Quantum mechanics assumes that it is fundamental because it defines all interactions within it in terms of its quantized properties while one could say that Einstein’s General Theory of Relativity defines it in terms of an emergent property of continuous space-time manifold because that’s how it defines reality.

Most would agree the best way of which to determine which one is fundamental would be to see if one can be explain in terms of the other.
For example it is impossible to explain the apparent continuous properties of space-time in terms of the discrete properties quantum mechanics associates with energy/mass because by definition something that is discrete cannot by definition be continuous.   However it is possible to explain how the continuous properties of space-time can be broken up into the discrete components of energy/mass that allows quantum mechanics to define it in those terms.

Quantum mechanics assumes that energy/mass is quantized based, in part on Schrödinger wave equation which is used to predict and define the quantized energy distribution of electrons in an atom in terms of the Principal number (n),  the Angular Momentum “â„“”   (l), Magnetic (m) and Spin Quantum Number(+1/2 and -1/2).

However as mentioned earlier it may be possible to define an emergent mechanism based on the reality of four dimensional space-time that can explain why the energy distribution in a atom is quantized.

Einstein gave us the ability to qualitatively and quantitatively convert the relativistic properties of a space-time environment to an equivalent one consisting of only four *spatial* dimensions when he defined its geometric properties in terms of the equation E=mc^2 and the constant velocity of light. This is because it allows one to redefine a unit of time he associated with energy in his space-time universe to unit of space in one consisting of only four *spatial* dimensions.

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

However this would allow explain how the spatial characteristics of the energy distribution quantum mechanics associated with the four quantum numbers can emerge from reality of environment consisting of four dimensional space-time or its four *spatial* dimension equivalent.  

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

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

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

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

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

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

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

In other words this defines the quantization or the particle properties of energy/mass in terms of an emergent property of four *spatial* dimensions. 

However the fact that one can derive the quantum mechanical properties of energy/mass by extrapolating the resonant properties of a wave in three-dimensional environment to a fourth *spatial* dimension means that one should also be able to derive the quantum numbers that define the properties of the atomic orbitals in those same terms.

As mentioned earlier there are four quantum numbers.  The first the Principal Quantum number is designated by the letter “n”, the second or Angular Momentum by the letter ” â„“” the third or Magnetic by the letter “m” and the last is the Spin or “s” Quantum Number.

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

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

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

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

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

Therefore the integer representing the first quantum number would correspond to the physical length associated with the wavelength of its fundamental resonant frequency.

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

Additionally it also tells us why in terms of the physical properties four dimensional space-time or four *spatial* dimensions an electron cannot fall into the nucleus is because, as was shown in that article all energy is contained in four dimensional resonant systems. In other words the energy released by an electron “falling” into it would have to manifest itself in terms of a resonate system. Since the fundamental or lowest frequency available for a stable resonate system in either four dimensional space-time or four spatial dimension corresponds to the energy of an electron it becomes one of the fundamental energy unit of the universe.

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

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

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

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

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

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

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

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

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

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

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

Therefore one can define the physically of the fourth or spin quantum number in terms of the direction a “surface” of three-dimensional space is displaced with respect to a fourth *spatial* dimension.  For example if one defines energy of an electron with a spin of -1/2 in terms of a downward directed displacement one would define a +1/2 spin as an upwardly directed one.

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

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

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

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

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

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

This shows how one can derive the physicality of the four quantum numbers of an emergent property of four *spatial* dimension or its space-time equivalent.

Later Jeff

Copyright Jeffrey O’Callaghan 2016

The post Quantum mechanics as an emergent property of space-time. appeared first on Unifying Quantum and Relativistic Theories.

But it will be easier if we first transpose or covert Einsteinâ€s space-time universe to one consisting of only four *spatial* dimensions because it will enable us to define the mechanism responsible how this emergence takes place in terms of a geometry which is directly related the position or spatial properties associated with quantum probabilities instead of their non-positional or temporal components.

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 time he associated with energy to a unit of space associated with position.  Additionally because the velocity of light is constant it allows for the defining of  a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words the symmetry of the mathematics he use to define his space-time environment makes it possible to define the location of the quantum-classical boundary not only in terms of four dimensional space-time but also in four *spatial* dimensions thereby making it easier to understand how these two worlds interact.

For example the fact that one can use Einsteinâ€s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions allows one, as was done in the article “Defining energy?” Nov 27, 2007 to derive all forms of energy including those associated with quantum systems in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This will allow as was shown in the article “Why is energy/mass quantized?” Oct. 4, 2007 to understand of the quantum properties energy/mass by extrapolating the laws of classical wave mechanics in a three-dimensional environment to a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

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

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

The 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?“

As mentioned earlier in the article “Defining energy?” Nov 27, 2007 showed all forms of energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However assuming energy is result of a displacement in four *spatial* dimension allows one to derive the most probable position of a particle in terms of its wave function by extrapolating the observations and classical laws associated with a three-dimensional environment to a fourth *spatial* dimension.

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

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

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

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

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

Similarly if a particle as was shown earlier is a result of a resonant system formed in space it would most probably be found were the magnitude of the vibrations in a “surface” of a three-dimensional space manifold is greatest and would diminish as one move away from that point.

However this also defines how quantum probabilities can emerge from an classical interaction of energy/mass with the geometry of four *spatial* dimensions or four dimensional space-time while the same time eliminating the need for Quantum Decoherence because it shows that the different elements in the quantum superposition of a wavefunction are the result of the relative spatial orientation or position of an observer with respect to the its most probable position.

In other words it justifies the framework and intuition of the probabilistic interpretation of quantum mechanics as an acceptable approximation of a classical environment without Quantum Decohernece.

It should be remember Einsteinâ€s genius allows us to choose to define a quantum system in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories 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 causality of the quantum mechanical interaction.

Later Jeff

Copyright 2015 Jeffrey O’Callaghan 

The post Do we really need Quantum Decoherence? appeared first on Unifying Quantum and Relativistic Theories.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Later Jeff

Copyright Jeffrey O’Callaghan 2015

The post Why does space exist? appeared first on Unifying Quantum and Relativistic Theories.

In first scenario, there would be enough matter in the universe to slow the expansion to the point it would come to a halt and gravitational forces would  cause it to begin contracting which eventually would result in a fiery death called the “Big Crunch.

In the other scenario, there would be too little matter to stop the expansion and everything would drift on forever, always slowing but never stopping. This would end in a vast, dark, and cold state: a “Big Chill,” as the stars faded and died out.

However the discovery of a force causing the expansion of the universe to accelerate called Dark Energy opened up the possibility that the galaxies, solar system, stars, planets, and even molecules and atoms could be shredded by the ever-faster expansion.  In other words the universe that was born in a violent expansion could end with an even more violent expansion called the Big Rip.

Most scientists would agree that the best way of determining which one these scenarios defines its ultimate fate would be to understand the forces involved based on the most successful theories we have regarding the macroscopic properties of the universe.
However modern theories only address two of them.  For example the laws of thermodynamics which defines the forces associated with heat early in the universe and Einstein General Theory of Relativity which defines the gravitational forces which effect its evolution are two of the most success theories we have.  Unfortunately neither of them, in their present form addresses the expansive force called Dark Energy.

This is true even though Einstein foresaw the existence of Dark Energy when he added a cosmological constant to his General Theory of Relativity to make it conform to his belief in a static universe. 

Granted he added it in an “adhoc” manner to force it, in keeping with physicists thinking at the time to predict a stationary universe.  However when it became clear that the universe wasn’t static, but was expanding Einstein abandoned the constant, calling it the ‘”biggest blunder” of his life.

But lately scientists have revived Einstein’s cosmological constant (denoted by the Greek capital letter lambda) to explain this mysterious force which as mentioned earlier is causing the expansion of our universe to accelerate even though they have been unable to Einstein integrate it into the theoretical structure of his General Theory of Relativity.

However we may find clue as to why by observing how our universe is expanding.

For example observations of the universe’s expansion tell us that three-dimensional space is expanding towards a higher spatial dimension not a time or space-time dimension.  

Therefore, to explain the how the expansive force called dark energy is accelerating the spatial expansion of the universe one would have to assume the existence of a another *spatial* or fourth *spatial* dimension in addition to the three spatial dimensions and one time dimension that Einsteinâ€s theories contain to account for that observation.

This would be true if Einstein had not given us a means of qualitatively and quantitatively converting the geometric properties of his space-time universe to one consisting of only four *spatial* dimensions.

He did this when he defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2 and the constant velocity of light because that provided a method of converting the displacement in space-time manifold he associated with energy to its equivalent displacement in four *spatial* dimensions.  Additionally because the velocity of light is constant he also defined a one to one qualitative and quantitative 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 four *spatial* dimensions.

The fact that the equation E=mc^2 allows us to quantitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions 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 displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of one in a space time manifold.

As mentioned earlier one reason why it is difficult to integrate the accelerated special expansion of three-dimensional space towards a higher space dimension into Einstein space-time universe because it does not define one. 

However it is easy to do if one redefined it, as was done above in terms of four *spatial* dimension because that higher spatial dimension would become an integral part of its theoretical structure.

Yet it also allows one to understand how and why Dark Energy is causing the accelerated spatial expansion of the universe and what its ultimate fate will be in terms the laws of thermodynamics and the concepts of Einstein’s theories.

We know from the study of thermodynamics that energy flows from areas of high density to one of low density very similar to how water flows form an elevated or “high density” point to a lower one.

For example, if the walls of an above ground pool filled with water collapse the molecules on the elevated two-dimensional surface of the water will flow or expand and accelerate outward towards the three-dimensional environment surrounding it while the force associated with that expansion decreases as it expands.

Additionally we know from observations of the cosmic background radiation that presently our three-dimensional universe has an average energy component equal to about 3.7 degrees Kelvin. 

However this means that according to concepts developed in the article “Defining energy” (mentioned earlier) the three-dimensional “surface” of our universe which has an average energy component of 3.7 degree Kelvin would be elevated with respect to a fourth *spatial* dimension.

Yet this means similar to the two dimensional surface of the water in the pool the particles that occupy that elevated region of three-dimensional space and the space they occupy will accelerate and flow or expand outward in the four dimensional environment surrounding it and that the force associated with that expansion will decline as it expands.

This shows how reformulating Einstein’s theories in terms of four *spatial* dimensions allows one to use the laws of thermodynamics to explain what the force called Dark Energy is and why it is causing the accelerated expansion of the universe in terms of those theories.

Many feel that because space is everywhere, the force called Dark Energy is everywhere, and its effects increase as space expands. In contrast, gravity’s force is stronger when things are close together and weaker when they are far apart.

However the law of conservation of energy/mass tells that energy/mass cannot be created or destroyed in a closed environment. Therefore because the universe is  us since, by definition is closed system the kinetic energy of the universeâ€s energy/mass cannot exceed its gravitational contractive properties of its mass because Einstein tells us that its kinetic energy is made up of that mass.

Therefore because some of the kinetic energy of some of its components is not directed towards its expansion because of the random motion of star and galaxies the total gravitational contractive properties of its energy/mass must exceed the kinetic energy of its expansive components. Which means at some point in time the gravitation contractive potential of its energy/mass must exceed the kinetic energy of its expansion because as just mentioned not all of its kinetic energy is directed towards its expansion. Therefore at that point, in time the universe will have to enter a contractive phase.

Some may disagree by saying that as the universe expands its energy is spread out over a larger volume so after a while it just vanishes so to speak or as some like to say that the universe experiences a heat death. However Einstein theories do not permit energy to just disappear or “die”. It unequivocally tells us that if the kinetic energy content in a closed environment decreases as it cools the mass content of that environment must increase irrespective of the volume of that environment. Therefore because by definition the universe is a closed system one must assume that any reduction in its overall energy content of the universe including its heat energy must be must be compensated for by an increase in its total attractive gravitational mass content.

In other words if this theoretical model is correct our universe has never ending future which exists between an icy death caused by Dark Energy and a fiery rebirth created by gravity.

Later Jeff

Copyright Jeffrey Oâ€Callaghan 2014

The post Fire or ice how will our universe end? appeared first on Unifying Quantum and Relativistic Theories.

“More is unknown about it than is known. We know how much dark energy there is because we know how it affects the Universe’s expansion. Other than that, it is a complete mystery. But it is an important mystery. It turns out that roughly 68% of the Universe is dark energy. Dark matter makes up about 27%. The rest – everything on Earth, everything ever observed with all of our instruments, all normal matter – adds up to less than 5% of the Universe. Come to think of it, maybe it shouldn’t be called “normal” matter at all, since it is such a small fraction of the Universe.
One explanation for dark energy is that it is a property of space.  Albert Einstein was the first person to realize that empty space is not nothing. Space has amazing properties, many of which are just beginning to be understood. The first property that Einstein discovered is that it is possible for more space to come into existence. Then one version of Einstein’s gravity theory, the version that contains a cosmological constant, makes a second prediction: “empty space” can possess its own energy. Because this energy is a property of space itself, it would not be diluted as space expands. As more space comes into existence, more of this energy-of-space would appear. As a result, this form of energy would cause the Universe to expand faster and faster. Unfortunately, no one understands why the cosmological constant should even be there, much less why it would have exactly the right value to cause the observed acceleration of the Universe.” 

Most scientists would agree the best case scenario would be to understand the causality of dark energy and how it interacts with its environment in terms of observations and our currently accepted theoretical models.

However, presently there are only two scientific disciplines that address those interactions.  The first or the laws of thermodynamics defines the forces associated with heat early in the universe’s evolution and the second or Einstein’s General Theory of Relativity defines how gravity influences that evolution.

Unfortunately neither of them, in their present form address the expansive force of Dark Energy and how or why it interacts with its environment to cause it to accelerate.

Yet one of the most obvious difficulties in integrating it into Einsteinâ€s space-time universe is that observations tell us that three-dimensional space is expanding towards a higher spatial dimension not a time or space-time dimension.  

Therefore, in order to explain the observed spatial expansion of the universe one would have to assume the existence of a another *spatial* or fourth *spatial* dimension in addition to the three spatial dimensions and one time dimension that Einsteinâ€s theories contain to account for that observation.

This would be true if Einstein had not given us a means of qualitatively and quantitatively converting the geometric properties of his space-time universe to one consisting of only four *spatial* dimensions.

He did this when he defined the geometric properties of a space-time universe and the dynamic balance between mass and energy in terms of the equation E=mc^2 and the constant velocity of light because it allows one to redefine a unit of time he associated with energy in his space-time universe to unit of space in a universe consisting of only four *spatial* dimensions. 

In other words by defining the geometric properties of a space-time universe in terms of the equation E=mc^2 and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

The fact that the equation E=mc^2 allows us to quantitatively derive the physical properties of energy in a space-time universe in terms of its spatial properties 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.

As mentioned earlier it is difficult to integrate the causality of three-dimensional space expanding towards a higher *spatial” dimension into Einstein space-time universe because it does not define a higher spatial dimension. 

However it is easy if one reformulates it, as was shown above to be possible in terms higher fourth *spatial* dimension.

Yet this also allows one to understand how and why the force called Dark Energy is causing an accelerated spatial expansion of our universe in terms of the laws of thermodynamics because it gives one the ability, as mentioned earlier to use his equations to qualitatively and quantitatively define energy in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimensions.

We know from the study of thermodynamics that energy flows from areas of high density to one of low density very similar to how water flows form an elevated or “high density” point to a lower one.

For example, if the walls of an above ground pool filled with water collapse the elevated two-dimensional surface of the water will flow or expand and accelerate outward towards the three-dimensional environment surrounding it while the force associated with that expansion decreases as it expands.

Yet we know from observations of the cosmic background radiation that presently our three-dimensional universe has an average energy component equal to about 3.7 degrees Kelvin. 

However this means according to concepts developed in the article “Defining energy” that the three-dimensional “surface” occupied by the particles in our universe which has an average energy component of 3.7 degree Kelvin would be elevated with respect to a fourth *spatial* dimension.  

Yet this means similar to the water molecules occupying the elevated two dimensional surface of the water in the pool, the particles occupying a region of three-dimensional space that is elevated because of its 3.7 degree temperature will flow and accelerate outward in the four dimensional environment surrounding it.

This shows how reformulating Einstein’s theories in terms of four *spatial* dimensions allows one to use the laws of thermodynamics to explain what the force called Dark Energy is and how it can be seamlessly integrated into his general theory of relativity.

Later Jeff

Copyright Jeffrey O’Callaghan 2014 

The post How Einstein may have explained Dark Energy appeared first on Unifying Quantum and Relativistic Theories.

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

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

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

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

(The reason will become obvious later.)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Later Jeff

Copyright Jeffrey O’Callaghan 2014

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

In first scenario, there would be enough matter in the universe to slow the expansion to the point where, like the baseball, it would come to a halt and the gravitational forces associated with it would result in it retracting causing it to crash together in a “Big Crunch.”

In the other scenario, there would be too little matter to stop the expansion and everything would drift on forever, always slowing and slowing but never stopping. This would end in a vast, dark, and cold state: a “Big Chill,” as the stars faded and died out.

However the discovery of Dark Energy or a force causing the accelerated expansion of the universe opened up the possibility that the galaxies, solar system, stars, planets, and even molecules and atoms could be shredded by the ever-faster expansion.  In other words the universe that was born in a violent expansion could end with an even more violent expansion called the Big Rip.
Most scientists would agree that the best way of determining which one these scenarios defines its ultimate fate would be to list all of the observations regarding the forces controlling its expansion and try to understand them based on the most successful theories we have regarding the macroscopic properties of energy/mass.

For example it is assumed by many that because space is everywhere, the force called Dark Energy is everywhere therefore its effects should increases as it expands.  In contrast, gravity’s force is stronger when things are close together and weaker when they are far apart.  Therefore many believe the expansion will continue at an ever increasing rate, eventually ripping space apart.

However if one views the observational evidence supporting the existence of Dark Energy in terms of the laws of thermodynamics and Einstein’s theories, it strongly suggests that it will weaken not increase as space expands and that eventually gravity will become the dominate force in our universe.

Observations of the expansive force called Dark Energy tell us that three-dimensional space is expanding towards a higher spatial dimension not a time or space-time dimension.  

Therefore, to explain the observed spatial expansion of the universe one would have to assume the existence of a another *spatial* or fourth *spatial* dimension in addition to the three spatial dimensions and one time dimension that Einstein’s theories contain to account for that observation.

This would be true if Einstein had not given us a means of qualitatively and quantitatively converting the geometric properties of his space-time universe to one consisting of only four *spatial* dimensions.

Einstein defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2.  However when he used the constant velocity of light to define that balance he provided a method of converting a unit of space he associated with mass to a unit of space-time he associated with energy.   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.

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 quantitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions 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.

As mentioned earlier it is difficult to integrate the causality of how three-dimensional space can be expanding towards a higher *spatial” dimension into Einstein space-time universe because it does not define a higher spatial dimension. 

However it is easy integrate it if one reformulates it, as was done above in terms higher fourth *spatial* dimension.

Yet it also allows one to understand how and why the expansive force called Dark Energy is causing the spatial expansion of our universe in terms of the laws of thermodynamics because it gives one the ability, as mentioned earlier to use his equations to qualitatively and quantitatively define energy in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimensions instead of one in a space-time environment.

We know from the study of thermodynamics that energy flows from areas of high density to one of low density very similar to how water flows form an elevated or “high density” point to a lower one.

For example, if the walls of an above ground pool filled with water collapse the elevated two-dimensional surface of the water will flow or expand and accelerate outward towards the three-dimensional environment surrounding it while the force associated with that expansion decreases as it expands.

Yet we know from observations of the cosmic background radiation that presently our three-dimensional universe has an average energy component equal to about 3.7 degrees Kelvin. 

However this means that according to concepts developed in the article “Defining energy” (mentioned earlier) the three-dimensional “surface” of our universe which has an average energy component of 3.7 degree Kelvin would be elevated with respect to a fourth *spatial* dimension.

Yet this means similar to the two dimensional surface of the water in the pool three-dimensional space will accelerate and flow or expand outward in the four dimensional environment surrounding it and that the force associated with that expansion will decline as it expands.

This shows how reformulating Einstein’s theories in terms of four spatial dimensions allows one to use the laws of thermodynamics to explain what the force called Dark Energy is and why it is causing the accelerated expansion of the universe in terms of the Einstein’s theories.

As mentioned earlier many feel that because space is everywhere, the force called Dark Energy is everywhere, and its effects increase as space expands. I n contrast, gravity’s force is stronger when things are close together and weaker when they are far apart.

However if the above theoretical model is correct than the magnitude of Dark Energy relative to gravitational energy will not continue to increase as the universe expands but will decrease because Einstein also told us that there is an equivalence between mass and energy and since mass is associated with the attractive properties of gravity it also tells us, because of that equivalence, the kinetic energy associated with the universeâ€s expansion also possess those attractive properties. However the law of conservation of energy/mass tells us that in a closed system the creation of kinetic energy cannot exceed the gravitational energy associated with the total energy/mass in the universe and that a reduction in one must be compensated for by an increase in the other.

This means the total gravitation potential of the universe must increase as it expands and cools approaching a maximum value at absolute “0” while at the same time the kinetic energy of its expansive components must decrease. Therefore, at some point in time, the universe MUST enter a contractive phase because the total gravitational potential must eventually exceed the kinetic energy of its expansion. This is would be true even though the gravitational potential of its kinetic energy components would be disturbed or “diluted” by a factor of c^2.

(Some may try to dismiss this by saying that as the universe expands its energy is spread out over a larger volume so after a while it just vanishes so to speak or as some like to say that the universe experiences a heat death.  However Einstein theories do not permit energy to just disappear or “die”.  It unequivocally tells us that if the kinetic energy content in a closed environment decreases as it cools the mass content of that environment must increase irrespective of the volume of that environment.  Therefore because by definition the universe is a closed system one must assume that any reduction in its overall energy content of the universe including its heat energy must be must be compensated for by an increase in its total attractive gravitational mass content.)

Therefore, just after the big bang when the concentration of energy and mass was high, gravitational force would predominate over Dark Energy because the distance between both its energy and mass components was relatively small.

However as the universe expands the its gravitational attractive forces will decrease more rapidly than the expansive force associated with Dark Energy because they are related to the square of the distance between them while those of the expansive forces of Dark Energy are more closely related to a linear function of the total energy of content of the universe. 

Therefore after a given period of time the expansive forces associated with Dark Energy will become predominate and the expansion of the universe will accelerate.

However as the universe expands and cools that force will decrease because as mentioned earlier similar to the two-dimensional surface of the water in a collapsed pool, the forces associated with that expansion will decrease as it expands.

This means that eventually gravitational forces will win because, as mentioned earlier thermodynamics tells us the total accelerative forces associated with Dark Energy will decease and therefore will eventually approach zero, while the total mass content and the gravitational attractive forces associated with it will remain constant as the universe expands even though they may be separated by a greater distant.

Therefore, gravity will eventually win the battle with dark Energy because as was just mentioned the forces associated with it approach zero as the expansion progress while those of gravity remain constant.

There can be no other conclusion if one accepts the validity of Einstein’s theories and the laws of thermodynamics because the theoretical arguments presented here are a base solely on their validity.

Later Jeff

Copyright Jeffrey O’Callaghan 2013

The post Gravity or dark energy: which one will win? appeared first on Unifying Quantum and Relativistic Theories.

Einstein told us that energy and mass are interchangeable however he did not define what mass is.  He only told us how mass interacts with space-time.

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

However Einstein’s inability to define or derive the casualty of mass is can be traced to the fact that he chose to define the energy associated with it in terms of four dimension space-time instead of defining the mass associated with energy in terms four *spatial* dimensions.

Yet Einstein gave us the ability to do this when used the equation E=mc^2 and the velocity of light to define the geometric properties of space-time because it allows one to convert a unit of displacement he associated with energy in a four dimensional space-time universe to an equivalent displacement a unit of mass would create in four *spatial* dimensions.  Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words because he defined the geometric relationship between energy and mass in terms of the constant velocity of light means that one can quantitatively and qualitatively define a one to one between the properties of energy in a space-time universe to the physical properties of mass four *spatial* dimensions.

This was the bases for assuming as was done in the article “Defining energy” Nov 27, 2007 that all forms of energy including thermo and inertia or momentum of mass 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 instead of one in a space-time environment.
However changing ones perspective on the geometric structure of the universe form one of space-time to four *spatial* dimensions not only gives one the ability to understand the causality of mass but also give one the ability derive its quantum mechanical properties as was done in the article “Why is energy/mass quantized?” Oct. 4, 2007″ in terms of its wave component and the resonant properties of four *spatial* dimensions.

(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 classical resonance to occur.

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

Classical mechanics tells us that resonant systems can only take on the discrete or quantized energies associated with a fundamental or a harmonic of their fundamental frequency.

However, this 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 resonant system associated with a particle.

Therefore, these resonant systems in a four *spatial* dimensions would define mass and its quantum mechanical properties 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.

This would allow one to, not only understand the causality of the absolute properties of mass such as inertia but it would allow us to derive all of its relativistic ones.

For example one can use these concepts to explain why the corresponding particle types across the three fundamental families of particles in the Standard Model listed in the table below have identical properties except for their mass, which 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 of its 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 of the environment they are occupying.

Thus suggest the reason “The corresponding particle types across the three families 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 energy 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 properties of classical resonance and the existence of four *spatial* dimensions.

However it also allows one to derive the absolute properties of mass associated with Newton’s first and second laws of motion because as was shown in the article “The Equivalence Principal: an alternative to space-time” July 15, 2008 all accelerations or forces (including gravitational) can be derive in terms of a curvature in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

(This curvature is analogous to the curvature in space-time Einstein assumed was responsible for gravitational forces.)

Newton’s first law of motion which defines the inertial properties of the mass of an object or particle states that “Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it”

However this is what one would expect if one assumes, as mentioned earlier the momentum of an object is caused by a displacement of a “surface” of a three-dimension space manifold with respect to a fourth *spatial* dimension because according those concepts it would tent to stay rest or once in motion would tend to stay in motion because its displacement would remain constant unless it interacted with an external force or as was shown in the article “The Equivalence Principal: an alternative to space-time” a three dimensional “surface” that was curved with respect to a fourth *spatial* dimension.

However it also allows on to understand the causality of Newton’s second law which defines the relationship between an object’s mass “m”, its acceleration “a”, and why the change in velocity of an object or particle is define by the equation is F = ma because as mentioned earlier, the rest mass of an object is directly proportional to a displacement a “surface” of three-dimensional space manifold with respect to fourth *spatial* dimension.  Therefore, as was shown in the article “Defining energy” there will be a 1 to 1 correspondence between it and the curvature in space associated with the energy required to make a unit change in its displacement with respect to a fourth *spatial* dimension.  Therefore the inertia of an object or its resistance to change in velocity would be directly related to its mass. 

In other words using Einstein’s field equations to redefine his space-time universe in terms of four *spatial* dimension allows one to not only understand and derive the causality of the relativistic properties of mass but also the absolute properties associated with its inertia without the need of assuming the existence of the Higgs Boson.

Later Jeff

Copyright Jeffrey O’Callaghan 2013

The post Deriving mass without the Higgs Boson appeared first on Unifying Quantum and Relativistic Theories.