Understanding the connection between space and time is difficult because we cannot see time or space even though we can perceive the void in space when it contains nothing

Additionally defining or describing what time is extremely difficult. Some define it only in the abstract saying that is an invention of the human consciousness that gives us a sense of order, a before and after so to speak of the changes that occur in our environment.  However one can define or describe space in terms of the void we can see between objects that it contains.
In other words time and space do not appear to share any physical qualities.

Even so physicists have derived the physical structure of the universe in terms of a mathematical model that combines space and time into a single interwoven space-time continuum.

However it is difficult to understand how in a space-time environment they can physically interact when, as was just mentioned neither of them have any common properties.

Granted using mathematics one can explain how they do in terms of abstract concepts but it does not explain how and why they do in physical terms.

Yet one can use the fact that the one of the primary functions of time is to define change to form a physical image of how it interacts with space to create it.

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

In other words he tells the physical properties of space and time are relative to an observer’s interpretation similar to how the measurements of their magnitudes are relative to an observer’s velocity because, as was show above one can reinterpret the mathematics associated with the space-time environment of both the General and Special Theories of Relativity purely in terms of its spatial components to create an identical one in only four *spatial* dimensions.  However one must be careful not to think of this as the physical replacement of the time dimension in Einstein’s space-time universe with a spatial one because according to his mathematics they simultaneously coexist in the same geometric plain.

However the fact that one can use Einstein’s theories to qualitatively and quantitatively define the displacement he associated with energy in a space-time universe in terms of four *spatial* dimensions is 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.

Doing would also allow one to form a physical image of how the geometric properties of space or time interact to create change because as mentioned earlier we can form a clear physical image of how a void in four spatial dimensions created by that displacement would cause change.

For example we can physically observe how the energy stored in the displacement of water in dam causes change in an environment when it is released or allowed to flow over it.  In other words we can form a physical image of the causality of the changing level of water in the dam in terms of its movement through the spatial void between the top and bottom of the dam.

Similarly one can form a clear physical image of how and why change would occur in  our three dimensional environment by assuming the energy stored in a spatial displacement in a “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension is released though the void that displacement creates in four dimensional space.

As was mentioned earlier it is difficult to form physical image of how time can interact with space because of its abstract properties.

However one can from a very clear image of how it does when one realizes that according Einstein theories the physical properties of space and time which as was shown above are relative to an observer coexist on in the same dimensional plain.  Therefore an observer who looks at his theories form a spatial perspective can easily understand how change occurs in a space time-environment in terms of the physical example of water flowing over a dam.

It should be remember Einstein’s mathematical model which defines the physical geometry of our universe tells us that an all objects must simultaneously exist in both a space-time environment and one consisting of four spatial dimension because as was shown above one can use his mathematics to define two identical universes; one in four dimensional time and another made up of only four *spatial* dimensions.  Which one we use to define a solution to a problem, as mentioned earlier is only dependent on how an observer interprets his mathematics. 

Later Jeff

Copyright Jeffrey O’Callaghan 2016

Quantum entanglement is defined “as a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot be described independently instead, a quantum state may be given for the system as a whole”.

Einstein referred to this as “spooky action at a distance” because it assumed that particles can interact instantaneously, regardless of distance separating them which according to his perception of reality this was not possible.
However if one accepts the reality of the space-time universe defined by Einstein one would realize that according the core principals of his theories there is nothing spooky about action at distance relative to an observers velocity. 

Even so he was so convince that he co-authored a paper with Podolsky–Rosen whose intent was to show that if Quantum Mechanics was a valid theory it could not be complete because it does not agree with most people’s perception of reality. The first thing to notice is that Einstein was not trying to disprove Quantum Mechanics in any way. In fact, he was well aware of its power to predict the outcomes of various experiments. What he was trying to show was that there must be a “hidden variable” that would allow Quantum Mechanics to become a complete theory of nature

The argument begins by assuming that there are two systems, A and B (which might be two free particles), whose wave functions are known. Then, if A and B interact for a short period of time, one can determine the wave function which results after this interaction via the Schrödinger equation or some other Quantum Mechanical equation of state. Now, let us assume that A and B move far apart, so far apart that they can no longer interact in any fashion. In other words, A and B have moved outside of each other’s light cones and therefore are spacelike separated.

With this situation in mind, Einstein asked the question: what happens if one makes a measurement on system A? Say, for example, one measures the momentum value for it. Then, using the conservation of momentum and our knowledge of the system before the interaction, one can infer the momentum of system B. Thus, by making a momentum measurement of A, one can also measure the momentum of B. Recall now that A and B are spacelike separated, and thus they cannot communicate in any way. This separation means that B must have had the inferred value of momentum not only in the instant after one makes a measurement at A, but also in the few moments before the measurement was made. If, on the other hand, it were the case that the measurement at A had somehow caused B to enter into a particular momentum state, then there would need to be a way for A to signal B and tell it that a measurement took place. However, the two systems cannot communicate in any way!

If one examines the wave function at the moment just before the measurement at A is made, one finds that there is no certainty as to the momentum of B because the combined system is in a superposition of multiple momentum eigenstates of A and B. So, even though system B must be in a definite state before the measurement at A takes place, the wave function description of this system cannot tell us what that momentum is! Therefore, since system B has a definite momentum and since Quantum Mechanics cannot predict this momentum, Quantum Mechanics must be incomplete.

In response to Einstein’s argument about incompleteness of Quantum Mechanics, John Bell derived a mathematical formula that quantified what you would get if you made measurements of the superposition of the multiple momentum eigenstates of two particles. If local realism was correct, the correlation between measurements made on one of the pair and those made on its partner could not exceed a certain amount, because of each particle’s limited influence on the other.

In other words he showed there must exist inequities in the measurements made on pairs of particles that cannot be violated in any world that included both their physical reality and their separability because of the limited influence they can have on each other when they are “spacelike” separated.

When Bell published his theorem in1964 the technology to verify or reject it did not exist. However in the early 1980s, Allen Aspect performed an experiment with polarized photons that showed that the inequities it contained were violated.

This meant that science has to accept that either the reality of our physical world or the concept of entanglement does not exist because they are mutually excessive.

However Einstein himself predicted the entanglement of particles that are moving at the velocity of light no matter how far apart they are in his Special Theory of Relativity because he showed us that  the separability or the distance between two points is dependent on the velocity of the observer with respect to what is being observed.

For example his theory tells the distance between the two objects A and B would be defined by their relative speed with respect to an observer.

Specifically he told us that it would be defined by

 

However this tell us the distance or length between observations measured between two photons or any particle moving at the speed of light from the perspective a photon would be zero no matter how far those observation might from the perspective of the observers making them because according to the concepts of relativity one could view the photons as being stationary and the observers as moving at the velocity of light.  This is true even if they are moving in opposite directions.

Therefore according to Einstein’s theory all photons which are traveling at the speed of light are physical entangled with all other photons that originated within a common system no matter how far apart or “spacelike” separated they may appear to be to all observers who are not traveling at the speed of light.

In other words inequities in the measurements made on pairs of photons should be violated in a world containing the physical reality of Einstein’s theory and separability because they are not “spacelike” separated when viewed from all reference frames which is not traveling at the speed of light.

This tells us that the hidden variable that would allow Quantum Mechanics to become a complete theory of nature is Einstein Theory of Relativity or the Relativistic properties of motion.

Additionally if quantum entanglement did not occur for photons that were space like separated then the physical reality of Einstein space-time universe as defined by his theory of Relativity must be discarded

One method for determining if this is the reason why Allen Aspect observed polarized photons violated Bells inequities would be to see if they are also violated by particles that were traveling slower that the speed of light because they would according to the Theory of Relativity could be “spacelike” separated.

In others words if it was observed that particles which were not traveling at the speed of light did not violate Bell’s inequity then it would support Einstein perception of reality and provide a physical verification for the causality in terms of the existence of space-time for one of the most puzzling aspects of quantum mechanics; that of quantum entanglement.

However if it is found that bell’s inequity is violated by particles moving slower than the speed of light then Einstein’s perception of reality would be invalidated because it demands that things which are “spacelike” separated can only have a limited influence one each other.

Yet one must be careful when performing the calculations because the distance separating the particles would not be determined by the distance between the end points as viewed by the experimenter but by relativistic distance as viewed from the particles,

Later Jeff

Copyright Jeffrey O’Callaghan 2016

Cosmologists have defined three different classifications of stars based on their elemental makeup.  Population I or those that contain relatively large concentrations of the heavy metals, Population II or those that have much less and Population III which are composed entirely hydrogen, helium and very small amounts of lithium and beryllium no heavy metals.  Although Population III, stars have not yet been observationally confirmed their existence is predicted in the Big Bang model.

According to that theory, the early universe consisted of hydrogen and helium, with trace amounts of lithium and beryllium, but no heavier elements. Through the process of stellar evolution, the first stars synthesized the metals from hydrogen and helium by nuclear reactions in their cores, which were then dispersed when they exploded.  Therefore, it is assumed the first stars to evolve would have lower metal content that those that came later.

However, as was mentioned earlier the fact that no Pop III stars have been observed despite the intense efforts by the cosmological community and the fact that the technology is advance enough to do so contradicts that assumption.

Even so many cosmologists still feel the big bang it is a valid model for describing evolution of our universe by suggesting that there are several reasons why they have not yet been observed.

The first is as the oldest population of stars, the majority of Pop III stars would have exhausted their fuel supplies long ago and would now be observed as remnants (white dwarfs, neutron stars or black holes), the original composition of which is nearly impossible to determine. However, this alone cannot explain the absence of Pop III stars, as those with the lowest masses should still be present (albeit difficult to observe due to their extremely low luminosities) in the Galaxy population today.

Another explanation is that stars sweep up gas from the interstellar medium as they move through it, and this may contaminate the outer layers of Pop III stars. This would give Pop III stars the appearance of metal-poor Pop II stars.

A more plausible explanation is that the metals produced in the cores of the Pop III stars have been dredged up to the surface by convection. Such ‘self-contaminated’ Pop III stars would also most likely be misclassified as metal-poor Pop II stars.

The currently favored explanation for the lack of observed Pop III stars is that the Pop III generation of stars were all high mass stars, with masses ranging from 60 to 300 times that of the Sun. In other words, no low mass Pop III stars were ever formed. This is supported by recent theoretical models, which show that primordial stars possessed much higher masses than the stars we see in the Universe today. If this bias in the mass distribution of primordial stars were the case, then all Pop III stars would have exhausted their fuel supplies long ago and would now be present only as remnants.

However, there are several other problems with the big bang model, which are not so easy to explain away.

For example the Big Bang theory postulates the universe emerged from what is called a singularity where the laws of physics breakdown and is expanding from the tremendously hot dense environment associated with it.  Additionally it assumes the momentum generated by the heat of that environment is sustaining the expansion.

However, it has difficulty explaining where the energy originated to cause its expansion.

The reason this presents a problem is because the law of conservation of energy/mass says that in a closed system it cannot be created or destroyed. 

However, proponents of the big bang model assume, as was just mentioned the energy powering the universe’s expansion came from a tremendously hot dense environment yet it cannot explain where the energy found in that environment came from.  In other words they would like us to believe that it was created out of nothing, which would be a violation of the law of conservation of energy/mass.

Additionally because it also assumes that it emerged from a singularity were the laws of physics do not apply they are unable to define the initial condition required to predict how that evolution began.  In other words the entire mathematical structure of the big bang model is based on an unknowable quantity which can be chosen to make it fit many different universes, including the one we occupy.

Yet there is another explanation for origin of our expanding universe that does not violate any of the accepted physical laws and makes a great deal more sense than assuming its expansive energy originated out of nothing.

We know from observations the equation E=mc^2 defines the equivalence between mass and energy in an environment and since mass is associated with the attractive properties of gravity it also tells us because of this equivalence the momentum associated with the universe’s expansion also posse those attractive properties.  However, the law of conservation of energy/mass tells us that in a closed system the creation of it cannot exceed the gravitational energy associated with the total energy/mass in the universe.

However, not all of the energy of associated with the universe’s expansion is directed towards it because of the random motion of its components.  For example, observations indicate that some stars and galaxies are moving towards not away us.  Therefore, not all of the energy present at the time of its origin is directed towards its expansion.

Additionally we know from observation that the universe is nearly flat with respect to its mass and energy.  Many physics assume this means that it will continue expand forever, but it is always slowing down, reaching a dead stop in an infinite amount of time.

However, because some of the momentum of its components is not directed towards its expansion the total gravitational contractive properties of will eventually exceed that of its expansive components.   Therefore, at some point in time its gravitation contractive potential must exceed the kinetic energy of its expansion because as just mentioned not all of its kinetic energy is directed towards its expansion.  Therefore, at that point, in time the universe will have to enter a contractive phase.

(Many physicists would disagree because recent observations suggest that a force called Dark energy is causing the expansion of the universe accelerate.  Therefore, they believe that its expansion will continue forever.  However, as was shown in the article “Dark Energy and the evolution of the universe” if one assumes the law of conservation of mass/energy is valid, as we have done here than the gravitational contractive properties of its mass equivalent will eventually have to exceed its expansive energy. Therefore, the universe must at some time in the future enter a contractive phase.)

We know from observations that heat is generated when we compress a gas and that this heat creates pressure that opposes further contractions.

Similarly, the contraction of the universe will create heat, which will oppose its further contractions.

The velocity of contraction will increase until the momentum of the galaxies, planets, components of the universe equals the radiation pressure generated by the heat of its contraction.

At this point in time, the total kinetic energy of the collapsing universe would be equal and oppositely directed with respect to the radiation pressure associated with the heat of its collapse. From this point on the velocity of the contraction will slow due to the radiation pressure and be maintained by the momentum associated with the remaining mass component of the universe.

However, after a certain point in time the heat and radiation pressure generated by its contraction will become great enough to ionize the remaining mass and cause it to reexpand because the expansive forces associated with the radiation pressure caused by its collapse will exceed the contractive forces associated with its mass.

This will result in the universe entering an expansive phase and going through another age of recombination when the comic background radiation was emitted. The reason it will experience an age of recombination as it passes through each cycle is because the heat of its collapse would be great enough to completely ionize all forms of matter.

However, at some point in time the contraction phase will begin again because as mentioned earlier its kinetic energy cannot exceed the gravitational energy associated with the total mass/energy in the universe.

Since the universe is a closed system, the amplitude of the expansions and contractions will remain constant because the law of conservation of mass/energy dictates the total mass and energy in a closed system remains constant.

This results in the universe experiencing in a never-ending cycle of expansions and contractions of equal magnitudes.

If this theoretical model is valid the heat generated by the collapse of the universe must raise the temperature to a point where most of the atomic nuclei become dissociated into their component parts and electrons would be strip off making the universe opaque to radiation.  It would remain that way until it entered the expansion phase and cooled enough to allow matter to recapture and hold on to them.

However, this model does not assume the universe had its beginning in a supper hot singularly as the big bang model suggest but in a slightly cooler environment were some nuclei that were created during the previous expansion and contraction phase would remain intact.

In other words, the reason why we have been unable to observe any Population III which are composed entirely hydrogen, helium and very small amounts of lithium and beryllium no heavy metals is because those heavy metals were already in the mix when they were formed.

One could quantify this scenario by calculating the temperature and pressure which would result the ratio the heavy metals to the lighter elements to be equal to what it is in the earliest stars that are observable.  Then starting from that point in time, using those as the initial parameters and the current laws of physics determine if the universe would have evolved to what is it today.  If so, it would have a tendency to be more creditable than the current Big Bang model because its beginning has a foundation in the laws of physics and not in a singularity as that model does.

Additionally it is true using the currently accepted laws of physics and the concept of a singularly as its starting point one can with considerable accuracy predict how our universe evolved.  However, those predictions are based on the initial conditions found in a singular and since as was just mention those laws cannot be applied to it they can never be fully validated.

However, the above theoretical model can make just as accurate perditions which can be fully validated or falsified because there is no place in the universes evolution where the laws of physics cannot be applied.

Later Jeff

Copyright 2016 Jeffrey O’Callaghan

One of the most puzzling questions in modern cosmology is why the density of matter and energy appears to be find tuned to the value that allowed life to evolve.

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 Einstein’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 universe’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

Here is an amazing fact: The matter we know that makes up all stars and galaxies only accounts for 5% of the content of the universe. The rest is called dark matter.  It does not interact with the electromagnetic force and therefore does not absorb, reflect or emit light, making it extremely hard to spot.  In fact, researchers are only able to infer its existence only from the gravitational effect it has on visible matter, which outweighs the visible matter roughly six to one, making up about 27% of 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 influence the gravity forces of the visible mass component our universe.

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 yet 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 are no currently known particles that have its 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 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 a portion of the missing mass found by Fritz Zwicky may be related to those field properties is not what 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 but as an irreversible physical, chemical, and biological change in physical space.  Therefore, it is hard to understand how the physical properties Einstein associated with space can interact with the non-physical properties of a time or a space-time dimension to create mass.

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 he 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.

The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the field properties of a space-time environment in terms of four *spatial* dimensions means as was done in the article “Defining energy?” Nov 27, 2007 that one can also define the gravitational properties mass in terms of a spatial displacement in field properties of four *spatial* dimension.

Therefore, according to Einstein if the continuous field properties of a three-dimensional space manifold were displacement with respect to a fourth *spatial* dimension a gravitational field would be created which because it is not made up of particles would not interact with light and therefore be Dark.

In other words, a portion of the gravitational forces associated with Dark Matter may not be the mass associated with particles but with the physical qualities Einstein in his speech “Aether and the theory of Relativity” tells us that a displacement of space must have

However, this contradicts the current worldview shared by most physicists and cosmologists that gravitational forces can only be created by mass 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 mass is made up of the continuous field properties of space when he theorized that all particles have a wave component because according to modern theories that is the only thing that can support continuous properties of a wave.

Additionally the electron diffraction by crystals in 1927 by Davisson and Germer provides experimental confirmation of this because that one can observe the transfer of momentum from a particles wave component to the electron caused by that interaction.

In other words, the mass we associate with 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 space or as was shown above mass the ability to oscillate 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 the mass and therefore the gravitational potential of particles.

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. Yet the most effective 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 and probably the most significant 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 force on the walls of ship lock created by the changing level of water from a ship in it by measuring how high it is above its surface because it is changing at the same rate.

As was mentioned earlier Einstein tells us a displacement in the continuous “surface” or field properties of a three-dimensional space manifold which are displaced with respect to a fourth *spatial* dimension would result in the creation of a gravitation field.

However, as it was with a ship one cannot measure the gravitational force on the “walls” of our universe generated by the mass associated with a displacement in a “surface” of three-dimensional space manifold because we and all our instruments are floating on that “surface”.

Yet as mentioned earlier we can determine the mass component of space by measuring how the inertial properties of its field components interact with crystals in experiments such as those conducted by Davisson and Germer

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 physical make up of dark matter

Later Jeff

Copy right Jeffrey O’Callaghan 2016

Something that is infinite or the quality of having no limits or end cannot exist or be a part of the physically observable environment we live in primarily because it is finite.

Some might disagree by pointing out that we cannot know the full extent of our universe because the speed of light puts limits on our ability to observe parts beyond a specific point.  However some could also argue that anything beyond that point is not in our observable universe and because of that it cannot be a part of it.

Yet even though Einstein’s theories does not mathematical rule out the possibility of an infinite universe it does not predict that one exists.

However the same cannot be said of Quantum Mechanics which mathematical defines mass, energy and forces in terms of a one dimensional point.  Infinities arise because the forces and energies associated with the integrals which define them become larger as they approach each other reaching infinity when they come in contact.

The difference between these quantum mechanical infinites and relativistic ones is that they occur with the limits of our observable universe.  In other words it predicts existence of masses, forces, and energies that are infinite within its finite boundaries.

Some might think this indicates the basic concepts of quantum mechanics that define our in terms of the mathematical properties of a one dimensional point is incorrect because most physicists and mathematicians would agree that the infinite entity cannot exist in a finite environment.

However its proponents disagree and have devised a clever method called renormalization which alters the mathematical relationships between the parameters in the theory to make these infinites disappear.

Granted even though one may be able to use renormalization to alter the mathematical relationships between point particles to eliminate infinites they cannot change the fact the point particle responsible for those infinities still exists before those alterations take place.  In other words it assumes they exist before renormalization takes place because if they did not there would be no need for renormalization.  Therefore even though the process of renormalization solves the mathematical problem of infinities it does nothing to solve the conceptual one that exist within the framework of quantum mechanics because it relies on the existence of point particles which as mentioned earlier are responsible for the infinites. `

Why then are we still using it to explain or predict that reality?

The most probable answer is because it predicts with amazing precision the results of every experiment involving the quantum world that has ever been devised to test it: so much so that many are willing to overlook the obvious fact that as was just mentioned the conceptual arguments use to make those predictions have a fatal flaw.

However we are not going to concern ourselves with resurrecting the conceptual content of quantum mechanics as has been the focus of the past three quarters of a century but instead will define another theory that can explain the behavior of energy/mass in terms of the properties of our observable environment in a way that eliminates the need for any “adhco” procedures such as renormalization to make it consistent with that behavior.

To do this one must be able to, in a logical and consistent manner using only the physical laws of our observable environment explain the existence of the four basic components of a quantum world: the fact that energy/mass is quantized, Planck’s constant, Heisenberg’s Uncertainty Principle and the reason one can use probabilities to define a particles position.

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

(Note: Einstein has already gave us a detailed mathematical description of this environment when he used the constant velocity of light to define the 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 mathematically derive a one to one correspondence between his space-time universe and one made up of only four *spatial* dimensions.)

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 an environment of four *spatial* dimensions.

(Louis de Broglie was the first to theorize that all particles are made up of matter waves.  His theories were later confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.)

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.

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

This shows how one can conceptually derive the quantum mechanical properties energy/mass in terms of wave properties of particles observed by Davisson and Germer by assuming that they are a result of resonant properties of four *spatial* dimensions.

In other words if one assumes as is done here that its mathematical properties of Schrödinger’s wave function are representative of wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension one can form a physical image of why energy/mass is quantized in terms of the properties of our observable environment.

However it also gives one the ability to define the physical boundaries of a particle and its energy in terms of the observable properties of our environment

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 or the “box” containing the wave component of Schrödinger’s wave function the article “Why is energy/mass quantized?” Oct. 4, 2007 associated with a particle. 

As mentioned earlier infinites arise in Quantum Mechanics when one applies the concept of mathematical one dimensional point to define mass, energy and forces results their integrals to become increasing larger as they approach each other reaching infinity when they come in contact. 

However the above theoretical concepts provides a solution because it shows that a particle’s energy is not confined to a one dimension point but instead exists in an extended spatial volume associated with its resonant structure.

Yet if true one must be able derive the physical meaning the other fundamental concepts of quantum mechanics like Planck’s constant or 6.626068 × 10-34 (kg*m2/s), Heisenberg’s Uncertainty Principle and the probabilities associated with Schrödinger’s wave function by extrapolating the laws of classical physics in a three-dimensional environment to a fourth *spatial* dimension.

Planck’s constant is one of fundamental components of Quantum Physics and along with Heisenberg’s Uncertainty Principle it defines the uncertainty in the ability to measure more than one quantum variable at a time.  For example attempting to measure an elementary particle’s position (â–²x) to the highest degree of accuracy leads to an increasing uncertainty in being able to measure the particle’s momentum (â–²p) to an equally high degree of accuracy.  Heisenberg’s Principle is typically written mathematically as â–²xâ–²p  Â³ h / 2  where h represents Planck constant

As mentioned earlier the resonant wave that corresponds to the quantum mechanical wave function defined in the article “Why is energy/mass quantized?” Oct. 4, 2007 predicts that a particle will most likely be found in the quantum mechanical “box” whose dimensions would be defined by that resonant wave.  However quantum mechanics treats particles as a one dimensional points and because it could be anywhere in it there would be an inherent uncertainty involved in determining the exact position of a particle in that “box”.

For examine the formula give above ( â–²xâ–²p  Â³ h / 2 ) tells us that uncertainty of measuring the exact position of the point in that “box” defined by its wavefunction would be equal to â–²xâ–²p  Â³ h / 2.   However because we are only interested in determining its exact position we can eliminate all references to its momentum.

However if we eliminate the momentum component from the uncertainty in a particle position become 6.626068 × 10-34 meters or Planck’s constant.

As mentioned earlier the uncertainty involved in determining the exact position of a particle is because it is impossible to determine were in the “box” defined earlier the quantum mechanical point representing that particle is located.  However as mentioned earlier Planck’s constant tells us that one cannot determine the position of a particle to an accuracy greater that 6.626068 × 10-34.  This suggest that Planck constant 6.626068 × 10-34 defines the physical parameters or dimensions of that “box” because it defines the parameters of where in a given volume of space a quantum particle can be found.

In other words it defines a physical interpretation of Planck’s constant or 6.626068 × 10-34 (kg*m2/s), and Heisenberg’s Uncertainty Principle by extrapolating the observable properties and laws of our three-dimensional environment to a fourth *spatial* dimension.

However it also gives one the ability to connect the probabilities associated with Schrödinger’s wave function to the observable reality of our three-dimensional environment.

As was mentioned one can conceptually derive the quantum mechanical properties of his function in terms of physical properties of a mater wave observed by Davisson and Germer by assuming that they are a result of resonant properties of four *spatial* dimensions.

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

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

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

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

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

Similarly a particle would most probably be found were the magnitude of the vibrations in a “surface” of a three-dimensional space manifold is greatest and would diminish as one move away from that point.

This shows how one can eliminate infinities from our understanding of the quantum properties of energy/mass while at the same time allow one to connect those properties to the observable realities of our environment.

Later Jeff

Copyright Jeffrey O’Callaghan 2016

The fact that we need two theories to explain the evolution of our universe means that one of them must have originated before the other.

For example Einstein’s relativistic and gravitational theories can explain predict the evolution of the large scale structure and movement of the stars and planets but cannot explain the structure of the atom.  Additionally it cannot be used to explain one of the most important aspects of the universe’s evolution: how atoms fuse together in stars to create enough energy to prevent their gravitational collapse.  While quantum mechanics explains the small scale structure of atom how they fuse together to prevent that from happening however it cannot be used to explain the evolutionary movement of the stars and planets.

Determining which on of these theory came first is difficult not only because no one was around to observe when they began but because they are defined in different units.  For example Einstein theories define the universe in terms of the temporal field properties of a space-time dimension while quantum theories do so in terms discrete quantized properties of position.  However if one can view them in terms of the same units one may be able to determine which one came first by showing how one could have evolved from the other.

Einstein gave us the ability to do this when he used the constant velocity of light in the equation E=mc^2 to define geometric properties of energy/mass 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 it would allow one to define both the evolution of gravity and the quantum mechanical properties of energy/mass in terms of a common property related to their spatial components.

This provides the bases for assuming, as was done in the article “Defining energy?” Nov 27, 2007 that all forms of energy including that associated with gravity and the quantized energy associated with Schrödinger’s wave equation in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

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

(Louis de Broglie was the first to predict the existence of a matter wave or the physical equivalent to Schrödinger’s wave equation when he theorized that all particles have a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer).

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

The existence of four *spatial* dimensions would give a “surface” of a three dimensional space manifold 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.

However these oscillations in four *spatial* dimensions would generate a classically resonating system or “structure” in it because it meets the requirements listed earlier for the creation of one.

These resonant structures are responsible for the quantum mechanical properties of energy/mass.

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

Yet it also allows one to define the boundary of a quantum system 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 associated with a particle in the article  Why is energy/mass quantized?” Oct, 4 2007. 

In other words one can understand how the quantum mechanical properties of energy/mass could have evolved from field properties Einstein’s theories if one assumes that it is a result of the resonate structured form by a matter wave in continuous field properties of space 

However if true one must also show how the probabilities associated with Schrödinger’s equation could have evolved out of that medium.

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

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 focal point.  Therefore their is a non-zero probability they could be found anywhere in our three-dimensional environment. 

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

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

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

In other words is it is possible to derive a scenario in which the concepts of quantum mechanics could have evolved out for the continuous field properties of an environment consisting of four dimensional space-time or four *spatial* dimensions.

As was mentioned earlier we can never by sure if Einstein’s theories or Quantum mechanics is the primary mover and creator of our universe because no one there when it began.  However the fact that one can derive the concepts of quantum mechanics using Einstein’s theories is a strong indicate that it came first.

In other words it suggests that the Quantum chicken was more than likely born out of a Relativistic egg.

It should be remember that Einstein’s genius and the symmetry of his mathematics allows us to choose whether to define the evolution of the universe in either four *spatial* dimensions or four dimensional space-time.

Later Jeff

Copyright Jeffrey O’Callaghan 2016

Quantum Decoherence was proposed to justify the framework and intuition of classical physics as an acceptable approximation: it is the mechanism by which the classical limit emerges from a quantum starting point and determines the location of the quantum-classical boundary.  Decoherence occurs when a system interacts with its environment in a thermodynamically irreversible way. This prevents different elements in the quantum superposition of the total system’s wavefunction from interfering with each other.
However one may eliminate the need for Decoherence by showing that one can explain how the quantum world emerges from a classical starting point by observing how matter and energy interact in a space-time environment.

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


Einstein gave us the ability to do this when he use the equation E=mc^2 and the constant velocity of light to define the geometric properties of space-time because that provided a method of converting a unit of time he associated with energy to a unit of space associated with position.  Additionally because the velocity of light is constant it allows for the defining of  a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

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

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


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

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

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

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 four *spatial* dimensions would be responsible for the discrete quantized energy associated with the quantum mechanical systems.

Yet it also allows one to define the boundary of a quantum system 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 associated with a particle in the article “Why is energy/mass quantized?“


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

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


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


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

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


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

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


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

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

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

It should be remember Einstein’s genius allows us to choose to define a quantum system in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the spatial as well as the time properties of our universe thereby giving us a new perspective on the causality of the quantum mechanical interaction.

Later Jeff

Copyright 2015 Jeffrey O’Callaghan 

There are many theories that attempt to explain what we observed in our three dimensional environment in terms of higher dimensions.  However they all suffer from the same problem in that the existence of those higher dimensions are primarily based on abstract on mathematical models.  The reason is because we as three dimensional beings are only able to observe objects in the three-dimensional environments we occupy.  Therefore we must rely on mathematics to guide us in understanding how their existence influences what we observe in our world.

Many feel the most promising is called string theory, which attempts to define all of the observed properties of our universe in as many as ten dimensions.
However, as is pointed out on page 51 of Lee Smolin book “The Trouble with Physics” all attempts at unifying physics through extra dimensions suffer from the same problem.  There are a few solutions that lead to the world we observe but there are many which do not.  One has to set the initial conditions, which are found by observing our world to determine which solutions define what we observe.  The use of this circular methodology means its validity is not based on its theoretical structure but on its flexibility.

In other words its validity is not based on connecting the observed properties of our environment to it but the randomly picking which the ones do the best job.

Einstein’s theories are very different in that they make specific predictions based on the existence of a single space-time environment that if found not to occur would invalidate it.

For example his theory tells us that light should bend as it passes by a massive object.

If this was not observed his theory would have to be discarded.

However 1919 Arthur Eddington lead an expedition to photograph the Total Eclipse of the Sun. The photographs revealed stars whose light had passed near sun had been bent exactly as Einstein had predicted. The experiment was repeated in 1922 with another eclipse with the same confirmation.

Additionally in past century since he proposed his theory there has not been any observations of our macroscopic universe that disagree with any of its predictions.

Even so this does not mean that we should assume that our universe is physically made up of four dimensional space-time because as with all multidimensional theories when Einstein derived the geometric properties of a space-time universe in terms of the constant velocity of light he also define another one with identical properties in terms of four *spatial* dimensions.

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

As was mentioned earlier the fact that light bends as it passes by massive objects doers not mean our universe is made up of four dimensional space-time because the symmetry of equations used to make that prediction also predicts one made up of only four *spatial* dimensions will do the same.

Therefore the fact that light bends as it passes by a mass cannot be used to eliminate that possibility.

However there is a experiment very similar to the one Arthur Eddington preformed that would resolve this ambiguity.

Einstein’s Theory of General Relativity tells that objects that create gravitational field cause time to “move” slower.  However due to the symmetry of his equations one could also say that time slowing down results in the formation of a gravitational field.  Therefore one must assume that a gravitational field must always be attractive because observations indicate that time only moves in one direction forward.

However the fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the energy 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 it can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension as well as one in a space-time dimension.

However unlike time which is observed to only move in one direction forward observations tell us that we can move in spatially in two directions up down backwards and forwards.

Therefore if the universe was made up of four *spatial* dimensions there should exist a form of mass that posses a negative gravitational potential.

One candidate for such a mass is antimatter.  We know from observations that in it posses an opposite electrical charge than its matter counterpart.  Therefore it is logical to assume that it posses a gravitational field that is oppositely directed from that of matter.

An experiment has be proposed that could determine if this is indeed true.

As describe in the New Scientist article “Antimatter mysteries 3: Does antimatter fall up?” Apr 29, 2009, it involves using uncharged particles to prevent electromagnetic forces from drowning out gravitational effects.  It will first 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.

In other words there is an experiment that could determine if our universe is physically composed of four dimensional space time or four *spatial* dimensions because as was mentioned earlier a universe physically composed of four dimensional space-time cannot support a negative gravitational potential while one made up of four spatial dimensions can.

Yet if found to be true it does not mean that Einstein’s theories are invalid because his theories and predictions were based on pure mathematics and as mentioned earlier a universe consisting of four dimensional space-time and four spatial dimensional are mathematically are equivalent in every respect.  

However it would require us to rethink our understanding of the physical geometry of our universe and the causality of gravitational forces.

Later Jeff

Copyright 2015 Jeffrey O’Callaghan

The Standard Model of Particle Physics and Quantum Mechanics give us a plausible reason why particles are what they are while Einstein theories give a reasonable answer to the question regarding why they come together to form planets stars and how they move in relation to each other.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Later Jeff

Copyright Jeffrey O’Callaghan 2015

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