Quantum mechanics assumes that it is fundamental because it defines all interactions within it in terms of its quantized properties while one could say that Einstein’s General Theory of Relativity defines it in terms of an emergent property of continuous space-time manifold because that’s how it defines reality.

Most would agree the best way of which to determine which one is fundamental would be to see if one can be explain in terms of the other.
For example it is impossible to explain the apparent continuous properties of space-time in terms of the discrete properties quantum mechanics associates with energy/mass because by definition something that is discrete cannot by definition be continuous.   However it is possible to explain how the continuous properties of space-time can be broken up into the discrete components of energy/mass that allows quantum mechanics to define it in those terms.

Quantum mechanics assumes that energy/mass is quantized based, in part on Schrödinger wave equation which is used to predict and define the quantized energy distribution of electrons in an atom in terms of the Principal number (n),  the Angular Momentum “â„“”   (l), Magnetic (m) and Spin Quantum Number(+1/2 and -1/2).

However as mentioned earlier it may be possible to define an emergent mechanism based on the reality of four dimensional space-time that can explain why the energy distribution in a atom is quantized.

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

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

However this would allow explain how the spatial characteristics of the energy distribution quantum mechanics associated with the four quantum numbers can emerge from reality of environment consisting of four dimensional space-time or its four *spatial* dimension equivalent.  

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

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

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

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

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

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

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

In other words this defines the quantization or the particle properties of energy/mass in terms of an emergent property of four *spatial* dimensions. 

However the fact that one can derive the quantum mechanical properties of energy/mass by extrapolating the resonant properties of a wave in three-dimensional environment to a fourth *spatial* dimension means that one should also be able to derive the quantum numbers that define the properties of the atomic orbitals in those same terms.

As mentioned earlier there are four quantum numbers.  The first the Principal Quantum number is designated by the letter “n”, the second or Angular Momentum by the letter ” â„“” the third or Magnetic by the letter “m” and the last is the Spin or “s” Quantum Number.

In three-dimensional space the frequency or energy of a resonant system is defined by the vibrating medium and the boundaries of its environment.

For example the energy of a standing wave generated when a violin string plucked is determined in part by the length and tension of its strings.

Similarly the energy of the resonant system the article ” Why is energy/mass quantized?” associated with atom orbitals would be defined by the “length” or circumference of the three-dimensional volume it is occupying and the tension on the space it is occupying.

Therefore the physicality of “n” or the principal quantum number would be defined by the fundamental vibrational energy of three-dimensional space that article associated with the quantum mechanical properties of energy/mass.

The circumference of its orbital would correspond to length of the individual strings on a violin while the tension on its spatial components would be created by the electrical attraction of the positive charge of the proton.

Therefore the integer representing the first quantum number would correspond to the physical length associated with the wavelength of its fundamental resonant frequency.

However, classical mechanics tells us that each environment has a unique fundamental resonant frequency which is not shared by others.

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

This defines physicality of the environment associated with the first quantum number in terms of an emergent property of four *spatial* dimensions and why it is unique for each subdivision of electron orbitals.  Additionally observations tell us that resonance can only occur in an environment that contains an integral or half multiples of the wavelength associated with its resonant frequency and that the energy content of its harmonics are always greater than those of its fundamental resonate energy.

This allows one to derive the physicality of the second “â„“” or azimuth quantum number in terms of how many harmonics of the fundament frequency a given orbital can support. 

In the case of a violin the number of harmonics a given string can support is in part determined by its length.   As the length increase so does the number of harmonics because its greater length can support a wider verity of frequencies and wavelengths.  However, as mentioned earlier each additional harmonic requires more energy than the one before it.  Therefore there is a limit to the number of harmonics that a violin string can support which is determined in part by its length.

Similarly each quantum orbital can only support harmonics of their fundamental frequency that will “fit” with the circumference of the volume it occupies.

For example the first harmonic of the 1s orbital would have energy that would be greater than that of the first because as mentioned earlier the energy associated with a harmonic of a resonant system is always greater than that of its fundamental frequency.  Therefore it would not “fit” into the volume of space enclosed by the 1s orbital because of its relatively high energy content.  Therefore second quantum number of the first orbital will be is 0. 

However it also defines why in terms of classical wave mechanics the number of suborbital associated with the second quantum number increases as one move outward from the nucleus because a larger number of harmonics will be able to “fit” with the circumference of the orbitals as they increase is size.

This also shows that the reason the orbitals are filled in the order 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, 5s is because the energy of the 3d or second harmonic of the third orbital is higher in energy than the energy of the fundamental resonant frequency of the 4th orbital.  In other words classical wave mechanics tells us the energy of the harmonics of the higher quantum orbitals may be less than that of the energy of the fundamental frequency of preceding one so their harmonics would “fit” into circumference of the lower orbitals

The third or Magnetic (m) quantum number physical defines how the energy associated with each harmonic in each quantum orbital is physically oriented with respect to axis of three-dimensional space.

For example it tells us that the individual energies of 3 “p” orbitals are physically distributed along each of the three axis of three-dimensional space.

The physicality of the fourth quantum or spin number has nothing to do with the resonant properties of space however as was shown in the article “Pauli’s Exclusion Principal: a classical interpretation” Feb. 15, 2012 one can derive its physicality by extrapolating the laws of a three-dimensional environment to a fourth *spatial* dimension.

Briefly the article “Defining potential and kinetic energy?” Nov. 26, 2007 showed all forms of energy including the angular momentum of particles can be defined in terms of a displacement in a “surface* of three-dimensional space manifold with respect to a fourth *spatial* dimension.  In three-dimensional space one can use the right hand rule to define the direction of the angular momentum of charged particles.  Similarly the direction of that displacement with respect to a fourth *spatial* dimension can be understood in term of the right hand rule.  In other words the angular momentum or energy of an electron with a positive spin would be directed “upward” with respect to a fourth *spatial* dimension while one with a negative spin would be associated with a “downwardly” directed one.

Therefore one can define the physically of the fourth or spin quantum number in terms of the direction a “surface” of three-dimensional space is displaced with respect to a fourth *spatial* dimension.  For example if one defines energy of an electron with a spin of -1/2 in terms of a downward directed displacement one would define a +1/2 spin as an upwardly directed one.

The physical reason why only two electrons can occupy a quantum orbital and why they have slightly different energies can also be derived by extrapolating the laws of a classical three-dimensional environment to a fourth *spatial* dimension.

There a two ways to fill a bucket.  One is by pushing it down and allowing the water to flow over its edge or by using a cup to raise it to the level of the buckets rim.

Similarly there would be two ways fill an atomic orbital according to the concepts presented in the article “Defining potential and kinetic energy?”.  One would be by creating a downward displacement on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* to the level associated with the electron in that orbital while the other would be raise it up to that energy level .

However the energy required by each method will not be identical for the same reason that it requires slightly less energy to fill a bucket of water by pushing it down below its surface than using a cup to fill it.

However it also explains why no two quantum particles can have the same quantum number because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement. 

Similarly the magnitude of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by two quantum particles with similar quantum numbers would greater than that caused by a single one.  Therefore, they will repel each other and seek the lower energy state associated with a different quantum number because the magnitude of the force resisting the displacement will be less for them if they had the same number.

This shows how one can derive the physicality of the four quantum numbers of an emergent property of four *spatial* dimension or its space-time equivalent.

Later Jeff

Copyright Jeffrey O’Callaghan 2016

The post Quantum mechanics as an emergent property of space-time. appeared first on Unifying Quantum and Relativistic Theories.

In other words to be consistent they should be able to define it in terms of its physicality.

Yet it is possible that time may be something which cannot be defined by a what but may be an effect similar to how color is not a something but is an effect cause by how light is reflected by a something.  If this is true physicist’s would have to find another way to define gravity other that one that depends on the interactions of space and time defined by Einstein.

Another question that is difficult to answer is if nothing in the universe changed would time still exist.

Answering this question may provide an answer as to what time is because if change is the causality of our perception of time then understanding what causes it in the space-time environment that physicist’s say we live may help us to understand how it is connected to our environment.

However, as Einstein suggested in the following quote time cannot not be physically connected to the process of change because it is a rigid unchanging component of a space-time environment defined by both his Special and General Theories of Relatively and therefore could not be responsible of the dynamic process associated with change.

“Since there exists in this four dimensional structure [space-time] no longer any sections which represent “now” objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three-dimensional existence.”

In other words according to Einstein the structure of space-time is ridge while the changes we associated with time are merely an illusion similar to the illusion of change created in a flip book when one rapidly flips through its pages containing series of pictures that vary gradually from one page to the next.

Yet this means if, as he suggested the time dimension is not responsible for the “evolution of a three-dimensional existence” some other geometric property of the our universe must be physically connected to it to allow change to propagated through it.

Therefore to understand the “evolution of a three-dimensional existence” one would have to explain how the change propagates through it without referring to a time dimension.

Einstein gave us the ability to do this when he defined the energy associated  with the evolution of a space-time environment in terms of the equation E=mc^2 the constant velocity of light because that provided a method of converting a unit time and redefine the energy in that environment to its equivalent in four *spatial* dimensions. Additionally because the velocity of light is constant he also defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words he tells the physical properties of a space-time geometry are related to an observer’s interpretation similar to how the measurements of their magnitudes are related an observer’s velocity.  This is because, as was show above one can reinterpret the mathematics associated with the time dimension in an environment consisting of four dimensional space-time with a spatial one to create one in only four *spatial* dimensions with identical properties.  However one must be careful not to think of this as the physical replacement of the time dimension in Einstein’s universe with a spatial one because according to his mathematics they coexist in the same geometric plain.

Additionally the fact that the equation E=mc^2 allows us to quantitatively derive energy in a space-time environment in terms of four *spatial* dimensions is the bases for assuming as was done in the article “Defining energy” Nov 27, 2007 that all forms of change can be derived in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of one in a space-time manifold.

Doing would also allow physicists to define gravity and energy in terms that do not depend on time or the interactions of space and time defined by Einstein.

Additionally it would allow one to understand how the geometric properties of space interact to create the change associated with time in terms of a physical image without using it because we can “see” or perceive how a void in space created by any displacement causes change where, as was mentioned earlier we cannot with time.

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

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

This suggest the change most associate with time may be an effect caused by an interaction of a fourth spatial dimension with our three dimension environment.

In other words similar to how an the color of an apple is an effect created by an interaction between light and its surface time may be the effect of a physical interaction of our three-dimensional environment with a four *spatial* dimension.

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

Later Jeff

Copyright Jeffrey O’Callaghan 2016 

The post Seeing time appeared first on Unifying Quantum and Relativistic Theories.

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

The problem was first mentioned by Robert Dicke in 1969. 

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

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

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

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

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

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a quantitative and qualitative means of redefining his temporal properties of a space-time universe in terms of the spatial ones of four *spatial* dimensions. 

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

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

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

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

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

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

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

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

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

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

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

Later Jeff

Copyright Jeffrey O’Callaghan 2016

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Later Jeff

Copyright 2015 Jeffrey O’Callaghan 

The post Do we really need Quantum Decoherence? appeared first on Unifying Quantum and Relativistic Theories.

However this is in direct conflict with how physicists define it in terms of the physical properties of a space-time dimension.

For example Einstein believed as the following quote demonstrates that time was a rigid physical component of a space-time environment defined by both his Special and General Theories of Relatively.

“Since there exists in this four dimensional structure [space-time] no longer any sections which represent “now” objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence.”

In other words according to Einstein the structure of space-time is ridge while the changes we perceive are merely an illusion similar to the illusion of change created in a flip book when one rapidly flips through its pages containing series of pictures that vary gradually from one page to the next.

However if one considered blocks of space-time as the pages of the flip book responsible for the illusion of change as Einstein did one still must still define the causality of the change on each page of that book which cannot be related to time if it is a ridge component of a space-time environment.

As mentioned earlier the idea of defining time terms of the physical properties of a space-time dimension conflicts with the abstract properties most associate with change.

Yet one could resolve this conflict while defining why changes occurs in each segment of a space-time environment if one can show that change and therefore time is an emergent property of the physicality most of us including physicists associate with space.  In other words if one can define the causality of change in terms of the physical properties of space then one could merge the abstract sense of order that our consciousness feels it has with its physical properties.

However to do this one must be able to understand the causes of change associated with time in terms of the perceive physical properties of space and then determine if one can integrate them into a theoretical model that is consistent with all of the other properties of that environment. 

Einstein gave us the ability to do this when he defined the energy associated with change in space-time environment in terms of  the equation E=mc^2 and the constant velocity of light because that provided a method of converting a unit time in that environment to its equivalent in four *spatial* dimensions.  Additionally because the velocity of light is constant he also defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

The fact that the equation E=mc^2 allows us to quantitatively derive energy in a space-time environment in terms of four *spatial* dimensions is the bases for assuming as was done in the article “Defining energy” Nov 27, 2007 that all forms of change can be derived in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of one in a space-time manifold.

As mentioned earlier Einstein believed it is more natural to think of physical reality in terms of a four dimensional existence, instead of the evolution of a three-dimensional existence even though he did not define the causality of change in that environment.

However as was shown earlier the symmetry of his mathematics means that he not only defined that “reality” in terms of four dimensional space-time but also in four *spatial* dimensions.

This enables one to derive the causality of change most associate with time in terms of the physical properties of the spatial dimensions instead of its abstract ones.

For example one can observe how a displacement in the geometry of three-dimensional space cases change by watching water flowing over a dam.

Similarly if as was shown above one defines energy in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of four dimensional space-time as was done in the article “Defining energy” Nov 27, 2007 one can define the transfer of energy associated with change in terms of the “level’ each segment of three-dimensional of space has with respect to a fourth *spatial* dimension.  In other words change can be defined as an emergent property of four *spatial* dimensions because as one moves though Einstein’s space-time environment each successive section of three-dimensional space would be at a different level with respect to a fourth *spatial* dimension. 

Granted due to the symmetrical nature of the arguments presented here one could argue that space is an emergent property of time.

However it is more consistent with observations of our three dimensional environment to assume that the changes most associate with time have their causality in the geometry of space because as was mentioned earlier we can see how that geometry causes change whereas the same cannot be done with respect to time because of its abstract properties.

Later Jeff

Copyright Jeffrey O’Callaghan 2015

The post The casualty of time. appeared first on Unifying Quantum and Relativistic Theories.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Later Jeff

Copyright Jeffrey O’Callaghan 2015

The post Why does space exist? appeared first on Unifying Quantum and Relativistic Theories.

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

Bohr summarized this reality as follows:…”however far the [quantum physical] phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms. The argument is simply that by the word “experiment” we refer to a situation where we can tell others what we have done and what we have learned and that, therefore, the account of the experimental arrangements and of the results of the observations must be expressed in unambiguous language with suitable application of the terminology of classical physics.

This crucial point…implies the impossibility of any sharp separation between the behavior of atomic objects and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear…. Consequently, evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be regarded as complementary in the sense that only the totality of the phenomena exhausts the possible information about the objects.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

For example Classical wave Mechanics tell us that because of the continuous properties of waves, the energy the article “Why is energy/mass quantized?” associated with a quantum system is free to move over the entire “surface” of three-dimensional space with respect to a fourth *spatial* dimension similar to how the wave generated by a vibrating ball on a surface of a rubber diaphragm are free to move or be distributed over its entire surface.  However to observer it one would have to touch its surface with a probe thereby restricting the wave motion of its surface.

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

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

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

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

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

Later Jeff

Copyright Jeffrey O’Callaghan 2015

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The post The observer effect in quantum mechanics: a classical interpretation appeared first on Unifying Quantum and Relativistic Theories.

This crucial point…implies the impossibility of any sharp separation between the behavior of atomic objects and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear…. Consequently, evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be regarded as complementary in the sense that only the totality of the phenomena exhausts the possible information about the objects.”

Albert Einstein and Leopold Infeld also addressed this issue in their book The Evolution of Physics, when they asked “what is light really? Is it a wave or a shower of photons? There seems no likelihood for forming a consistent description of the phenomena of light by a choice of only one of the two languages. It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do.”

In other words the quantum world has duel non overlapping realities: one consisting of waves; the other particles and which one we observe depends on how we observe it.

This is in stark contrast to the classical one we all live in which defines only one reality based on cause and effect.

However one of the reasons it has been it is so difficult to understand why these dual realties exist may be because too much attention has been focused on the mathematics that describe it and not enough on their physical meaning in our classical environment. 

Another reason may be because most have tried to integrate them into a space-time environment even though they are primarily defined in terms of the spatial properties of probabilities.

This suggest we may be able to better understand why the quantum world possess two distinct realties based on the single reality of a classical world of cause and effect if we view them in terms of spatial properties instead of their space-time ones.

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

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

However defining the dimensional properties of quantum system in terms of its spatial instead of its time components would allow one to understand why a quantum environment possess two distinct realities by extrapolating the laws governing cause and effect in the classical world to them.

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

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

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

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

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

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

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

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

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

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

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

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

The confinement of the “upward” and “downward” oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries of the resonant system associated with the particle component of its wave properties in the article “Why is energy/mass quantized?” Oct. 4, 2007.

In other words one can use classical wave mechanics to explain why a quantum system can possess both wave and particle properties.

However it does not help us to understand why they define two non-overlapping realties. 

In other words it does not help us to understand why if one devises and experiment to observe its particle properties one cannot at the same time observe its wave reality while if one observes its particle reality one cannot observe it wave properties.

However one can use the properties of classical reality to understand the causality of the complementary or dual real of quantum mechanics.

For example Classical Mechanics tell us that because of the continuous properties of waves, the energy the article “Why is energy/mass quantized?” Oct. 4, 2007 associated with a quantum system would be free to move over the entire “surface” of three-dimensional space with respect to a fourth *spatial* dimension similar to how the wave generated by a vibrating ball on a surface of a rubber diaphragm would be free to move over its entire surface.  However to observe the movement of the rubber diaphragm one must physically touch it with a probe thereby restricting its movement

Similarly to observe the movement of a quantum system one must use a probe which would restrict its movement.

However this also allows one to understand why observing a quantum system effects its reality as is demonstrate in the double slit experiment.

In this experiment the wave reality of a quantum system is demonstrated by the bright and dark interference bands produced on the screen after being allowed to freely pass through between two slits on a screen, However, it is always found to be absorbed at the screen at discrete points, as individual particles (not waves), while the interference pattern appears as varying density of these particle hits on the screen. Furthermore, its particle reality is demonstrated when someone puts detectors at the slits he finds that each detected photon passes through one slit (as would a classical particle), and not through both slits (as would a wave).

These results demonstrate the principle of wave–particle duality.

In the first part of this experiment the wave properties of a quantum system defines its reality because it is allowed to move freely through space. This would be analogous to classical reality of sound waves created by a random source in that they show no properties of quantization. 

However classical wave mechanics tells us that if one if one restrict the movement of a wave as is done in a pipe organ it will form a quantized resonant system.

For example if one restricts sound waves as is done in an organ pipe its output becomes quantized because it amplifies one of its wave components while diminishing all others.

As the article “Why is energy/mass quantized?” Oct. 4, 2007 showed the particle “reality” of a quantum system is the result of the restricting its wave “reality” which must always happen when an observation is made.

In other words as the reason why the particle reality of a quantum environment only occurs when an observation is made is because that act restricts the movement of its wave reality thereby creating the resonant structure associated with its particle properties defined in the article “Why is energy/mass quantized?” Oct. 4, 2007.

In other words the reason the interference pattern appears as varying density of these particle hits on the screen in the double slit experiment is because as was mentioned earlier observing a quantum system requires one to restrict its wave prosperities thereby causing the resonant system the article “Why is energy/mass quantized?” Oct. 4, 2007 associated with its particle really.

Additionally their varying density occurs because these resonant systems will most likely occur where the magnitude of the wave component is maximum and drop off as it decreases.  Therefore their position on the screen will form a wave interference pattern .

The reason why the two realties are complimentary or cannot be simultaneous observed is similar to why one cannot observe ice and water at the same time.  For example in an environment consisting of water that is well below freezing the reality is frozen water while its reality when it is above freezing is water.  Additionally our classical experiences tell us that these two states are complementary because they cannot be both at the same time but have to one or the other.

Similarly in an unobserved quantum environment the wave reality exists because is it allows to move freely through space while as was shown above the restrictions caused by observation makes its particle properties or reality become predominate.

This shows even though a quantum environment consists of two non-overlapping contradictory pictures of reality one can fully understand their existence by applying the cause and effect relationship of a classical reality to it.

Later Jeff

^{Copyright Jeffrey O’Callaghan 2015}

The post The dual realities of quantum mechanics: a classical explanation appeared first on Unifying Quantum and Relativistic Theories.

The most obvious is that it violates one of most treasured laws of science that of the law of conservation of mass/energy.

That law tells us that the kinetic energy of the universeâ€s energy/mass cannot exceed its.combined total.  However that is exactly what would have to happen for the Big Rip to occur. 

For example for a rocket to escape or be “Rip” from the earth’s gravitational influence one must provide it with more kinetic energy than the gravitational potential of its energy/mass.

Similarly for the universe to be “Rip” apart one would have to provide its components with enough kinetic energy to overcome the total gravitational potential of its energy/mass.

However as was just mentioned the law of conservation energy/mass tells us that since by definition the universe is a closed system the kinetic energy of the its components cannot exceed the total energy of its gravitational components.

In other words if we are to assume that the universe will be Rip apart by Dark Energy we must also assume that energy/mass can be created and that the law of conservation or energy/mass is invalid.

Yet there is also an inconsistency with the assumption that universe would continue to expand indefinitely resulting in what has come to be called the Big Freeze. 

This inconsistency revolves around the fact that the equation E=mc^2 which defines the equivalence between mass and energy in an environment tells us that, because of it, the kinetic energy associated with the universe’s expansion also possess the gravitational potential associated with mass while the law of conservation of energy/mass tells us that at as the universe expands and cools the gravitational potential of the kinetic energy loss associated with that cooling must be returned to the universe.  Granted it would be disturbed or deluded by a factor of c^2 however it would still increase the total gravitational potential of the universe’s energy/mass.

Yet this means as the universe cools the total gravitational potential of its energy/mass must increase.  Therefore at some point in time its gravitation potential will increase to the point where it will be greater than the kinetic energy associated with its expansion resulting in it entering a contraction phase because it is decrease while the other is increasing.

There can be no other conclusion if one accepts the validity of Einstein’s General Theory of Relativity and the law of conservation energy/mass.

As was mentioned earlier the article “Why the Big Rip cannot happen” June 15. 2015 showed why the assumption that Dark Energy would “rip” apart the universe is untenable if one assumes the validity of the law of conservation of energy/mass while the other possible end to our universe or the big freeze is also ruled out for the reasons stated above.

However that means the only viable option for the end our universe is the big crunch if the currently accepted laws of physics eliminates the Big Freeze and the Big Rip because those same laws tell us as was just shown  the total gravitation potential of the universe must increase as it expands and cools approaching a maximum value at absolute “0” while at the same time the kinetic energy of its expansive components must decrease.  Therefore, at some point in time, the universe will enter a contractive phase because the total gravitational potential will eventually exceed the kinetic energy of its expansion.  This is would be true as mentioned earlier even though the gravitational potential of its Kinetic energy components would be disturbed or diluted by a factor of c^2.

Therefore at that point, in time the universe will have to enter a contractive phase.

In other words the only one of the three options our universe has to end it life that is supported by today’s scientific understanding of its evolutionary mechanism is the Big Crunch

Later Jeff

Copyright 2015 Jeffrey O’Callaghan

The post The “reality” of the Big Crunch appeared first on Unifying Quantum and Relativistic Theories.

For example one of the most obvious problems of assuming the universe will Rip apart is that it violates one of most treasured laws of physics that of the law of conservation of mass/energy.

That law tells us the kinetic energy of the universeâ€s expansion associated with the big bang and the accelerative forces of Dark Energy cannot exceed the total combined energy of its energy/mass.  However that is exactly what would have to happen for the Big Rip to occur. 

For example for a rocket to escape or be “Rip” from the earth’s gravitational influence one must provide it with more kinetic energy than the combined gravitational potential of both its and the earth’s energy/mass.

Similarly for the universe to be “Rip” apart one would have to provide its components with enough kinetic energy to overcome the total gravitational potential of its energy/mass.

However as was just mentioned the law of conservation energy/mass tells us that since by definition the universe is a closed system the kinetic energy of the universe’s components cannot exceed the gravitational potential of its energy/mass.

Therefore if we are to assume that the universe will be Rip apart by Dark Energy we must also assume that energy/mass can be created and that the law of conservation of energy/mass is invalid.

However as also mentioned early the best way of to understand why the Big Rip” cannot occur is to show, using the currently accepted theoretical models and laws of physics to understand why Dark energy is causing the accelerated expansion of our universe and why, based on those laws and theoretical models it theoretical models why it cannot possibly cause it to be rip apart.

Einstein’s General Theory of Relativity, the previewing theory governing the evolution of the universe tells us that its future depends the interaction of the contractive force of gravity, the expansive force associated with the kinetic energy left over from the Big bang and Dark Energy.

Unfortunately in its present form it cannot address the causality of the expansive force of Dark Energy and how or why it would interact with its environment to cause it to accelerate because observations tell us that three-dimensional space is expanding towards a higher spatial dimension not a time or space-time dimension.  

Therefore, in order to explain the observed spatial expansion of the universe one would have to assume the existence of a another *spatial* or fourth *spatial* dimension in addition to the three spatial dimensions and one time dimension that Einsteinâ€s theories contain to account for that observation.

This would be true if Einstein had not given us a means of qualitatively and quantitatively converting the geometric properties of his space-time universe to one consisting of only four *spatial* dimensions.

He did this when he defined its geometric properties in terms of the equation E=mc^2 and the constant velocity of light because it allows one to redefine a unit of time he associated with energy in his space-time universe to an equivalent unit of space in a universe consisting of only four *spatial* dimensions. 

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

The fact that the equation E=mc^2 allows us to quantitatively and qualitatively derive the physical properties of energy in a space-time universe in terms of its spatial properties is the bases for assuming, as was done in the article “Defining energy” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

As mentioned earlier it is difficult to integrate the causality of why three-dimensional space expanding towards a “higher” spatial dimension into Einstein space-time universe because it does not define a higher spatial dimension. 

However it is easy if one reformulates it, as was shown above to be possible in terms higher fourth *spatial* dimension because a higher dimension is an integral part of its theoretical structure.

Yet this also allows one to understand how and why the force called Dark Energy is causing an accelerated spatial expansion of our universe in terms of the laws of thermodynamics because it gives one the ability, as mentioned earlier to use Einstein’s equations to qualitatively and quantitatively define energy in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimensions.

We know from the study of thermodynamics that energy flows from areas of high density to one of 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 surrounding it while the force associated with that expansion decreases as it expands.

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 according to concepts developed in the article “Defining energy” that the three-dimensional “surface” occupied by the particles in our universe which has an average energy component of 3.7 degree Kelvin would be elevated with respect to a fourth *spatial* dimension.  

Yet this means similar to the water molecules occupying the elevated two dimensional surface of the water in the pool, the particles occupying a region of three-dimensional space that is elevated because of its 3.7 degree temperature will flow and accelerate outward in the four dimensional environment surrounding it.

In other words by reformulating Einstein’s theories in terms of four *spatial* dimensions one can use the laws of thermodynamics to explain what the force called Dark Energy is and why it is causing the accelerated expansion of the universe in terms of Einstein’s theories.

Many feel that because space is everywhere, the force called Dark Energy is everywhere so therefore its effects will increase as space expands.  In contrast, gravity’s force is stronger when things are close together and weaker when they are far apart.  Therefore they feel the rate at which the universe expands will increase as time go by resulting in galaxies, stars, the solar system, planets, and even molecules and atoms would be shredded by the ever-faster expansion.  In other words the universe that was born in a violent expansion could end with an even more violent expansion called the Big Rip.

However if the above theoretical model is correct than the magnitude of Dark Energy relative to gravitational energy will not continue to increase as the universe expands but will decrease because, similar to the water in a collapsed pool the accelerative forces associated with its will decline as it expands. 

Yet, because the laws of conservation the total quantity of the universeâ€s energy/mass remains constant throughout its history its gravitational potential will also.  Therefore in the future the gravitational contractive forces associated with it will exceed the expansive forces associated with Dark Energy because, as mentioned earlier according to this theoretical model its accelerative forces should decrease as the universe expands.

This would be true even though its components may be separated by extremely large distances because, as just mentioned if the above theoretical scenario is correct the force associated with dark energy will decease relative to gravity as time goes by.

However observations also suggest that early in the universe evolution the gravitational forces exceeded the expansive forces of Dark Energy.

The reason is that according the above theoretical model, just after the big bang when the concentration of energy and mass was high, the gravitational forces with it would predominate over Dark Energy because the distance between both its energy and mass components was relatively small.

However as the universe expands its gravitational attractive forces will decrease more rapidly than the expansive force associated with Dark Energy because they are related to the square of the distance between them while those of the expansive forces of Dark Energy are more closely related to a linear function of the total energy of content of the universe. 

Therefore after a given period of time the expansive forces associated with Dark Energy will become predominate and the expansion of the universe will accelerate.

However as the universe expands and cools that force will decrease because as mentioned earlier similar to the two-dimensional surface of the water in a collapsed pool, the forces associated with it will decrease as it expands.

This means that eventually gravitational forces will predominant  because, as mentioned earlier the laws of thermodynamics tells us the total accelerative forces associated with Dark Energy will decease and therefore will eventually approach zero, while the total mass content and the gravitational attractive forces associated with it will remain constant as the universe expands even though they may be separated by a greater distant.

Therefore. gravity will eventually win the battle with Dark Energy because as was just mentioned the forces associated with it approach zero as the expansion progress while those of gravity remain constant.

There can be no other conclusion if one accepts the validity of Einstein’s theories and the laws of thermodynamics because the theoretical arguments presented are a base solely on their validity.

In other words if someone spends the time, as we done above analyzing what observations have taught us about Dark Energy and integrating them into Einstein’s Theories one would one find that the assumption that it would “Rip” the universe apart does not have foundation in logic or science.

It should be remember that Einstein’s genius allows us to choose whether to view Dark Energy in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of energy/mass and the constant velocity of light.

Later Jeff

Copyright 2015 Jeffrey O’Callaghan

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