The standard interpretation of his mathematics suggests that gravity is cause by a displacement in a three-dimensional space manifold with respect to time.

However an equally valid one defines gravity in terms of an environment consisting of only four *spatial* dimensions because by defining its geometric properties in terms of the equation E=mc^2 and the constant velocity of light gives one the ability to redefine a unit of time he associated with gravity in his space-time universe to unit of space in one consisting of only four *spatial* dimensions.
In other words it gives us mathematical way to convert a universe composed of four dimensional space-time to one made up of four *spatial* dimensions because one can define distance in it in terms of time times the constant velocity of light.

Even though these two interpretations yield the exactly the same numerical results describing our universe there is a very significant qualitative difference in that we observe we can only move in one direction forward with respect to a time dimension while in the spatial dimensions we can move in two direction upward or downwards backwards or forward.

This is significant because if gravity is caused by displacement in a three-dimensional space manifold with respect to spatial not a time dimension it may be possible to create a negative or antigravity potential in space.

In other words if gravity is cause by a displacement in a three dimensional space manifold with respect to a spatial instead of a time dimension it, at least in theory should possible to create an oppositely directed displacement which for all practical purposes would repel the gravitational field of normal matter and cause it to be propelled thought space.

It should be remember the existence of a time or space time dimension is the based exclusively on Einstein’s mathematics because no one has or will ever be able to directly observe it.

However the same could be said about a fourth *spatial* dimension in that it cannot be directly observed. But there is an experiment that could without ambiguity determine if our universe is physically made up of four *spatial* dimensions or four dimensional space-time.

As describe in the NewScientist article “Antimatter mysteries 3: Does antimatter fall up?” Apr 29, 2009, it is possible use uncharged particles to prevent electromagnetic forces from drowning out gravitational effects of antimatter. First we will be required to build highly unstable pairings of electrons and positrons, known as positronium, then excite them with lasers to prevent them annihilating too quickly. Clouds of antiprotons will rip these pairs apart, stealing their positrons to create neutral antihydrogen atoms.

Pulses of these anti-atoms shot horizontally through two grids of slits will create a fine pattern of impact and shadow on a detector screen. By measuring how the position of this pattern is displaced, the strength – and direction – of the gravitational force on antimatter can be measured

However if it is found the gravitational field of antiparticles opposes that of particles then we will be required to rethink our understanding gravity because Einstein’s Theory of General Relativity tells that objects that create gravitational field cause time to “move” slower with respect to a region of space that does not contain mass. In other words Einstein theory tells if antiparticle posses a negative gravitational potential time should be accelerated or move in the “opposite direction” were they exist with respect to the slowing he associated with gravity; something which would be observable in particle accelerators if it were to happen. The fact that this has not been observed tells us if antiparticles do have a negative gravitational potential it cannot be related to the physical property of a time dimension.

However as was mentioned earlier the fact that one can use Einsteinâ€s equations to qualitatively and quantitatively redefine the energy he associated with gravity in a space time environment in terms of four *spatial* dimensions would give us a viable explanation for the negative gravitational potential antimatter that would be consistent with his theories.

Later Jeff

Copyright Jeffrey O’Callaghan 2018

The post Antigravity propulsion; a real possibility. appeared first on Unifying Quantum and Relativistic Theories.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Later Jeff

Copyright Jeffrey O’Callaghan 2014

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

We have shown throughout this blog and its companion book “The Reality of the Fourth *Spatial* Dimension” there would be many theoretical advantages to defining space in terms four *spatial* dimensions instead of four-dimensional space-time.

One of them is that it would allow one to understand the classical origins of Heisenberg’s Uncertainty Principle by extrapolating observations of a three-dimensional environment to a fourth *spatial* dimension. 

For example In the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown it is possible to understand its quantum mechanical properties 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 form of energy/mass would be responsible for the discrete quantized quantum mechanical properties of particles.

However, it did 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.

However if this is true that one should be able to explain why the other properties of quantum systems are what they are in the same terms

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.

However, Quantum Mechanics mathematically defines the position and momentum of a particle in terms of non-dimensional point.

Therefore according to the above concepts 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 movement 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 use 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 define 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 the one dimensional point 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 through 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 in terms of classical mechanics why 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.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

The post A classical interpretation of Heisenberg’s Uncertainty Principal appeared first on Unifying Quantum and Relativistic Theories.

Einstein told us that it is made up of a dynamic balance between the properties of space and time.

For example he told us that space is a sort of multidimensional fabric, where the presence of mass causes the fabric of space-time to curve.  However he did not tell us anything about its composition.  Granted he did tell us what occurs when mass is present however he said nothing about space without mass.  In other words he simply told use how space reacts when mass is present.
However it is difficult to form a clear picture of how the physical properties of mass can interact with time because it is not perceived by most as matter or space but as an irreversible physical, chemical, and biological change in physical space.  So it is difficult to understand how mass can change time in a space-time dimension because it by definition is change.  In other words it does not make any sense to say that when mass is present in space it changes change.

Yet Einstein gave us the ability to solve this conundrum and develop more direct understand how and why the fabric of space is effected by mass when he used the equation E=mc^2 and the constant velocity of light to define the geometric properties of space-time.  This is because that provided a method of converting a unit of time associated with energy in a space-time dimension to unit of space associated with mass 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.

One of the many theoretical advantages to doing this is that it allows one to define the fabric of space in terms of physical properties of mass because it tells us why it causes the fabric of space-time to curve. For example one can see how moving a mass from one point to another physically changes the space it occupies which agrees with as mentioned earlier with what most of us perceive time to be.

In other words it tells us that mass must be an integral part of fabric of space.

However Einstein’s theory defines mass only in terms of the continuous field properties of space-time which means if one is to accept his theory one must also assume that there is continuous field of mass throughout space.  In other words it tells us that it is made up of that field.

This is true despite the fact that many believe that mass only exists in its particle or quantized form.

But observations tell a different story.

For example Louis de Broglie was the first to predict space is made up of the field 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.

In other words the space we associate with the particles must be composed of the field properties of mass because that is the only thing that could be responsible for the wave component of particles.  However this means the space the wave is moving through also must be made up of it to.

If this is true why then do we only observe its particle properties?

One can understand why by extrapolating the laws of governing resonance in a three-dimensional environment, as was done in the article “Why is energy/mass quantized?” Oct. 4, 2007 to the field properties of the wave Davisson and Germer to a fourth *spatial* dimension instead of four dimensional space-time.

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 continuous field properties of mass 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 the field properties of space would be responsible for it particles properties.

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

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

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

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

However there are at least two reasons why we are unable to directly observe the field properties of mass. The first is because all observations require an exchange of energy between what is being observed and the observer.  However the most effective and efficient way for nature to transfer information to our instruments is, as was shown in the article “Why is energy/mass quantized?“ in a resonate system made up of the field properties of mass.  Therefore in all measurements the particle properties associated with its resonant system will always be predominant over its field ones.

The second is that to directly measure a quantity there must be a physical difference between what is being measured and what is doing the measuring.  For example one cannot measure the changing level of water in a ship lock from a ship in it by measure how high it is above the surface of the water ship is floating in because it is changing at the same rate.

Similarly one cannot measure the field properties of the mass component of space because the field properties in the measuring instrument are changing at the same rate.

However we can indirectly measure how the field properties of mass interact with particles as was shown by in 1927 by Davisson and Germer observation of electron diffraction by crystals

This shows that the fabric or our cosmos is made continuous field of mass.

Unfortunately for those who believe that all mass must be contained in particles the logic for that conclusion is based purely on observations and the validly of Einstein theories.  Therefore to deny the existence of a continuous field of mass and the fact that it is the fabric of the cosmos one would have to deny the validity of Einstein theories.

It should be remember Einsteinâ€s genius allows us to choose to define all environments in either space-time or one consisting of four *spatial* dimension when he defined their geometry in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the quantum and field properties of space thereby giving us a new perspective on their interactions.

Later Jeff

Copy right Jeffrey O’Callaghan 2012

The post The fabric of the cosmos appeared first on Unifying Quantum and Relativistic Theories.

For the past 50 years, the Standard Model of Particle Physics has given us a complete mathematical description of the particles and forces that shape our world.  It predicts with so much accuracy the microscopic properties of particles and the macroscopic ones of stars and galaxies that many physicists feel that it is the ultimate theory of matter and energy.

But as Charles Seife mentions on page 142 of his book Alpha & Omega “Taken literally the plain vanilla form of the Standard model does not say anything about particle mass at all: in fact if theorists try to put mass in to its equations they blowup and become meaningless.”

In 1964 Peter Higgs showed that one can solve this problem and explain the origins of their inertial or rest mass is if one assumes space is permeated by what is called a Higgs field.

He was able to show that if a particle changes its velocity or accelerates, then the Higgs field should exert a certain amount of resistance or drag which according to his theory is the origin of mass.  In a slightly more precise terminology, the origin of mass is an interaction between a particle and the (nonzero) Higgs field.  It also assumes the disturbance created by mass as it moves through this field would have to generate the particle called the Higgs boson.

The only problem is that it is has been extremely difficult to identify the Higgs Boson (the particle the Standard Model associates with the Higgs field) because of the relatively few times it has been observed in the swarm of particles created in modern particle accelerators.

This is problematic for its proponents because the Standard Model tells us it should be created more frequently than it has been in the high energy environments of particle accelerators like The Large Hadron Collider (LHC)

This means that scientists should be careful before saying that they have discovered is the Higgs Boson predicted by the Standard Model.

This is especially relevant because there is an alternative explanation for mass that is based on the observable and therefore verifiable properties of three-dimensional space and does not require the analysis of a few isolated events as is required to verify the existence of the Higgs Field.

Observations of our three-dimensional environment tell us the total potential energy of an object or particle is related to position or its relative displacement with respect to some other position.  For example the potential energy of water in a bucket is in part determined by the height of its surface relative to the surface of the table it is resting on.  However, its potential energy is greater if one measures it relative to the floor on which the table is resting.

Unfortunately one cannot use the same logic to explain the potential energy of mass in the Standard Model because it defines in terms of a space-time environment which is not computable with one based solely on the properties of a spatial one as is the above example.

This would be true if Einstein had not used the equation E=mc^2 and the constant velocity of light to define the geometric properties of a space-time because that provided a method of converting a unit of space-time he associated with energy to unit of space associated with position 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.

The fact that one can use Einsteinâ€s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions is one bases for assuming, as was done in the article “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 according to the concepts in that article one could define the inertial or rest mass of an object or particle by extrapolating the observations of the potential energy of the water in a bucket resting on the surface of a table to a displacement in a “surface” of a three-dimensional volume with respect to a fourth *spatial* dimension.  In other words one could define the energy associated with mass in terms of a spatial displacement of a three-dimensional volume with respect to a fourth *spatial* dimension for the same reason as one can define the energy of the water in the bucket as being related to its displacement with respect to the table top.

In other words one can define the physicality of the Higgs field in terms of a displacement in the field properties of a four *spatial* dimension or space-time.

However if as was shown above one assumes that the Higgs field is made up geometric properties of four *spatial* dimensions or four dimensional space-time allows one to understand why it does what it does in terms of a physical image based our three dimension environment.

Isaac Newton defined inertia or mass as being responsible for why an object at rest will remain at rest, and an object in motion will remain in motion in a straight line at a constant speed.

This is because also allows one to derive the energy associated with the momentum or constant relative velocity of an object or particle in terms of those scalar field properties buy adding the displacement associated with its rest mass to the one the article “Defining energy?” Nov 27, 2007 associated with constant velocity. (The relative velocity 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 it allows on to understand in terms of a physical image based on our three dimensional environment how a  “linear” displacement in the field properties of a three-dimension space with respect to a fourth *spatial* dimension or the Higgs field is responsible for why particle have mass and the energy associated with its relative motion.

However it can also explain why an object or particle resists acceleration and why that resistance is directly proportional to its mass because as that article showed a curvature in a “surface” of a three dimensional space manifold with respect to a four *spatial* dimensions is responsible for all accelerations.  However because as was shown earlier there is a one to one correspondence between it and the space-time curvature Einstein indicated was responsible for mass it would be directly proportional to it.  Therefore the interaction of mass with the slope of a curvature in a “surface” of a three-dimensional space and it would be directly proportional to its mass.  This means the acceleration a mass experiences when it interacts a curvature in either in either an environment consisting of space-time or four *spatial dimensions proportional to its mass.  In other words there should according to these concepts outline above be a one to one correspondence between the mass of an object or particle and the acceleration it experiences for a given force.

However this is exactly what Isaac Newton’s Second law of motion tells us that “The acceleration of a body is directly proportional to the net force F acting on the body, and is inversely proportional to the mass m of the body, i.e., F = ma.

This not only provides an consistent explanation for the existence of mass but also solves one of the major conceptual problems associated with the Higgs field and Newton’s first law of motion or an object at rest will remain at rest unless acted on by an unbalanced force while an object in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

This is because it assumes the origin of mass is an interaction between a particle and the (nonzero) Higgs field and “that a disturbance created by mass as it moves through this field generates the particle called the Higgs boson” one also must assume that mass exchanges energy with the environment associated with the Higgs field.  However this means that all objects will experience an unbalance force as it moves through that environment because that is the only way it can cause a disturbance in it.

Yet this contradicts Newtown’s laws of motion and the observation that objects and particles maintain a constant velocity as they move through space because if it was true that mass is a result of an unbalance force or interaction between it and the Higgs field we would observe that they do not maintain a constant velocity while moving through space.

However according to the concepts outlined above mass is a result of an unchanging “linear” displacement in a “surface” of a three dimensional volume with respect to a fourth *spatial* dimension.  Therefore these concepts conceptually agree with both observations of the movement of particles or objects and Newton laws because as just mentioned the displacement in the “surface” three dimensional space associated with both mass and a constant velocity is unchanging and therefore does not require an interaction with its environment.

This demonstrates that one does not have to assume the existence of new of unique field such as the Higgs field to explain why particles have mass and inertia because Einstein showed us that it can be explained by extrapolating observations made in our of a three-dimensional environment to a fourth *spatial* dimension.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

The post The physicality of the Higgs fields appeared first on Unifying Quantum and Relativistic Theories.

Later he talks about the ratio of gravitational attraction to electrical repulsions:

“The ratio of the gravitational attraction to electrical repulsions is given by a number with 42 digits tailing off.  (The exact number was given in a diagram as Gravitation attraction / Electrical repulsion = 1/(4.17 X 10^42) Now therein lies a very deep mystery.  Where could such a tremendous number come from?  If you ever had a theory, from which both of these things are to come how could they come in such disproportion?  What equation has a solution which has for two kinds of forces an attraction and repulsion with that fantastic ratio.”

However, one may be able to show that gravity and electricity are different aspect of the same thing and derive “this fantastic ratio” if one extrapolates the laws of classical physics in a three-dimensional environment to a fourth *spatial* dimension as done in this blog.

Because as the article “Why is energy/mass quantized?” Oct. 4, 2007 showed one can derive the quantum mechanical properties of electrical forces 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.

There are 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.

The existence of four *spatial* dimensions would give the “surface” of three-dimensional space (the substance) the ability to oscillate spatially 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.

Therefore, these bi-directional oscillations in a “surface” of a 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 us 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.

This shows that one can understand the origins of the quantum mechanical properties of an electromagnetic wave in terms of classical mechanics if one assumes that it is a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth “spatial” dimension.

However as the article “The Photon: a matter wave?” Oct. 1, 2007 one can also understand the origins electrical forces and their quantum mechanical properties by extrapolating the laws of classical wave mechanics in a three-dimensional environment to a matter wave moving on a “surface” of a three-dimensional space manifold with respect to  fourth *spatial* dimension.

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

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

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

This would define the causality of the attractive forces of unlike charges associated with the electromagnetic wave component of a photon because it tells us a force would be developed by a differential displacement of a point on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, it also provides a classical mechanism for understanding why similar charges repel each other because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement.

Similarly the magnitude of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by two similar charges will be greater than that caused by a single one. Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two similar charges than it would be for a single charge.

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

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

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

This shows how one can understand electric and magnetic forces by extrapolating laws of classical mechanics in a three-dimensional environment to a displacement in a “surface” of a three-dimensional space with respect to a fourth *spatial* dimension.

The reason why electromagnetic forces are quantized is because as mentioned earlier its energy is propagated through space in quantized resonant systems defined in the article “Why is energy/mass quantized?”

However as the article “Gravity in four *spatial* dimensions” Dec. 15, 2007 showed one also can derive gravitational forces in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension by extrapolating the laws of classical physics in a three-dimensional environment to a fourth “spatial” dimension

One can understand how by comparing the forces on objects would experience in four *spatial* dimensions to those experienced by a marble on a rubber diaphragm with a rod pushing down it.

The surface of the diaphragm will represent the “surface” of three-dimensional space the marble, the energy/mass of an object and the rod will represent the “W” axis of a fourth *spatial* dimension.

(The “W” axis of the fourth *spatial* dimension was defined in the article “Embedded dimensions Oct. 27, 2007″)

If the end of the rod is orientated perpendicular to the “surface” of the diaphragm and is allowed to touch it without putting any pressure on it, the surface of the diaphragm will remain flat. The marble on the flat diaphragm would not move.

However, if pressure is applied to the rod, the “surface” of the diaphragm will become displaced and will no longer be perpendicular to the rod.

Gravitational forces will then have a tangential component along the displacement in the “surface” of the rubber diaphragm. The tangential component of the gravitational force directed along the “surface” of the diaphragm will cause the marble to move towards the apex of the depression

Similarly objects interacting with a displacement in “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension will experience a differential force directed towards the apex of that curvature. This force is called gravity.

(This curvature is analogous to the space-time curvature or displacement Einstein postulated is responsible for gravity.)

This would make gravitational and electrical forces different aspects of the same thing because it defines both in terms of the physical properties of a displacement in a “surface” of a three-dimensional space manifold with respect to a four *spatial* dimensions.

However, they also share a common property defined by the E=mc^2 because it defines the ratio of all forms of energy including electrical to the gravitational energy contained in mass.

If true one should be able to define a mechanism responsible for why “The ratio of the gravitational attraction to electrical repulsions is given by a number with 42 digits tailing off” in terms of the equation E=mc^2 and the fact that they are both have a common origin in a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Solving the equation E=m*c^2 for “m” gives m=E/c^2. This would define the ratio of electrical to its gravitational energy/mass equivalent because as mentioned earlier it defines the ratio of electrical to the gravitational energy associated with mass.

The law of gravitation states that the forces between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them or m x m/d^2

If one then substitutes E/c^2 for “m” in that equation one gets F=(E/c^2)^2/r^2.  This would define the ratio of the attractive properties of gravity to the repulsive properties of electrical energy in terms of the geometry of four *spatial* dimensions.

Using 3.0 x 10^10 cm/sec for the speed of light (c) and substituting we obtain for the ratio of electrical to gravitation forces to be F=E/(3.010^10 cm/sec)^4/r^2 or F=E/(8.1X 10^41 cm/sec).

This value represents the ratio of “Gravitation attraction / Electrical repulsion” Richard Feynman was referring to in the earlier quote from his book “The Character of Physical Laws” because it numerically defines the ratio of gravitational to electrical forces.

The theoretical result of 1/8.1 X 10^41 differs from the experimental value of 1/(4.17 X 10^42) because the equation of E=mc^2 that defines the ratio between gravitational and electrical energy tells us that some of the electrical energy in a system is derived from its mass or gravitational component.  Therefore, one must subtract the quantity of the gravitational equivalent of the electrical forces associated with that mass from the above derived value to obtain the experimental value.

Therefore it appears one can solved the “very deep mystery” as to why the inverse square law can be applied to both gravitational and electric forces by “making electricity and gravity different aspects the same thing” if one assume as we have done they are both caused by a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension and answers Mr. Feynman’s question as to “how could they (gravitational and electrical forces) come in such disproportion”.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

The post Linking gravitational and electrical forces appeared first on Unifying Quantum and Relativistic Theories.

However, this may be because the wavefunction defines existence in terms of the spatial properties of matter while Einstein defines it terms of its time or space-time properties.

This suggests that one may be able to explain what happens to the wave function when a measurement is made if one could convert or transpose time in Einstein’s space-time universe to its spatial equivalent in four *spatial* dimensions.
Einstein gave us the ability to do this when he use the equation E=mc^2 and the constant velocity of light to define the geometric properties of space-time because it provided a method of converting a unit of time in 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.

For example the article “Why is energy/mass quantized?

” Oct. 4, 2007 showed one can physical derive the quantum mechanical properties of energy/mass by extrapolating the laws of classical wave mechanics in a three-dimensional environment to a matter wave on a “surface” of a three-dimensional space manifold with respect to  a fourth *spatial* dimension.

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

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

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

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

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

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

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

(In the article “The geometry of quarks” Mar. 15, 2009  the internal structure of quarks, a fundament component of particles was derived in terms of a resonant interaction between a continuous energy/mass component of space and the geometry of four *spatial* dimensions)

However classical mechanics tell us that because of the continuous properties of waves the energy the article “Why is energy/mass quantized?” 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 putting a vibrating or oscillating ball on rubber diaphragm will create a displacement which will be disturbed over its entire surface while the magnitude of that displacement will decrease as one moves away from the point of contact.

However, this means if one extrapolates the mechanics of the rubber diaphragm to a “surface” of a three-dimensional space manifold one must assume the oscillations associated with each individual quantum system must be disturbed thought the entire universe while spatial displacement associated with its energy defined in the in the article “Defining energy?” Nov 27, 2007 would decrease as one move away from its position.  This means there would be a non-zero probability they could be found anywhere in our three-dimensional environment because, as mentioned earlier the article “Why is energy/mass quantized?” shown 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 also tells us a resonance would most probably occur on the surface of the rubber sheet were the magnitude of the vibrations is greatest and would diminish as one move away from that point,

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

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

Yet it also explains in terms of the observable reality of our environment what happens to the wave function when a measurement is made because to make one energy must be redirected towards the measurement instrument.  In other words the wave function does not collapse but is physically redirected towards the observing instrument at the point of observation and would continue on that path until another observation is made.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

The post Solving the Measurement Problem appeared first on Unifying Quantum and Relativistic Theories.