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.

However these laws suggest the existence of another more fundamental one that physically defines their causality.
For example Einstein told us that time dilates and space contracts as the energy and momentum of reference frames increase.

In other words there appears to a one to one correspondence between the effects momentum and energy has on the dimensional properties of space-time.

However the fact that the energy and momentum have a common effect on those properties suggests there may be a physical connection between them and their conservation laws.

For example Einstein told us the mass of a particle created in accelerators increases the curvature in space-time causing the physical distance between two points external to it to decrease by a measurable amount.  If that particle decays that curvature returns to where it was before that mass was created.  In other words physical properties of space are conserved in the creation, destruction or redistribution of mass.  Additionally he also told us that concentrating it in the form of a particle causes time to dilate by a measurable amount with respect to its external space-time environment and when that particle decays time is returned to normal rate of change. 

In other words in all reactions involving mass the physical properties of space-time are conserved because they always return to their original value before it was either created or destroyed.

One can also connect the causality of the law of conservation of all forms of energy to the physical properties of a space-time environment.

For example it can be shown the causality of charge conservation is also directly related to the symmetries of the space-time environment defined by Einstein.

However it will be easier to explain if one coverts it to its equivalent in four *spatial* dimensions.

(The reason will become obvious later on in this discussion.)

Einstein gave us the ability to do this when defined the geometric properties of space-time in terms of the constant velocity of light because that provided a method of converting a unit of time in a space-time environment to a unit of space in four *spatial* dimensions. Additionally because the velocity of light is constant he also defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

The fact that one can use Einsteinâ€s theories to qualitatively and quantitatively derive the displacement he associated with 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 including those associated with charge can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This allows one to derive the physical properties of charge in terms a displacement in that “surface” with respect to a fourth *spatial* dimension.

For example if one raises a cup of water above its surface it will be given a measurable amount of potential energy with respect to that surface while at the same time a force will be developed that will be directed downward towards it.  Additionally the level of the water will be lowered by the exact amount that was removed by the lifting of the cup above its surface.  If one pours the water back the levels will return it original depth.  In other words the level of the water is conserved due to the symmetry of its surface levels.

However as was shown in the article “Defining energy” Nov 27, 2007 if one raises, with respect to a fourth *spatial* dimension the volume of three-dimension space associated with a charge it will be given a measurable amount of potential energy with respect to that “surface” while at the same time a force will be developed that will be directed downward towards it.  Additionally the energy level of three-dimensional space not associate with that charge will be lowered by the exact same amount.  If one calls the volume space that was raised up a negative charge one would call the lowering of the “surface” of three dimension space caused by that a positive charge. If one neutralizes the negative charge by bring it in contact with that “surface” it will return to its original level and the charge will be neutralized.  This shows how one can derive the causality of charge conservation in term of the symmetry imposed by Einstein theories. 

In other words symmetry imposed by Einstein’s space-time environment means that charge must be conserved because the creation of one must always be offset by the other.

This is true in environments consisting of either four *spatial* dimensions or four dimensional space-time because as was shown earlier they are quantitative and qualitative interchangeable.

However it also allows one to understand how the conservation laws of nature are physically connected to each other in terms of the physical geometry of our universe.

It should be remember Einsteinâ€s genius allows us to choose to derive the conservation laws either a space-time environment or one consisting of four *spatial* dimension when he defined their environments in terms energy and the constant velocity of light. This interchangeability broadens the environment encompassed by his theories thereby giving us a new perspective on the origins of the conservation laws of physics.

Later Jeff

Copyright Jeffrey O’Callaghan 2016

The post The conservation of space-time. appeared first on Unifying Quantum and Relativistic Theories.

For example the density of mass to energy in the early universe must have been very close to a specific value to explain how stars could have evolved because if their concentrations were not it would depart rapidly from the one that would allow them to form over cosmic time.  Calculations suggest that it could not have departed more than one part in 10⁶² from that value.   This leads cosmologists to question how the initial density came to be so closely fine-tuned to this ‘special’ value that would have allowed stars and therefore life to evolve.
This has come to be called the flatness problem because the density of matter and energy which affects the curvature of space-time must have very specific value to give it the flat geometry required for stars to form and life to evolve.  In other words if the energy of the universe expansion was much larger it would have overpowered gravity preventing the formation of stars while if gravity was to strong they would have formed to quickly thereby not give life as we know it time to evolve.  `

The problem was first mentioned by Robert Dicke in 1969. 

The most commonly accepted solution among cosmologists is cosmic inflation or the idea that the early universe underwent an extremely rapid exponential expansion by a factor of at least 10⁷⁸ in volume, driven by a negative-pressure vacuum energy density.

This solves the flatness problem because the act of inflation actually flattens the universe.  Picture a uninflated balloon, which can have all kinds of wrinkles and other abnormalities, however as the balloon expands the surface smoothes out.  According to inflation theory, this happens to the fabric of the universe as well.

However, many view the inflationary theory as a contrived or “adhoc” solution because the exact mechanism that would cause it to turn on and then off is not known.

Yet, if one defines energy/mass density of our universe in terms of its spatial properties instead of the temporal ones of four dimensional space-time one can explain and predict why it has the correct proportions to cause its geometry to be hospitable to life as we know it by extrapolating the laws of classical physics in a three-dimensional environment to one of four *spatial* dimensions.

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

However, doing so makes easier to understand the mechanisms responsible for creating a flat universe that would enable life to evolve because flatness is associated more with the properties of spatial environment than those of a temporal one.

For example it would allow one to derive the momentum and the gravitational potential of the universe mass components as was done in the in the article “Defining potential and kinetic energy?” Nov. 26, 2007 in terms of, oppositely directed curvatures in “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  In other words if one can define the gravitational potential of mass in terms of a depression in its “surface” one could derive momentum of its expansion in terms of elevation in it.

This differs from Einsteinâ€s theoretical definition of energy in that he only defines mass or its gravitational potential in terms of a temporal displacement in a four dimensional space-time manifold.

This difference is significant to our understanding of the shape or flatness of our universe because it allows one to define the geometry of its mass component in terms the spatial properties of a “downward” directed curvature in a “surface” of a three-dimensional space manifold with respect to a four *spatial* dimensions while defining its energy component in term an upwardly directed one.

Additionally Einstein’s equation E=mc^2 and Second Law of Thermodynamics tells us there would be a dynamic relationship between the curvature created by the gravitational potential of the universeâ€s mass and the oppositely directed momentum of its expansion.  In other words because that law tell us that energy flows from area of high density to low; if the energy density was too high in the early universe it would have been channeled into creating more matter while if the matter component was excessive it would have been converted to energy. 

Granted it also tells us the curvature caused by its energy component is c^2 greater than that caused by mass but it also tells the one caused by mass would be more concentrated and therefore deeper than the one caused by energy.  However the deeper curvature associated with mass would be offset by the shallower and more draw out curvature associated with energy thereby make the universe flat and therefore hospitable to life as we know it.

This process would be similar to what happens to interstellar gas as it collapses to form a star.  The gas heats due to its contraction which causes energy to be created by nuclear reactions in its core converting mass to energy which opposes further gravitational collapses.  If too much energy is created it will escape from the star allowing gravity to take over again. 

After a given about of time the creation of energy is exactly offsets gravity and the star enters a period where the curvature in space associated with its energy exactly matches the oppositely directed curvature associated with its gravity and no further change takes place making its spatial geometry be flat because the curvatures counteract each other.  Additional this geometry would be frozen in time until the star evolved to new stage in its life.

Similarly the equation E=mc^2 tells us in the early universe there was an interchange between energy and the creation of mass in the form of baryons and the components of dark matter.  Additional as was the case in the formation of a star the second law of thermodynamic tells us that energy flows from areas higher density to lower ones while E=mc^2 tells us if the energy density was too high in the early universe it would have been channeled into creating baryons and dark matter while if they were too abundant they would have been converted to energy.

In other words second law of thermodynamic and E=mc^2 tells us as the universe evolves it would move towards a flat geometry because as was just mentioned if its energy density was too high it would have been channeled into creating mass while if its mass were to abundant it would have been converted to energy.  This geometry would become frozen in time when the universe cooled enough for its mass and energy components to become stable.

This shows why one does not have to assume that a complicated change of events must have occurred such as inflation to give our universe the geometry needed to support beginnings of life because as was shown above that story is told by the Second Law of Thermodynamics and Einstein’s equation E=mc^2.

Later Jeff

Copyright Jeffrey O’Callaghan 2016

The post The story of life in four spatial dimensions. appeared first on Unifying Quantum and Relativistic Theories.

For example as long as you are not actually observing an electron, its behavior is that of a wave of probability however moment you do it is becomes a particle.  But as soon as you are not looking at it it behaves like a wave again. That is rather weird, and no ordinary idea of classical objectivity can accommodate it.”

Bohr summarized this reality as follows:…”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 done and 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 objects.

In other words the choice one makes on how to observe a quantum object determines if it is a particle or wave.

This behavior is exposed by the double slit experiment in which a coherent source of light illuminates a screen after passing through a thin plate with two parallel slits cut in it. The wave reality of light causes the light waves passing through both slits to interfere, creating an interference pattern of bright and dark bands on the screen. However, when being observed, the light is always found to be absorbed as discrete particles, called photons.
However one of the reason it is so difficult to understand how observation effects a quantum system may be because too much attention has been focused on its  mathematical properties and not enough on its physical meaning in a space-time environment.  This is made even more difficult because they are defined in terms of the spatial properties of a quantum system instead of its space-time properties.

This suggest one may be able to obtain a better understanding of what happens when one observes it if one could view it in terms its spatial instead of its time or space-time properties.

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

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 redefining the physical properties of quantum system in terms of its spatial instead of its time components would allow one to derive a single picture of its wave and particle characteristics thereby allowing one to understand how observation effects our perception of it.

For example the article “Why is energy/mass quantized?” Oct. 4, 2007 showed one can derive its physicality by extrapolating the laws of classical wave mechanics in a three-dimensional environment to a matter wave on a “surface” of a three-dimensional space manifold with respect to  a fourth *spatial* dimension.

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

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

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

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

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

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

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

Yet it also allowed one to derive the physical boundaries responsible for the creation of a particle in terms of the geometric properties of four *spatial* dimensions.

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

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

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

However assuming its wave energy is result of a displacement in four *spatial* dimension instead of four dimensional space-time as was done in the article “Defining energy?” Nov 27, 2007 allows one to not only derive the physicality of its particle component as was just done but also the reason why when you are not actually observing it its behavior is that of a wave however moment you do it is becomes a particle with a physically defined position. 

For example Classical wave 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 is free to move over the entire “surface” of three-dimensional space with respect to a fourth *spatial* dimension similar to how the wave generated by a vibrating ball on a surface of a rubber diaphragm are free to move or be distributed over its entire surface.  However to observer it one would have to touch its surface with a probe thereby restricting the wave motion of its surface.

Similar the wave reality of a quantum system that is not being observed is allow to freely move though space as is done in the double slit experiment when it moves though the slits undetected thereby allowing is wave reality become observable as demonstrated by a diffraction pattern on a screen placed behind the slits.

In other words similar to the rubber diaphragm there is a probability that its wave reality could be found anywhere on the “surface” of three dimensional space.

However if we decide to restrict or redirect some of its energy by probing or observing it becomes a particle that appears to be at a specific place in space and time because as was shown in the article “Why is energy/mass quantized? the act of observation confines its wave component to specific volume thereby allowing the resonant system that article showed was responsible for its particle reality to become reality.

In other words by assuming space it composed of four spatial dimensions instead of four dimensional space-time one can understand why the act of observation defines the reality of a quantum environment by extrapolating our experiences in a three-dimensional environment to a fourth *spatial* dimension.

It should be remember that Einsteinâ€s genius allows us to choose whether to define the reality of a quantum system in either a space-time environment or one consisting of four *spatial* dimension when he derived its physical geometry in terms of the constant velocity of light.

Later Jeff

Copyright Jeffrey O’Callaghan 2015

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

For example the article “Why is energy/mass quantized?” Oct. 4, 2007 showed one can physical derive the quantized wave properties of electromagnetism  by extrapolating the field properties of classical wave mechanics in a three-dimensional environment to a matter wave on a “surface” of a three-dimensional space manifold with respect to  a fourth *spatial* dimension.

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

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

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

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

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

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

Hence, these resonant systems in four *spatial* dimensions would be responsible for the discrete quantized energy associated with the quantum mechanical properties of a photon or electromagnetic field.

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

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

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

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

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

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

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

It should be remember that Einstein’s genius allows us to choose whether to create physical images of an unseen “reality” in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of the constant velocity of light.

Later Jeff

Copyright Jeffrey O’Callaghan 2015

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

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.

Unfortunately there is absolutely no direct observational or experiment evidence supporting its physicality. 

In fact one of the most persistent observations regarding time is that it is not directly perceived in terms of a physical entity such as matter or space but only as a measure of an irreversible physical, chemical, or biological change in a physical system.

However this suggests as was shown in the article “Defining what time is.” Sept 20, 2007 time may only be a non-physical measurement of the sequential ordering of a physical, chemical, or biological change in space similar how a unit of length is a non-physical measure of a change in the ordering of the position of an object in space. This is because similar to time, length is not perceived as matter or space but only as a non-physical measure of where an object is located with respect to a given point in space.

Yet this appears to contradict the assumption that time or a space-time dimension is or has the properties of a physical entity because as mentioned earlier most of us do not perceived it as having the physical properties of matter or space.

However, what is even more damaging to the concept that it has physical properties is that they are not required to define relativistic properties of our universe as many physics seem to think.

This is because Einstein gave us a way of converting a unit of time in a space-time dimension to unit of space in four *spatial* dimensions when he used the constant velocity of light to define its geometric properties.  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.

However using Einstein’s equations as is suggested above to redefine the universe in terms of four *spatial* dimensions instead of four dimension space-time would allow one to understand its relativistic properties in terms of the observable properties of the spatial dimensions while maintaining the same quantitative predictive powers as those associated with a space-time dimension because as mentioned earlier there is a one to one correspondence between them.

For example  the article “Embedded dimensions” Oct 22, 2007 showed that one can derived all forms of energy including gravitational and kinetic in terms of a displacement or curvature in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension and why one must assume that kinetic energy is a result of an oppositely directed displacement in its “surface” than the one associated with gravity.

The conclusion that the causality of kinetic energy is a result of an oppositely directed displacement in a “surface” of three-dimensional space with respect to the one associated with gravity is based on the observation that they are oppositely directed.  For example, the kinetic energy of an orbiting satellite is oppositely directed with respect to the gravitational energy associated with the planet it is orbiting.  Therefore, if one defines gravity in terms of a “depression” in a “surface” of a three-dimensional space manifold with respect to fourth *spatial* dimension one should define kinetic energy in terms of a oppositely directed “elevation” in that “surface”.

However this means according the definitions given in the article “Embedded dimensions” the total energy/mass of an object would be equal to the sum of the displacements of a “surface” of a three-dimensional space manifold caused by the rest mass of an object and that caused by its relative velocity.

Therefore, the energy/mass of an object would be dependent on its relative motion because one must add the energy of its motion to its rest energy/mass.

This defines the mechanism responsible for why the energy/mass of an object increases when viewed by an observer who is in relative motion to it in terms of the geometry of four *spatial* dimensions.

The following analogy can be used to understand and define the relativistic properties length and time

Assume that two “2 dimensional creatures” are living on the surface of two pieces of paper resting on a desktop.

Also, assume the two creatures can view the surfaces of the other piece of paper, which are separated a pencil.

If the diameter of the pencil is increased, the curvature between the surfaces of the two pieces of paper will increase.

Each of these creatures, when viewing the other piece of paper will only perceive the two-dimensional translation of the three-dimensional curvature generated by the pencil.

Therefore, each will view the distance between two points on the surface of the other as shorter since they will view that distance as a two-dimensional translation of a three-dimensional curvature in the surface of the paper and each will measure the distance between them on their piece of paper as being longer then they would if they viewed it on the other piece.

Similarly, because three-dimensional beings could only “view” a three-dimensional translation of a “curvature” or displacement in four *spatial* dimension caused by the motion of a reference frame they will measure distance or length in them as being longer than they would be if viewed as an observer who is not in relative motion to it.

The “movement” of “time” on both surfaces will also be affected.

Each of the two dimensional creatures mentioned earlier will view the others “time” as moving slower because the three-dimensional curvature in the paper makes the distance between events longer than the two dimensional translation of those events.  Therefore, it will take longer for events “move” through the curvature in three-dimensional space relative to the time it would take for them to move along two dimension translation of that surface.

Earlier it was mentioned that the magnitude of the displacement or “curvature” an object generates in a fourth *spatial* dimension is dependent on its velocity.

However as mentioned earlier, we have defined time as only being the measure or the “distance between” the sequential ordering of the causality of an event.

Therefore time will become dilated in reference frames that are in motion because of the curvature generated in three-dimensional space by its relative motion, three-dimensional beings in that reference frame will view the distance between events to be longer in it than it would if they were in motion relative to it.  Therefore, they will view time in a reference frame that is in motion relative to them as moving slower than if they were in that reference frame because events in those reference frames will have a greater separation.

The velocity of light is constant despite the relative motion of an observer because the foreshortening or shortening of the length or distance the light travels is proportional to the motion of the observer.  Therefore, the velocity of light will be constant in all reference frames despite the relative velocities of the observers to those reference frames because velocity is defined in terms of distance divided by time.

It should be remember this scenario applies to all forms of energy including gravitational because, as the article “Embedded dimensions” Oct. 22, 2007 showed, three-dimensional beings perceive energy in terms of the magnitude of a “curvature” in “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

The Lorentz transformations derived from this theoretical model will take on the same form as the Lorentz transformations derived from Relativity.

This is because this theoretical model postulates that a displacement or curvature in “surface” of a three-dimensional space manifold, with respect to a fourth *spatial* dimension caused by the gravitational or kinetic energy of an object is proportional to the velocity of light.

Therefore, because both Relativity and the above mechanism predict a physical shortening of length and a slowing of time are related to the geometry of space, the form of the Lorentz transformations associated with the foreshortening length and slowing of time will be identical for both of these models.

However, this theoretical model differs from that of Relativity’s in that it defines the magnitude of a foreshortening of length and a slowing or dilation of time in terms of a “curvature” in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of curvature in four dimensional space-time manifold.

As mentioned earlier the article “Defining energy” derived the mechanism responsible for gravity in terms of a “curvature” in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, it was shown earlier that a curvature in a “surface” of a three-dimension space manifold with respect to a four *spatial* dimension was responsible for length foreshortening and time dilation.

Therefore, because both gravitational and the kinetic energy of relative motion are derived from a common “curvature” in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension they will have a similar effect on physical properties of length and time.

This means both Relativity and this paper predict an observer in a gravitational field will measure the length of an object to be shorter and passage of time to be slower with respect to an observer who is located outside of a gravitational field.

However, as mentioned earlier this paper defines this shortening of length and slowing of time in a gravitational field in terms of four *spatial* dimension instead of four-dimensional space-time manifold.

The “relative” characteristics of a “curvature” in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension associated with kinetic and gravitational energy would also make it impossible for an observer to determine if an acceleration is caused by gravitational or kinetic energy such as that from an exhaust of a rockets engine.

This is because the mechanism defined above indicates the magnitude of a force associated with both gravitational and kinetic energy is related to the absolute magnitude of a “curvature” a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, because a three-dimensional observer can only observe the three-dimensional effects of a curvature in four *spatial* dimensions he or she could not determine whether he or she is in a gravitational field or an accelerated reference frame.

This means the concepts contained in this article would make identical qualitative and quantitative and predictions with respect to the relativistic properties of space and time and the inability to determine the casualty of acceleration in terms of the physical properties of four *spatial* dimensions instead of four dimensional space-time because they are based on the analytical and qualitative properties of Einstein’s experimentally verified equation E=mc^2.

As mentioned earlier the primary reason why most scientist assume the physicality of time or a space-time dimension is because the foundation of modern cosmology is based on the physical existence of time or Einstein’s space-time dimension.

Yet as this article shows one can make the same quantitative and qualitative predictions regarding them by assuming they are caused by a physical interaction between the third and fourth *spatial* dimension and not one made up of time.

However this article also suggests the reason why scientists are unable physically observe time or a space-time dimension is because its existence is based on the illusion that it is responsible for the relativistic properties of space, time and energy/mass.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

The post The illusion that is time. appeared first on Unifying Quantum and Relativistic Theories.