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.

The uncertainty principal of quantum mechanics tells us that we cannot know or observe the precise amount of energy contained in microscopic physical system over very short intervals of time. 

Some physicists feel that because they cannot know the precise “reality” of the amount of energy contained in microscopic physical system, it must fluctuate around a given point even though it is a vacuum which does not contain anything that can physically fluctuate.  They call the energy generated by the uncertainty principal quantum fluctuations or vacuum energy.

However, this means they are defining the “reality” of a vacuum in terms of their inability to know or define its reality.
However we have shown throughout this blog there are many theoretical advantages to defining the universe in terms of four *spatial* dimensions instead of four-dimensional space-time.

One is that it would allow us to understand the “reality” of a quantum vacuum by using our imagination to extrapolate the reality of a three-dimensional environment to a fourth *spatial* dimension.

Einstein gave us this ability when he used the velocity of light to define the geometric properties of time in a space-time environment because it allows one to convert a unit of time in it to a unit of a space identical to those of our three-dimensional space.  Additionally because the velocity of light is constant it is possible to defined a universe made up of four *spatial* dimensions that makes predictions identical to those he had attributed to four dimensional space-time.

This as mentioned earlier this would allow one to understand the reality of a quantum environment in terms of the classical laws physics.

For example in the article “Why is mass and energy quantized?‘“ Oct. 4, 2007 it was shown that one can understand the quantum properties of energy/mass by extrapolating the resonant properties of a three-dimension environment to a matter wave moving on a continuous “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 could be meet by one 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 a continuous 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 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 other words one can understand the reality of a quantum environment in terms of the laws of classical physics if one views in terms of four *spatial* dimensions.

However, if true one may be able to define the “reality” of quantum vacuum by as mentioned earlier using one imagination to extrapolate observations of a three-dimensional environment to four *spatial* dimensions instead of relying, as many physicists seem to on their inability to observe them.

Casimir theorized that quantum fluctuations in a vacuum would cause a force to be developed between two uncharged metallic plates in a vacuum without an external electromagnetic field acting on them, if they were placed a few micrometers apart.  This contradicts classical reasoning because, the lack of an external field also means that there is no field between the plates, and therefore no force would be measured between them.  However if this field is instead studied using quantum electrodynamics, it is seen that the plates are affect the virtual photons which constitute the field, and generate a net force either an attraction or a repulsion depending on the specific arrangement of the two plates.

This force was first measured by Dutch physicists Hendrik B. G. Casimir and Dirk Polder in 1948 while participating in research at Philips Research Labs.  

They found its strength falls off rapidly with the distance between the plates and that it is only measurable when the distance between them is extremely small.  On a sub micrometer scale, this force becomes so strong that it becomes the dominant force between uncharged conductors.  In fact, at separations of 10 nm—about 100 times the typical size of an atom the Casimir effect produces the equivalent of 1 atmosphere of pressure, the precise value depending on surface geometry and other factors.

However, this is what one would expect if the quantum mechanical properties of vacuum were as was shown in the article “Why is mass and energy quantized?” a result of a resonant system form by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Observations of waves in a classical environment indicate the number of 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 the same concept can be applied to two uncharged metallic plates in a vacuum, because even without any external electromagnetic field the electromagnetic components of the atoms in each plate are vibrating because they are not at absolute zero they have thermal energy.  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 either constructively or destructively at certain points in space.  The number of harmonic oscillators or, as some physicist’s call them quantum fluctuations in the space between two plates would decrease as the gap between them decreases.  In other words, the smaller the gap between the plates the fewer number of quantum fluctuations that gap could support.

This means as was shown in the article ”Why is mass and energy quantized?“ there will be a greater number harmonic oscillators or quantum fields 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 harmonic oscillations outside of the gap would be greater than inside of it.

However, it also tells us there will be places where the distance between them will be equal to the wavelength associated with a fundamental or harmonic of the fundamental frequency of electromagnetic oscillations.  At those distances their energy will reinforce force each other and would 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 and attractive or repulsive force to be developed by extrapolating the reality of a three-dimensional environment to a fourth *spatial* dimension.

We know the reality of the wave properties of particles because in 1927 Davisson and Germer observed they are diffracted by crystals.  Additionally we can observe the reality and properties of a resonant system in three-dimensional space.

This suggests the Casimir effect may not be due to our inability to know the precise “reality” of the amount of energy contained in microscopic physical system but to the physical observable reality of the wave properties of a particle.

However, it also means the “reality” of a quantum vacuum could be defined, as was done in the article ”Why is mass and energy quantized?“ by extrapolating the laws of classical three-dimensional space to a fourth “spatial* dimensions instead of the non “reality” of quantum field theory.

Later Jeff

Copyright Jeffrey O’Callaghan 2010

The post Understanding the “reality” of a quantum environment appeared first on Unifying Quantum and Relativistic Theories.