Absolutely not, because those laws as proposed by Einstein prevent that from happening.

The existence of a singularity at the center of a black hole is often taken as proof that the theory of general relativity has broken down, which is perhaps not unexpected as it occurs in conditions where quantum effects should become important.

In the center of a black hole many believe a gravitational singularity occurs which contains a huge mass in an infinitely small space. In other words density and gravity become infinite while space-time curves infinitely. This would result in the laws of physics as we know them cease to operate. As the eminent American physicist ** Kip Thorne **describes it, it is "the point where all laws of physics break down".

**U****nfortunately, everyone including Kip Thorne is wrong because as was just mentioned the laws proposed by Einstein governing the existence of space-time tell us that a singularity can never repeat never exist in a black hole.**

The existence of a singularity is based on a mathematical solution developed in 1915, by Karl Schwarzschild who proposed based on Einstein theories the gravitational field of a star greater than approximately 2.0 times a solar mass would stop the movement of time. Additionally, it is assumed that his solution identified a radius for any given mass, known as the Schwarzschild radius, where, if that mass could be compressed to fit within that radius, no known force or degeneracy pressure could stop it from continuing to collapse into a gravitational singularity or black hole. Thus, where the radius of the body is less than its Schwarzschild radius, everything, even photons of light, must inevitably fall into the central body called a singularity or a one-**dimensional** object in space-time.

However, the according to the relativistic laws Einstein proposed for his space-time universe the time dilatation it associated with a gravitational field would prevent matter form collapsing beyond the event horizon of a black hole to form a singularity .

**In other words, the very theory is used to predict the existence of a black hole also prevents the formation of a singularity and the laws of physics, as defined by Einstein from breaking down in its space-time environmen**t.

To understand why one must analyze how he define the relativistic properties of space-time and how it interacts with matter in a gravitational field.

For example, as a star contacts and its circumference decreases, the time dilation on its surface will increase. At a certain point called the event horizon the contraction of that star will produce a gravitational field strong enough to stop the movement of time. Therefore, the critical circumference defined by Karl Schwarzschild is a boundary in space where time stops relative to the space outside of that boundary.

However, the existence of a singularity mentioned earlier is based on the assumption that time continues to move for matter even after it has past the event horizon of a black hole.

However, this is a direct contraction of the relativistic properties of time as described in Einstein theories.

In Kip S. Thorne book "Black Holes and Time Warps", he describes how in the winter of 1938-39 Robert Oppenheimer and Hartland Snyder computed the details of a stars collapse into a black hole using the concepts of General Relativity. On page 217 he describes what the collapse of a star would look like, form the viewpoint of an external observer who remains at a fixed circumference instead of riding inward with the collapsing stars matter. They realized the collapse of a star as seen from that reference frame would begin just the way every one would expect. "Like a rock dropped from a rooftop the stars surface falls downward slowly at first then more and more rapidly. However, according to the relativistic formulas developed by Oppenheimer and Snyder as the star nears its critical circumference the shrinkage would slow to a crawl to an external observer because of the time dilatation associated with the relative velocity of the star’s surface. The smaller the circumference of a star gets the more slowly it appears to collapse because the time dilation predicted by Einstein increases as the speed of the contraction increases until it becomes frozen at the critical circumference.

However, the time measured by the observer who is riding on the surface of a collapsing star will not be dilated because he or she is moving at the same velocity as its surface.

Therefore, the proponents of singularities say the contraction of a star can continue until it becomes a singularity because time has not stopped on its surface even though it has stopped with respect to an observer who remains at fixed circumference to that star.

But one would have to draw a different conclusion if one viewed time dilation in terms of the gravitational field of a collapsing star.

Einstein showed that time is dilated by a gravitational field. Therefore, the time dilation on the surface of a star will increase relative to an external observer as it collapses because, as mentioned earlier gravitational forces at its surface increase as its circumference decrease.

This means, as it nears its critical circumference its shrinkage slows with respect to an external observer who is outside of the gravitation field because its increasing strength causes a slowing of time on its surface. The smaller the star gets the more slowly it appears to collapse because the gravitational field at its surface increase until time becomes frozen for the external observer at the critical circumference.

Therefore, the observations of an external observer would make using conceptual concepts of Einstein’s theory regarding time dilation caused by the gravitational field of a collapsing star would be identical to those predicted by Robert Oppenheimer and Hartland Snyder in terms of the velocity of its contraction.

**However, it also tells us, the laws of physics developed by Einstein for a space-time environment are not violated in black hole with respect to all external observers because the time dilation associated with its gravitational field would not allow the collapse of matter beyond its critical circumference to a singularity. **

However, Einstein developed his Special Theory of Relativity based on the equivalence of all inertial reframes which he defined as frames that move freely under their own inertia neither "pushed not pulled by any force and Therefore, continue to move always onward in the same uniform motion as they began".

This means that one can view the contraction of a star with respect to the inertial reference frame that, according to Einstein exists in the exact center of the gravitational field of a collapsing star.

(Einstein would consider this point an inertial reference frame with respect to the gravitational field of a collapsing star because at that point the gravitational field on one side will be offset by the one on the other side. Therefore, a reference frame that existed at that point would not be pushed or pulled relative to the gravitational field and would move onward with the same motion as that gravitational field.)

**(However, some have suggested that a singularity would form in a black hole if the collapse of a star was not symmetrical with respect to its center. In other words, if one portion of its surface moved at a higher velocity that another towards its center it could not be consider an inertial reference frame because it would be pushed or pulled due to the differential gravity force cause be its uneven collapse. But the laws governing time dilation in Einstein’s theory tell us that time would move slower for those sections of the surface that are moving faster allowing the slower ones to catch up. This also tells us that every point on the surface of star will be at the event horizon at the exact same time and therefore its center will not experience any pushing or pulling at the time of its formation and therefore could be considered an inertial reference frame.)**

The surface of collapsing star from this viewpoint would look according to the field equations developed by Einstein as if the shrinkage slowed to a crawl as the star neared its critical circumference because of the increasing strength of the gravitation field at the star’s surface relative to its center. The smaller it gets the more slowly it appears to collapse because the gravitational field at its surface increases until it becomes frozen at the critical circumference**.**

Therefore, because time stops or becomes frozen at the critical circumference for all observers who is at the center of the clasping mass and the contraction cannot continue from their perspectives.

**However, it also tells us, the laws of physics developed by Einstein for a space-time environment are not violated in black hole with respect to an observer who is at the its center because the time dilation associated with its gravitational field would not allow the collapse of matter beyond its critical circumference to a singularity. **

Yet, Einstein in his general theory showed that a reference frame that was free falling in a gravitational field could also be considered an inertial reference frame.

As mentioned earlier many physicists assume that the mass of a star implodes when it reaches the critical circumference. Therefore, an observer on the surface of that star will be in free fall with respect to the gravitational field of that star when as it passes through its critical circumference.

This indicates that point on the surface of an imploding star, according to Einstein’s theories could also be considered an inertial reference frame because an observer who is on the riding on it will not experience the gravitational forces of the collapsing star.

However, according to the Einstein theory, as a star nears its critical circumference an observer who is on its surface will perceive the differential magnitude of the gravitational field relative to an observer who is in an external reference frame or, as mentioned earlier is at its center to be increasing. Therefore, he or she will perceive time in those reference frames that are not on its surface slowing to a crawl as it approaches the critical circumference. The smaller it gets the more slowly time appears to move with respect to an external reference frame until it becomes frozen at the critical circumference.

Therefore, time would be infinitely dilated or stopped with respect to all reference frames that are not on the surface of a collapsing star from the perspective of someone who was on that surface.

However, the contraction of a star’s surface must be measured with respect to the external reference frames in which it is contracting. But as mentioned earlier Einstein’s theories indicate time in its external environment would become infinitely dilated or stop when the surface of a collapsing star reaches its critical circumference.

Therefore, because time stops or becomes frozen at the critical circumference with respect to the external environment of an observer who riding on its surface the contraction cannot continue because motion cannot occur in an environment where time has stopped.

**However, it also tells us, the laws of physics are not violated in black hole with respect to all riding on the surface of a star because the time dilation associated with its gravitational field the collapse of matter beyond its critical circumference to a singularity. **

This means, as was just shown according to Einstein’s concepts time stops on the surface of a collapsing star from the perspective of all observers when viewed in terms of the gravitational forces the collapse of matter must stop at the critical circumference.

This contradicts the assumption made by many that the implosion would continue for an observer who was riding on its surface.

** In other words, **based on the conceptual principles of Einstein’s theories relating to time dilation caused by a gravitational field of a collapsing star it cannot implode to a singularity as many physicists believe because it causes time to freeze at its critical circumference with respect to all observers and therefore must maintain a quantifiable minimum volume which is equal to the one defined by Karl Schwarzschild.

**However, this means the laws of physics as defined by Einstein do not break done when a singularity forms at the center of a black hole because as was shown above those laws tell us its formation is not supported by those laws. Therefore it cannot be taken as proof that the laws as defined by General Theory Relativity has broken down, because those same laws prevent that from happening **

There can be no other conclusion if one accepts the validity laws as defined by Einstein Relativistic Theories and of the physical observations of the time dilation associated with a gravitational field.

Later Jeff

Copyright 2020 Jeffrey O’Callaghan

One cannot deny that Quantum mechanics, the theory that defines the tiny world of particles and Einstein’s theories, the one that defines what we see through a telescope have been the most successful scientific theories of modern times However, attempts to bring these two theories together and define "A Theory of Everything" have been unsuccessful.

However, the fact that we have been unable to do so suggests that one or both of these theoretical models does not describe the true nature of reality because the world we see through a telescope must have its foundations in the world of the very small therefore they must be connected.

There can be many reasons for this. One is that foundational assumptions of either or both of them is incorrect. In other words, the world of the tiny may not be governed by probabilities as quantum theory suggests or the world, we see though a telescope may not be ruled by relativistic properties of four dimensional space-time.

*H***owever, there is another possibility that many have over looked *** is that even though their mathematics makes very accurate perditions of experimental observations they do not accurately define reality of their operating environments. *

For example, Einstein mathematically defined the physical structure of the universe in terms of the geometry four dimensional space-time*.*

However, when using the constant velocity of light and the velocity of objects that do not move at that speed to define its geometric properties he provided a way of mathematical converting a unit of time in a space-time universe to unit of space in one physically consisting of only four *spatial* dimensions.

In other words, their is an equally valid interpretation of his mathematics in terms of only four spatial dimensions.

*Since both of these solutions that of four dimensional space-time and four spatial dimensions would yield the same numerical results it gives one a different way of connecting his theories to those of Quantum mechanics based on the physical properties of four spatial dimensions instead of four dimensional space-time.*

Quantum Theory on the other hand defines tiny world of particles in terms of the non physical probabilities associated with SchrÃ¶dinger wave equation which as mentioned earlier no one has been able to physical connect to the space-time universe define by Einstein.

However, the fact that Einstein provided an alternative solution to his mathematics in terms of four spatial dimensions suggests it may be possible to make that connection and therefore define a Theory of Everything by using the alternative solution of four spatial dimension that his theory provides instead of one based on four dimensional space-time.

For example the article "Why is mass quantized?" Oct. 4, 2007 showed one could derive the quantum mechanical properties of energy in terms of a resonant "system" or structure formed by a energy wave on the surface of a three-dimensional spatial manifold with respect to a fourth *spatial* dimension.

Briefly that article showed the four conditions required for resonance to occur in a three-dimensional 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 can be meet in one consisting of terms of four spatial dimension.

Its continuous properties would allow an energy wave on a "surface’ of a three-dimensional space manifold to oscillate with respect to a fourth *spatial* dimension thereby fulfilling one of the requirements for resonance to occur.

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

Therefore, these oscillations in a continuous non-quantized field of energy would meet one of the requirements mentioned above for the formation of a resonant system or "structure" in space.

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

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

These resonant systems in a space-time environment would be responsible for the incremental or discreet energy associated with quantum mechanical systems.

Another requirement for a resonate system to be formed is that the wave must be confined to specific volume of space.

However, one can also define the confinement of the resonant component of a particle and therefore establish a physical connection to the wave particle duality quantum mechanics associates with energy in terms of the relativistic properties of four *spatial* dimensions.

In 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?".

**In other words, an energy wave in four *spatial* dimensions will maintain its wave properties unless it is confined to three by an observation, therefore it it always be view as a particle when an observation is made and any energy left over from the formation of its resonate structure will be radiating from the point of observation in the form of light or an energy wave.**

The physics of wave mechanics also tells us that due to their continuous properties the energy waves 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 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 are a result of vibrations or oscillations in a "surface" of three-dimensional space is correct 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.

(Some may question the fact that the energy wave associated with particle would be distributed over the entire universe. However, the relativistic properties of space-time and four spatial dimensions tell that distance perceived by objects or particles in relative motion is dependent on their velocity which become zero at the speed of light. Therefore, from the perspective of an energy wave moving at the speed of light, the distance between all points in the universe along it velocity vector is zero. In other words, it’s energy is distributed or simultaneous exists at every point in the universe along its velocity vector. There can be not other conclusion if one accept the validity of Einstein’s theories.)

As mentioned earlier the article â€œ__Why is energy/mass quantized?__â€ shown a quantum particle is a result of a resonant structure formed by an energy wave on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Yet the science of 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, by interpreting Einstein space-time theories in their equivalent four spatial dimension one can connect the non physical probabilities associated with SchrÃ¶dinger wave equation to the reality of the world defined by him.

**Additional it shows, by changing our interpretation of Einstein’s theories from four dimensional space-time to it equivalent in four spatial dimensions allows one to clearly understand the physical connection between the probabilistic world of quantum theory and the relativistic world of his theories, thereby allowing one to form a Theory of Everything. **

**Later Jeff **

**Copyright Jeffrey O’Callaghan 2019**

Dark energy appears to contradict many of our ideas about the way the universe works. For example, light waves move energy though emptiness of space while Einstein’s equation, E = mc2, tells us that matter and energy are interchangeable, merely different forms of the same thing. However, energy is supposed to have a source either matter or radiation but Dark Energy exists even when space is devoid of all matter and radiation.

For example, Einstein defined the origin mass and its energy of in terms of curvature or displacement in the field properties of space-time not in terms of matter or radiation. In other words, he defined them as a geometric property of the universe. Therefore, it is possible that Dark Energy may not be related to matter or radiation but to the geometry of those field properties similar to how he defined matter.

Specifically, Einstein defined gravitational energy in terms of positive displacement in the space-time field of our universe which causes mass/energy to become concentrated at the apex of that curvature. This suggest, since Dark energy is a force that opposes gravity that it could be caused by an opposite directed or negative displacement in geometry of that field.

However, one of the problem integrating Dark Energy into Einstein’s space-time model is the fact that it is causing special expansion of the universe which his space-time model cannot accommodate because it does not include higher spatial dimension for it to expand to. In other words, because his theories contain only three-spatial dimensions there is no higher spatial one for our universe to expand to.

Granted one can assume that space is expanding relative to itself but that would mean that it must extend to infinity because if it did have a boundary its outer most region would have to be moving with respect to a higher or fourth spatial dimension which would require rewriting his theory to accommodate it.

Additionally, the theoretical model called the Big Bang which most cosmologists accept as the definitive origin for both space and time tell us that it cannot be infinite because it assumes its expansion began not from an infinite volume but form one from within the boundaries of a singularity.

But Einstein provided a solution this problem when defined the magnitude of the gravitational energy in terms of time and the constant velocity of light because that provided a method of converting a unit of time in a space-time environment to unit of space in four *spatial* dimensions. In other words, because light travel a unique distance for a given time interval it gives us mathematical way to converting a universe composed of four-dimensional space-time to one made up of four *spatial* dimensions. Additionally, because the velocity of light is constant, he also defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

**The fact that one can use Einstein’s theories to qualitatively and quantitatively derive the *spatial* properties of time in space-time universe in terms of four *spatial* dimensions is one the bases of assuming as was done in the article â€œDefining energyâ€ Nov 27, 2007 that all forms of energy including gravity and those associated with Dark 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. **

**In other words, one can not only use Einsteinâ€™s equations to quantitatively and qualitatively derive how both Dark and gravitational energy interacts with time in a space-time dimension but also how it would interact with its *spatial* equivalent in four *spatial* dimensions.**

As was mentioned earlier, one problem integrating Dark Energy into Einstein’s space-time model is the fact that it is causing special expansion of three-dimensional space which his model cannot accommodate because it does not include a higher spatial dimension for it to expand towards. However, redefining his theories in terms its equivalent in four *spatial* dimensions resolves this issue because it defines a higher spatial one in which our three-dimensional space can expand towards.

However, it also provides a logically consistent causality for Dark Energy in terms of his theories since he defined gravity in terms of a depression or positive curvature in a "surface" of a three-dimensional space manifold with respect to fourth *spatial* dimension it would be logical to conclude, due their opposing nature that Dark energy is an elevation or negative curvature in that "surface".

This would also allow one to use Einstein’s theories to understand how Dark Energy is causing the spatial expansion of our universe in terms of either a space-time environment or one made up of fourth *spatial* dimension because as was shown in above these two environments are interchangeable in his theories.

For example, if the walls of an above ground pool filled with water collapse the potential energy associated with the elevated two-dimensional surface of the water will flow or expand and accelerate outward towards the three-dimensional environment sounding it.

However, we know from the study of hydrodynamics that energy "flows" from areas of high density to ones with a low density very similar to how water flows form an elevated or "high density" point to a lower one.

Yet we also know from the observations of the cosmic background radiation that presently our three-dimensional universe has an average energy component equal to about 3.7 degrees Kelvin.

However, if one accepts Einstein’s theories the three-dimensional "surface" of our universe which has an average energy component of 3.7 degree Kelvin one must assume it would be elevated with respect to a fourth *spatial* dimension.

In other words, if the "surface" of a three-dimensional manifold was elevated with respect to a fourth *spatial* dimension by the energy associated with the cosmic background radiation as Einstein tell us must then it would be accelerated outward for the same reason as the water in a pool whose sides had collapsed.

This allows one qualitatively understand the casually of the accelerated expansion of our universe in term of the physical image of water accelerating out of collapsed pool.

The reason why Dark Energy was not the predominant force in the early universe was because its gravitational energy was more concentrated at that time because as the equation defining tells us, its force diminishes with respect to the square of the distance between masses. Therefore, when the volume of the universe was relatively small its gravitational component determined its expansion rate. However, as its volume increased Dark Energy took over because the gravitational component of the universe’s mass become less concentrated and therefore weaker with respect it.

Some may feel that this is an over simplification of what appears on the surface to be a rather complex phenomena such as Dark Energy but is no more simplistic than the one used to help us understand how gravity works in a space-time environment. Granted the math behind this concept may be complex and difficult to understand as it is with the gravitational curvature in space-time. However, that does not mean that we cannot use it to understand its causality.

It should be remembered; Einsteinâ€™s genius allows us to choose to define our universe in either a space-time environment or one consisting of four *spatial* dimension when he defined its geometry in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories thereby giving us a new perspective on the how matter energy space and time interact.

Later Jeff

Copyright Jeffrey O’Callaghan 2019

because it can stop the collapse of matter no matter how massive an object is.

Einstein told us a gravitational field causes time to dilate and in 1915,Karl Schwarzschild proposed based on Einstein theories the gravitational field of a star greater than approximately 2.0 times a solar mass would stop the movement of time. Additionally, it is assumed that his solution identified a radius for any given mass, known as the Schwarzschild radius, where, if that mass could be compressed to fit within that radius, no known force or degeneracy pressure could stop it from continuing to collapse into a gravitational singularity or black hole. Thus, where the radius of the body is less than its Schwarzschild radius, everything, even photons of light, must inevitably fall into the central body called a singularity or a one-**dimensional** object in space-time.

**However, according to Einstein there is one "force or degeneracy pressure" that will stop it from continuing to collapse into a gravitational singularity and that is time. **

To understand how and why one must analyze how he defined the relativistic properties of space-time and how it interacts with matter in a gravitational field.

For example, as a star contacts and its circumference decreases, the time dilation on its surface will increase. At a certain point called the event horizon the contraction of that star will produce a gravitational field strong enough to stop the movement of time. Therefore, the critical circumference defined by Karl Schwarzschild is a boundary in space where time stops relative to the space outside of that boundary.

However, the existence of a singularity mentioned earlier is based on the assumption that time continues to move for matter even after it has past the event horizon of a black hole.

Yet, this is a direct contradiction of the relativistic properties of time as described in Einstein theories.

In Kip S. Thorne book "Black Holes and Time Warps", he describes how in the winter of 1938-39 Robert Oppenheimer and Hartland Snyder computed the details of a stars collapse into a black hole using the concepts of General Relativity. On page 217 he describes what the collapse of a star would look like, form the viewpoint of an external observer who remains at a fixed circumference instead of riding inward with the collapsing stars matter. They realized the collapse of a star as seen from that reference frame would begin just the way every one would expect. "Like a rock dropped from a rooftop the stars surface falls downward slowly at first then more and more rapidly. However, according to the relativistic formulas developed by Oppenheimer and Snyder as the star nears its critical circumference the shrinkage would slow to a crawl to an external observer because of the time dilatation associated with the relative velocity of the star’s surface. The smaller the circumference of a star gets the more slowly it appears to collapse because the time dilation predicted by Einstein increases as the speed of the contraction increases until it becomes frozen at the critical circumference.

However, the time measured by the observer who is riding on the surface of a collapsing star will not be dilated because he or she is moving at the same velocity as its surface.

*Therefore, the proponents of singularities say the contraction of a star can continue until it becomes a singularity because time has not stopped on its surface even though it has stopped with respect to an observer who remains at fixed circumference to that star.*

But one would have to draw a different conclusion if one viewed time dilation in terms of the gravitational field of a collapsing star.

Einstein showed that time is dilated by a gravitational field. Therefore, the time dilation on the surface of a star will increase relative to an external observer as it collapses because, as mentioned earlier gravitational forces at its surface increase as its circumference decrease.

This means, as it nears its critical circumference its shrinkage slows with respect to an external observer who is outside of the gravitation field because its increasing strength causes a slowing of time on its surface. The smaller the star gets the more slowly it appears to collapse because the gravitational field at its surface increase until time becomes frozen for the external observer at the critical circumference.

Therefore, the observations of an external observer would make using conceptual concepts of Einstein’s theory regarding time dilation caused by the gravitational field of a collapsing star would be identical to those predicted by Robert Oppenheimer and Hartland Snyder in terms of the velocity of its contraction.

**However, it also tells us, the force of time is stronger that the gravitational forces of a black hole with respect to all external observers because when it freezes it prevents the further gravitational collapse of matter beyond the critical circumference with respect to them.**

However, Einstein developed his Special Theory of Relativity based on the equivalence of all inertial reframes which he defined as frames that move freely under their own inertia neither "pushed not pulled by any force and therefore, continue to move always onward in the same uniform motion as they began".

This means that one can view the contraction of a star with respect to the inertial reference frame that, according to Einstein exists in the exact center of the gravitational field of a collapsing star.

(Einstein would consider this point an inertial reference frame with respect to the gravitational field of a collapsing star because at that point the gravitational field on one side will be offset by the one on the other side. Therefore, a reference frame that existed at that point would not be pushed or pulled relative to the gravitational field and would move onward with the same motion as that gravitational field.)

(However some have suggested that a singularity would form in a black hole if the collapse of a star was not symmetrical with respect to its center. In other words if one portion of its surface moved at a higher velocity than another towards its center it could not be consider an inertial reference frame because it would be pushed or pulled due to the differential gravitational force cause be its uneven collapse. But the laws governing time dilation in his theory tell us that time would move slower for those sections of the surface that are moving faster allowing the slower ones to catch up. This also tells us that every point on the surface of star will be at the event horizon at the exact same time and therefore its center will not experience any pushing or pulling at the time of its formation and therefore could be considered an inertial reference frame.)

The surface of collapsing star from this viewpoint would look according to the field equations developed by Einstein as if the shrinkage slowed to a crawl as the star neared its critical circumference because of the increasing strength of the gravitation field at the star’s surface relative to its center. The smaller it gets the more slowly it appears to collapse because the gravitational field at its surface increases until time becomes frozen at the critical circumference.

Therefore, because time stops or becomes frozen at the critical circumference for all observers who are at the center of the clasping mass the contraction cannot continue from their perspectives.

*However, it also tells us, the force of time is stronger than the gravitational forces of a black hole with respect to all observers located at its center because when it freezes with respect to them it prevents the further collapse of matter beyond the critical circumference.*

However, Einstein in his general theory showed that a reference frame that was free falling in a gravitational field could also be considered an inertial reference frame.

As mentioned earlier many physicists assume that the mass of a star implodes when it reaches the critical circumference. Therefore, an observer on the surface of that star will be in free fall with respect to the gravitational field of that star when as it passes through its critical circumference.

This indicates that point on the surface of an imploding star, according to Einstein’s theories could also be considered an inertial reference frame because an observer who is on the riding on it will not experience the gravitational forces of the collapsing star.

However, according to the Einstein theory, as a star nears its critical circumference an observer who is on its surface will perceive the differential magnitude of the gravitational field relative to an observer who is in an external reference frame or, as mentioned earlier is at its center to be increasing. Therefore, he or she will perceive time in those reference frames that are not on its surface slowing to a crawl as it approaches the critical circumference. The smaller it gets the more slowly time appears to move with respect to an external reference frame until it becomes frozen at the critical circumference.

Therefore, time would be infinitely dilated or stopped with respect to all reference frames that are not on the surface of a collapsing star from the perspective of someone who was on that surface.

However, the contraction of a star’s surface must be measured with respect to the external reference frames in which it is contracting. But as mentioned earlier Einstein’s theories indicate time in its external environment would become infinitely dilated or stop when the surface of a collapsing star reaches its critical circumference.

Therefore because time stops or becomes frozen at the critical circumference with respect to the external environment of an observer who riding on its surface the contraction cannot continue because motion cannot occur in an environment where time has stopped.

**However, it also tells us, the force of time is stronger that the gravitational forces of a black hole with respect to an observer who is riding on it because when it freezes with respect to its external environment it prevents further the collapse beyond the critical circumference.**

This means, as was just shown according to Einstein’s concepts because time and movement stops on the surface of a collapsing star from the perspective of all observers when viewed in terms of gravitational forces, the collapse of matter must stop at the critical circumference. This contradicts the assumption made by many that the implosion would continue for an observer who was riding on its surface.

In other words,** **based on the conceptual principles of Einstein’s theories relating to time dilation caused by the gravitational field of a collapsing star it cannot implode to a singularity as many physicists believe because it causes time to freeze at its critical circumference with respect to all observers. Therefore it must maintain a quantifiable minimum volume which is equal to the one defined by Karl Schwarzschild.

This tells us either the conceptual ideas developed by Einstein are incorrect or there must be an alternative solution to the field equations based on the General Theory of Relativity that many physicists used to predict the existence of a singularity because as has just been shown the theoretical predications made by them with respect to the time dilation associated with a gravitational field tell us it cannot exist. Therefore, according to his theories a black hole must have a solid surface at the event horizon which is made up of matter in its most basic form because it cannot be compacted any more.

*However, it also tells us time is a force more powerful than the gravitational field of a black hole because it has the ability to freeze the collapse of matter at its event horizon no matter how massive it is.*

In other words, time is the most powerful in the universe because it can stop the collapse of matter in a black holes.

There can be no other conclusion if one accepts the validity Einstein Relativistic Theories and of the physical observations of the time dilation associated with a gravitational field.

Later Jeff

Copyright Jeffrey O’Callaghan 2019

In the early 1990s, one thing was fairly certain about the expansion of the universe. It might have enough energy density to stop its expansion and recollapse, it might have so little energy density that it would never stop expanding, but gravity was certain to slow the expansion as time went on.

However, in 1998 observations of very distant supernovae by the Hubble Space Telescope (HST) that showed that, a long time ago, the universe was actually expanding more slowly than it is today. So, the expansion of the universe has not been slowing due to gravity, as everyone thought, it has been accelerating. No one expected this, no one knew how to explain it. But something was causing it.

Since then we have not been able to derive the causality of what has been called Dark Energy even though we know how much of it there is because we know how it affects the universe’s expansion. Other than that, it is a complete mystery. It turns out that roughly 68% of the universe is dark energy while Dark matter makes up about 27%. The rest – everything on Earth, everything ever observed with all of our instruments, all normal matter – adds up to less than 5% of the universe.

One explanation for Dark Energy is that it is a property of space. Albert Einstein was the first person to realize this when he postulated that empty space is not nothing. The first property that he discovered is that it is possible for more space to come into existence. One version of Einstein’s gravity theory, which contains a cosmological constant, makes a second prediction: "empty space" can possess its own energy.

However, even though in 1917, he added this energy in terms of cosmological constant to his equations which some fell would provide one of simplest mathematical explanations for Dark Energy it is difficult for many to conceptually integrate it with the physical imagery that is provided by his theory.

Yet one of the difficulties forming one may be because Einstein chose to define energy in terms of time or a space-time dimension while the expansion of Dark Energy effects the spatial not the time properties of our universe.

However, he did provide a way to understand the spatial expansion associated with it in terms of physical image similar to the one he provided for energy while at the same time defining the causality of the potential energy in space.

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

This fact that one can use Einsteinâ€™s theories to qualitatively and quantitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is one the bases of assuming as was done in the article â€œDefining energy?â€ Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a â€œsurfaceâ€ of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

In other words, one can not only use Einsteinâ€™s equations to from physical image of how Dark Energy interacts with space in terms of four-dimensional space-time but also in terms of four spatial dimensions.

For example, we know from the study of thermodynamics that energy flows from areas of high to ones with low density very similar to how water flows form an elevated or â€œhigh densityâ€ point to a lower one.

Yet we also know from observations of the cosmic background radiation that presently our three-dimensional universe has an average energy component equal to about 3.7 degrees Kelvin.

In other words, according to Einstein’s space-time theories the "surface" of three-dimensional space when viewed, as was shown above from its spatial equivalent would be elevated with respect a fourth *spatial* dimension. This suggest the potential energy Einstein had associated with space was a result of the displacement of the "surface" of three dimensional space with respect to a fourth spatial dimension due to the residual energy of the big bang.

One can understand how this energy would be responsible for the expansion of the universe by comparing it to how the potential energy of water in an above ground pool expands when the walls collapse. In other words when the walls of an above ground pool collapse the elevated two-dimensional surface of the water will expand and accelerate outward towards the three-dimensional environment sounding it.

Similarly if the â€œsurfaceâ€ of a three-dimensional manifold was elevated with respect to a fourth *spatial* dimension as Einstein tell us as it would be if one redefined his space-time universe in terms of four spatial dimension then it would be accelerated outward for the same reason as the water in a pool whose sides had collapsed.

In other words, one can explain the origins of Dark Energy or the potential energy of space in terms of the physical image of water accelerating out of collapsed pool.

Some may feel that this is an over simplification of what appears on the surface to be a rather complex phenomena such as Dark Energy but is no more simplistic that the one use to help us understand how gravity works in a space-time environment.

It should be remembered that Einsteinâ€™s genius and the symmetry of his mathematics allows us to choose whether to define the forces associated with gravity and Dark Energy in either four *spatial* dimensions or four-dimensional space-time.

Later Jeff

Copyright 2019 Jeffrey Oâ€™Callaghan

Dark Energy is a repulsive force that is the dominant component (69.4 percent) of the universe. The remaining portion consists of ordinary matter and dark matter. Dark Energy, in contrast to both forms of matter, is relatively uniform in time and space and is gravitationally repulsive, not attractive, within the volume it occupies. The nature of Dark Energy is still not well understood.

However if you have a Universe full of stuff it’s virtually impossible to keep it static. The fabric of our Universe, at least in General Relativity, must either expand or contract on the largest scales. But if you have a Universe filled with Dark Energy, as we appear to have, something even more troubling happens: the total amount of energy contained within our observable Universe increases over time, with no end in sight. Doesn’t this violate the conservation of energy?

That depends on what is responsible for that energy.

Einstein was aware, while working on is General Theory of Relativity that it is virtually impossible to keep a Universe full of stuff static so 1917, he added a cosmological constant to his equations. Some believe this would provide one of simplest mathematical explanations for Dark Energy however it is difficult for many to conceptually integrate it with the physical imagery that is provided by his theory.

For example, in Einstein’s General Theory of Relativity he derived gravity in terms of a curvature in a space-time metric. One can form a relatively simple physical image of it based on how objects such as a ball is accelerated on a curved two dimensional surface on the earth and then extrapolating that to a curvature in a space-time metric.

Yet one of the difficulties some may have in forming a similar image of Dark Energy is because Einstein chose to define gravity in terms of time or a space-time dimension while the expansion of Dark Energy appears to be related to the spatial not the time properties of our universe.

However he did provide a way to understand the spatial expansion associated with it in terms of physical image similar to the one he provided for gravity while at the same time answering the question razed earlier if it violated the conservation laws of physics.

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

This fact that one can use Einstein’s theories to qualitatively and quantitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is one the bases of assuming as was done in the article â€œDefining energyâ€ 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.

In other words one can not only use Einstein’s equations to quantitatively and qualitatively derive how energy interacts with time in a space-time dimension but also how it would interact with its spatial equivalent in four *spatial* dimensions.

The study of thermodynamics tells us those particles with high temperature or energy move or flow to areas of low energy very similar to how water flows form an elevated or “high energy” point to a lower one.

However the fact that Einstein defines energy in terms of field properties of space-time means that one must also consider the thermodynamics of those fields. In other words because he defined energy in terms of a dimensional properties of space we must assume even with no particle matter present that it contains energy. In other words one must apply the concept of thermodynamics to those field properties.

For example if the walls of an above ground pool filled with water collapse the elevated two-dimensional surface of the water will flow or expand and accelerate outward towards the three-dimensional environment sounding it.

Yet we know from observations of the cosmic background radiation that presently our three-dimensional universe has an average energy component equal to about 3.7 degrees Kelvin.

However this means that according to concepts developed in the article â€œDefining energy” (mentioned earlier) the three-dimensional “surface” of our universe which has an average energy component of 3.7 degree Kelvin would be elevated with respect to a fourth *spatial* dimension.

As was mentioned earlier Einstein gave us the ability to define energy in terms of a spatial displacement in a “surface” of a three dimensional space manifold with respect to a forth *spatial* dimension as well as a time dimension. Therefore, similar to the surface water in a pool if that “surface” was elevated with respect to a fourth *spatial* dimension as Einstein tell us as it must be because, as was just mentioned it has the energy associated 3.7 degree Kelvin then it would accelerate outward for the same reason as the water in a pool whose sides had collapsed.

In other words one can qualitatively understand the casually of the Dark energy in term of the physical image of water expanding out of a collapsed pool.

However if this theoretical model is correct it means that Dark Energy would not violate the conservation laws because it would be compensated for by the cooling of the universe and not with a physical component of space similar to how energy released from the water in a dam is does violate the conservation laws because it is compensated for by the loss of its potential energy.

In other words the total amount of energy contained within our observable Universe does not increase over time because the energy of its expansion is compensated for by its loss of energy due to its cooling.

It should be noted there is nothing new or revolutionary about this concept because, as was shown above, it is consistent with the Einstein General and special Theories Relativity and all of the currently accepted laws of physics that govern the evolution of the universe.

Yet some may feel that this is an over simplification of what appears on the surface to be a rather complex phenomena such as Dark Energy but is no more simplistic that the one use to help us understand how gravity works in a space-time environment. Granted the math behind this concept may be complex and difficult to understand as it is with the gravitational curvature in space-time however that does not mean that we cannot use it to understand its causality.

It should be remember that Einsteinâ€™s genius and the symmetry of his mathematics allows us to choose whether to define the forces associated with gravity and Dark Energy in either four *spatial* dimensions or four dimensional space-time.

Later Jeff

Copyright 2019 Jeffrey O’Callaghan

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In the early 1990s, one thing was fairly certain about the expansion of the universe. It might have enough energy density to stop its expansion and recollapse, it might have so little energy density that it would never stop expanding, but gravity was certain to slow the expansion as time went on. Granted, the slowing had not been observed, but, theoretically, the universe had to slow. The universe is full of matter and the attractive force of gravity pulls all matter together. Then in 1998 observations made by the Hubble Space Telescope (HST) of very distant supernovae that showed that, a long time ago, the universe was actually expanding more slowly than it is today. So the expansion of the universe has not been slowing due to gravity, as everyone thought, it has been accelerating. No one expected this, no one knew how to explain it. But something was causing it.

More is unknown than is known. We know how much Dark Energy there is because we know how it affects the universe’s expansion. Other than that, it is a complete mystery. But it is an important mystery. It turns out that roughly 68% of the universe is dark energy. Dark matter makes up about 27%. The rest – everything on Earth, everything ever observed with all of our instruments, all normal matter – adds up to less than 5% of the universe. Come to think of it, maybe it shouldn’t be called “normal” matter at all, since it is such a small fraction of the universe.

According to Nasa’s universe web site one explanation for Dark Energy, as Albert Einstein suggested is that it is a property of space. In other words he was the first person to suggest that empty space is not nothing. The first property that Einstein discovered is that it is possible for more space to come into existence. Then one version of Einstein’s gravity theory, the version that contains a cosmological constant, makes a second prediction: “empty space” can possess its own energy. Because this energy is a property of space itself, it would not be diluted as space expands. As more space comes into existence, more of this energy-of-space would appear. As a result, this form of energy would cause the universe to expand faster and faster. Unfortunately, no one understands why the cosmological constant should even be there, much less why it would have exactly the right value to cause the observed acceleration of the universe”

However following Einstein lead we may find the answer these questions by attempting to understand exactly how and why space is expanding in terms of his space-time model.

For example Einstein’s Special and General Theories of Relativity is based on the relative simple concept of a space-time metric. Granted the math required to determine the how space and time interact on objects can be very complicated however understanding or visualizing how space-time effect them is relative easy to do.

However one of the difficulties in understanding how three-dimensional properties of space are expanding is defining what it is expanding into because only place it can go according his theories is towards a time dimension.

Granted one can assume that space is expanding relative to itself but that would mean that it must extend to infinity because if it did have a boundary its outer most region would have to be moving with respect to something.

However, the theoretical model called the Big Bang which most cosmologists accept as the definitive origin for both space and time tell us that it cannot be infinite because it assumes its expansion began not from and infinite volume but form one with boundaries called a singularity.

Additionally because three-dimensional space is undergoing a spatial expansion it is difficult to understand how three-dimensional space can physically expanding towards time dimension because time does not have physical physical properties of the spatial dimensions.

But Einstein gave us the ability to develop a better understanding of the expansion of three dimensional 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 because that provided a method of converting a unit of time he associated with energy in space-time to unit of space one can associate 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 fact that one can use Einstein’s theories to qualitatively and quantitatively derive the *spatial* properties of time in space-time universe in terms of four *spatial* dimensions is one the bases of assuming as was done in the article â€œDefining energyâ€ 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.

In other words one can not only use Einstein’s equations to quantitatively and qualitatively derive how energy interacts with time in a space-time dimension but also how it would interact with its *spatial* equivalent in four *spatial* dimensions.

In other words his theories tell us that three-dimensional space can expand towards a fourth *spatial* dimension as well as a time dimension.

We know from the study of thermodynamics that energy flows from areas of high to ones with low density very similar to how water flows form an elevated or “high density” point to a lower one.

For example if the walls of an above ground pool filled with water collapse the elevated two-dimensional surface of the water will flow or expand and accelerate outward towards the three-dimensional environment sounding it.

Yet we know from observations of the cosmic background radiation that presently our three-dimensional universe has an average energy component equal to about 3.7 degrees Kelvin.

However this means that according to concepts developed in the article â€œDefining energy” (mentioned earlier) the three-dimensional “surface” of our universe which has an average energy component of 3.7 degree Kelvin would be elevated with respect to a fourth *spatial* dimension.

Similar to the water in a pool whose sides had collapsed, if the “surface” of a three-dimensional manifold was displaced with respect to a fourth *spatial* dimension as Einstein tell us as it must be if one redefines his space-time universe in terms of four *spatial* dimension then it would be accelerated outward.

In other words one qualitatively understand the casually of the accelerated expansion of our universe in term of water accelerating out of collapsed pool.

This suggests the accelerative force dark energy is caused by the fact that the base line Einstein used to define energy in a space time is displaced with respect to its zero point.

Some many question this because if true it means that over time the expansion rate should decrease because similar to the water in a pool its velocity should decrease as it expands and its energy dissipates.

However the universeâ€™s expansion to appears to be accelerating. as the graphic shows, instead of slowing down as this model suggests it should. The reason is because it assumes there are two factors that determine its expansion rate: the attractive forces of gravity which would cause it to slow and Dark Energy which case it to expand.

However since gravitational forces are inversely proportional to distance its effects are reduce by the increasing distance between their components cause by the physical expansion of space and the kinetic energy imparted to its gravitational mass components by the big bang while if the above model is correct the only thing that effects Dark Energy is the magnitude of the *spatial* displacement of three-dimensional space with respect to fourth *spatial* dimensions. In other words the contractive forces of gravity should be according the above model decreasing faster that the expansive forces of Dark Energy because of their increase rate of separation relative to dark energy Therefore the expansive force of dark energy would appear to be increasing even though it may be constant or decreasing over the course of time.

This could be verified by determining the ratio of the energy is lost by the gravitational force as a result of the universe’s expansion and kinetic energy imparted to the its mass components and see if it corresponds to the energy required to explain the observed increase in its acceleration.

In other words one can explain the observed properties of Dark Energy in terms of a *spatial* displacement a “surface” of three dimensional space with respect to a fourth *spatial* dimension as well as with respect to a time dimension because in Einstein’s mathematics tells us they are interchangeable.

Some may also feel that this is an over simplification of what appears on the surface to be a rather complex phenomena such as Dark Energy but is no more simplistic that the one use to help us understand how gravity works in a space-time environment. Granted the math behind this concept may be complex and difficult to understand as it is with the gravitational curvature in space-time however that does not mean that we cannot use it to understand its causality.

It should be remember that Einsteinâ€™s genius and the symmetry of his mathematics allows us to choose whether to define the forces associated with gravity and dark energy in either four *spatial* dimensions or four dimensional space-time.

Later Jeff

Copyright 2019 Jeffrey O’Callaghan

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Here is an amazing fact: The matter we know of 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.

There have been several proposed answers to what it is.

One proposed by “Quantum Field Theory of Interacting Dark Matter/Dark Energy: Dark Monodromies” suggests that Dark Matter is made up of heavy particles with masses which are very sensitive to the value of dark energy are strongly constrained. Quintessence-generated long range forces and radiative stability of the quintessence potential require that such dark matter and dark energy are completely decoupled. However, if dark energy and a fraction of dark matter are very light axions, they can have significant mixings which are radiatively stable and perfectly consistent with quantum field theory. Such models can naturally occur in multi-axion realizations of monodromies. The mixings yield interesting signatures which are observable and are within current cosmological limits but could be constrained further by future observations.

However, it not only defies logic but also common sense to assume that dark matter is made up of “heavy particles with masses” because one would think that a heavy particle would be easier to observe than lighter ones which we are able to observe.

For too long physicists have ignored common sense and logical arguments which are based on a perception of our observable universe such as assuming “”Dark Matter is made up of heavy particles” because if it was we should be able to observe it. They create all kinds of crazy ideas such “Quintessence-generated long range forces and radiative stability” to justify their arguments that do not have any bases in the reality of our observable world.

However physics by definition is an observational science. In other words physicists must not base their theoretical models only the of end results experiment but also on observing the processes by which those results were obtain.

For example Albert Einstein in his theory of Special Relativity, determined the laws of physics are the same for all non-accelerating observers by showing that space and time were interwoven into a single continuum known as space-time.

However as he worked on the equations defining gravity in his General Theory of Relativity, he realized that massive objects would cause a distortion or curvature in the space-time field of his Special Theory of Relativity. Imagine setting a large body in the center of a trampoline. The body would press down into the fabric of space-time causing it to dimple. A marble rolled around the edge would spiral inward toward the body, pulled in much the same way that the gravity of a planet pulls at rocks in space.

In other words Einstein based his theoretical conclusions that a curvature in space-time is responsible for gravity not only on his mathematics but on his observation of how objects in the world around him interact with their environment.

Additionally, in his General Theory of Relative he told us that energy and mass are interchangeable in terms of the field properties of a space-time environment and the equation E=mc^2. In other words he defined energy and mass in terms in terms of the continuous field properties he associated with a space-time environment. This suggests a portion of the missing mass found by Fritz Zwicky may be related to those field properties not what most associate with the mass of objects or particles.

Yet, for some it may be difficult to integrate the physical imagery provided by his theory to understand how a field consisting of space and time can have the properties of Dark Matter because time is not perceived by most as having the properties of matter. In other words because time does not have any observable physical properties it is difficult to form a physical image of how it can interact with the space to create matter.

But Einstein gave us the ability to develop more direct understand how and why those field properties 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 it provided a method of converting a unit of time he associated with energy in space-time to unit of space one can associate 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.

In other words he gave us the ability to understand how the field properties of four dimensional space-time can be responsible for Dark Matter in terms of a physical image based solely on the observable properties of the spatial dimensions.

The fact that one can use Einsteinâ€™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 â€œDefining energy?â€ Nov 27, 2007 that one can also define the gravity in terms of a spatial displacement in its field properties.

In other words according to Einstein mathematics if the continuous field properties of a three-dimensional space manifold were displaced or offset with respect to a fourth *spatial* and or time dimension a gravitational field would be created.

For example the potential energy of the water in a dam over a flat “surface” is determined by its height with respect to that surface. However some of its energy is stored in the environment it occupies because the pressure it exerts on the surface of the earth where it was located will cause that surface to become depressed or offset with respect to where it was before it was filled. Therefore, to accurately measure its full potential energy one would not only have to measure how much energy is stored in the water but how much is stored in the offset it creates in its environment. In other words one cannot get an accurate measure of the potential energy of the water in a dam by just measuring its height above the bottom because one must add to that energy is stored in the in the environment it is occupying.

Similarly Einstein’s space-time mathematics tells us the same thing, that the gravity is not only caused by the quantity of matter in a given volume but also the magnitude of the energy store in its environment.

Unfortunately we are only able to measure gravitational force from the center of the mass of planets, stars, and galaxies which means we are only measuring its potential energy in terms of the “height” with respect to the “flat surface” of space-time before the object was there. However as was just mentioned Einstein tells us that some of their gravitational energy will be stored in the offset they cause in the space-time environment they are occupying. Therefore to get a true sense of the total gravitational energy in the universe one must take into account the energy stored the fabric of space.

This energy stored in the fabric of space-time created by matter is responsible for the gravitational energy associated with Dark Matter. The reason it does not interact with light or is Dark is because it is not created by matter but by the energy stored in the continuous flied properties of space-time, the medium light travels on.

Later Jeff

Copy right Jeffrey O’Callaghan 2019

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Why many physicists chose to define the universe in terms of the physical properties of a time or space-time dimension instead of four *spatial* dimensions is puzzling because, as was shown in the earlier article “Defining time” Sept 20, 2007 there is no observational evidence supporting it having physical properties.

But even more damaging is that assuming it is composed of four *spatial* dimensions instead of four-dimensional space-time, would allow physicists more logical and consistent explanation **based on physical observations** or our environment for time dilation, length foreshortening, the mass increases associated with relative velocities, gravitational and kinetic energy than can be provided by space-time concepts of the Special and General Theories of Relativity.

Einstein himself defined a universe composed of four *spatial* dimension * and* one of four-dimensional space-time when he mathematically defined its geometric properties in terms of the constant velocity of light. This is because it allows one to redefine a unit of time he associated with energy in his space-time universe to unit of space in a one consisting of only four *spatial* dimensions.

However as was mentioned earlier viewing the universe in terms of four *spatial* dimensions instead of four-dimensional space-time, would allow one to define the mechanism responsible for time dilation, length foreshortening, the mass increases associated with relative velocities, and gravity **based on the physical observations instead of the abstract mathematical properties of the Special and General Theories of Relativity.**

One of the advantages of deriving all forms of energy in terms of their spatial instead of their time or space time properties is that it allows one to form a physical image of the opposing nature of kinetic and gravitational forces in terms of our observable properties of our environment

For example we observe that the kinetic energy associated a satellite opposes the gravitational energy of the object it is orbiting.

*However because of observations of our three-dimensional environment tell us one can move in two directions upward or downwards in a *spatial* dimension one can form a clearer image of opposing properties of these forces by defining gravity in terms of a “downward directed” displacement in a surface of a three-dimensional space manifold with respect to a fourth spatial dimension while define kinetic energy in terms of oppositely or upward directed or up displacement in that surface. Granted the one can do the same using the properties of a space-time dimension however it is much more difficult to understand the opposing nature of these force because we only observe time to move in one direction forward. *

This is the observational basis for defining, as was done in the article “Defining potential and kinetic energy?” gravitational and kinetic energy in terms of oppositely directed movements or displacements in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

In other words if one defined the energy/mass in a volume associated with mass in terms of downward directed displacement in a “surface” of a three-dimensional space manifold with respect to a four *spatial* dimension one would define the energy associated with its relative motion in terms of an oppositely or upward displacement in that “surface”.

This would allow one to form a physical image of the relative mass increase due to relative velocities based on observation of our three-dimensional world because according to the concepts contained in that article the total energy/mass of an object would be equal to the sum of the displacements of a “surface” of a three-dimensional space manifold caused by its rest mass and that caused by their relative velocities.

However defining space in terms of four spatial dimension not only provides observational basis for causality of the gravity and kinetic energy but it also provides an explanation for the casualty of time dilation and the length foreshortening in gravitational environments and moving reference frames based on physical observations made in a three-dimensional environment.

The following analogy can be used to understand and define the relativistic properties length and time based on observations made in a three-dimensional environment.

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

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

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

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

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

Similarly, because three-dimensional beings could only “view” a three-dimensional translation of a “curvature” or displacement in four *spatial* dimension caused by the relative motion of a reference frame they will measure distance or length in them as being longer than they would be if viewed as an observer who is in relative motion to it.

This is the mechanism responsible for the relativistic properties of length in terms of the geometry of four *spatial* dimensions.

The two-dimensional creatures in the earlier example will also notice that time is effected by a curvature in the surface of their paper.

Each of them will view the others â€œtimeâ€ as moving slower because the three-dimensional curvature in the paper makes the distance between events longer than the two dimensional translation of that curvature. Therefore, it will take longer for events “move” through a curvature in three-dimensional space on the surface of the others piece of paper relative to the time it would take for it to move thought the two-dimensional translation of that curvature.

Earlier it was mentioned that time can be defined as only being the measure or the “distance between” the sequential ordering of the causality of an event.

Therefore time would be dilated with respect to a reference frame that is external to a gravitational field or was in motion because as mentioned earlier the length of the arc generated in three-dimensional space by a gravitational field or the kinetic energy of relative motion to be longer than the cord of that arc. Therefore, the distance between events would be greater for an observer in those reference frames than for one who is outside of it. However, this means an observer outside of those reference frames would measure the time between those events as being dilated with respect to an observer who is inside because the time required for objects to move between events in that reference frame will be longer.

As mentioned earlier article both â€œGravityâ€ and kinetic energy can be define in terms of a 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 manifold.

However, this means that one can define the foreshortening of the length of an object in relative motion or in a gravitational field in terms of the cord to the arc generated by that curvature. This is because the cord of an arc created by that displacement is always shorter than the arc itself and since three-dimensional beings can only observe the three-dimensional cord of an arc in four-dimensional space they would view the length of the objects to be shorter when viewed in relative motion or in a gravitational field.

However it would also provide a mechanism for the time dilatational associated with gravity and motion that is consistent with our observations of three-dimensional space.

This shows one the benefits of viewing Einstein relativistic theories in terms of four *spatial* dimension is that it allows one to form a more logical and consistent explanation **based on physical observations** or our environment for time dilation, length foreshortening, the mass increases associated with relative velocities, gravitational and kinetic energy than can be provided by the space-time concepts of the Special and General Theories of Relativity.

As was shown earlier Einsteinâ€™s mathematics allows us to choose to define our universe in terms of either a space-time environment or one consisting of only four *spatial* dimension when he defined its geometry in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories thereby giving us a new perspective on its relativistic properties.

Later Jeff

Copyright 2017 Jeffrey O’Callaghan

Is time travel possible?

The laws of physics in the microscopic world suggest that it is because the physical processes they define at the subatomic level appear to be either entirely or mostly time symmetric. In other words the theoretical statements that describe them remain true if the direction of time is reversed. However, the opposite is true in the macroscopic world in that there is an obvious direction (or *flow*) of time. In others words, process in our macroscopic environment are observed to be asymmetric with respect to the direction of time appearing to rule out the possibility of traveling backwards in it.

Therefore, one way to understand why we as a civilization have been unable devise a mechanism for traveling back in time may be to understand difference between the macroscopic and microscopic worlds with respect to it because in one it seems possible while in the other it appears not to be.

**Entropy** appears to be the only quantity in the macroscopic world that “picks” a particular direction for time. As one goes “forward” in time, the second law of thermodynamics says the entropy or disorder of an isolated system will increase when no energy is consumed. In other words many in the scientific community believe the reason a system composed of multiple units must always move in forward with respect to time because to go back to a previous configuration one must add energy to it.

However, one cannot apply the concept of entropy to the microscopic world of atoms to determine its direction with respect to time because the entropy or relative disorder of system composed of signal entities such as an atom does **not **spontaneously increase as it moves through it. Therefore, one cannot use it to define its direction in microscopic systems because it does not quantifiably change as one “moves” through time.

Yet both these definitions define the direction or flow of time in terms of the physical configuration of its spatial components. For example, entropy or relative disorder of system composed of a signal atom does **not **spontaneously increase as it moves through time because its spatial position can only be reference to itself. This differs form systems that contain multiple entities in that the spatial configuration of its units can be compared to others in that system. The only difference between them with regards to defining their entropy with respect to the movement of time is what their spatial locations are reference to.

However the fact that we have been unable to move backwards in time in the microscopic universe suggests the casualty of time in that environment may not be related to the physical movement of an entity but to the causality of a quantifiable change in the spatial components of a system similar to the one that gives us direction for time in a macroscopic system.

For example in a multiunit system the causality of the increased entropy associated with the forward movement of time is directly related to its thermodynamic energy because it is what quantifies the direction of the changing spatial disorder in a system. Similarly in a single component system the sequential ordering of the causality of it moving to the left and then to the right will always define the direction of time in terms of its changing spatial position. In other words on can define the direction of time in both in terms of the causality of the systems spatial components.

As was mentioned earlier the second law of thermodynamics which defines the passage of time in the macroscopic world is based on a statistical definition was developed by Ludwig Boltzmann does not hold with strict universality: any system can fluctuate to a state of lower entropy.

However scientists have observed billions of particle collisions in which two particles collide to produce other particles however they have never observed two particles spontaneous coming together to form one particle even though statistically speaking they should happen much more often than in multi particle systems because they have considerably less complexity.

Therefore understanding the causality of the change in the position component of entities in both macro and microscope system may tell us if travel time travel is possible.

As was shown in the earlier article “Defining what time is” Sept. 20, 2007 defining the direction of time in terms of the sequential ordering of the causality of events would a provide a consistent direction for time in all environments because the causality of an atom moving to the left in both single or multiple component system would always be proceeded by the causality of that the same atom moving to the right; even though, as was mentioned earlier the behavior of the atom is not *qualitatively* different in either case. This would be true in both our physical and mathematical perceptions of time.

In other words defining it in terms of the sequential ordering of the causality of an event is consistent with the observation that events appear to always move forward in time in both the macroscopic universe and the microscopic world of particle accelerators because the casualty of particle breaking up into different parts must always proceed those parts coming together.

*Some might think that it is not possible to tell the order in which events occurred without using time as a reference. However one can use the spatial properties of a system to determine it because the first event in a series would only be connected to the one before it while all other would be connected not only to that one but to the one after it. In other words one could determine the order in which the events occurred by referencing them to the one that has only one spatial connection and following the single line of events back towards there origin.*

However this also rules out any possibility of one traveling through time because if it is only a measure of the sequential ordering of the causality of events then similar to all measurements it does not have physical properties so because one cannot travel through or in something that does not have a physical structure time travel is physically possible.

Is time travel possible?

The laws of physics in the microscopic world suggest that it is because the physical processes they define at the subatomic level appear to be either entirely or mostly time symmetric. In other words the theoretical statements that describe them remain true if the direction of time is reversed. However, the opposite is true in the macroscopic world in that there is an obvious direction (or *flow*) of time. In others words, process in our macroscopic environment are observed to be asymmetric with respect to the direction of time appearing to rule out the possibility of traveling backwards in it.

Therefore, one way to understand why we as a civilization have been unable devise a mechanism for traveling back in time may be to understand difference between the macroscopic and microscopic worlds with respect to it because in one it seems possible while in the other it appears not to be.

**Entropy** appears to be the only quantity in the macroscopic world that “picks” a particular direction for time. As one goes “forward” in time, the second law of thermodynamics says the entropy or disorder of an isolated system will increase when no energy is consumed. In other words many in the scientific community believe the reason a system composed of multiple units must always move in forward with respect to time because to go back to a previous configuration one must add energy to it.

However, one cannot apply the concept of entropy to the microscopic world of atoms to determine its direction with respect to time because the entropy or relative disorder of system composed of signal entities such as an atom does **not **spontaneously increase as it moves through it. Therefore, one cannot use it to define its direction in microscopic systems because it does not quantifiably change as one “moves” through time.

Yet both these definitions define the direction or flow of time in terms of the physical configuration of its spatial components. For example, entropy or relative disorder of system composed of a signal atom does **not **spontaneously increase as it moves through time because its spatial position can only be reference to itself. This differs form systems that contain multiple entities in that the spatial configuration of its units can be compared to others in that system. The only difference between them with regards to defining their entropy with respect to the movement of time is what their spatial locations are reference to.

However the fact that we have been unable to move backwards in time in the microscopic universe suggests the casualty of time in that environment may not be related to the physical movement of an entity but to the causality of a quantifiable change in the spatial components of a system similar to the one that gives us direction for time in a macroscopic system.

For example in a multiunit system the causality of the increased entropy associated with the forward movement of time is directly related to its thermodynamic energy because it is what quantifies the direction of the changing spatial disorder in a system. Similarly in a single component system the sequential ordering of the causality of it moving to the left and then to the right will always define the direction of time in terms of its changing spatial position. In other words on can define the direction of time in both in terms of the causality of the systems spatial components.

As was mentioned earlier the second law of thermodynamics which defines the passage of time in the macroscopic world is based on a statistical definition was developed by Ludwig Boltzmann does not hold with strict universality: any system can fluctuate to a state of lower entropy.

However scientists have observed billions of particle collisions in which two particles collide to produce other particles however they have never observed two particles spontaneous coming together to form one particle even though statistically speaking they should happen much more often than in multi particle systems because they have considerably less complexity.

Therefore understanding the causality of the change in the position component of entities in both macro and microscope system may tell us if travel time travel is possible.

As was shown in the earlier article “Defining what time is” Sept. 20, 2007 defining the direction of time in terms of the sequential ordering of the causality of events would a provide a consistent direction for time in all environments because the causality of an atom moving to the left in both single or multiple component system would always be proceeded by the causality of that the same atom moving to the right; even though, as was mentioned earlier the behavior of the atom is not *qualitatively* different in either case. This would be true in both our physical and mathematical perceptions of time.

In other words defining it in terms of the sequential ordering of the causality of an event is consistent with the observation that events appear to always move forward in time in both the macroscopic universe and the microscopic world of particle accelerators because the casualty of particle breaking up into different parts must always proceed those parts coming together.

*Some might think that it is not possible to tell the order in which events occurred without using time as a reference. However one can use the spatial properties of a system to determine it because the first event in a series would only be connected to the one before it while all other would be connected not only to that one but to the one after it. In other words one could determine the order in which the events occurred by referencing them to the one that has only one spatial connection and following the single line of events back towards there origin.*

However this also rules out any possibility of one traveling through time because if it is only a measure of the sequential ordering of the causality of events then similar to all measurements it does not have physical properties so because one cannot travel through or in something that does not have a physical structure time travel is physically possible.

Latter Jeff

Copyright 2016