The effects of vacuum energy can be experimentally observed in various phenomena such as the accelerated expansion of the universe and the Casmir effect.

Unfortunately as was just mentioned there is a very large discrepancy between the values observed for the Casmir made by Quantum Field Theory and those of vacuum energy that it assumes is responsible for the universe’s expansion. 

For example the Casimir effect is a small attractive or repulsive force which acts between two close parallel-uncharged conducting plates, which many physicists believe is due to quantum vacuum fluctuations of the electromagnetic field.

According to modern quantum theory, a vacuum is full of fluctuating electromagnetic waves of all possible wavelengths, which imbue it with a vast amount of energy.  Casimir realized that between two plates, only those electromagnetic waves whose wavelengths fit a whole number of times into the gap should be counted when calculating the vacuum energy.   As the gap between the plates is narrowed, fewer waves can contribute to the vacuum energy and so the energy density between the plates falls below the energy density of the surrounding space.  This generates either an attractive or a repulsive force depending on the specific arrangement of the two plates.  This is because Quantum theory requires that each of these vibration be quantized and therefore the field, at each point in space would be a simple harmonic oscillator that has the energy of the particle associated with the force that Casimir observed to be pushing the plates together.

However as was just mentioned there is very large discrepancy between the observed vacuum energy density quantum mechanics associates with the Casmir effect that it associates with our expanding universe.

Nevertheless one may be able to understand why if instead of deriving vacuum or zero point energy purely from a mathematical perspective as Quantum Field Theory does one derives it from the observations associated with the Casimir effect.

For example in the article ”Why is mass and energy quantized?“ Oct.4, 2007 it was shown that one can derive the quantum mechanical properties of energy/mass and electromagnetic waves by extrapolating the laws of classical resonance in a three-dimensional environment to matter wave in four *spatial* dimension. 

(Louis de Broglie was the first to predict the existence of wave properties of a  when he theorized that all particles have a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.) 

(Einstein gave us the ability to do this 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 four *spatial* dimensions.)

Briefly, that article 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 composed of four.

The existence of four *spatial* dimensions would give the field properties of energy/mass (the substance) the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established in a field consisting energy/mass.

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 units of the universe.

However it can also be shown they are responsible for the Casimir effect because observations of resonant systems in a classical environment indicate the number of simple harmonic oscillators that can be established in a given environment is dependent on the distance or “gap” between the “end points” of their environments.

But this same concept can be applied to two uncharged metallic plates in a vacuum, because even without an external electromagnetic field the electromagnetic components of the atoms in each plate are vibrating or have thermal energy because they are not at absolute zero.  These random vibrations of their electromagnetic components will result in a random electromagnetic field to be generated between the plates.

However, classical wave mechanics tells us these random electromagnetic vibrations would be reinforced only at certain points in space.  The number of simple harmonic oscillators in the space between two plates formed by this reinforcement would decreases as the gap between them decreases.  In other words, the smaller the gap between the plates the fewer number of quantum fields or particles that gap could support.

This means as was shown in the article ”Why is energy/mass quantized?“ there will be a greater number simple harmonic oscillators impacting the plates from outside of the gap than between it.  This will cause a force that will push the plates together because the energy density associated with the harmonic oscillations outside of the gap would be greater than inside of it.

However, it also tells us there will be also be places where the distance between the plates will be equal to the wavelength associated with a fundamental or harmonic of the fundamental frequency of these oscillations.  At those distances their energy will reinforce force each other and push them apart.

Therefore, if one assumes as us done here that the quantum mechanical properties of energy/mass are a result of a resonant system in four *spatial* dimension one can understand why the specific arrangement of the two plates causes an attractive or repulsive force to be developed by extrapolating the properties of a three-dimensional environment to a fourth *spatial* dimension.

However it also shows the reason zero-point energy predicted by quantum mechanics is so much higher than what is observed in the Casmir effect is because, according to it each zero point mode of oscillation is subject to the Heisenberg uncertainty principle.  That produces a tiny amount of energy in each point, but the number of modes is enormous.  Since energy density is mathematically determined by multiplying the density of modes times the energy per mode the product of the tiny point source of energy times the huge spatial density of modes yields a very high theoretical zero-point energy density per cubic centimeter.

Yet as was shown above the Casmir effect may not be the result of the summation of a large number of individual zero point harmonic oscillators acting individually but only those that are defined by a fundamental resonant property of space and distance between the plates.  In other words every point in space may not experience random fluctuations as is required by quantum field theory but instead it may have a fundamental oscillating frequency that requires a volume that is larger that of a single point. 

In other words the magnitude of vacuum energy would be defined by the fundamental harmonic of space and not by the random fluctuations associated with the zero point energy of a quantum vacuum.

However one can use the known the value for both the Casmir effect and as mentioned earlier the accelerated expansion of the universe to mathematically determine the energy associated with that fundamental harmonic and determine if it agrees with the observed value of each.

This would give one the ability to experimentally verify or falsify the hypotheses outlined above because as was mentioned earlier vacuum energy is assumed not only responsible for the Casimir effect but also for the accelerated expansion of the universe.

Later Jeff

Copyright Jeffrey O’Callaghan 2016

The post The vacuum catastrophe: A classical interpretation appeared first on Unifying Quantum and Relativistic Theories.

For example in his General Theory of Relativity he derived gravity in terms of a curvature in the geometry of space and time.

Additionally he showed us one can understand why in terms of the physical image of a marble on a curved surface of a rubber diaphragm.  The marble follows a circular pattern around the deformity in the surface of the diaphragm. Similarly planets revolve around the sun because they follow a curved path in the deformed “surface” of space-time.

In other words he was able to integrate the physicality of gravity into our consciousness in terms of a physical image based on the reality of a marble moving on a curved surface.

However he was unable to do the same for electrical forces even though he felt, as documented by the American Institute of Physics  “that electromagnetism and gravity could both be explained as aspects of some broader mathematical structure”.  

“From before 1920 until his death in 1955, Einstein struggled to find laws of physics far more general than any known before. In his theory of relativity, the force of gravity had become an expression of the geometry of space and time. The other forces in nature, above all the force of electromagnetism, had not been described in such terms. But it seemed likely to Einstein that electromagnetism and gravity could both be explained as aspects of some broader mathematical structure. The quest for such an explanation — for a “unified field” theory that would unite electromagnetism and gravity, space and time, all together — occupied more of Einsteinâ€s years than any other activity.

One reason may be because electrical force appears to be more closely related to the spatial not the time properties of our universe because they can be both attractive and repulsive whereas gravity is unidirectional attractive force. 

In other words because time is only observed to move in one direction forward, it is difficult to incorporate the bidirectional component of electrical forces in terms of a physical image based on the geometry of space-time.  However it is much easer if one defines them in terms of the geometry four *spatial* dimensions because one can more two directions, backwards of forwards in a spatial dimension. 

Einstein gave us the ability to do this when he used the velocity of light and the equation E=mc^2 to define 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 defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by mathematically defining the geometric properties of time in his space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions thereby giving one the ability to define the bidirectional components of electrical forces in terms of the multi directional properties of the spatial dimensions.

The fact that one can use Einsteinâ€s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with gravity in terms of four *spatial* dimensions is one bases for assuming, as was done in the article “Defining energy?” Nov 27, 2007 that all forms of energy including gravitational and electromagnetism 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.

This would have allowed him to form a physical image of electrical force as was done in the article “What is electromagnetism?“ Sept, 27 2007 in terms of the differential force caused by the “peaks” and “toughs” of a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly it showed it is possible to derive the electrical properties of electromagnetism by extrapolating the laws of Classical Wave Mechanics in a three-dimensional environment to a matter wave moving on a “surface” of three-dimensional space manifold with respect to a fourth *spatial* dimension.

A wave on the two-dimensional surface of water causes a point on that surface to be become displaced or rise above or below the equilibrium point that existed before the wave was present.  A force will be developed by the differential displacement of the surfaces, which will result in the elevated and depressed portions of the water moving towards or become “attracted” to each other and the surface of the water.

Similarly a matter wave on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension would cause a point on that “surface” to become displaced or rise above and below the equilibrium point that existed before the wave was present.

Therefore, classical wave mechanics, if extrapolated  to four *spatial* dimensions tells us a force will be developed by the differential displacements caused by a matter wave moving on a “surface” of three-dimensional space with respect to a fourth *spatial* dimension that will result in its elevated and depressed portions moving towards or become “attracted” to each other.

This defines the causality of the attractive forces of unlike charges associated with the electromagnetic wave component of a photon in terms of a force developed by a differential displacement of a point on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, it also provides a classical mechanism for understanding why similar charges repel each other 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 similar charges will be greater than that caused by a single one.  Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two charges than it would be for a single charge.

One can define the causality of electrical component of electromagnetic radiation in terms of the energy associated with its “peaks” and “troughs” that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement.

However, Classical Mechanics tells us a horizontal force will be developed by that perpendicular or vertical displacement which will always be 90 degrees out of phase with it.  This force is called magnetism.

This is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls matter horizontally towards the apex of that displacement.

This shows how one can define a physician image for the causality electrical forces in terms by extrapolating the laws of classical mechanics in a three-dimensional environment to consisting of four dimensional space time or four *spatial* dimensions.

However viewing electromagnetism in terms of its spatial instead of its time properties allows one to understand its quantum mechanic properties in of a physical image based on the observable properties of waves in three dimensional space.

However it also allows one to integrate the quantum mechanical properties of  electromagnetism into the continuous field properties General Relativity

For example the article “Why is energy/mass quantized?” Oct. 4, 2007 showed one can physical derive the quantized wave properties of electromagnetism  by extrapolating the field properties 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.

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 a matter wave the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the “surface” of a three-dimensional space manifold 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.

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 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 properties of a photon or electromagnetic field.

Yet one can also define its boundary conditions in terms of the classical laws space and time.

For example 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 the field properties of mass 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?“

In other words one can form a physical image of why electromagnetic energy is quantized in terms of the same wave properties that was earlier was associated with its attractive and repulsive properties.

As mentioned earlier Einstein felt “that electromagnetism and gravity could both be explained as aspects of some broader mathematical structure”. 

The above discussion vindicates that belief because it shows that one can not only incorporate gravity and the continuous wave properties of electromagnetism but also its  quantum properties into a broader mathematical structure by rewriting the space-time field concepts of General Theory of Relativity in terms of four *spatial* dimensions

It should be remember that Einstein’s genius allows us to choose whether to create physical images of an unseen “reality” 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.

Later Jeff

Copyright Jeffrey O’Callaghan 2015

The post Incorporating electromagnetism in General Relativity appeared first on Unifying Quantum and Relativistic Theories.

However this interpretation is at odds with the reality of the classical or deterministic world most of us appear to live in because it assumes that for a given set of initial conditions there can only be one outcome while the probabilistic interpretations of quantum mechanics assumes there can be an infinite number.
However many of the standard interpretations of quantum mechanics assume that probability is the fundamental property of the universe, while alternative interpretations explain it as an emergent or a second-order consequence of various limitations of the observer or the environment he or she is occupying when making an observation.

Determining which is the correct way of interpreting it is difficult because due to the limitation imposed on observers by uncertainty principle we can never be sure what is happening on the quantum scale when an observation is made.

Yet that does not mean that we cannot extrapolate what we can learn from observing our four dimensional space-time environment to the quantum world to help us understand what happens when we make an observation.

However we will find it beneficial to redefine Einstein space-time model of the universe into its equivalent in four spatial dimensions.

(The reason for this will become obvious later on)

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 it he associated with energy to unit of space we feel he would have associated with mass. 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.

As mentioned earlier Quantum mechanics assumes one can only determine the future evolution of a particle in terms of the probabilistic values associated with its wave function which is in stark contrast to the Classical “Newtonian” assumption that one can assign precise values of future events based on the knowledge of their past. 

In other words in a quantum system Schrödinger’s wave equation plays the role of Newtonian laws in that it predicts the future position or momentum of a particle in terms of a probability distribution.

This accentuates the fundamental difference between quantum and classical mechanics because the latter defines the reality of future events in terms of pervious events whereas quantum mechanics defines them based on the “non-classical” reality of the sum total of all possible events that can occur.  

However as mentioned earlier one may be able to understand the physical reason why these two theories define the reality of events differently if, as was done earlier one redefine Einstein’s space-time concepts in terms of four spatial dimensions.

In the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown one can understand the physicality of quantum properties energy/mass 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.

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 a matter wave the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the “surface” of a three-dimensional space manifold 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.

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 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 resonant interaction between a continuous energy/mass component of space and the geometry of four *spatial* dimensions.)

However, if a quantum mechanical properties of particle is a result of a matter wave on a “surface” of three-dimensional space with respect to a fourth *spatial* dimension, as this suggests one should be able to show that it is responsible for the uncertainties and probabilistic predictions made by Schrödinger and his wave equation regarding the position and momentum of particles.

Classical wave mechanics tells us a waveâ€s energy is instantaneously constant at its peaks and valleys or the 90 and 270-degree points as its slope changes from positive to negative while it changes most rapidly at the 180 and 360-degree points.

Therefore, the precise position of a particle could be only be defined at the “peaks” and “valleys” of the matter wave responsible for its resonant structure because those points are the only place where its energy or “position” is stationary with respect to a fourth *spatial* dimension.  Whereas it’s precise momentum would only be definable with respect to where the energy change or velocity is maximum at the 180 and 360-degree points of that wave.  All points in between would only be definable in terms of a combination of its momentum and position.

However, to measure the exact position of a particle one would have to divert or “drain” all of the energy at the 90 or 270-degree points to the observing instrument leaving no energy associated with its momentum left to be observed by another instrument.  Therefore, if one was able to precisely determine position of a particle he could not determine anything about its momentum.  Similarly, to measure its precise momentum one would have to divert all of the energy at the 180 or 360 point of the wave to the observing instrument leaving none of its position energy left to for an instrument which was attempting to measure its position.  Therefore, if one was able to determine a particles exact momentum one could not say anything about its position.

The reason we observe a particle as a point mass instead of an extended wave is because, as mentioned earlier the article ”Why is energy/mass quantized?“ showed energy must be packaged in terms of its discrete resonant properties.  Therefore, when we observe or “drain” the energy continued in its wave function, whether it be related to its position or momentum it will appear to come from a specific point in space similar how the energy of water flowing down a sink drain appears to be coming from a “point” source with respect the extended volume of water in the sink.

As mentioned earlier, all points in-between are a dynamic combination of both position and momentum.  Therefore, the degree of accuracy one chooses to measure one will affect the other. 

For example, if one wants to measure the position of a particle to within a certain predefined distance “m” its wave energy or momentum will have to pass through that opening.  However, Classical Wave Mechanics tells us that as we reduce the error in our measurement by decreasing that predefine distance interference will cause its energy or momentum to be smeared our over a wider area thereby making its momentum harder to determine.  Summarily, to measure its momentum “m”kg / s one must observe a portion the wavelength associated with its momentum.  However, Classical wave mechanics tell us we must observe a larger portion of its wavelength to increase the accuracy of the measurement of its energy or momentum.  But this means that the accuracy of its position will be reduced because the boundaries determining its position within the measurement field are greater.

However, this dynamic interaction between the position and momentum component of the matter wave would be responsible for the uncertainty Heisenberg associated with their measurement because it shows the measurement of one would affect the other by the product of those factors or m^2 kg / s.

Yet because of the time varying nature of a matter wave one could only define its specific position or momentum of a particle based on the amplitude or more precisely the square of the amplitude of its matter wave component.

This defines the physical reason in terms of four *spatial* dimensions for why we are unable to measure the exact position and moment of a quantum system.

However it also defines the reason why the probably functions of quantum mechanics are an emergent or a second-order consequence of various limitations of the observer or the environment and not a fundamental property of our universe because as was just shown the physicality of four *spatial* dimension places limitations on our ability to define the initial conditions or momentum and position of a quantum system we are measuring. 

In other words the reason quantum mechanics can only predict the probability of an event occurring is because of the limitations the physical properties of four *spatial* dimension places on an observer.

This shows why we should view the probabilistic properties of quantum mechanics as an emergent or a second-order consequence of the limitations of the four *spatial dimension or space-time environment he or she is occupying when making an observation and not a fundamental property of the universe.

Later Jeff

Copyright Jeffrey O’Callaghan 2014

The post Is Quantum Mechanics a Fundamental or emergent property of space-time? appeared first on Unifying Quantum and Relativistic Theories.

Robert Oerter, on page 83 of his book “The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics” said “Quantum mechanics has completely undermined the mechanistic view of the universe, by removing not one but two of its foundations. First, according to the Heisenberg uncertainty principle, it is impossible, even in principle, to determine the exact position and velocity or momentum of each particle in your body. The best that can be done, even for a single particle, is to determine the quantum state of the particle, which necessarily leaves some uncertainty about its position, velocity or momentum. Second, the laws of physics are not deterministic but probabilistic: given the (quantum) state of your body, only the probabilities of different behaviors could be predicted.”

To a certain extent this is true however the same can be said for our inability to determine the exact position and momentum of many macroscopic objects in our environment.

For example in “reality” we can cannot determine or measure the exact position or momentum of the planets as they obit the sun because we do not have the ability, even with modern computers to calculate the gravitational effects all of the other objects in our universe, such as the planets or stars have on them.  In other words we can only determine their most probably macroscopic positions or momentum based on an incomplete set of initial conditions.  However we do not deny the mechanistic view of planetary science, in part because we can understand or determine the mechanism responsible for why they move the way they do and why we cannot determine their exact position or momentum though observations of the “reality” of our environment.  In others words because we define the measurements of their positions and momentum in terms of the “reality” or the ability to observe the conditions under which they interact we assume that they occupy a deterministic environment.

However the reason we view the quantum world as being non-mechanistic is in part because we cannot observe or understand a mechanism responsible for why the components of its environment interact the way they do.  Therefore we can only base its “reality” on our inability to measure the position or momentum of its components.  In others words we define it only in terms of measurements and not on observations of the conditions of responsible for those measurements.

Yet this is exactly how planetary scientists define the deterministic “reality” of planetary motion because as mentioned earlier, the influence other objects have on them makes it impossible to determine the exact position or momentum of a planet.

Some would say that this is not a valid comparison because we could at least, in theory refine our observations and computing power enough to be able to determine a planets initial conditions precisely enough to predict where it will be in the future.

But that still does not explain why modern science presently assumes that the motion of the planets is mechanistic on a microscopic scale when at the moment is it not.

As mentioned earlier the reason they feel justified in believing that it is, in part because they can define a mechanism in terms of a deterministic “reality” they can observed.

If it was not for this belief they would have to assume that environments the planets occupy fully agree with the non-mechanistic assumptions of quantum mechanics.

However one can define a mechanism in terms of the deterministic “reality” of our observable environment that would explain why the quantum mechanical world appears to be non-deterministic.

For example in the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown it is possible to understand the quantum mechanical properties of energy/mass by extrapolating the laws of classical resonance in a deterministic three-dimensional environment to a matter wave 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 be meet by a matter wave in four *spatial* dimensions.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

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

Therefore the discrete or quantized energy of resonant systems in a continuous form of energy/mass would be responsible for the discrete quantized quantum mechanical properties of particles.

However, that does not explain how the boundaries of a particleâ€s resonant structure are defined.

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 of the “box” containing the resonant system the article “Why is energy/mass quantized?” associated with a particle.

In quantum mechanics, the uncertainty principle asserts that there a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position x and momentum p, can be simultaneously known.

However, as mentioned earlier one can define a mechanistic “reality” for that environment in terms of the geometry of the four *spatial* dimensions because quantum mechanics mathematically defines the position and momentum of a particle in terms of one dimensional point.

Therefore according to the above concepts there would be an uncertainty in determining its exact position because that one dimensional point could be found any within the volume of the three-dimensional “box” mentioned above.

Similarly there would be an uncertainty in measuring its momentum, again because quantum mechanics defines it in terms of the movement of a one dimensional point.  Before one could determine a particle’s momentum one would have to know its exact position in the box at the “end” points were one measured its velocity.  However, as mentioned above that non-dimension point representing a particle could be found anywhere in the box containing the resonant structure that define a particle in the article “Why is energy/mass quantized?“  Therefore one could not determine its exact velocity and therefore its momentum because there will always be an uncertainty as to where in the box the non-dimensional point that represents a particle is relative to the dimensions of the “box” when a measurement is taken.

This shows that one can define a deterministic mechanism in terms of the “reality” of our observable environment responsible for the non-deterministic measurements associated with quantum mechanics.

In other words it  define a classical mechanismsf or Heisenberg uncertainty principle or why it is impossible, even in principle, to determine the exact position and velocity of each particle in your body.

As mentioned earlier we can cannot determine or measure the exact position or momentum of the planets as they obit the sun because we do not have the ability even with modern computers to calculate the gravitational effects all of the other objects such planet or stars in our universe have on them.  However we assume that they occupy mechanistic environment because we can define the measurements of their positions and momentum in terms of the “reality” or the ability to observe the conditions under which they interact.

We can and may never be able precisely measure the momentum and position of particle in a quantum environment however if we assume that the above mechanism is valid then one also has to assume that that environment is mechanistic for the same reasons we assume that the motion of the planets is mechanistic.

What should determines if an environment is mechanistic is not the fact that we can precisely measure the position or momentum of its component because if it was we could not consider the motion of the planets mechanistic because presently we cannot.  What determines if an environment is mechanistic is if we can define a valid mechanism in terms of our observable “reality” that can explain and predict why we measure what we do even if we cannot observe all of its components.

If we let our inability to make precise measurements of the position or momentum of the planets or particles define “reality” then we must assume that they do not exist however if we can use our “reality” to define a mechanism responsible for why we cannot precisely make those measurements then must we assume that the environments we are measuring are “real” even though it may be impossible to precisely measure the positions and momentum of their components. 

Later Jeff

Copyright Jeffrey O’Callaghan 2014

The post Should measurement define "reality" appeared first on Unifying Quantum and Relativistic Theories.

“However far the quantum physical phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms. The argument is simply that by the word “experiment” we refer to a situation where we can tell others what we have learned and that, therefore, the account of the experimental arrangements and of the results of the observations must be expressed in unambiguous language with suitable application of the terminology of classical physics.

This crucial point…implies the impossibility of any sharp separation between the behavior of atomic objects and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear…. Consequently, evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be regarded as complementary in the sense that only the totality of the phenomena exhausts the possible information about the object.”

In other words he did not think that it was possible to use classical concepts to integrate the wave and particle characteristics of a quantum particle into a single picture therefore he felt that there exits a physical division between the macroscopic world of classical objects and the microscopic world of quantum particles. 

However this may not be the true and one can understand why if one views the universe in terms of four *spatial* dimensions instead of four dimensional space-time.

(The reason will become obvious later.)

Einstein gave us the ability to do this when he used the velocity of light to define the geometric properties of space-time because it allows one to convert a unit of time in his space-time universe to a unit of a *spatial* dimension identical to those in our three-dimensional universe .  Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by mathematically defining the geometric properties of a space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions.

The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions is one bases for assuming as was done in the article “Defining energy?” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

However it also allows one to understand the wave particle duality of energy/mass or its complementary property in terms of the concepts of classical physics.

For example the article, “Why is energy/mass quantized?” Oct. 4, 2007 showed that one can explain and understand the physicality of its particle properties in terms of the classical concept of waves by extrapolating the laws of resonance in a three-dimensional environment to a matter wave moving on “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension.  It also explains why all energy must be quantized or exist in these discrete resonant systems when observed.

Briefly it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in a matter wave moving in four *spatial* dimensions.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established in four spatial dimensions.

Observations of a three-dimensional environment show the energy associated with resonant system can only take on the incremental or discreet values associated with a fundamental or a harmonic of the  fundamental frequency of its environment.

Similarly the energy associated with resonant systems in four *spatial* dimensions could only take on the incremental or discreet values associated a fundamental or a harmonic of the fundamental frequency of its environment.

Therefore these resonant systems in would be responsible incremental or discreet energy associated with quantum mechanical systems.

This allows one to define the particle properties of energy/mass in terms of the classical concepts of a wave.

However, one can define its wave properties in terms of the classical concepts of a particle in terms of the boundaries of its resonant structure.

In classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space. 

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate “up” or “down” with respect to a fourth *spatial* dimension.

The confinement of the “upward” and “downward” oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries of the resonant system associated with a particle in the article “Why is energy/mass quantized?“

However it also defines the particle properties of waves in terms of the classical concept of resonant properties of a box because its physical properties define its frequency and energy.

This also provides the ability to understand the inseparability of the wave particle duality of energy/mass because it clearly demonstrates how one is depend on the other.

However it also explains why quantum systems either display the properties of a particle or a wave when measured because if one wants to measure the total energy contained in a given volume of space one will observe it as a particle while if one want to measure how it is propagated through space one must observe its wave properties.

Additionally it defines a classical reason why particles sometimes behave like wave and sometimes like particle and why it is impossible simultaneously observe these two different properties.

As shown earlier the energy contained in a quanta of space associated with a particle would be defined by the energy associated with the wavelength of its resonate structure.  In other words to observe or measure the particle properties of a given volume of space one has to sample all of its energy leaving nothing of its wave component to measure.  Similarly if one wants to observe or measure fully the wave energy of a quantum of space one would have to sample all of its energy leaving none of its particle properties.

(If one does not want to observe all of the energy in a given volume of space then one would expect that the difference would be made up by the emission of a photon or other particle whose energy would correspond to that difference.)

The reason why one cannot simultaneously measure both its wave and particle properties is because as mentioned the energy of a particle is defined by the wave properties of its resonant structure.  Since the resonant system that defines a particle is the smallest unit of its resonate structure if one measures its particle properties there would be no wave energy left for measuring its wave proprieties while if someone measure its wave energy there would be no energy left to support its particle properties. Therefore making one of these measurements precludes the other.

This demonstrates how one can integrate the wave and particle characteristics of a quantum particle into a single picture and why the  physical division between the macroscopic world of classical objects and the microscopic world of quantum particles as was assumed by Bohr many not exist. 

Later Jeff

Copyright Jeffrey O’Callaghan 2014

The post A classical interpretation of the complementary principal appeared first on Unifying Quantum and Relativistic Theories.

The wave–particle duality postulates that all particles exhibit both wave and particle properties. A central concept of quantum mechanics, this duality addresses the inability of classical concepts like "particle" and "wave" to fully describe the behavior of quantum-scale objects.  Standard interpretations of quantum mechanics explain this paradox as a fundamental property of the Universe, while alternative interpretations explain the duality as an emergent, second-order consequence of various limitations of the observer.

However it may be possible to understand it in classical terms if one assumes the universe is composed of four *spatial* dimensions instead of four dimensional space time.

(The reason will become obvious later)

The double slit experiment is made up of "A coherent source of photons illuminating a screen after passing through a thin plate with two parallel slits cut in it.  The wave nature of light causes the light waves passing through both slits to interfere, creating an interference pattern of bright and dark bands on the screen.  However, at the screen, the light is always found to be absorbed as discrete particles, called photons.
When only one slit is open, the pattern on the screen is a diffraction pattern however, when both slits are open, the pattern is similar but with much more detailed.  These facts were elucidated by Thomas Young in a paper entitled "Experiments and Calculations Relative to Physical Optics," published in 1803.  To a very high degree of success, these results could be explained by the method of Huygens–Fresnel principle that is based on the hypothesis that light consists of waves propagated through some medium.  However, discovery of the photoelectric effect made it necessary to go beyond classical physics and take the quantum nature of light into account.

However the most baffling part of this experiment comes when only one photon at a time impacts a barrier with two opened slits because an interference pattern forms which is similar to what it was when multiple photons were impacting the barrier.  This is a clear implication the particle called a photon has a wave component, which simultaneously passes through both slits and interferes with itself.  (The experiment works with electrons, atoms, and even some molecules too.)"

Yet as mentioned earlier one can derive the fact that a photon exhibits both the characteristics of a particle and wave in terms of classical concepts by transposing or converting the space-time geometry of relativity to one of four *spatial* dimensions and the spatial properties quantum mechanics associates with its energy.

Einstein gave us the ability to do this when he used he used the velocity of light to defined the geometric properties of space-time because it allows one to convert a unit of time in his space-time universe to a unit of space in an environment consisting four *spatial* dimensions.  Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by mathematically defining the geometric properties of a space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

The fact that one can use Einstein’s equations to qualitatively and qualitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions is one bases of assuming as was done in the article “Defining energy?” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

However it also allows one to understand the wave particle duality of photon and all other particles as is demonstrated in Thomson’s double slit experiment in terms of the concepts of classical physics.

For example the article, "Why is energy/mass quantized?" Oct. 4, 2007 showed that one can use the concept developed in the article “Defining energy?” to explain and understand the physicality of the wave properties of all particles including a photon by extrapolating the laws of classical resonance in a three dimensional environment to a matter wave moving on “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension.  It also explains why all energy must be quantized or exists in these discrete resonant systems when observed.

Briefly it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in a matter wave moving in four *spatial* dimensions.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in four spatial dimensions.

As was shown in that article these resonant systems in four *spatial* dimensions are responsible for its quantum mechanical properties.

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 units of the universe.

However, it does not explain how the boundaries of a particleâ€s resonant structure are defined.

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 spatial boundaries of the resonant system associated with a particle in the article "Why is energy/mass quantized?"

This provides the ability to understand, in classical terms the inseparability of the wave-particle duality of energy/mass that is demonstrated in Thomson’s double slit experiment is because clearly demonstrates how the one is dependent on the other.

Briefly it shows the reason why the interference patterns remains when one photon at a time is fired at the barrier with both slits open or "the most baffling part of this experiment" is because, as mentioned earlier it is made up of a resonant system or "structure" therefore it occupies an extended volume which is directly related to the wavelength of its particle system.

This means a portion of a particles energy could simultaneously pass both slits, if the diameter of its volume exceeds the separation of the slits and recombine on the other side to generate an interference pattern. 

It also explains why the interference pattern disappears,when a detector is added to determine which slit a photon has passed through.  The energy required to measure which one of the two slits its energy passes through interacts with it causing the wavelength of that portion to change so that it will not have the same resonant characteristics as one that passed through the other slit   Therefore, the energy passing thought that slit will not be able to interact, in most cases with the energy passing through the other one to form an interference pattern on the screen.

It also defines in classical terms  the reason, why the measurements of energy/mass takes the form particles and not waves in Thomson’s double slit experiment

As mentioned earlier, the article "Why is energy/mass quantized?" showed energy must be propagated through space in quantized resonant systems if one applies the concept of classical mechanics to a matter wave on "surface" of a three-dimension space.  Therefore, because its energy must be propagated through space to be observed the energy impacting the screen will have the discrete non-wavelike characteristics of a particle.

Richard Feynman the farther of Quantum Electrodynamics or "OED" realized the significance of this experiment because it demonstrates the inseparability of the wave and particle properties of particles and felt a complete understanding of quantum mechanics could be gleaned from carefully thinking through its implications.

The above article demonstrates why.

It shows the quantum mechanical particle and wave properties of energy/mass displayed in the double slit experiment can be understood if one assumes they are made up of a resonant system in a moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Latter Jeff

Copyright Jeffrey O’Callaghan 2013

The post Thomson’s double slit experiment in four spatial dimensions appeared first on Unifying Quantum and Relativistic Theories.

However the reason may be because gravity is not propagated by a particle such as a photon but by field properties of space.

The currently accepted view among most cosmologist and physicist is that all forces mediated by particles.  This viewpoint is support the success the Standard Model of Particle Physics has had in explaining and predicting the observed properties of electromagnetic energy, weak, and strong nuclear forces in terms of particles.  It makes very accurate and verifiable predictions of the nature and causality of those forces in terms of particle interactions.

However it falls short of being a complete theory of fundamental interactions because it cannot or does not incorporate the full theory of gravitation as described by General Relativity.  This is because Einstein’s General Theory of Relativity derives gravity in terms of a continuous curvature in the field properties of four-dimensional space-time and not in terms of the discontinuous properties of the quantum.

This fact makes it extremely difficult to conceptually integrate them because something that is discontinuous cannot be by definition continuous.
However it may be possible to integrate gravity with the particle properties of the forces defined in the Standard Model if instead of assuming they are propagated by particles one assumes that the particle properties of all forces are propagated by the fields.

It is easier to explain the mechanism responsible for creating the gravity or quantum of gravitational force by redefine Einstein’s space-time universe into one consisting of only four *spatial* dimensions.

(The reason will become obvious latter in the article)

Einstein gave us the ability to do this when he used he used equation of E=mc^2 and the constant velocity of light to defined gravity in terms geometric properties of space-time because it allows one to convert a unit of time in his space-time universe to a unit of space.  Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by 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 it allows one to define a physical mechanism that would responsible creating a particle or quanta of space-time in terms of the field properties of four *spatial* dimensions.

For example the article “Why is energy/mass quantized?” Oct. 4, 2007 showed it is possible to explain the discontinuous properties of space by extrapolating the laws classical resonance in a three-dimensional environment to a matter wave on a continuous “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

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

Therefore these discrete or quantized energy of resonant systems in a field consisting of four *spatial* dimensions would be responsible for the particle characteristics the standard model associates with the propagation of gravity electromagnetic energy, weak, and strong nuclear forces.

However, it does not explain how or why we observed them in terms of discontinuous properties of a particle instead of the continuous properties of a field as the above theoretical model and Einstein Theories predicts we should.

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 defines the mechanism responsible for the quantization of the field properties of space associated with energy/mass in the article “Why is energy/mass quantized?“.

Quantum mechanics defines the smallest possible unit of space and increment of energy in terms of Planck’s length “h” while defining the size of an individual quantum of force in terms of the equation E = h c / L. 

In other words the physical size of the fundamental quanta of all forces is not the same as is suggest by the Standard Model of Particle Physics and quantum mechanics but varies with their energy and the higher energy there is the smaller its volume.

However this means the length and therefore the volume of a Graviton would be considerably larger when compared to the volume associated with a quantum unit of the electromagnetic weak or strong forces because of its relatively low energy content with respect to theirs.

The theoretical evidence to support this conclusion is provided by the fact that the energy of a quantum of force is mathematically defined by its frequency and wavelength.  This means a higher energy particle with a shorter wavelength would occupy a smaller volume than lower energy ones.

Observational evidence can be found in the fact that quanta of the strong and weak forces can only be observe in particle accelerators capable of generating the energy required to magnify their environment enough to allow for us to observe them.

In other words the reason why we can observe quanta of the strong and weak forces is because we can create experimental apparatus that can magnify the environment to the point where they become visible.

While a quantum of a less energetic electromagnetic force associated with visible light is observable because it size is comparable to the size to the sensing apparatus in the cones and rods in the eyes use to detect it.

However electromagnetic forced is about a million billion billion billion billion (10^42) times stronger than gravitational.

Using the same logic one reason why we have been unable to observe a Graviton may be because we have been unable to construct an observing platform a million billion billion billion billion (10^42) larger than the one need to observe quanta of electromagnetic force of the same strength. 

However the relatively large size of a Graviton or an individual quanta of gravity predicted by quantum mechanics suggests another reason why we have been unable to observe it.

We know from observations that gravitational forces act on much smaller scales than the physical size of an individual Graviton predicted by quantum mechanics. However this means that we should observe that the orbital energy of objects should also be quantized.

Some may disagree by saying that the size of the quantum unit of gravitational force is too small relative to the mass of objects that the effect of its quantization would be unobservable.

However the equation that defines the size of a Gravitron ( E = h c / L ) tells us that it would relatively large with respect to the orbits of many of the observable planets.  Additionally the force of gravity is always attractive or only acts in one direction therefore the effects of its quantization would be cumulative

In other words if gravity is propagated by the graviton the cumulative effects over the life of the universe should be observable with the increased sensitivity and high resolution of modern instrumentation.

Therefore one must assume that Einstein was correct we he defined gravity in terms of its field and not the quantum properties of space-time because if it was propagated by the Graviton then quantum mechanics tells us due to its relative large size that we should have observed discrete regions of space where orbits of stars planets and moons are not found.

This strongly suggest the reason why we have been unable to observe a Graviton is because gravity is not propagated it but by the field properties of space.

Later Jeff

Copyright Jeffrey O’Callaghan 2013 

The post Finding the graviton appeared first on Unifying Quantum and Relativistic Theories.

We think so.

Many including Albert Einstein and Erin Schrödinger, had difficulty accepting the “reality” of quantum mechanics because many of its concepts appear to contradict those of our observable universe.

For example in a quantum system Schrödinger’s wave equation defines the field properties of its environment and predicts the future distribution of a particle’s position only in terms of the abstract properties of probabilities.

However many including Einstein and Schrödinger define reality in terms of what they see or touch.

For example, Einstein used the observable “reality” of the interactions of electromagnetic energy with a photoelectric material to derive the quantum mechanical properties of energy/mass while using the observable properties of light in our three-dimensional environment to define his space-time universe.

In other words his conclusion that electromagnetic energy is quantized was based on the physical “reality” of the environment sounding the photoelectric material and how electromagnetic energy interacted with it, not on the abstract probabilities associated with quantum fields.

However the abstract properties of probabilities do share a common characteristic with Einstein’s space-time universe in that time or a space-time dimension have never be seen or touched and therefore they like the probability functions of quantum field theory are, by definition abstract quantities.

Fortunately they also have a common element, as mentioned earlier in the physically observable non-abstract properties of the *spatial* dimensions because the probabilities associated with Schrödinger’s wave equation are expressed in terms of the spatial properties of position.

Therefore because they share a common connection to the observable “reality” of our three-dimensional spatial environment one should be able to define the physical “reality” of both Einstein space-time dimension and the field properties of quantum mechanics in terms of their non-abstract spatial components.
Einstein gave us the ability to do this when he used the constant velocity of light in the equation E=mc^2 to define geometric properties of energy/mass 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 defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

The fact that one can use the Einsteinâ€s equations to qualitatively and qualitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is one bases for assuming, as was done in the article “Defining energy?” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

One of the theoretical advantages of modeling the existence of energy/mass on four *spatial* dimensions instead of four dimension space-time is it allows one to derive the “reality” of a quantum fields in terms of the observable non-abstract properties of our three-dimensional environment.

The physical “reality” of the field properties energy/mass in four *spatial* dimension was developed in the article “Electromagnetism in four *spatial* dimensions” Sept 27, 2007 where it was shown the forces associated with an electromagnetic field can be explained and predicted in terms of matter wave on field consisting of four *spatial* dimensions.

Briefly it showed that one can derive its field properties by extrapolating the observable non-abstract properties of a three-dimensional environment to a fourth *spatial* dimension.

For example a wave on the two-dimensional surface of water causes a point on that surface to be become displaced or rise above or below the equilibrium point that existed before the wave was present.  A force will be developed by the differential displacement of the surfaces, which will result in the elevated and depressed portions of the water moving towards or become “attracted” to each other and the surface of the water.

Similarly a matter wave on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension would cause a point on that “surface” to become displaced or rise above and below the equilibrium point that existed before the wave was present.

Therefore observations  of our three dimensional “reality”, if extrapolated  to four *spatial* dimensions tells us the force developed by the differential displacements caused by a matter wave moving on a “surface” of three-dimensional space with respect to a fourth *spatial* dimension will result in its elevated and depressed portions moving towards or become “attracted” to each other.

This defines the causality of the attractive forces of unlike charges associated with the electromagnetic wave component of a photon in terms of a force developed by a differential displacement of a point on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, it also provides a non-abstract mechanism for understanding why similar charges repel each other because observations of wave on the surface of water tell us 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 similar charges will be greater than that caused by a single one.  Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two charges than it would be for a single charge.

One can define the causality of electrical component of electromagnetic radiation in terms of the energy associated with its “peaks” and “troughs” that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement.

However, observations of our three dimensional environment tell us a horizontal force will be developed by that perpendicular or vertical displacement which will always be 90 degrees out of phase with it.  This force is called magnetism.

This is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls matter horizontally towards the apex of that displacement.

This shows how one can explain and predict the continuous field properties of electromagnetism by extrapolating the observable non-abstract properties of our three dimensional environment to a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, as was shown in the article “The Photon: a matter wave?” Oct. 1, 2007 the quantum field properties of four *spatial* dimension can also be derived by extrapolating the observable non-abstract resonant properties of a three-dimensional environment to one consisting of four *spatial* dimension.

There are 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.

The existence of four *spatial* dimensions would give the continuous surface or field of three-dimensional space manifold (the substance) the ability to oscillate spatially with respect to a fourth *spatial* dimension 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 in four *spatial* dimensions, 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 incremental or discreet values associated a fundamental or a harmonic of the fundamental frequency of its environment.

These resonant systems in four *spatial* dimensions are responsible for the incremental or discreet field energies associated quantum and electromagnetic field theories.

However if true one must also show how the probabilities associated with Schrödingerâ€s equation could have evolved out of those field properties.

Classical mechanics tell us that because of the continuous properties of waves, the energy the article “The Photon: a matter wave?” Oct. 1, 2007 associated with all quantum systems such as a photon 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 focal point of the balls oscillations.

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 “Defining energy?” Nov 27, 2007 would decrease as one moves away from its focal point.  Therefore their is a non-zero probability they could be found anywhere in our three-dimensional environment. 

Classical Wave Mechanics also 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 this is exactly what is predicted by Quantum mechanics in that one can only define a particle’s position or momentum in terms of the probabilistic values associated with vibrations of its wave function.

This shows how one can define the “reality” of the continuous field associated with Schrödinger’s wave equation and its associated probabilities in terms of a physical mechanism based on the observable non-abstract “reality” of our three-dimensional environment.

Latter Jeff

Copyright 2013 Jeffrey O’Callaghan

The post The reality of Quantum Fields appeared first on Unifying Quantum and Relativistic Theories.

One is that it would allow for understanding of the physical significance of Planck’s constant in terms of the laws of classical physics.

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 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.

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 be meet by a matter wave in an environment of four *spatial* dimensions.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

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 means that one can theoretically derive the quantum mechanical properties of Schrödinger’s wave function in terms of the physicality of resonant properties of four *spatial* dimensions if one assumes as is done here that its mathematical properties are representative of wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However it also gives one the ability to understand the physical meaning of Planck’s constant or 6.626068 × 10^-34 (kg*m2/s) by extrapolating the laws of classical physics in a three-dimensional environment to a fourth *spatial* dimension.

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 or wave function the article “Why is energy/mass quantized?” Oct. 4, 2007 associated with a particle. 

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  ³ 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?” 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  ³ 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  ³ 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 × 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 × 10^-34.  This suggest that Planck constant 6.626068 × 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.

This shows how one can define and understand the physicality of Planck’s constant by extrapolating the laws of classical physics in three-dimensional environment to a fourth *spatial* dimension if one assumes as is done here that the quantum mechanical properties of the wave function are cause by a resonant structure in four *spatial* dimensions.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

The post The physical significance of Planck’s constant appeared first on Unifying Quantum and Relativistic Theories.

For example the Copenhagen interpretation tells us that a particle is spread out as a wave over the entire universe and only appears in a specific place when a conscience observer looks at it.  Therefore it assumes the act of measurement or observation creates its physical reality and that of the universe.  However because only conscience human beings can be observers it implies that nothing can exist without them being there to observe them.

Not only is it a bit self centered for humans to assume that they (humans) are the sole arbiters of the physicality of the universe but it is also shows how out of touch with reality those who believe in it are for the simple fact that the is overwhelming scientific evidence that humans physically evolved over a finite period of time.  However, if one assumes that atoms exist only after being observed by a human one must also assume that humans evolved out of something that did not exist.

However one of the reasons many scientist believe this is because they feel it is the only way to resolve the physical conflicts they find between the experimental observations of the microscopic realm of the atom and the “reality” we see in our macroscopic universe.
For example quantum mechanics assumes that all energy/mass is encapsulated in what is called a wave function which collapses into the reality most of us associate with our particle world only when it is observed. 

However as Greene, Brian points out in his book “The Fabric of the Cosmos: Space, Time, and the Texture of Reality” (Kindle Locations 3750-3752).

“No one has been able to explain how an experimenter making a measurement (observation) cause a wavefunction to collapse? In fact, does wavefunction collapse really happen, and if it does, what really goes on at the microscopic level? Do any and all measurements cause collapse?

The name give to the inability to define what happens to the wave properties of energy/mass when a measurement or observation is made is called the measurement problem and has given rise to different interpretations of quantum mechanics.  Many of these interoperations assume that Schrödinger wave function defines an atom in terms of the linear superposition of its particle and wave states even though actual measurements always find the physical system in a definite state.   Additionally experiments tell us that any future evolution must be based on the state the system was discovered to be in when the measurement was made and not on its history, meaning that the measurement “did something” to the process under examination.   Many believe whatever that “something” may be does cannot be explained in terms of classical theories.

However, it can be shown that one can explain and understand the “something” that happens when a measurement of the wave function is made by extrapolating the theoretical concepts of classical mechanics in a three-dimensional environment to a fourth *spatial* dimension.

In the article “A classical Schrödingerâ€s wave equation” Mar. 15, 2010 it was shown one can derive the physical reality of the quantum mechanical properties of energy/mass associated with Schrödinger’s wavefunction by extrapolating observations of classical three-dimensional space to a fourth *spatial* dimension.

Briefly 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.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

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

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

However, these are the similar to the quantum mechanical properties associated with the wavefunction in that it only takes on the discontinuous or discreet energies associated with the formula E=hv where “E” equals the energy of a particle, “h” or Planckâ€s constant would correspond to the energy associated with the fundamental frequency of four *spatial* dimensions and “v” equals the frequency of its wave component.

This shows how one can not only define the physicality of the quantum mechanical properties of Schrödinger wavefunction but also of Planck’s constant by extrapolating the classical laws governing resonant system in a three-dimensional environment to a resonant system formed by a matter wave moving in four *spatial* dimensions. 

However it also gives one the ability to understand why evolution of a quantum system is effected by observation or measurement.

Classical mechanics tells us that one should be able predict the future evolution of a system based on its history.  In other words if one knew every detail of a systems history one could measure its future evolution with complete certainty.  However it also tells us that one must interact with a system and therefore change its history to make a measurement.  Therefore, the laws of classical mechanics tell us that one must base the future evolution of a system on new history created by a measurement. 

Yet this is precisely what we observed in a quantum environment in that the act of measurement creates a new history for a system.  The only difference between a classical and a quantum environment is that in the latter the act of measurement always makes significant change which cannot be ignored in determining the future of the environment. 

However this does not mean that one cannot use the conceptual “reality” defined by classical mechanics to understand the physicality of the quantum world because as mentioned earlier classical mechanics also tells us the act of measurement must affect the future evolution of a system.

The other as of yet unanswered question that Brian Breen brought up in his book involving what happens to the quantum mechanical wave function when a measurement is made can also be found in classical mechanics.

As mentioned the earlier article “A classical Schrödingerâ€s wave equation” showed that one can derive the quantum mechanical properties of energy/mass in terms of a resonant structure by physically extrapolating the laws of classical mechanics to wave in a quantum environment.

This tells us that because of the continuous properties of waves, the energy associated with a quantum system would be distributed throughout an extended volume of space 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 a three-dimensional space manifold one must assume the oscillations associated with each individual quantum system must be disturbed throughout the entire universe while the displacement created by its wave energy 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 was shown earlier a quantum mechanical system is a result of a resonant structure formed by wave oscillations which are disturbed throughout space.

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

Yet this also means the wave function does not collapse but its evolution is redirected towards the observer.

In other words it answers the question “how an experimenter making a measurement (observation) causes a wave function to collapse” Greene, Brian asked in his book “The Fabric of the Cosmos: Space, Time, and the Texture of Reality” by using the laws of classical mechanics to define the quantum environment and “explain ”  show that the act of observation does not cause the collapse of the wavefunction but only redirects its evolution towards the observer.

It should be remember that we are not trying to quantify our quantum experiences but only to explain how and why we experience it the way we do in terms of the “realty” most of us associate with our classical world.

Later Jeff

Copyright 2012 Jeffrey O’Callaghan

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