Later Neils Bohr sought to explain them by using the Rutherford model of the atom as a nucleus surrounded by electrons and the new ideas of quantum mechanics.  Bohr assumed that electrons orbit the nucleus at certain discrete, or quantized, radii, each with an associated energy.  He also assumed that when electrons “fall” from larger to smaller orbits, they release electromagnetic radiation obeying the Planck-Einstein relationship.  Because the energies of the orbits are quantized, so are the wavelengths. Bohr’s model explains both the Balmer series and the Rydberg constant and ushered in a new era of understanding atoms through quantum mechanics.

However Bohr felt that that no explanation of why electrons orbited in discrete, or quantized radii was needed because using that theoretical model based on that assumption was able to make very accurate prediction of energies of Balmer series.

Einstein disagreed because he felt that “If a new theory (such as that associated with Bohr’s model of the hydrogen atom) was not based on a physical image simple enough for a child to understand, it was probably worthless.”

In other words he felt that if Bohr’s explanation of the Balmer series was to have any value one should be able to form a physical image of how and why the spectral lines in the Balmer series have the energy they do.

The importance of explaining theoretical concept in physical terms was demonstrated by Einstein when addressing one of the more troubling aspect of Newton’s gravity theory.

Most, including Newton were troubled by the fact that that his gravitational theory meant ” that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact…That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.”

However Einstein realized that one can understand how gravity “may act upon another at a distance through a vacuum” by extrapolating the physical image of how objects move on a curve surface in a three-dimensional environment to a curved four dimensional space-time manifold. This allowed him to conceptually understand gravity in terms of a physical image based on our three-dimension environment.

In other words the mathematics developed by Newton was only able to quantitatively predict gravitational forces while Einstein gave us the ability to conceptually understand how and why “one body may act upon another at a distance” by physically connecting it to the reality of what we can see and touch.

However up until now no one has been able to define a physical model clear enough to explain the quantum mechanical model Bohr hypnotized was responsible for the spectral emissions associated with the Balmer series in terms of a space-time environment.

One reason for both Einstein’s and modern scientist’s inability to define one can be traced to the fact that they chose to define their energies in terms of four dimensional space-time instead four *spatial* dimensions because most view reality in terms of the physicality of the spatial dimensions instead of a time or space-time dimension.

This is true even though Einstein’s space-time theories give us a detailed physical image how a curvature in a space-time manifold can be responsible for gravity by extrapolating the image of an object moving on a curved two dimensional “surface” in a three dimensional environment to four dimensional space-time.  However this image only contains reference to the physicality of the spatial dimensions and not a time or space-time dimension.

This suggests that one may be able to develop a physical image how and why the energy levels in a hydrogen atom are what they are by converting or transposing Einstein’s space-time universe which defines energy in terms of geometry of space-time to one that defines it in terms of  the physicality of the spatial dimensions..

Einstein gave us the ability to do this when he used the constant velocity of light and the equation E=mc^2 to define the dynamic balance between mass and energy because that provided a method of converting the time displacement he associated with energy in a space-time universe to one to a spatial one in a universe consisting of only four *spatial* dimensions.  Additionally because the velocity of light is constant he also allows us to defined a one to one quantitative and qualitative 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 mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of only four *spatial* dimensions.

This fact is the 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 if true one should be able to form a physical image of why the energy of each of the Blamer lines are what they are by extrapolating the physicality of the spatial dimensions to a fourth *spatial* dimension.

In other words one would should be able to define why the elections associated with the Principal Quantum number (n), the Angular Momentum “â„“” (l) Magnetic (m) and Spin Quantum Number (+1/2 and -1/2) have the energy they do by extrapolating the laws of a classical environment to a fourth *spatial* dimension while at the same time excluding all other energies.

In the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown one can derive the quantum mechanical properties of energy/mass by extrapolating the laws governing resonance in a three-dimensional environment to a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

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

The existence of four *spatial* dimensions would give the “surface” of a three-dimensional space manifold (the substance) the ability to oscillate spatially with respect to it thereby fulfilling one of the requirements for resonance to occur.

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

Therefore, these oscillations on a “surface” of three-dimensional space, would meet the requirements mentioned above for the formation of a resonant system or “structure” in space.

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

Similarly the energy associated with resonant systems in four *spatial* dimensions could only take on the 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 energy associated with quantum mechanical systems.

However the fact that one can derive the quantum mechanical properties of energy/mass by extrapolating the resonant properties of a wave in three-dimensional environment to a fourth *spatial* dimension means that one should as mentioned earlier be able to define why Principal Quantum number (n),  the Angular Momentum “â„“”  (l) Magnetic (m) and Spin Quantum Number(+1/2 and -1/2) have the energy they do by extrapolating the laws of a classical environment to a fourth *spatial* dimension while at the same time excluding all other energies.

In three-dimensional space the frequency or energy of a resonant system is defined by the vibrating medium and the boundaries of its environment.

For example the resonant energy of a standing wave generated when a violin string plucked is determined in part by the length and tension of its strings.

Similarly the energy of the resonant system the article “Why is energy/mass quantized?” associated with atom orbitals would be defined by the “length” or circumference of the three-dimensional volume it is occupying and the “tension” on the space it is occupying.

Therefore the physicality of “n” or the principal quantum number would be defined by the fundamental vibrational energy of three-dimensional space that article associated with the quantum mechanical properties of energy/mass.

The circumference of its orbital would correspond to length of the individual strings on a violin while the tension on its spatial components would be created by the electrical attraction of the positive charge of the proton.

Therefore the integer representing the first quantum number would correspond to the physical length associated with fundamental vibrational energy of three-dimensional space which in terms is dependent on the tension created by the electrical attraction of the proton and electron.

However, classical mechanics tells us that each environment has a unique fundamental resonant frequency which is not shared by others.

The reason an electron does not fall into the nucleus is because as was shown in the article “Why is energy/mass quantized?” all energy is contained in four dimensional resonant systems.  Therefore the fundamental frequency or wavelength of four dimensional space would define the minimum energy and therefore the physical size of the first quantum orbital.

This defines physicality of the environment associated with the first quantum number and why it is unique for each subdivision of electron orbitals.  Additionally observations tell us that resonance can only occur in an environment that contains an integral or half multiples of the wavelength associated with its resonant frequency and that the energy content of its harmonics are always greater than those of its fundamental resonate energy.

This allows one to derive the physicality of the second “â„“” or azimuth quantum number in terms of how many harmonics of the fundament frequency a given orbital can support. 

In the case of a violin the number of harmonics a given string can support is in part determined by its length.   As the length increase so does the number of harmonics because its greater length can support a wider verity of frequencies and wavelengths.  However, as mentioned earlier each additional harmonic requires more energy than the one before it.  Therefore there is a limit to the number of harmonics that a violin string can support which is determined in part by its length.

Similarly each quantum orbital can only support harmonics of their fundamental frequency that will “fit” with the circumference of the volume it occupies.

For example the first harmonic of the 1s orbital would have energy that would be greater than that of the first because as mentioned earlier the energy associated with a harmonic of a resonant system is always greater than that of its fundamental frequency.  Therefore it would not “fit” into the volume of space enclosed by the 1s orbital because of its relatively high energy content.  Therefore second quantum number of the first orbital will be is 0. 

However it also defines why in terms of classical wave mechanics the number of suborbital associated with the second quantum number increases as one move outward from the nucleus because a larger number of harmonics will be able to “fit” with the circumference of the orbitals as they increase is size.

This also shows that the reason the orbitals are filled in the order 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, 5s is because the energy of the 3d or second harmonic of the third orbital is higher in energy than the energy of the fundamental resonant frequency of the 4th orbital.  In other words classical wave mechanics tells us the energy of the harmonics of the higher quantum orbitals may be less than that of the energy of the fundamental frequency of preceding one so their harmonics would “fit” into circumference of the lower orbitals

The third or Magnetic (m) quantum number physical defines how the energy associated with each harmonic in each quantum orbital is physically oriented with respect to axis of three-dimensional space.

For example it tells us that the individual energies of 3 “p” orbitals are physically distributed along each of the three axis of three-dimensional space.

The physicality of the fourth quantum or spin number has nothing to do with the resonant properties of space however as was shown in the article “Pauliâ€s Exclusion Principal: a classical interpretation” Feb. 15, 2012 one can derive its physicality by extrapolating the laws of a three-dimensional environment to a fourth *spatial* dimension.

Briefly the article “Defining potential and kinetic energy?” Nov. 26, 2007 showed all forms of energy including the angular momentum of particles can be defined in terms of a displacement in a “surface* of three-dimensional space manifold with respect to a fourth *spatial* dimension.  In three-dimensional space one can use the right hand rule to define the direction of the angular momentum of charged particles.  Similarly the direction of that displacement with respect to a fourth *spatial* dimension can be understood in term of the right hand rule.  In other words the angular momentum or energy of an electron with a positive spin would be directed “upward” with respect to a fourth *spatial* dimension while one with a negative spin would be associated with a “downwardly” directed one.
Therefore one can define the physically of the fourth or spin quantum number in terms of the direction a “surface” of three-dimensional space is displaced with respect to a fourth *spatial* dimension.  For example if one defines energy of an electron with a spin of -1/2 in terms of a downward directed displacement one would define a +1/2 spin as an upwardly directed one.

The physical reason why only two electrons can occupy a quantum orbital and why they have slightly different energies can also be derived by extrapolating the laws of a classical three-dimensional environment to a fourth *spatial* dimension.

There a two ways to fill a bucket.  One is by pushing it down and allowing the water to flow over its edge or by using a cup to raise it to the level of the buckets rim.

Similarly there would be two ways fill an atomic orbital according to the concepts presented in the article “Defining potential and kinetic energy?“.  One would be by creating a downward displacement on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* to the level associated with the electron in that orbital while the other would be raise it up to that energy level .

However the energy required by each method will not be identical for the same reason that it requires slightly less energy to fill a bucket of water by pushing it down below its surface than using a cup to fill it.

However it also explains why no two quantum particles can have the same quantum number because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement. 

Similarly the magnitude of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by two quantum particles with similar quantum numbers would greater than that caused by a single one.  Therefore, they will repel each other and seek the lower energy state associated with a different quantum number because the magnitude of the force resisting the displacement will be less for them if they had a different number.

This shows how one can explain why spectral emissions specifically those of the Balmer series have the energy they do and the four quantum numbers in terms of emergent property of four *spatial* dimensions or four dimensional space-time by extrapolating the laws of a classical three-dimensional environment to them.

It should be remember that Einsteinâ€s genius allows us to choose whether to define the physicality of the atomic orbitals 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 Spectral emissions as an emergent property of space-time appeared first on Unifying Quantum and Relativistic Theories.

However it is by definition is an abstract creation of the mind and therefore is not physically connected to the observable real world, most of us believe we live in.

Therefore, we can never be sure the equations developed by science accurately define the physicality of those laws or the real world they are describing.

This is true even though they make accurate predictions because unless there is a way of physically connecting the mathematical worlds create by the intellect to the observable world we live in science cannot be sure that is has chosen the correct set of facts that defines its existence.
Granted the mind can systematical quantify the natural world as the mathematics of quantum mechanics does with great accuracy but that does not necessarily mean it tell us anything about the reality of how or why that quantification takes place.

For example there are an infinite number of ways one can mathematically describe the fact that there are two apples on a table. One can predict why based on the assumption that there were originally four apples and two were taken away or assume that originally there were six and four were taken away.  However if there were only four apples to begin with the mathematical description using six apples even though accurately quantifies the existence of two apples it does not describe their world because in “reality’ that world did not contain six apples.

Similarly just because the mathematics of quantum mechanics can very accurately predict the quantitative observation of the particle world does not mean that it defines why it is that way.

Einstein was often quoted as saying “If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless.”

He realized for science to make a claim that they have organized the natural world into a single set of patterns or laws that describe why we perceive its  “reality” the way we do they must be able to conceptually connect the independent models developed by our minds to the reality of natural world that exists outside of it.

For example Newton in a letter to Bentley in 1693, talks about a conceptual problem he has with his gravity theory by rejecting the action at a distance that it requires.

“It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact…That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.”

However Einstein realized by extrapolating the physical image of how objects move on a curve surface in a three-dimensional environment to a four dimensional space-time manifold one could explain how gravity “may act upon another at a distance through a vacuum” in terms of a curvature in space and time.   This enables one to understand gravity based on a physical image formed by the “reality” of what we can see and touch in our three-dimension world.

In other words he was able to connect the observable reality of our three dimensional world to the mathematical one he had created in his mind to explain gravity in terms of a physical imaged form in our three dimensional world.

Unfortunately many of today scientists seem to be ignoring the lessons taught to us by Einstein.  They chose to look for reality only in terms of abstract mathematics instead of the physical imagery given to us by the “reality” of what we can see and touch.

The reason may be because it is easier to alter an abstract environment based on mathematics to conform to an observational inconsistency than it is to alter one based on physical imagery.

For example Quantum theory makes predictions based on the random properties of a probability function.  However because the abstract properties of probabilities which are not physically connected to our world, all its predictions no matter how inconsistent they are with the world they are describing can be incorporate into it.

This is in sharp contrast to the space-time environment defined by Einstein in that projecting the physical image of objects moving on a curve surface in our three-dimensional environment physically connects it to a four-dimensional space time-environment

For example a single instance of a mass being gravitational repelled instead of attracted would contradict the physical imagery define by Einstein and would be extremely if not impossible to explain because no one has ever observe objects rolling up hill in our three-dimensional environment.  In other words because he defined gravity in terms of a physical image based on how objects move on a curve surface in a three-dimensional environment it makes observations like two masses gravitational repelling each other virtually impossible to incorporate into it.

However because quantum mechanics is based on probabilities anything that can happen eventually will.  Therefore it is virtually impossible to find any observation in the real world that contradicts it.  However this can only happen in an abstract environment which is not bound by the physicality of our observational world.

As mentioned earlier unless science can conceptually connect the mathematical worlds created by the intellect to the observable world we live in we cannot say that we know or understand anything physical laws that we assume define its reality.

But why should science put in the effort to understanding our theoretical models in terms of the physical “reality” of our world when both the abstract mathematical foundation of quantum mechanics and the physical imagery of Einstein’s theories make very accurate predictions of future events.

Because the mission of a science is to define the real world in terms of what we perceive in our environment not to perceive an abstract mathematical environment to define what we want it to be.

Later Jeff

Copyright 2014 Jeffrey O’Callaghan

The post The mathematics of the real world appeared first on Unifying Quantum and Relativistic Theories.

As Steven Weinberg said “Mass tells space-time how to curve while space-time tells mass how to move”.

In other words Einstein was only able to explain how the field properties of space interact to create gravity while the Standard Model defines how the asymmetry of those fields gives particles their mass.

However this suggests that one may be able to integrate the Standard Model into Einstein’s concept of gravity if one can define a common physical mechanism responsible for how Higgs field breaks the symmetry of space-time to create mass while at the same time explaining how and why its field properties interact to create gravity.

Einstein gave us a method for accomplishing this when he said “If a new theory (such as that associated with the Higgs boson) was not based on a physical image simple enough for a child to understand, it was probably worthless.”

For example Newton was troubled by the fact that that his gravitational theory meant .” that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact…That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.”

However Einstein realized that one can understand how gravity “may act upon another at a distance through a vacuum” by extrapolating the physical image of how objects move on a curve surface in a three-dimensional environment to a curved four dimensional space-time manifold. This allowed him to conceptually understand gravity in terms of a physical image based on our three-dimension environment.

In other words the mathematics developed by Newton was only able to quantitatively predict gravitational forces while Einstein gave us the ability to conceptually understand why “one body may act upon another at a distance” by physically connecting it to the reality of what we can see and touch.

However, as mentioned earlier he was unable to tell us what mass is, he was only able tell us how mass interacts with space-time.

Similarly the Standard Model is able to define mass in terms of the symmetry breaking properties of the Higgs field however it is unable to define in terms of a physical image of how it interacts with the field properties of space-time to create gravity or the forces associated with mass.

This fact is difficult to understand because the Standard model is based on a Relativistic Quantum Field theory which has its foundation in Einstein’s Theories.  Therefore one would think that it would be easy to integrate it into them.

However Einstein’s and modern scientist’s inability to connect the Standard Models explanation for mass to Einstein’s explanation of gravity can be traced to the fact that they chose to define the universe in terms of energy instead of mass.

Einstein told us that a curvature in the field properties of space-time is responsible for gravitational energy and because of the equivalence between energy and mass defined by his equation E=mc^2 one must also assume that it is responsible for mass.

This suggest that one may be able to incorporate Einstein’s explanation of the gravity into the Standard Model if one converts or transposes the his space-time universe which defines field properties of energy in terms of geometry of space-time to one that defines mass of in terms of its field properties.

Einstein gave us the ability to do this when he used the constant velocity of light and the equation E=mc^2 to define the dynamic balance between mass and energy because that provided a method of converting the space-time displacement he associated with energy in a space-time universe to one we believe he would have associated with mass in a universe consisting of only four *spatial* dimensions.  Additionally because the velocity of light is constant he also allows us to defined a one to one quantitative and qualitative 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 mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

The fact that the equation E=mc^2 allows us to both qualitatively and quantitatively derive the spatial properties of energy in a space-time universe in terms of its spatial properties in four *spatial* dimensions is the bases for assuming as was done in the article “Defining energy” Nov 27, 2007 that all forms of energy/mass, including that associated with the Higgs field 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 changing ones perspective on the geometric structure of the universe form one of space-time to four *spatial* dimensions, as was just shown to be possible gives one the ability to define the physical mechanism by which the Higgs Field or the field properties of four *spatial* dimensions interacts with particles to create mass and why they are quantized in terms of a physical image formed in our three-dimensional environment.

For example one can form a physical image of why mass is quantized, as was done in the article “Why is energy/mass quantized?” Oct. 4, 2007 by extrapolating the image of a wave and its resonant properties in three dimension environment to one made up of four *spatial* dimensions.

This would be analogous to how Einstein, as mentioned earlier was able to explain gravity by extrapolating the physical image of how objects move on a curved surface of three-dimension space to one consisting of four dimensional space-time.

(Louis de Broglie was the first to predict the existence of the wave properties of mass 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).

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 be meet in one consisting of four.

The existence of four *spatial* dimensions would give a matter wave that Louis de Broglie associated with a particle the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for 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 respect to a fourth *spatial* dimension at a 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.

Physical observations of our three dimensional environment tell us that resonant systems can only take on the discrete or quantized energies associated with a fundamental or a harmonic of their fundamental frequency

Therefore, these resonant systems in the field properties of four *spatial* dimensions would define mass and its quantum mechanical properties in terms of the Standard Model because of the fact that the volumes of space containing them would have a higher concentration of energy and therefore the mass associated with those volumes would be greater.

However can also understand in terms of a “physical image” of the boundaries of the point particles of the Standard Model using the above concepts.

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.

(The reasons why particles can be treated as a mathematical points in the Standard Model is because according to the above theoretical model the components of their energy/mass and forces associated with them would be evenly distributed around the centre of mass or the resonant structure in the article “Why is energy/mass quantized?” Oct. 4, 2007)

However this suggest the symmetry breaking properties the Standard Model associates with the Higgs field may be related to the geometric properties of four *spatial* dimensions.

If true one should be able to use those field concepts to explain how it interacts with particles to give them mass and why the mass of the corresponding particle types across the three fundamental families of particles in the Standard Model listed in the table below grows larger in each successive family.

As mentioned earlier the article “Why is energy/mass quantized?” showed that one can derive the mass of a particle in terms of the energy contained within a resonant system generated by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension while the article “Defining energy” showed that one can derive the energy or temperature of an environment in terms a displacement in the same three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore using the concepts developed in those articles one could derive the total mass of a particle in terms of the sum of the energies associated with that resonant structure and the displacement in the “surface” of three-dimensional space associated with the energy of the environment it is occupying.

Yet Classical Mechanics tells us there will be specific points in space where the matter wave that Louis de Broglie associated with a particle can interact with the energy content or temperature of its environment to form a resonant system.

Therefore, the mass of each family member would not only be dependent on the energy associated with the resonant system that defined their quantum mechanical properties in the article “Why is energy/mass quantized?” but also on temperature or energy of the environment they are occupying.

Thus suggest the reason “The corresponding particle types across the three families in the Standard Model have identical properties except for their mass, which grows larger in each successive family.” is because of an interaction between the resonant properties defined in the article “Why is energy/mass quantized?” and the mass content of the environment they are occupying.

This means the particles in the first family would be found in relativity low energy environments, are relatively stable, and for the most part can be observed in nature.  However, the particles in the second and third families would be for the most part unstable and can be observed only in high-energy environments of particle accelerators.  The exception is the Muon in the second family, which is only observed in the high-energy environment of cosmic radiation.

The relative masses of the fundamental particles increases in each successive family because the higher-energy environments where they occupy would result in the corresponding particles in each successive family to be formed with a greater relative “separation” in the “surfaces” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, the corresponding particles in the second family will have a greater mass than the particles in the first family because the “separation”, with respect to a fourth *spatial* dimension of the three-dimensional space manifold associated with them is greater than the “separation” associated with the first family.

Similarly, the corresponding particles in the third family will have a greater mass than those in the second family because the “separation”, with respect to a fourth *spatial* dimension, of the three-dimensional space manifold associated with them is greater than the spatial “separation” associated with the second family.

Additionally the corresponding particle types across the three families have “identical properties” because as shown in the article “The geometry of quarks” Mar. 15, 2009 they are related to the orientation of the “W” axis of the fourth *spatial* dimension with the axis of three-dimensional space.  Therefore, each corresponding particle across the three families will have similar properties because the orientation of the “W” axis of the fourth *spatial* dimension with respect to the axis of three-dimensional space is the same for the corresponding particles in all of the families.

This explains why “The corresponding particle types across the three families having identical properties except for their mass, which grows larger in each successive family” in terms of the asymmetrical field of four *spatial* dimensions.

However it also shows how one can use the asymmetrical field properties of four *spatial* dimensions or the Higgs Field to understand the causality of the masses of the fundamental particles in the Standard model in terms of a physical image based on the “reality” of what we can see and touch in our three dimensional environment.  This is similar to how Einstein, as mentioned earlier was able to shown that a mass “may act upon another at a distance through a vacuum” by extrapolating the physical image of how objects move on a curve surface in a three-dimensional environment to a curved four dimensional space-time manifold.

As mentioned earlier the article “Why is energy/mass quantized?” showed that one can derive the total mass of all particles in terms of the sum of energy contained within a resonant system generated by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension and the energy associated with displacement in the “surface” of three-dimensional space associated the environment it is occupying.

However if one assumes, as was done above the Higgs field is created by a spatial displacement in the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension one can also understand how its asymmetric properties interacts with particles to create their mass in terms of the physical image formed by water in a dam.

This is because the potential energy of water molecule in a dam is defined by its asymmetrical spatial separation with respect to the bottom of the dam.

Similarly, according to the above theoretical model, the potential energy or mass contained in particles would be defined by an asymmetrical displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

In other words it gives one the ability to define the asymmetrical properties the Standard Model associates with the Higgs field in terms of a physical image of water in a dam because as mentioned earlier its potential energy is in part dependent on the height of the dam while that of a particle would be dependent on magnitude of the spatial separation or the “height” of the three-dimension space manifold it is occupying with respect to a fourth *spatial* dimension.

However, as was mentioned earlier Einstein also defined gravity in terms of an asymmetrical displacement or curvature or a “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension or a space-time manifold.

This suggest that one may be able to unite the Standard Model with Einstein’s concept of gravity with if one can find a way of integrating the effects an asymmetrical curvature in “surface” of a three-dimensional manifold with respect to either space-time or a higher or fourth *spatial* dimension would have on a particle with the asymmetrical properties of the Higgs field.

It should be remember that Einstein’s genius allows us to choose whether to view the reality of the Higgs Field in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of energy/mass and the constant velocity of light.

Later Jeff

Copyright Jeffrey O’Callaghan 2014

The post Integrating the Standard Model into Einstein’s gravitational theory appeared first on Unifying Quantum and Relativistic Theories.

In other words can one use our everyday experiences to understand the irrationality behind many of the assumptions made by quantum mechanics and integrate them into the space-time environment in which we all live

For example the paradoxical wave–particle behavior of energy/mass, one of the fundamental concepts defining Quantum mechanics defies the “reality” of the four dimensional world we live in because of its inability to describe/define how quantum-scale objects can simultaneously exist as waves and particles.  Many have tried to explain it 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 is possible to explain the wave–particle duality of the quantum world in terms of the “reality” of classical concepts and four dimensional space-time by redefining Einstein’s space-time environment to its equivalent four spatial dimension counterpart because it will allow one to directly apply classical concepts of Newtonian space to the wave properties quantum mechanics associates with particles.

(The reasons will become obvious latter.)

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 four dimensional space-time universe to a unit of a space in an environment consisting  four spatial dimensions which identical to those of our three-dimensional 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 mathematically defining the geometric properties of time 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 and gave us the ability to redefine the curvature or displacement he associated with energy/mass in a space-time environment to a spatial displacement in a fourth *spatial* dimension.

This, as mentioned earlier will allow us to understand the reasons behind the paradoxical wave–particle duality of light when it is partially reflected by two surfaces, as outlined on pages 17 thru 23 of Richard P Feynman book “QED The Strange Theory of Light and Matter” in terms of the laws of classical physics.

On those pages he writes that by placing two glass surfaces exactly parallel to each other one can observe how the photons of light reflected from the bottom surface interact with those reflected from the top surface.  Depending on the distance between the glass surfaces he can determine, by using a photo detector, that four percent or 4 out of 100 photons reflected from the lower surface of the glass could add up to as many as 16 or none at all when they interact with the photons reflected from the upper surface of the glass because of the reinforcement of the reflected wave energy from the bottom and top surfaces of the glass.

In other words the 4 photons reflected from the surface of the bottom piece of glass would interact with the incident ones to that surface creating from 0 to 8 photons while the 4 photons reflected from the surface of the top piece of glass would interact with the incident ones to it creating 0 to 8 more photons for a total of 0 to 16 photons.

These observations by Mr. Feynman support a wave theory of electromagnetic radiation because according to it, the energy associated with the interference of the 4 photons reflected from the bottom surface with 4 from the top will result in energy variations that corresponds to the energy of 0 to 16 photons.

However, wave theory also predicts the energy variations should be continuous.

In other words, the energy of the reflected photons should be able to take on any value between 0 and the combined energies associated with 16 photons.

Unfortunately, for the wave theory of light, the energy of the reflected photons Richard Feynman observed in the above experiment only took on integral values equal to the energy of the photons that originally struck the surface of the glass.  This indicates that their energy is not transmitted by a wave but by a particle.

However this observational paradox can be resolved if particles are, as mentioned earlier are viewed in terms four *spatial* dimension instead of four dimensions space-time because it shows their behavior can be described in terms of a resonant “structure” generated by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

For example in the article “Why is energy/mass quantized?” Oct. 10, 2007 it was shown one can derive both the wave and particle properties of energy/mass and a photon by extrapolating the laws of classical of resonance in a three-dimensional environment to a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Additionally it showed that all energy must be propagated in these resonant systems.

Briefly it showed the four conditions required for resonance to occur in a classical Newtonian environment, an object, or substance with a natural frequency, a forcing function at the same frequency as its natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

The existence of four *spatial* dimensions would give the “surface” of three-dimensional space (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 if one extrapolates the laws of classical wave mechanics to a fourth *spatial* dimension these oscillations in a “surface” of a three-dimensional space manifold would generate a resonant system or “structure” in space. 

Classical mechanics tell us resonant system can only have the incremental or discrete energy associated with its fundamental or a harmonic of its fundamental frequency.

Similarly the incremental or discrete energies associated with individual photons in Richard Feynman’s experiment could be explained by assuming that they are a result of the fundamental or a harmonic of the fundamental frequency resonant properties of four *spatial* dimensions.

This shows how one can derive the quantum mechanical properties of energy/mass and a photon by extrapolating the laws of classical wave mechanics to a matter wave on a “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension.

However, one can also describe the physicality of a particle in terms of the wave properties 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 associated with a particle in the article “Why is energy/mass quantized?“

This provides the ability to understand how and why a photon can have the properties of both a wave and a particle because it clearly defines their interdependence in terms of the laws of Classical wave mechanics

However it also defines the physical reality of particle-wave duality in terms of the classical properties of a matter wave moving on the “surface” of a three dimension space manifold with respect to a fourth *spatial* dimension or four dimensional space-time environment because remember, as was show earlier they are equivalent

For example, the wave like interference of photons he observed would be due to the wave properties of the resonant “system” defined in the article “Why is energy/mass quantized?“.

If the distance between the two glass surfaces in Richard Feynman’s experiment is equal to half of the wavelength of the resonant “system” associated with a photon, classical wave mechanics tell us the interference of its wave properties would interfere and will, as mentioned earlier yield the energy associated with 0 photons.

If the distance between two glass surfaces is equal to its wavelength of they will reinforce each other and yield the energy associated with 16 photons.

However, it also tells us the reason the energy variations caused by their interference are quantized and not continuous as wave theory predicts they should is because, as was shown in the article “Why is energy/mass quantized?” the resonant properties of four *spatial* dimensions means that their energy would be propagated in the discrete quantized values associated with the fundamental or harmonic of fundamental frequency of four *spatial* dimensions or space-time environment they are occupying.

Yet this also defines the reason the wave properties of 8 reflected photons reinforce themselves to create the energy associated with16 photons is because Classical wave mechanics tells us that when two waves of the same frequency interact their frequency will or does not change.  Therefore if energy is propagated in discrete quantized values associated with the wavelength or frequency of a resonant system the reinforcement of the wave properties of 8 photons must be carried away in the integral or discreet energies associated with resonant systems of up to 16 photons of the same frequency as those original 8 photons.

This indicates that viewing the quantum mechanical world of wave–particle duality in terms of the geometric properties of a resonant “system” generated by a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension allows one to derive its “reality” by extrapolating the laws of classical mechanics in three-dimensional environment to a fourth *spatial* dimension.

It should be remember Einsteinâ€s genius allows us to chose if we want to resolve all paradoxes between the microscopic world of quantum mechanics and the macroscopic world of Relativity either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of energy/mass and the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the spatial as well as the time properties of our universe thereby giving us a new perspective on the physical relationship of particles and waves

Later Jeff

Copyright Jeffrey O’Callaghan 2014

The post The geometry of a particle wave appeared first on Unifying Quantum and Relativistic Theories.

Unfortunately many physicists attempt to define reality based solely on what they measure and do not attempt to conceptually integrate those measurements into the realty we see around us.

One example can be found in Brian Clegg book Before the Big Bang: The Prehistory of Our Universe (p. 137) where he describes how Neils Bohr reacted when Heisenberg proposed his uncertainty principal.
“When Heisenberg first told his boss, Neils Bohr, about the uncertainty principle, he put it across in the form of an imaginary microscope. He described a particle as an electron passing through a make-believe ultra powerful microscope. We use light to examine the object, so a beam of photons (quantum particles just as the electron is) is constantly crashing into the electron. The result is that the electronâ€s path is changed. You canâ€t look at a quantum particle without changing things. Heisenberg is said to have been reduced to tears when Bohr ripped his idea to pieces. Heisenberg had assumed that until the microscope scanned the electron, the electron had an exact position and momentum. He thought it was the process of observing it that messed things up. But actually, Bohr pointed out, the uncertainty was more fundamental than that. There was no need to observe the electron for uncertainty to apply: it was inherent to the nature of a quantum particle.”

In other words Neils Bohr said that because we will never be able to observe an electron without changing it or its environment one must simply accept the fact that we will never be able to understand why it behaves the way it does in terms of the “reality” we see around us.

However the science of physics is defined as “the asking fundamental questions regarding how and why matter and energy interact while demanding the answers be validated by observations.

Yet this definition appears to conflict with Neils Bohr assertion that the uncertainty principal is inherent to the nature of a quantum particle because that immunizes it from such questions.

Additionally he said since it is true that uncertainty principal is inherent to the nature of the unseen world of a quantum particle “Everything we call real is made of things that cannot be regarded as real”.

Yet if one uses his philosophy that “reality” does not exist then the observations used to define that principal also cannot be real or exist because one cannot observe something that does not exist.  In other words the very arguments Neils Bohr uses to support his concept of the uncertainty principal leads to it invalidation.

However history has shown us that one of the advantages to defining the universe that we cannot and will never be able to see in terms of the “reality” of our observable environment is that it limits the ability of our imagination to create nonexistent or fantasy worlds to support them.

For example Einstein mathematically derived the force of gravity in terms of a curvature in a four dimensional space-time universe.  However even though he knew that he would never be able to physically observe how a time dimension interacts with the three spatial dimensions he attempted and succeeded in explaining how a curvature in a space-time environment can result in the force gravity by watching how a marble moved on a curved surface in our observable three dimensional universe.

In other words Einstein not only mathematically quantified the measurements of the force of gravity but he also provided a qualitative explanation of how it could act at distance by anchoring it to the observable properties of an object moving on a curved surface in three-dimensional environment.

This methodology is in sharp contrast to how Newton defined gravity in that he simply accepted the fact that he was able to accurately quantify it using the concept of action at a distance even though he was aware that it disagreed, as the following excerpt from a letter he wrote to Bentley with the “reality” he saw around him.

“It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact…That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.

However Einstein’s unwillingness to accept action at a distance gave him the ability more accurately quantify gravity while providing an understanding of how it could act at a distance by aqs mentioned earlier anchoring it to the “reality” of our three-dimensional environment.  Additional it showed that Newton’s concept of absolute space and time only existed in the fantasy world of his imagination because according to Einstein gravity is caused by their variability.

This shows the power of attempting to understand the unobservable in terms of the observable by anchoring it to the “reality” of what we see around us and why we should be skeptical about accepting the validity of the uncertain principal based on Neils Bohr assertion that it is inherent to the nature of a quantum particle

However what is even more damaging to his ideology of blindly accepting a mathematical interpretation of the uncertainty principle, is that it is possible (much as Einstein did) to extrapolate the observable properties of our three dimensional environment to a quantum one as was done in the article “A classical interpretation of Heisenbergâ€s Uncertainty Principal” Dec. 1 2012 to explain and predict how and why it behaves the way it does.

However before we begin we must first reformulate Einstein space-time concept to their spatial equivalent.

(The reason will become obvious latter)

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

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe as was done in the article “The “Relativity” of four spatial dimensions” in terms of geometry of only four *spatial* dimensions.

On advantage to doing this is that it gives one a different perspective on the “reality” of the quantum environment and the uncertainty principal in terms of the observable properties of our three dimensional universe.

For example the article “Why is energy/mass quantized?” Oct. 4, 2007 demonstrated it is possible to understand 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 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 field of four spatial dimensions could explain the discrete quantized quantum mechanical properties of particles.

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 boundaries of the “box” containing the resonant system the article “Why is energy/mass quantized?” associated with a particle and why quantum systems behave the way they do.

However not only using the properties of a fourth *spatial* dimension allow one to understand why energy/mass in our three-dimensional world in terms of our experiences but it can also be used to explain the uncertainty principle

For example 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.

As mentioned earlier one can define a mechanism responsible of the uncertainty principal in terms the geometry of the four *spatial* dimensions because Quantum Mechanics mathematically defines the position and momentum of a particle in terms of non dimensional point.  This means there would be an uncertainty in determining its position because that point could be found anywhere within the volume of the “box” mentioned above.

Similarly there would be an uncertainty in measuring its momentum, again because quantum mechanics defines it in terms of a non dimensional point.  Therefore before one could determine a particle’s momentum one would have to know the exact position of the “end” points one uses to measure 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 defined a particle in the article “Why is energy/mass quantized?“  Therefore one could not determine its exact velocity and momentum because there will always be an uncertainty as to where the non dimensional point representing a particle is in the box when the measurement was taken

The reason why one cannot simultaneously measure both with complete accuracy is because the act of measure its momentum or position requires one to access different segments the “box” containing particle.

For example if one wants to make the most accurate measurement possible of its momentum internal to the box one would have to measure the time it took for it to transverse a given segment of it.  However this means that one could not determine its position because it would be changing throughout the entire time that it took it to transverse that portion of the box.

However if one wanted to make the most accurate measurement possible of its position internal to the box it would have to be stationary with respect to the box’s geometry meaning that one could not determine its monument because it would not be moving.  Since these two measurements required one to access different segments of a particles geometry they are mutually exclusive. 

Therefore one cannot simultaneously measure a particle position x and momentum p with complete accuracy.

This defines why, in terms of the reality we see around us there is a 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 it also tells us we should always attempt to conceptually integrate our theoretical models into the “reality” of what we “see” around us because it allows one to physically connect the abstract properties of a theoretical environment created by our imagination to the reality of the worlds they are describing thereby limiting its ability to create fantasy worlds such as the one Neils Bohr believed in to explain their theoretical models.

Later Jeff

Copyright Jeffrey O’Callaghan 2014

The post Should we let our imaginations define reality? appeared first on Unifying Quantum and Relativistic Theories.

Most scientist would agree the best way of accomplishing this would be to determine if one can be explained in terms of the other.

For example can one explain why many proponents of quantum mechanics assume that a particle simultaneously exists everywhere in space until it is observed or measured in terms of the classical laws that govern our macroscopic environment.  

In Brian Greene book “The Fabric of the Cosmos: Space, Time, and the Texture of Reality” (Kindle Locations 1825-1836) he explains the difference between the probabilistic world of quantum mechanics and the deterministic world of Newtonian mechanics.

“According to Newton, if we knew in complete detail the state of the environment (the positions and velocities of every one of its particulate ingredients), we would be able to predict (given sufficient calculation prowess) with certainty whether it will rain at 4:07 p.m. tomorrow; if we knew all the physical details of relevance to a craps game (the precise shape and composition of the dice, their speed and orientation as they left your hand, the composition of the table and its surface, and so on), we would be able to predict with certainty how the dice will land. Since, in practice, we canâ€t gather all this information (and, even if we could, we do not yet have sufficiently powerful computers to perform the calculations required to make such predictions), we set our sights lower and predict only the probability of a given outcome in the weather or at the casino, making reasonable guesses about the data we donâ€t have.

However one of the most fundamental laws of classical mechanics is that each cause has a specific effect and that identical causes will have identical effects.  However it also states that random causes will have random outcomes and that one can determine the probability of a certain event occurring based on the randomness of its cause.

Yet many feel that one cannot apply the concepts of Classical Newton physics to the quantum world because as Brian Greene points out in his book The Fabric of the Cosmos: Space, Time, and the Texture of Reality (Kindle Locations 1833-1836), “The probability introduced by quantum mechanics is of a different, more fundamental character (than classical Newton probabilities) Regardless of improvements in data collection or in computer power, the best we can ever do, according to quantum mechanics, is predict the probability of this or that outcome. The best we can ever do is predict the probability that an electron, or a proton, or a neutron, or any other of natureâ€s constituents, will be found here or there. Probability reigns supreme in the microcosmos.”
However if someone strikes a pool ball on a pool table in a dark room and cannot measure or determine initial conditions there is an extremely high probability that he will find it on the table when he turns on the light.  However, he or she does not assume that the balls simultaneously exist on every point on its surface until the light is turned. Additionally one can apply Newton’s laws and the probability of the different initial conditions associated with that event to determine the final resting place of the pool balls on the table after the light is turn on.  I think most would consider someone mentally deficient if he tried to convince us that the pool balls simultaneous existed every at every point on the surface of the pool table when the light off and only materialize when it was turn on just because he could not see how they got there.

Similarly why do some make the outlandish claim that a particle simultaneously exists in at every point in space and only materializes when it is observed based on the fact that they cannot “see” or measure the initial conditions and how they traveled to a specific point in space.

The reason is because quantum mechanics does not deal with evolution of a measurement but only with its outcomes. Therefore, because we in the macroscopic world and cannot “see” the initial condition responsible the evolution of a quantum system many assume that its entire history must be probabilistic. 

However, as with the balls on a pool table the finial resting place of them and all quantum systems would be definable only in terms of the random probabilities of their initial conditions if one cannot “see” or determine them even if its evolutionary history conforms to Newton’s laws.

This shows how one can explain probabilistic outcomes of experiments in the quantum world in terms of the classical laws of the macroscopic world by assuming randomness of their outcomes is due to a lack of knowledge of their initial condition and not due the the probabilistic properties of their evolution. 

Granted as Brian green pointed out nature may prevent us from ever develop the technology to precisely measure the initial conditions of a quantum system.  However, as was shown above that does not means we cannot find an explanation of what we cannot see in the microcosmos in terms of what we can see in the macro cosmos.

In other words it is a fallacy to assume that the quantum mechanical probabilities of the micro cosmos lack or cannot be explained by the determinism of the macro cosmos.

Later Jeff

Copyright Jeffrey O’Callaghan 2013

The post The quantum fallacy appeared first on Unifying Quantum and Relativistic Theories.

In Plato’s allegory “The cave” he describes how people who have been chained to a cave wall view the world outside of it.  “The people watch shadows projected on the wall by things passing in front of a fire behind them, and begin to ascribe forms to these shadows. According to Plato’s Socrates, the shadows are as close as the prisoners get to viewing reality. He then explains how the philosopher is like a prisoner who is freed from the cave and comes to understand that the shadows on the wall do not make up reality at all, as he can perceive the true form of reality rather than the mere shadows seen by the prisoners.
However he could have been talking about today’s scientists who are locked into a worldview that projects shadows that cannot be made to agree with the reality of the world they are living in.

For example Quantum theory defines the existence of particles in terms of a mathematically generated probability function and that they do not exist until a conscience observer looks at it.  In other words it assumes the act of observation or measurement creates the physical reality of our particle world.  However because only conscience beings can be observers it implies that it cannot exist without them being there to observe it.

However if one assumes reality exist only after someone observes it one must also assume that we humans evolved out of something that did not exist.

This seems to contradict the most common definition of reality: that it is an environment with a set of physical properties that exists even when there are no observers present.  In other words most believe the world exist in even when no one is there to observe it.

Plato’s in his allegory “The Cave” he tells us that one should base his or her interpretation of reality on direct physical observations of the “shadows” they cast on the cave walls because he feels it is the only way to connect their existence to the reality of the world outside of it.

However the  proponents of quantum mechanics face an even greater problem than those who reside in Platoâ€s cave because they assume that reality and existence is defined in terms of abstract mathematical probabilities which by definition do not have physical properties; therefore they are unable to cast shadows on the reality of the non-abstract environment that exists all around us. 

In other words the reality defined by quantum mechanics cannot create or define the physicality of the shadows projected on the walls of our world or cave as Plato calls it because they themselves do not have any.

Some would argue the fact that quantum mechanics can accurately predict what we observe in the world in terms of the abstract nature of probability functions means that what we perceive as the reality does not exist. 

However as Plato pointed out our only connection to reality is though the observation of the “shadows” it displays on our physical or material world.  Yet because of the abstract nature of probability functions of quantum mechanics they, by definition can never be part or interact with that world.  Therefore because we can physicality observe of the “shadows” of the quantum mechanical world in our environment isn’t it more likely the abstract one defined by quantum mechanics does not exist while those of the world that we can see and touch do.

Einstein was often quoted as saying “If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless.”

He realized as Plato did that reality can only be discovered by forming a physical image of what its shadows are telling us.

For example Newton in a letter to Bentley in 1693, talks about a conceptual problem he has with his gravity theory by rejecting the action at a distance that it requires.

“It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact…That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.”

Einstein looked at the shadows of reality cast by gravity and realized they could be created by a universe made up of four dimensional space-time.  He extrapolated the physical image of how objects move on a curve surface in a three-dimensional environment to a curved four dimensional space-time manifold to show that it can explain and predict how gravity “may act upon another at a distance through a vacuum” in terms of a curvature in space and time.   This allowed him to understand the reality behind the shadows we can see in our three-dimension world in terms of a physical image based on the existence of four dimension space-time.

In other words he was able to explain the gravitational shadows on the Newtonian cave walls in terms of a physical image cast by four dimensional space-time on them.

As Plato would say he perceived the true form of reality based on a physical image of the shadows seen by its prisoners.

Unfortunately many of today scientists seem to be ignoring the lessons taught to us by Plato and Einstein.  They chose to look for reality in terms of abstract mathematics instead of the physical imagery given to us by its shadows.

The reason may be because it is easier to alter an abstract environment based on mathematics to conform to an observational inconsistency that it is to alter one based on physical imagery. 

For example Quantum theory makes predictions based on the random properties of a probability function.  However because its abstract properties are not connected to any physical images of our world all observations no matter how inconsistent they are with the physical world it is describing can be incorporate into it.

This is in sharp contrast to the space-time environment defined by Einstein in that projecting the physical image of objects moving on a curve surface in a four-dimensional environment directly connects it to the physicality of the shadows it casts on our three-dimensional environment.

For example a mass that was repelled by gravity instead of begin attracted would contradict the physical model define by Einstein and would be extremely if not impossible to explain according to that model because that would mean that we should observe objects rolling up hill in our three-dimensional environment.  In other words because he defined gravity in terms of a physical image based on how objects move on a curve surface in a three-dimensional environment it makes observations like two masses repelling gravitational each other impossible to incorporate into it.

If however if some observation happened to contradict complimentary principal of quantum mechanics such as simultaneously observing both the particle and wave properties mass it could easily explained in terms of the fact that its probability functions tell us that anything that can happen eventually will  This makes it impossible to find an observation that would contradict it because it tells us the even the impossible is possible if we wait long enough.  However this can only happen in an abstract environment which is not bound by the physicality of our observational world because in that world we observe that some things just cannot happen.

But why should science put in the effort to understand the physical reality behind the shadows of our world when both the abstract mathematical foundation of quantum mechanics and the physics imagery of Einstein’s theories make very accurate predictions of future events based on the past. 

Because the mission of a science is to define reality in terms of what we perceive in the world around us which by definition is not abstract.

Later Jeff

Copyright Jeffrey O’Callaghan 2013

The post Plato’s lesson on quantum mechanics. appeared first on Unifying Quantum and Relativistic Theories.

In other words we assume we are conscience beings because we can perceive a world outside of ourselves however that world is created by our conscience ability to interpret it or as Friedrich Nietzsche put it “There are no facts, only interpretations”

This circular definition presents a very real problem for scientists because it is their task to objectively identifying the true nature of reality.
The problem arises because objectivity is based on analyzing observable phenomena that we become consciously aware of.  Therefore human beings are only indirectly connected to reality through their consciousness’s ability analyze it.

This means our understanding of objective reality is always clouded by our conscience perceptions, belief systems and the prevailing level of knowledge in the world because as just mentioned our conscience is an integral part of how science defines it.

Therefore, because of the circular nature of how science defines objective reality and conscience many feel it is an illusion that can never be fully grasped by any human being.

For example to the people of the middle ages, the fact that world was flat was an undisputed truth. If you traveled far enough, you would fall off. That perception or “knowledge” of reality was just as real to our predecessors as is the modern notion that the world is round.

Even so many feel that science has transformed the collective reality that most people experience.  Newton identified a whole range of laws that govern natural phenomena by observing the world.  These laws became the new reality for the people of his time although none of them actually exist in nature.  They were only human constructs developed by our conciseness to assist in understanding of the nature of the reality of the world we can see.

More recently Quantum mechanics defined the “reality” or state of a quantum system in terms of the mathematical probability function that can only exist or can be “seen” by the human conciseness.  However, it does not tell us anything about the state or “reality” of the world outside of our conciseness because it is based on abstract mathematical properties that only exist in the conciseness.

However due to circular nature of reality and conciseness the only thing that gives scientist’s the right to assume they understand its objective properties is to physically connect the worlds created by the intellect such as Isaac Newton to world through observing it.

Yet that same circular property gives some such as the proponents of quantum mechanics the right to say the only way to define objective reality is in terms of the ideas that exist in our conscience.

This means the best that science will ever be able to do is to define it based on the collective illusions of the reality that most of us believe in.

Latter Jeff

Copyright Jeffrey O’Callaghan 2011

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The ability to define a mechanism which can resolve the conflict between Maxwell’s classical wave theory of light and the quantization of the electromagnetic field confirmed by the photoelectric effect is one of them.

In the article “Why is mass and energy quantized?” Oct 4, 2007 it was shown that one can understand and derive both the quantum mechanical and wave properties of energy/mass by extrapolating the laws of a classically resonating three-dimensional environment to a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Additionally it was showed why all forms of energy must be propagated in these resonant systems.

(The concept of a particle having a wave component was first formulated in 1924, when Louis de Broglie he theorized they have a wave properties.  However he was unable to resolve the conflict between it and the quantum mechanical properties of a photon associated with the photoelectric effect.)  

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 spatially with the frequency associated with the energy of that event.

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

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

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

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

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.

Yet one cans also define the boundary of a quantum system in terms of the spatial properties of four spatial dimensions.

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 a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries associated with a particle in the article “Why is energy/mass quantized?“

The photoelectric effect is perhaps the most direct and convincing evidence of the existence of photons and the “corpuscular” nature of light and electromagnetic radiation.  That is, it provides undeniable evidence of the quantization of the electromagnetic field and the limitations of the classical field equations of Maxwell.

This conclusion is based on the observation that the emission of electrons begin as soon as electromagnetic energy of a given frequency strikes the photoelectric material.  This is inconsistent with the wave theory of light because it predicts the delayed emissions of electrons.

In addition, it was observed that varying the intensity of the light does not change the velocity of the electrons ejected but only their numbers, however increasing the frequency does.

Einstein in 1905 successfully explained these observations by assuming the incident light consisted of individual quanta, called photons, that interacted with the electrons in the metal like discrete particles, rather than as continuous waves and that each one carried the energy E = hf, where h is Planck’s constant and f is the frequency.  Therefore, increasing the intensity of the light corresponded to increasing the number of incident photons per unit time (flux), while the energy of each photon remained the same (as long as the frequency of the radiation was held constant). 

These assumptions explain why varying the intensity of the light does not change the velocity of the electrons ejected but only their numbers because according Einstein’s photonic concepts that would result in increasing the number of photons with the same energy thereby causing a greater number of electrons to be ejected.  However, because each photon has the same energy the electrons effect by them would carry the same average energy when ejected.  Additionally it would also explain why increasing the frequency “f” of the incident radiation would increase their average energy because that would increase the average energy of the photons striking the photoelectric material thereby their increasing average energy.

However, assuming as we have done that the quantization of the electromagnetic field is a result of a resonant system formed by a matter wave on “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension allows one to resolve the conflict between those properties and Maxwell’s classical wave interpretation of light.  This is because, it allows one to extrapolate the laws classical wave mechanics in a three-dimensional environment to a fourth *spatial* dimensions to explain its quantization.

Classical Wave Mechanics tells us resonant system must be quantized or have the discrete energies associated with their fundamental or a harmonic of their fundamental frequency.

Yet this means that one could interpret Planck’s constant or “h” in the equation Einstein used to calculate the energy of photon as the energy associated with the fundamental resonant frequency in four *spatial dimensions that defined a photon in the article “Why is mass and energy quantized?”.  Therefore, every photon would have a multiple “h” of that energy.

The reason why, as Einstein noted, “increasing the intensity of the incident radiation causes greater numbers of electrons to be ejected, each carrying the same average energy” is because each photon had the identical frequency and therefore, as was shown in the article “Why is mass and energy quantized?” would contain the same energy.  However this means that increasing the intensity of the incident radiation must mean a proportional an increase in the number of photons striking the photo electric material.  Therefore it follows that increasing the intensity of the incident radiation would cause greater numbers of electrons to be ejected, each carrying the same average energy.   However it allows his concepts to integrated into Maxwell’s wave theory of light because as was shown in that article the energy of a photon is related to the wave properties of its resonant structure.

Additionally, as Einstein also noted as one increased the frequency the average energy of the emitted electrons increases.  This is consistent with the classical wave interpretation of the resonant system associated with a photon in the article “Why is mass and energy quantized?” because it defines their quantized energy in terms of the frequency of a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimensions.  This means that according to Classical Wave Mechanics its quantized energy will be directly related to its frequency of that matter wave and therefore increasing its frequency will also increase the energy of the ejected elections.

The reason why delayed emission is not observed is because as was shown in that article energy can only be propagated in these resonant systems.  Therefore if the energy associated with a quantized resonant “system” of a photon of a given frequency is sufficient it will instantly eject an individual electron off a photoelectric surface while none will be f it is not.

This shows how one can resolve the conflict between Maxwell’s wave theory of light and the quantization of the electromagnetic field confirmed by the photoelectric effect by assuming that the quantization of an electromagnetic field is caused by a resonant system formed by a matter wave moving on a “surface” of three-dimensional space manifold with respect to a fourth *spatial* dimension.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

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One is that it could allow for the development of a theoretical link between gravity, mass and inertia in terms of interactions between a third and fourth *spatial* dimension.

Newton, in his laws of motion defined how the inertia of an object interacts with its environment and the effect forces have on them.  However, he was unable to define the causality of gravity or inertia.

Einstein was able to define the causality of gravity and the relativistic properties of motion in terms of a four-dimensional space-time manifold but he was unable to define the causality of inertia. 

However, as mentioned earlier one can derive the causality of both if one redefines Einstein’s space-time universe in terms of four *spatial* dimension.

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 that provided a method of converting a unit of space-time associated with energy to unit of space associated with position.  Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

This was the basis for, as was done in the article  “Defining energy” Nov. 26, 2007 for defining all forms of energy including inertia or momentum in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

While the article “The “Relativity” of four spatial dimensions” Dec. 01, 2007 showed that one can derive the causality of all forces or accelerations including gravitational in terms of an interaction of a mass with the slope of a curvature in a “surface” of a three-dimensional space.  Additionally it was shown the magnitude of gravitational mass was directly proportional to the magnitude of the displacement caused by that curvature.

(This curvature is analogous to a curvature in a four-dimensional space-time manifold Einstein theorized was the causality of gravitational accelerations.)

Therefore, according to the theoretical concepts presented in those articles the magnitude of the momentum of an object would be defined by the sum of two components.  The first would be the displacement in a “surface” of a three-dimensional space associated with the rest mass of an object, whose magnitude as the article “The “Relativity” of four spatial dimensions” Dec. 01, 2007 showed is defined by the magnitude of that mass.  While second would be the magnitude of a displacement in that “surface” that the article “Defining energy” Nov. 26, 2007 associated with ita momentum of its relative motion.  (The momentum of an object at rest with respect to other objects is zero so the displacement of three-dimensional space with respect to those objects would also be zero.)

In other words to define the total energy of an object or particle in motion one would have to add the displacements in a “surface” of a three-dimensional space manifold associated with its rest mass to that associated with its relative motion.

However the article “Defining energy” Nov. 26, 2007 also derives the causality of inertia in terms of the constant geometric displacement of a “surface” of a three dimensional space manifold with respect to four *spatial* dimension associated while showing why there will be a 1 to 1 correspondence between it and the curvature in space required to make a unit change in its displacement with respect to a fourth *spatial* dimension.

In other words it derives the causality of Newton’s law of inertia or the fact that “Every body remains in a state of rest or constant velocity unless acted upon by an external unbalanced force” in terms of a linear displacement in a “surface” of a three dimension space manifold with respect to fourth *spatial* dimension because that displacement would remain unchanged unless in interacted the curvature associated with an accelerative force defined in the “The “Relativity” of four spatial dimensions” Dec. 01, 2007

Additionally because as that article showed there is a one to one correspondence between the rest mass or inertia of an object and the magnitude of the curvature in a “surface” of a three-dimensional space associated with its gravitational component the relative accelerations of all objects will be the same in all gravitational fields.

This defines a causal link between the inertia, mass and gravity in terms of a geometric interaction between the third and a fourth *spatial* dimension.

Later Jeff

Copyright Jeffrey O’Callaghan 2010

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