Quantum mechanics assumes that a particle is in a superposition of several states or positions based on the mathematical properties of Schrödinger’s wave equation before an observation is made.  It also assumes that when it is observed it collapses resulting the particle it represents having a single or unique position.

When the Copenhagen interpretation was first introduced Neils Bohr found it was necessary to assume the collapse of wave function to distinguish the quantum from the classical world.  This allowed it to develop without distractions from interpretational worries.  Nevertheless since then that it meaning has be hotly debated because if it is a fundamental properties of nature as many have assumed it would contradict the classical or Newton assumption that the world is deterministic.

MIT lecture 3:The Wave Function

However the science of physics is devoted to understanding the physical process responsible for creating the "reality" of our observable environment based on observing the physical interaction of its real not imagined components.

One of the reason it has been so difficult to understand what happens to the position component of a quantum system when it is observed may be because too much attention has been focused on the mathematical aspects of the wave function and not enough on its physical meaning in a space-time environment.  This is made even more difficult because the concept of superposition is defined in terms of the spatial properties of a quantum system instead of its space-time properties.

This suggest one be able to obtain a better understanding of what happens to it if one could view it in terms its spatial instead of it 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 Einstein’s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions is one bases for assuming as was done in the article “Defining energy?” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However defining the dimensional properties of quantum system in terms of its spatial instead of its time components would allow one to derive the physicality of the wave functioned associated with Schrödinger’s equation by extrapolating the observable properties of our reality to the quantum world it describes.

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 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 similar resonant interaction between three and four dimensional space.)

However assuming its 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 Schrödinger’s equation as was just done but also the physical reason why its particle components would be in superpositioned state before an observation is made.

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 similar to how the wave generated by a vibrating ball on a surface of a rubber diaphragm are disturbed over its entire surface while the magnitude of the displacement it causes 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 three-dimensional space one must assume the oscillations associated with each individual quantum system must be disturbed thought the entire universe while the spatial displacement associated with its energy defined in the in the article “Defining energy?” Nov 27, 2007 would decrease as one moves 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?” shows that a quantum mechanical system is a result of a resonant structure formed by the oscillations on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Classical Wave Mechanics 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 vibrations of its wave function

Additionally this tells us that the wave function does not collapse but its energy is redirected towards the observer and as was shown in the article Why is energy/mass quantized? he would record its redirected energy in term of discrete quantized properties associated with a particle.

As mentioned earlier the science of physics is devoted to understanding the physical process responsible for creating the "reality" of our observable environment based on observing the physical interaction of its real not imagined components.

Yet even though we may never be able to directly observe the fourth *spatial* dimension we can verify its existence by observing the effects it has on our observable three-dimensional environment similar to how Einstein was able to conclude that gravity was a result of a curvature in a space time environment.

Later Jeff

Copyright Jeffrey O’Callaghan 2015


 

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In 1933 Fritz Zwicky a Swiss astronomer, was trying to measure the mass of a galactic cluster using two different methods. First he tried to infer it from the rational speed of the galaxies around the center of the clusters.  Just like kids on a merry-go-round have to hold on to avoid being ejected, galaxies are held together in a spinning galactic cluster by the gravitational force provided by the matter it contains because if there were not enough matter to create this force, the galaxies would simply scatter.

He then compared his result with the mass evaluated from the light the galaxies shed. He realized that there was way more matter in the cluster than what was visible or baryonic matter. This matter of an unknown type generated a gravitational field without emitting light; hence its name, dark matter.

Further observations suggest the baryonic or visible forms of matter in the universe only comprise approximately 5 to 10% of the mass required to account for the total gravitational energy in the universe.

The search for this missing mass has focus on three different types of particles or objects that would be invisible or would not interact with electromagnetic energy while at the same-time influenced by the gravity forces of the visible mass component our universe.

 3D Dark Matter Density Field Simulation

The first or Axions are very light particles with a specific type of self-interaction that makes them a suitable CDM candidate.  Axions have the theoretical advantage that their existence solves the Strong CP problem in QCD, but have not been detected.

The second or MACHOs or Massive Compact Halo Objects are large, condensed objects such as black holes, neutron stars, white dwarfs, very faint stars, or non-luminous objects like planets. The search for these consists of using gravitational lensing to see the effect of these objects on background galaxies. Most experts believe that the constraints from those searches rule out MACHOs as a viable dark matter candidate.

Finally WIMPs or Dark matter which is composed of Weakly Interacting Massive Particles. There is no currently known particle with the required properties, but many extensions of the standard model of particle physics predict such particles. The search for WIMPs involves attempts at direct detection by highly sensitive detectors, as well as attempts at production by particle accelerators. WIMPs are generally regarded as the most promising dark matter candidates. The DAMA/NaI experiment and its successor DAMA/LIBRA have claimed to directly detect dark matter particles passing through the Earth, but many scientists remain skeptical, as null results from similar experiments seem incompatible with the DAMA results.

However Einstein suggested another possibility in the speech "Aether and the theory of Relativity" he made on May 5th 1920 at the University of Leyden Germany where he indicated that The General Theory of Relativity predicts, that "space is endowed with physical qualities"

"Recapitulating, we may say that according to the General Theory of Relativity space is endowed with physical qualities; in this sense, therefore, there exists Aether. According to the General Theory of Relativity space without Aether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time, nor therefore any space-time intervals in the physical sense. But this Aether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts, which may be tracked through time. The idea of motion may not be applied to it."

However Einstein only endowed space with the field properties of a space-time dimension and not the physical qualities of mass.  Therefore if one accepts the validity of his theory the physical properties he was referring to must be a result of those field properties not those of mass in its particle form.  This suggests the missing mass found by Fritz Zwicky may be related to those field properties not those most associate with the mass of objects or particles.

Yet it is difficult to form a clear picture of how a field consisting of space-time can have the physical properties of Dark Matter because as was shown in the article "Defining what time is" Sept. 20, 2007 time is not perceived by most as matter or space but as an irreversible physical, chemical, and biological change in physical space.  Therefore it is difficult to understand how the physical properties Einstein associated with space or Dark Matter can interact with the non physical properties of a time or a space-time dimension to create a gravitational field.

But Einstein gave us the ability to solve this and develop more direct understand how and why the field properties of space-time can be responsible for Dark Matter when he used the equation E=mc^2 and the constant velocity of light to define the geometric properties of mass in a space-time universe.  This is because that provided a method of converting a unit of time 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.

This tells us that one can use Einstein’s theory to define gravitational potential in terms of the continuous field properties of four *spatial* dimensions which means if one is to accept his theory one must also assume that space contains a continuous field of mass.

However this contradicts the current world view shared by most physicists and cosmologists that mass only exists in its particle or quantized form.  This is true even though 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 mass we associate with the particles must be composed of the oscillation in the field properties of space because that is the only thing that could be responsible for their wave components.  Therefore those fields must also have the properties associated with mass.

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 observed particle to be composed of 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 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 the mass component of space. 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.

This is why as mentioned earlier its field properties are only observable in terms of the interference of the wave properties particles as was demonstrated by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.

The second is that to 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 on 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 would be changing at the same rate.

However as mentioned earlier 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

The above discussion not only defines why we cannot directly observer Dark Matter but also how it creates gravitational potential in terms of the field properties of four dimensional space-time or four *spatial* dimensions.

Unfortunately for those who disagree the above conclusion is based purely on observations and the validly of Einstein theories.  Therefore to deny the existence of a continuous field of Dark Matter and it gravitational influence one would have to deny the validity of Einstein theories.

It should be remember Einstein’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 2015

 

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