On the one hand quantum physics tells that the universe is made up of discrete units of energy/mass while relativistic physics tells us it is composed of a continuous field of space-time

Unfortunately these two ideas do not work well together because a continuous field by definition cannot be made up of discrete parts as is suggested by quantum mechanics.
Some have tried to merge them by defining what is has come to be called a relativistic quantum field theory.  It assumes that particles can be understood as the quanta of some quantum field which in essence elevates fields to the most fundamental objects in nature and that each type of field generates its own particular type of particle.

However, you cannot have it both ways because by definition a field is continuous and saying they can be understood in terms of some quantum field does not mean that you have connected them to the continuous properties of a relativistic space-time field or any field for that matter.  All it does is elevate its size to that of the entire universe because by definition a field is continuous throughout its entire domain.  Therefore if the fundamental component of the universe is a quantum field as quantum field theory suggests then it could only contain one quantum entity because if it contained more the continuity of the field would be broken.  In words saying one can understand the continuous properties of a field in terms of a quantum field is like saying that one can understand why a circle is round is because it is a circle. 

Another reason why it is so difficult to conceptually to integrate Quantum theory with the field properties of Einstein’s theories is because it defines space in terms of a field consisting of time or a space-time dimension while Quantum theory defines itself in terms of its spatial properties of energy/mass.  

For example Schrödinger’s wave equation only defines the probability of a particle will be located in a given volume of space without giving a reference to time while Einstein defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2.

Yet one can overcome the difficultly by redefining the field properties of space-time Einstein associated with energy/mass to its spatial properties Quantum field theory associates with it. 

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

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

One of the theoretical advantages to assuming that the universe is made up of four *spatial* dimensions instead of four dimensional space-time is that it allows one to derive the quantum mechanical properties of energy/mass in terms of the field properties of four *spatial* dimensions instead of defining the field properties of space in terms of its quantum mechanical properties as is done in quantum field theory.

The field properties of four *spatial* dimension was developed in the article “Electromagnetism in four *spatial* dimensions” Sept 27, 2007 where it was shown the forces associated with an electromagnetic field can be explained and predicted in terms of matter wave on a continuous field consisting of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly it showed that one can derive its properties by extrapolating the laws of Classical Wave Mechanics to a field consisting of fourth *spatial* dimensions.

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 the force 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 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 explain and predict the electrical and magnetic field properties of an electromagnetic wave by extrapolate 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 a fourth *spatial* dimension.

However, as was shown in the article “The Photon: a matter wave?” Oct. 1, 2007 the quantum field properties of four *spatial* dimensions can be explained and predicted by extrapolating the resonant properties of field in a three-dimensional environment to one consisting of four *spatial* dimension.

There are 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.

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

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

Therefore, these oscillations in four *spatial* dimensions, would meet the requirements mentioned above for the formation of a resonant system or “structure” in space. 

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

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

These resonant systems in four *spatial* dimensions are responsible for the incremental or discreet field energies associated with relativistic quantum field theories.

This shows that it is possible to logically and consistently explain and predict the quantum mechanical field properties energy/mass in a microscopic environment by assuming that space is composed of four *spatial* dimensions instead of four dimensional space-time.

However it also shows it is more logical and consistent with observations to assume that our universe is fundamentally composed of fields not quanta of energy/mass as is assumed by quantum field theory

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

Latter Jeff

Copyright 2013 Jeffrey O’Callaghan

The post Particles or fields you cannot have it both ways appeared first on Unifying Quantum and Relativistic Theories.

For example, a classical approach would be to observe how matter and energy interact with our environment and then attempt to define a mechanism, based on those observations that will explain and predict their causality.
This was the method was used Newton to develop the laws of gravity.

Newton observed the orbits of the planets and realized they had something in common in that their positions could be predicted if one assumed their movements were a result of force emanating from mass itself.  This observation was reformulated into Newton’s gravitational theory. 

This method gave him the ability to check, through observations the validity of his theory because he could observe how the planets physically interacted with their spatial environments to define their positions.

However, Newton was unable to define the casualty of the force associated with his law of gravity.

That was left to Einstein.

He realized the causality of gravity could be explained and predicted by assuming that time and space is physically connected.  This idea was became known as “The General Theory of Relativity”.

However, Einstein had to use a different approach than Newton to verify his theory because the physical properties of time or a space time-dimension cannot be directly observed.

Therefore, because he could not directly observe time or a space-time dimension he not only had to assume it had physical properties but also how it would interact with space to cause gravity.

However, this approach, unlike the one used by Newton does not give physicists the ability to verify through observations how the interaction of space and time can explain gravity because, as mentioned earlier no has ever observed the physical properties of time or a space-time dimension.  Therefore, they must rely on how they think they would interact to verify Einstein’s theory.

Physics is an observational science because, as it name implies it is devoted to the understanding of how and why matter and energy physically interact to create the structure of the universe.  Therefore, physicists should use caution when assuming the existence of a parameter, such as a physical property of time that is unobservable because there is no way for them to observational verify that it has those properties.

It has been shown throughout this blog that one could define the casualty of gravity in terms of four identical *spatial* dimensions instead of four-dimensional space-time.

One advantage to do so is that would give physicists an observational basis for determining how they would interact because they could extrapolate the interactions of the three spatial dimensions they can observe to understand that how a fourth *spatial* dimension would interact with them.

Therefore, even though, as was shown in the article “Embedded Dimensions” Oct. 22, 2007 physicists will never be able to directly observe the properties of a fourth *spatial* dimension they can use observations of three-dimensional space as a basis for deriving how they would interact with three-dimensional space to cause gravity.

Additional we can observe how objects are effected by a curvature in a two dimensional surface with respect to the third spatial dimension.

For example water will flow and become concentrated at the lowest point on a curved surface in three dimensional space.

Similarly one could extrapolate that behave to a four spatial dimensions  energy will flow and become concentrated in the form of mass at the lowest point in a curved “surface” of a three dimensional space manifold with respect to a fourth spatial dimension.

In other words one does not have to assume the physical properties of a fourth spatial dimensions or how it would interact with the three dimensions we can observe if one bases their physical properties on our observations of them.

Einstein not only had to assume the physical properties of time but he also had to assume how it would interact with space to form a space-time dimension that could account for the properties of gravity.

Therefore, assuming gravity is a result of an interaction of three-dimensional space with a fourth *spatial* dimension, as we have done should have more scientific credibility than one based on a space-time dimension because observations of our three-dimensional environment provide a basis for understanding how it would physically interact with it. 

Later Jeff

Copyright 2008 Jeffrey O’Callaghan

The post What is Physics about? appeared first on Unifying Quantum and Relativistic Theories.

“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“.

Unfortunately, Einstein did not have access to the data concerning the quantum “qualities” of mass and electromagnetic energy when developing his theories as we do today, such as the Louis de Broglieâ€s observation made in 1924 that all particles have a wave component.  If he had he may have chosen to define gravity in terms of four *spatial* dimensions instead of four-dimensional space-time because, as was shown in the article “Gravity in four *spatial* dimensions” Dec. 15, 2007 he could have done it that way.

This is because even the smallest particle, according to Broglie observations must have a wave component.  Therefore, a continuous medium must be available to support it.  Einstein would have realized this medium would have to be made up of a continuous non-quantized field of energy/mass because by definition a wave can only be propagated on a continuous surface.

He also may have due to the spatial properties of a transverse of the energy/mass wave Louis de Broglie observed chose to define energy in our environment in terms of its spatial not time properties because a transverse wave can only be propagated by a spatial displacement with respect to the surface it is moving on.

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

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

Additionally this would have provided a way to integrate quantum properties of energy/mass into both his Special and General Theories of Relativity using the concepts of classical physics.

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

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

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

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

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

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

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

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

However redefining Einstein’s space time concepts in terms of four *spatial* dimensions would also allow one to integrate electromagnetism into them.

For example 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 the force 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 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

The electrical component of electromagnetic energy is a result of the force associated with the “slope” of a curvature created by the “peaks” and “troughs” of a matter wave that is perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that “vertical” displacement

Classical Mechanics tells us a horizontal force will be developed by a 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.

As was shown above redefining Einstein’s space-time concepts in terms of their spatial equivalent allows one to not only allows one to ingrate the quantum properties of energy/mass into the continuous field properties of his space time universe but also give one classical understanding of how to incorporate electromagnetism into it.

Later Jeff

Copyright Jeffrey O’Callaghan 2008

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