic components of a quantum world: the fact that energy/mass is quantized, Planck’s constant, Heisenbergâ€s Uncertainty Principle and the reason one can use probabilities to define a particles position.

For example in the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown it is possible to explain and predict the quantum mechanical properties of energy/mass associated with SchrÃ¶dinger’s wave function by extrapolating the laws of classical resonance in a three-dimensional environment to a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

(Note: Einstein has already gave us a detailed mathematical description of this environment when he used the constant velocity of light to define the geometric properties of space-time because it allows one to convert a unit of time in his four dimensional space-time universe to a unit of space in a one consisting of only four *spatial* dimensions. Additionally because the velocity of light is constant it is possible to mathematically derive a one to one correspondence between his space-time universe and one made up of only four *spatial* dimensions.)

(Louis de Broglie was the first to theorize that all particles are made up of matter waves. His theories were later confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.)

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.

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 the energy of a resonant system can only take on the discrete or quantized values associated with its resonant or a harmonic of its resonant frequency.

This shows how one can conceptually derive the quantum mechanical properties energy/mass in terms of wave properties of particles observed by Davisson and Germer by assuming that they are a result of resonant properties of four *spatial* dimensions.

In other words if one assumes as is done here that its mathematical properties of SchrÃ¶dinger’s wave function are representative of wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension one can form a physical image of why energy/mass is quantized in terms of the properties of our observable environment.

However it also gives one the ability to define the physical boundaries of a particle and its energy in terms of the observable properties of our environment

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 geometric boundaries or the “box” containing the wave component of SchrÃ¶dinger’s wave function the article “Why is energy/mass quantized?” Oct. 4, 2007 associated with a particle.

As mentioned earlier infinites arise in Quantum Mechanics when one applies the concept of mathematical one dimensional point to define mass, energy and forces results their integrals to become increasing larger as they approach each other reaching infinity when they come in contact.

However the above theoretical concepts provides a solution because it shows that a particle’s energy is not confined to a one dimension point but instead exists in an extended spatial volume associated with its resonant structure.

Yet if true one must be able derive the physical meaning the other fundamental concepts of quantum mechanics like Planck’s constant or 6.626068 Ã— 10^-34(kg*m2/s), Heisenbergâ€s Uncertainty Principle and the probabilities associated with SchrÃ¶dinger’s wave function by extrapolating the laws of classical physics in a three-dimensional environment to a fourth *spatial* dimension.

Planck’s constant is one of fundamental components of Quantum Physics and along with Heisenbergâ€s Uncertainty Principle it defines the uncertainty in the ability to measure more than one quantum variable at a time. For example attempting to measure an elementary particleâ€s position (â–²x) to the highest degree of accuracy leads to an increasing uncertainty in being able to measure the particleâ€s momentum (â–²p) to an equally high degree of accuracy. Heisenbergâ€s Principle is typically written mathematically as â–²xâ–²p Â³ h / 2 where h represents Planck constant

As mentioned earlier the resonant wave that corresponds to the quantum mechanical wave function defined in the article “Why is energy/mass quantized?” Oct. 4, 2007 predicts that a particle will most likely be found in the quantum mechanical “box” whose dimensions would be defined by that resonant wave. However quantum mechanics treats particles as a one dimensional points and because it could be anywhere in it there would be an inherent uncertainty involved in determining the exact position of a particle in that “box”.

For examine the formula give above ( â–²xâ–²p Â³ h / 2 ) tells us that uncertainty of measuring the exact position of the point in that “box” defined by its wavefunction would be equal to â–²xâ–²p Â³ h / 2. However because we are only interested in determining its exact position we can eliminate all references to its momentum.

However if we eliminate the momentum component from the uncertainty in a particle position become 6.626068 Ã— 10^-34 meters or Planck’s constant.

As mentioned earlier the uncertainty involved in determining the exact position of a particle is because it is impossible to determine were in the “box” defined earlier the quantum mechanical point representing that particle is located. However as mentioned earlier Planck’s constant tells us that one cannot determine the position of a particle to an accuracy greater that 6.626068 Ã— 10^-34. This suggest that Planck constant 6.626068 Ã— 10^-34 defines the physical parameters or dimensions of that “box” because it defines the parameters of where in a given volume of space a quantum particle can be found.

In other words it defines a physical interpretation of Planck’s constant or 6.626068 Ã— 10^-34(kg*m2/s), and Heisenbergâ€s Uncertainty Principle by extrapolating the observable properties and laws of our three-dimensional environment to a fourth *spatial* dimension.

However it also gives one the ability to connect the probabilities associated with SchrÃ¶dinger’s wave function to the observable reality of our three-dimensional environment.

As was mentioned one can conceptually derive the quantum mechanical properties of his function in terms of physical properties of a mater wave observed by Davisson and Germer by assuming that they are a result of resonant properties of four *spatial* dimensions.

For example Classical mechanics tells us that the energy of a vibrating or oscillating ball on a rubber diaphragm would be disturbed over its entire surface while the magnitude of those vibrations would decrease as one move away from the focal point of the oscillations.

As mentioned earlier the article “Why is energy/mass quantized?” Oct. 4, 2007 shown a quantum object is a result of a resonant structure formed on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This shows how one can eliminate infinities from our understanding of the quantum properties of energy/mass while at the same time allow one to connect those properties to the observable realities of our environment.

Later Jeff

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Why does space exist?

jeffocal — Thu, 01 Oct 2015 09:00:18 +0000

The Standard Model of Particle Physics and Quantum Mechanics give us a plausible reason why particles are what they are while Einstein theories give a reasonable answer to the question regarding why they come together to form planets stars and how they move in relation to each other.

For example both Einstein’s General Theory of Relativity define existence in terms of a space-time geometry. However it only defines the forces it encompasses and not how they come together to create space or as John Wheeler put it “Matter tells space how to curve. Space tells matter how to move.”

But this does not tell us what space is made of it only tells us how matter interacts with it to cause it to move in the space-time environment defined by him.

Granted it is possible in the abstract mathematical world of Einstein’s theories to fully define an environment without addressing the question as to why it is there as he seems to have done. However his theories are based on a universe where cause and effect rule. Therefore if they are valid one should be able to define why it exists in terms of those parameters.

However Einstein also told us that in a space-time environment there is a causal link between mass and energy defined by E=mc^2 and space. For example converting energy to mass causes the curvature in space-time to increase while changing mass to energy causes it to decrease.

This suggest that their maybe a causal link between mass and the existence of space.

However it is difficult to form a clear picture of how mass can interact with time to create space because as was shown in the article “Defining what time is” Sept. 20, 2007 most view time not in terms of the physical properties of space but as an irreversible physical, chemical, and biological change in it. Therefore it is difficult to understand how these abstract properties of change can interact with mass to create the physicality of the world we live in.

However Einstein gave us the ability to solve this dilemma and develop more direct understanding of how and why mass can interact with the physical geometry of our universe to form space when he used the equation E=mc^2 and the constant velocity of light to define the geometric properties of mass in a space-time universe. This is because that provided a method of converting a unit of time in a space-time to unit of space in four *spatial* dimensions. Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

This makes it possible as was shown in the article â€œDefining energyâ€ Nov 27, 2007 to derive all forms of motion caused by mass, in terms of a physical displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

In other words one can use Einsteinâ€s theories to redefine how and why mass can tell space how to curve and how space tells matter how to move based exclusively on the physicality most associate with space instead of non-physical properties of time.

However this also provides a way of understanding why space is here in terms of an interaction between matter and energy defined by Einstein.

For example when the air in a balloon is cooled it becomes more concentrated the magnitude of the curvature in its surface increases and its volume decreases while heating it causes it to expand resulting in decreasing its curvature and increasing its size.

In other words the balloon owes its existence and structure to the dynamic forces of the air pushing its two dimensional “surface” towards a third dimension because if they were not there it could not maintain in physical structure.

Similarly Einstein theories tell us if mass is converted to energy the magnitude of the curvature in space-time and the strength of the gravitational field associated with it decreases while converting energy to mass causes an increase in the curvature of space-time and the gravitational field associated with it.

Yet as mentioned earlier it is difficult to form a clear picture of how three-dimensional space can interact with time to form the structural boundary by which the dynamic forces of energy and mass can push against to causes its curvature to change because of its abstract properties.

However one can develop a much clearer understanding of how the dynamic properties of mass and energy can interact to create the physical structure of space if one redefines Einstein space-time universe as was done earlier to its equivalent in four spatial dimensions.

For example as mentioned earlier the structure of a balloon is the result of its two-dimensional membrane or manifold restricting or preventing the air in the balloon from moving freely in the third spatial dimension.

Similarly the “surface” of a three-dimensional manifold would present a barrier for all things made up of mass from moving freely in to the fourth *spatial* dimension because they are three dimensional objects.

However it also gives one the ability to form a physical image of why space is there in terms of the energy contain space pushing on the “surface” of a three-dimensional manifold causing it to expand towards a fourth *spatial* dimension.

In other words similar to a balloon when energy becomes more concentrated in the form of mass the curvature in the surface of space increases and its volume to decreases while making it less concentrated by changing mass to energy causes it to expand resulting in decreasing its curvature and increasing its physical size.

Thus suggests that space exists because of a interaction of mass and energy with the physical geometry of our universe.

It should be remember these same concepts can applied to universe consisting four dimensional space-time because as was shown earlier Einstein gave us the ability to define the physical relationship be energy, mass and the geometry properties of space in terms of either its spatial or time properties.

In other words the existence of three-dimensional space depends on the energy pushing the “surface” of a three-dimensional space manifold towards a higher fourth dimension which can ether be made up of time or another spatial dimension.

It should also be remember that the reason for this article was not to define the what space is made or what its geometry is only why it is here. Those questions will be answered in future articles.

Later Jeff

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The physical meaning of Schrödinger wave equation

jeffocal — Sat, 01 Aug 2015 09:52:42 +0000

Quantum mechanics defines our observable environment only in terms of the probabilistic values associated with SchrÃ¶dingerâ€s wave equation.

However it is extremely difficult to define a set of statements which explains how those probabilities are physically connected to it even though it has held up to rigorous and thorough experimental testing.

This may be the reason most physicists consider quantum mechanics only in terms of its mathematical formalization instead trying to understand the meaning of it in terms of the space-time environment we occupy.
For example in 1924 Louis de Broglie was the first to realize all particles are physically composed of a matter wave as the discovery of electron diffraction by crystals in 1927 by Davisson and Germer) verified. However in his paper, â€œTheory of the double solutionâ€œ he unsuccessfully attempted to define a physical interpretation of SchrÃ¶dinger equation in classical terms of space and time.

As is pointed at his biography on the nobleprize.org web site in “1951, he together with some of his younger colleagues made another attempt, one which he abandoned in the face of the almost universal adherence of physicists to the purely probabilistic mathematical interpretation of, Bohr, and Heisenberg.”

However the fact that no has been able to physically connect those probabilities to our environment does not change the fact that there must be one because if there wasn’t they could not interact with it to create the physicality of observable world upon which those probabilities are based.

As mentioned earlier Louis de Broglie and his colleagues tried unsuccessfully to find a physical interpretation of SchrÃ¶dinger equation in classical terms of space and time.

However the reason for their failure may be due to the fact that it is related to the spatial not time dependent properties of the wave function.

If so one may be able to establish the connection by looking at it in terms of its spatial properties instead of the space-time one Louis de Broglie and his colleagues used.

Einstein gave us the ability to do this defined the geometric properties of space-time in terms of the constant velocity of light and a dynamic balance between mass and energy because that provided a method of converting a unit of time in a space-time environment of unit of space in four *spatial* dimensions. Additionally because the velocity of light is constant he also defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

This would have allowed Louis de Broglie to physically connect the probabilities associated SchrÃ¶dinger equation to the quantum properties of a matter wave in terms of a physical or spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension as was done in the article “Why is energy/mass quantized?” Oct. 4, 2007.

Briefly that article showed that one can do this by assuming they are caused by the formation of a resonant system on a “surface” of a three-dimensional space manifold with respect to fourth “spatial” dimension. This is because it showed the four conditions required for resonance to occur in a three-dimensional 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 made up of four.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established on a surface of a three-dimensional space manifold.

In other words Louis de Broglie would have been able to physicality connect the the quantum mechanical properties of his particle waves to SchrÃ¶dinger equation in terms of the discrete incremental energies associated with a resonant system in four *spatial* dimensions if he had assume space was composed of it instead of four dimensional space-time.

Yet it also would have allowed him to define the physical boundaries of a quantum system in terms of the geometric properties of four *spatial* dimensions.

However assuming the energy associated with Louis de Broglie particle wave is result of a displacement in four *spatial* dimension instead of four dimensional space-time as was done earlier would allows one to connect the probabilities associated with SchrÃ¶dinger equation to the physicality of our observable environment we all live in.

For example Classical mechanics tells us that the energy of a vibrating or oscillating ball on a rubber diaphragm would be disturbed over its entire surface while the magnitude of those vibrations would decease as one move away from the focal point of the oscillations.

This shows how one can physically connect the probabilities associated SchrÃ¶dinger wave equation to our observable environment by redefining it in terms of four *spatial* dimensions.

Later Jeff

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An Aristotelian perspective on Dark Matter and Quantum Mechanics

jeffocal — Mon, 01 Jun 2015 09:01:56 +0000

Many of us would define nothing as being the absence of everything.

One would think that some as simple as that would be easy to define.

However history has shown that it is not the case.

For example Parmenides argued that “nothing” cannot exist because to speak of a thing, one has to speak of a thing that exists. Therefore nothing (or empty space) cannot exist because one cannot speak of it.
While Aristotle countered the logical problem posed by Parmenides by distinguishing things that are matter and things that are space. In this scenario, space is not “nothing”, but a receptacle in which objects of matter can be placed. Therefore the void (as “nothing”) is different from space and is removed from consideration.

However understanding the difference between space and “the void” or nothing not only had relevance to the Greek philosophers but also to modern scientists because the science of “nothing” is an integral part of modern theories of our universe.

For example both Einstein’s General and Special Theories of Relativity define existence in terms of a space-time geometry. However it only defines the forces it encompasses and not what they were acting on or the material aspects of their environment. In other words it defines them in terms of existence of “nothing”.

Granted it is possible in the abstract mathematical world of Einstein’s theories to fully define an environment in terms of nothing, as he seems to have done however we do not live in that world we live in the real world in which forces can only act on physical objects.

One could also consider the other bed rock of modern science or quantum mechanics as being based on the existence of nothing because it defines a reality in which particles do not exist until an observation is made. In other words it assumes they materialize out of nothing at a specific point in space.

However if one assumes that forces are the result of an interaction between space and time as Einstein did then one also must assume that space cannot be made up of nothing because if it was one would have to also assume that forces are also made up of nothing. Therefore they could not exist because as Parmenides point out “nothing” cannot exist.

The fact that Einstein was aware of this was made evident in the speech “Aether and the theory of Relativity” he made on May 5th 1920 at the University of Leyden Germany where he indicated “The General Theory of Relativity predicts, that “space is endowed with physical qualities” “Recapitulating, we may say that according to the General Theory of Relativity space is endowed with physical qualities; in this sense, therefore, there exists something he called Aether. According to the General Theory of Relativity space without it is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time, nor therefore any space-time intervals in the physical sense.”

Yet it is difficult to form a clear picture of how the something that makes up space or the “ponderable media” Einstein mention above can interact with time because as was shown in the article “Defining what time is” Sept. 20, 2007 time is not perceived by most as matter or a “ponderable media” as Einstein called it but only as an irreversible physical, chemical, and biological change in physical space. Therefore it is difficult to understand how these abstract properties could interact with space to create the physicality of the world we live in.

However Einstein gave us the ability to solve this dilemma and develop more direct understanding of how and why space and time can interact with when he used the equation E=mc^2 and the constant velocity of light to define the geometric properties of matter in a space-time universe. This is because that provided a method of converting a unit of time associated with energy in a space-time dimension to unit of space in four *spatial* dimensions. Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

This makes it possible as was shown in the article â€œDefining energyâ€ Nov 27, 2007 to derive all forms of energy and forces, including gravitational in terms of a physical displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension

In other words one can use Einsteinâ€s theory to redefine forces and how they interact to create our world based exclusively on the physicality most associate with space instead of non-physical properties of time.

For example, we know from observations water in a dam exerts a force on its walls which is stationary with respect to time. Therefore it cannot be logically explained in terms of Einstein’s space-time environment because the water is not moving thought time yet it still generates force.

However this problem is irreverent if one views all forces including those that do not vary with time, such as forces created by water in a dam as was done in the article â€œDefining energyâ€ Nov 27, 2007 in terms of the physical separation of a three-dimensional volume with respect to a fourth *spatial* dimension because it shows how they can interact with geometric property of space to create them

Yet this still does not tell us what the “nothing” Aristotle told us that the objects of matter can be placed in is made of.

Einstein gave us a clue when he showed that there exists a dynamic balance between energy, mass and the surface of three-dimensional space similar to the balance that exists between the air in a balloon and its surface.

For example when the air pressure in a balloon is reduced by cooling and becomes more concentrated the magnitude of the curvature in its surface increases while heating it causes it to expand resulting in decreasing its curvature.

Similarly Einstein theories tell us if one views them in terms of their spatial instead of their time properties as was done â€œDefining energyâ€ Nov 27, 2007 when energy is concentrated in the form of mass, the energy pressure on the “surface” of three-dimensional space is reduced thereby increasing magnitude of its curvature and the strength of the gravitational field associated with it while decreasing the mass in a given volume of space by converting it to energy causes space to expand thereby decreasing its curvature and the gravitational field associated with that volume.

In other words Aristotle would say the receptacle or space which matter objects such as all of the particles known to science occupy is made up geometric properties of space which is supported by a dynamic balance between mass and energy.

Some may disagree by claiming that all of a particle’s energy/mass is concentrated in its volume and that the intervening space contains nothing.

However observations suggest otherwise.

For example we know that gravitational and electrical energy permeate space therefore we cannot say that it is empty because it does contain energy which according to Einstein also has the properties of mass or the substance he referred to in his speech mentioned earlier.

However this means that space is not composed of nothing as many of the proponents of Einstein theories believe but is made up of energy/mass.

Yet If one accepts the Aristotelian perspective that space is not nothing and the logic of the arguments presented above then Einstein does not leave us much choice but to assume â€œthe voidâ€ or the space between particles is made up of energy/mass which would according to his theories posses gravitation potential.

In other words the Aristotelian philosophy that space is not “nothing”, but a receptacle in which objects of matter (or energy) can be placed provides a basis for assuming that a portion of the gravitational potential associated with Dark matter may not be due to the existence of particles but due to the existence of space itself.

However Aristotelian belief that the “nothing” many call space is something also provides the conceptual foundation for the quantum mechanical properties of energy/mass and how particles can appear out of nothing as is assumed by many of its proponents.

For example one can by extrapolating the laws governing resonance in a three-dimensional environment, as was done in the article â€œWhy is energy/mass quantized?â€ Oct. 4, 2007 to the physicality of Aristotelian space can explain why particles seem to appear out of nothing.

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 â€œsomethingâ€of space to oscillate spatially with the frequency associated with the energy of that event.

The oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established space.

Therefore, these oscillations in a “surface” of a three-dimensional space manifold would meet the requirements mentioned above for the formation of a resonant system or “structure” in four-dimensional space if one extrapolated them to that environment.

Classical mechanics tells us the energy of a resonant system can only take on the discrete or quantized values associated with its fundamental or a harmonic of its fundamental frequency.

These resonant systems formed in a by space are responsible for the discrete quantized energy associated with the quantum mechanical systems.

In other words particles do not appear out of nothing but do as was shown above appear as out of the energy/mass of space or as Aristotle’s may have said the thing that is space.

This shows why Aristotle’s realization that there are “things that are matter and things that are space” opens the door to a possible explanation for some of the greatest mysteries of modern science such as the origin of Dark Matter and how particles can seemly appear out of empty space.

Later Jeff

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The road to reality and why physicists have not found it.

jeffocal — Fri, 01 May 2015 09:15:28 +0000

How does science especially physics help us to understand what we cannot see, or touch.

There are some who believe the best way to advance it is to observe the environment and then extrapolate those observations to the unobservable.

Isaac Newton used this approach to derive the law of gravity by making the assumption that mass generates an attractive gravitational force on all objects based on physical observations he made on the earth. The universality of its existence is based on the fact that one can determine the motion of all objects in the universe by assuming this force was responsible for it.

However, we cannot “see” a gravitational force. How then can we be sure that it really exists?

The answer is we cannot. However one reason why most believe it does is based on the fact it allows us to predict and explain the motion of objects that we can see and those that we cannot.

For example the position of Neptune was mathematically predicted using Newton’s concept of gravity before it was directly observed.

However, Quantum mechanics takes the opposite approach and assumes one can understand the laws of nature only by observing the results experiments and not the environment that surrounds them.

For example it defines the position of a particle by in terms of a mathematical probability distribution but says nothing about how it got there.

This differs from the Newtonian method in that it defines the solution to where an object is in terms of how it got there whereas quantum mechanics as motioned earlier defines it only in terms of where it is.

Both of these methods are valid because they give scientists the ability to make accurate predictions of future events.

However physics as the name implies is the science that deals with physical properties of matter, energy, and the forces that guide their interactions and not with abstract mathematics. Therefore, physicists should look to their observable properties as the primary vehicle and then mathematics to guide them understanding of the environment.

Unfortunately many seem to have gotten lazy in their pursuit of reality. Instead of taking the time and effort to fully understand the physicality of an environment many scientists make a few observations and turn to mathematics not observations to interconnect them.

For example The Big Bang Theory of cosmic evolution postulates the universe had its beginnings in a hot infinitely dense expanding environment. Using this assumption scientists have been able to successfully explain and predict many of the observed properties of our universe including the relative abundance of the elements and the formation of galactic clusters.

However, they have had considerable difficulty explaining why different regions of the universe that have not been causally connected to each other have the same temperature and other physical properties. This should not be possible, given that the exchange of information (energy, or heat, etc.) can only take place at the speed of light. This inconsistency between theory and observations is what cosmologists call the Horizon Problem.

In 1980 Alan Guth, Andrei Linde, Paul Steinhardt, and Andy Albrecht proposed a solution by modifying the Big Bang theory to include a short $10 âˆ’ 32$ second period of exponential expansion (dubbed “inflation”) within the first minutes of the universe’s history.

However, as was mentioned in the article “The Horizon Problem” Apr. 15, 2011 there is absolutely no observational basis for defining what caused this rapid inflation to begin or end. Therefore, some say it is an “ADHOC” or contrived explanation of a flaw in original the Big Bang Theory.

Even so within a few years of its publication it became the general accepted explanation based almost exclusively on mathematical arguments that reportedly verified it.

However, its rapid acceptance to the exclusion of others meant many of the resources that could be used to make more detailed observations and possibly find a less “ADHOC” one or one that is based more on observations less on mathematics were unavailable to those who wished to look for them

Our criticism is not with the inflation model per say but with those who after making a few tentative calculations determined that it provides the only solution and then proceeded to bully all others to accept it or get “out of town” so to speak.

Newton’s gravitational theory took many years of observing the relationship of the tides to the position of the moon, how an object moved on earth and in space before it was formulated. Granted he may have “alleluia” moment when he was able to connect them but that was because he made the very time consuming effort to observe and understand their environment.

Yet unlike the inflationary model Newton’s ideas were not accepted by the scientific establishment for many decades after their publication even though they made extremely accurate perditions of future events which is in sharp contrast to the inflationary model which makes only vague general predictions.

However this meant that many keep looking for alternatives and developed the observational technologies to advance them. Even though none were found for almost 200 years those investigations were important to the advancement of science because divergent ideas promote divergent types of investigations which inherently leads to a better understanding of the environment.

For example, many of the advancements made in 17 and 18 centuries optics were a direct result of the need to make more accurate observations of the movement of planets to either verify or refute Newton’s laws.

Recently there have been several observations such as those associated with Dark Energy and Matter that are extremely difficult to integrate into the inflationary model and other currently accepted theories of our universe evolution.

However, as mentioned earlier the quick and almost universal acceptance by the scientific establishment of the inflationary model has and most probably will continue to inhibit the search for alternatives and the scientific advancement that would have inevitably occurred if other ideas had been considered.

Observing the environment takes considerable time and effort.

Newton publish his “PhilosophiÃ¦ Naturalis Principia Mathematica” containing his gravitational theory many years after he had formulated it because we believe he want to make sure that it was observationally correct even though he knew the mathematics it contained were unquestionable.

The problem with physics is not so much related to the science but the rush to judgment which we believe is based on the desire of many to be the first to propose and get credit for a solution to the extent that they do not take the time and effort to verify that it agrees not only mathematically but also with the observational environment their ideas encompassed.

Later Jeff

In “The crises of our time, it becomes increasingly clear,are
the necessary impetus for the revolution now under way.
And once we understand nature’s transformative powers,
we see that it is our powerful ally, not a
force to feared or subdued.”
Thomas Kuhn

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A classical interpretation of the wave function collapse

jeffocal — Wed, 01 Apr 2015 11:51:54 +0000

Quantum mechanics assumes that a particle is in a superposition of several states or positions based on the mathematical properties of SchrÃ¶dinger’s wave equation before an observation is made. It also assumes that when it is observed it collapses resulting the particle it represents having a single or unique position.

When the Copenhagen interpretation was first introduced Neils Bohr found it was necessary to assume the collapse of wave function to distinguish the quantum from the classical world. This allowed it to develop without distractions from interpretational worries. Nevertheless since then that it meaning has be hotly debated because if it is a fundamental properties of nature as many have assumed it would contradict the classical or Newton assumption that the world is deterministic.
However the science of physics is devoted to understanding the physical process responsible for creating the “reality” of our observable environment based on observing the physical interaction of its real not imagined components.

One of the reason it has been so difficult to understand what happens to the position component of a quantum system when it is observed may be because too much attention has been focused on the mathematical aspects of the wave function and not enough on its physical meaning in a space-time environment. This is made even more difficult because the concept of superposition is defined in terms of the spatial properties of a quantum system instead of its space-time properties.

This suggest one be able to obtain a better understanding of what happens to it if one could view it in terms its spatial instead of it time or space-time properties.

Einstein gave us the ability to do this when he use the equation E=mc^2 and the constant velocity of light to define the geometric properties of space-time because it provided a method of converting a unit of time he associated with energy to unit of space associate with position. Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

However defining the dimensional properties of quantum system in terms of its spatial instead of its time components would allow one to derive the physicality of the wave functioned associated with SchrÃ¶dingerâ€s equation by extrapolating the observable properties of our reality to the quantum world it describes.

For example the article â€œWhy is energy/mass quantized?â€ Oct. 4, 2007 showed one can derive its physicality by extrapolating the laws of classical wave mechanics in a three-dimensional environment to a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

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 the frequency associated with the energy of that event.

The oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established space.

Classical mechanics tells us the energy of a resonant system can only take on the discrete or quantized values associated with it fundamental or a harmonic of its fundamental frequency.

Hence, these resonant systems in four *spatial* dimensions would be responsible for the discrete quantized energy associated with the quantum mechanical systems.

(In the article “The geometry of quarks” Mar. 15, 2009 the internal structure of quarks, a fundament component of particles was derived in terms of a similar resonant interaction between three and four dimensional space.)

However assuming its energy is result of a displacement in four *spatial* dimension instead of four dimensional space-time as was done in the article â€œDefining energy?â€ Nov 27, 2007 allows one to not only derive the physicality of SchrÃ¶dingerâ€s equation as was just done but also the physical reason why its particle components would be in superpositioned state before an observation is made.

Classical mechanics tell us that because of the continuous properties of waves, the energy the article â€œWhy is energy/mass quantized?â€ associated with a quantum system would be distributed throughout the entire “surface” a three-dimensional space manifold with respect to a fourth *spatial* dimension similar to how the wave generated by a vibrating ball on a surface of a rubber diaphragm are disturbed over its entire surface while the magnitude of the displacement it causes will decrease as one moves away from the point of contact.

However, this means if one extrapolates the mechanics of the rubber diaphragm to a “surface” of three-dimensional space one must assume the oscillations associated with each individual quantum system must be disturbed thought the entire universe while the spatial displacement associated with its energy defined in the in the article â€œDefining energy?â€ Nov 27, 2007 would decrease as one moves away from its position. This means there would be a non-zero probability they could be found anywhere in our three-dimensional environment because, as mentioned earlier the article â€œWhy is energy/mass quantized?â€ shows that a quantum mechanical system is a result of a resonant structure formed by the oscillations on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Classical Wave Mechanics tells us a resonance would most probably occur on the surface of the rubber sheet were the magnitude of the vibrations is greatest and would diminish as one move away from that point,

Similarly an observer would most probably find a quantum system were the magnitude of the vibrations in a “surface” of a three-dimensional space manifold is greatest and would diminish as one move away from that point.

However as mentioned earlier this is exactly what is predicted by Quantum mechanics in that one can define a particle’s exact position or momentum only in terms of the probabilistic values associated with vibrations of its wave function

Additionally this tells us that the wave function does not collapse but its energy is redirected towards the observer and as was shown in the article Why is energy/mass quantized? he would record its redirected energy in term of discrete quantized properties associated with a particle.

As mentioned earlier the science of physics is devoted to understanding the physical process responsible for creating the “reality” of our observable environment based on observing the physical interaction of its real not imagined components.

Yet even though we may never be able to directly observe the fourth *spatial* dimension we can verify its existence by observing the effects it has on our observable three-dimensional environment similar to how Einstein was able to conclude that gravity was a result of a curvature in a space time environment.

Later Jeff

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