The Big Bang Theory is the leading explanation about how the universe began. At its simplest, it says the universe as we know it started with a small singularity, then inflated over the next 13.8 billion years to the cosmos that we know today.18The_math_errors_in_the_Big_Bang_Theory

Because current instruments don’t allow astronomers to peer back at the universe’s birth, much of what we understand about the Big Bang Theory comes from mathematical formulas and models. Astronomers can, however, see the "echo" of the expansion through a phenomenon known as the cosmic microwave background.

The idea the universe was smaller in the beginning was supported by Edwin Hubble in 1929 it expanding.

Later, a few physicists led by George Gamow a proponent of the big bang model showed an expanding universe meant that it might have had its beginning in a very hot infinitely dense environment, which then expanded to generate the one we live in today.

They were able to show only radiation emitted approximately 300,000 years after the beginnings of the expansion should be visible today because before that time the universe was so hot that protons and electrons existed only as free ions making the universe opaque to radiation. This period is referred as the age of "recombination".

Additionally, they predicted this Cosmic Background Radiation or what was left over from the age of recombination would have cooled form several thousand degrees Kelvin back when it was generated to 2.7 today due to the expansion of the universe.  Many thought its discovery 1965 by Penzias and Wilson provided its verification

However, there was a problem with assuming the universe begin as an expansion of in an infinitely dense hot environment because one would expect it and the Cosmic Background Radiation to be homogeneous because an infinitely dense environment must have been, by definition homogeneous. Therefore, if the universe was homogeneous when it began it should still be.

But the existence of galactic clusters and the variations in the intensity of the cosmic background radiation discovered by NASA’s WMAP satellite showed the universe is not and therefore, was not homogeneous either now or at the time when the Cosmic Background Radiation was emitted.

Many proponents of the big bang model assume that these "anisotropy" in the universe are caused by quantum fluctuations in the energy density of space. They define quantum fluctuations as a temporary change in the energy of space caused by the uncertainty principle.

However, there is an error in the math used to predict both effects the expansion of singularity at its origin and quantum fluctuations in the energy density of space would have on the evolution of the universe.

Einstein mathematics tell us time slows as the gravitational or energy density increases and will eventually stop if it becomes great enough.  While observation of black holes provides verification of his math because it is observed that time does slow to a stop when it reaches a critical energy density at its event horizon.  Additionally, Schwarzschild was able to use Einstein’s math to calculate the radius of a black hole were the energy density would be great enough to stop time.

This means the math used by the proponents of the big bang is INCORRECT if they did not include the effect the energy density around a singularity or quantum fluctuation would have on its evolution.

This is because observationally verified math of Schwarzschild tells us there is a minimum radius the total energy content of the universe can occupy for time to move forward. Since evolution cannot occur in an environment where time has stopped that is also MINIMUM RADIUS of the universe which could expand form which IS larger than a singularity.

In other words, if they had included the effect energy density has on time, they would have realized that the universe could not have originated from a singularity.

Some may say that the energy density of expanding universe would not effect the rate at which time passes but they would be wrong because Einstein’s tells us it is only related to differential energy density. In other words, he tells us the rate at which time slows and where it would stop and prevent further expansion would be determined by the differential energy density between the center of its expansion and its outer edge.  This point would define the minimum volume it would have to have before its expansion could take place.

However, there is a similar error in the math behind the assumption that quantum fluctuations are responsible for "anisotropy" in Cosmic Background Radiation because energy could not expand from one because the energy density surrounding it would cause time to stop.  Therefore, quantum fluctuation could not affect the evolution of the universe or be responsible for "anisotropy" in Cosmic Background Radiation because as was just mentioned evolution cannot occur in an environment where time has stopped.

Some might disagree because they say the energy in a singularity and that contained in a quantum fluctuation would be powerful enough to overcome the stopping of time predicted by Einstein mathematics.  However, they would be wrong because the mathematics of Einstein tells that when the energy density reaches a certain level time will stop.  It does not say that an increase beyond that point will allow time to move again.

As was mentioned earlier, current instruments don’t allow astronomers to peer back at the universe’s birth, much of what we understand about the Big Bang Theory comes from mathematical formulas and model

However, we may be able to define the origin of the present universe in terms of its observable properties.

We still have not been able to determine if the universe will continue to expand indefinitely or if it will eventually collapse in on itself. However, if one assumes it does, we could develop a mathematically model which would tell us when the heat generated by its collapse would be enough to cause it to re-expand.  Additionally, one could determine if that heat occurred AFTER that required to free protons and electrons from each other thereby allowing another age of "recombination" when it started to re-expand.

This would also give mathematicians the ability to more precisely determine the age of universe because we can observe when age of "recombination" occurred and project back from that point in time to when the additional heat generated by its continued collapse was great enough to cause it to re-expand.

In others words we have the ability to define the origin of the present universe and anisotropy" in Cosmic Background Radiation in terms of a mathematical model based on real time observations of the present universe. 

The science of Astrophysics is base almost exclusively on observations.  Therefore, the question they must ask themselves is "If we have two models for the origin of the universe that predict the same outcome which one should we assume is correct?"  The one that make is predictions based on the observable properties of our present universe or one that defines it origins in terms of the unobservable properties of a singularity.

Copyright Jeffery B O’Callaghan Nov. 2020Road to unification part  2007 thru 2010  EbookPlease visit our  Facebook group The Road to unification of Quantum and Relativistic theories if you would like to comment or

 Road to unification part  2007 thru 2010  EbookPlease visit our  Facebook group The Road to unification of Quantum and Relativistic theories if you would like to comment or

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Quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics.  In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction.

However, as of yet no one has been able to integrate gravity into its theoretical structure.

Yet one can use the wave properties of a quantum field to explain how Einstein’s definition of gravity in his General Theory of Relativity can be used to accomplish that.

Einstein in his General Theory of Relativity explains gravity as a distortion of space-time caused by the presence of matter or energy while defining its magnitude in terms of the concentration of matter or energy in a given volume of space-time

Therefore, to incorporate Quantum field into Einstein General Theory of Relativity one must explain how the interaction of a photon with electrically charge particles causes a distortion in space-time associates with gravity.

As was mentioned earlier QED defines the interaction of charged particles in terms of the exchange of photons.  However, it defines the exchange of photons in terms of the electromagnetic wave properties of a quantum field.

However, one can use the wave definition of that quantum field to define how it interacts with field properties of Einstein General Theory of Relativity to create the distortion in space-time that defines gravity.

For example, the photonic properties of an electromagnetic wave can be defined by extrapolating the laws of classical resonance in a three-dimensional environment to an electromagnetic wave on a "surface" of a three-dimensional space manifold with respect to a time dimension.

This is because one can 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 its natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in an environment consisting of four-dimensional space-time.

The existence of four-dimensional space-time would give an energy wave the ability to oscillate spatially on a "surface" the third spatial dimension with respect to the time dimension thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the "surface" of a three-dimensional space manifold 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-time if one extrapolated them to that environment.

Classical wave 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-dimensional space-time would be responsible for photonic properties of a quantum field.

Yet one can also define how and why an electromagnetic wave interacts with charge particles terms of the physical properties of space-time to create the resonant structure associated with photonic properties of a quantum field.

For example, in our three-dimensional world, 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.

However, the edge of the paper provides a boundary that reflects those oscillation back on itself, thereby creating a resonant wave on the surface of the paper.

Similarly, an electromagnetic wave in three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate “up” or “down” while moving through time.

However, if it is prevented from moving thought time by interacting with an electrically charged particle its wave energy will be reflected back on itself, thereby concentrating it in a resonant standing wave on the "surface" three-dimensional space with respect to the time dimension.

As was mentioned earlier, Einstein in his General Theory of Relativity explains gravity as a distortion of space-time caused by the presence of matter or energy.  While defining its magnitude in terms of the concentration of matter or energy in a given volume of space-time.

In other words, one can integrate gravity with Quantum electrodynamics definition of how matter interact with light in terms of how that interaction results in increase the energy density in the volume of space-time where that interaction takes place.

Copyright Jeffrey O’Callaghan Nov 2020

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Einstein tells us and it has been observed the rate at which time moves is slower is all environments where the gravitation density is greater than where it is being observed from. (please see graphic)   This means, the further we look back in time, where the gravitational density of the universe was greater the slower time would move and for events to occur from the of the present than they actually did.  In other words this would suggest that it evolved faster in the past and therefore is younger that the present value if considers the Relativistic slowing of time when determining the expansion rate of the universe.  12Gravity_time_dilation_and_the_accelerating_universe

However, we also know the gravitational density of the universe has a nonlinear slowing effect on its expansion because its attractive properties decrease as the volume of the universes increase due to its expansion.   In other words, the gravitational density has an opposite effect on its expansion. Therefore, to determine the actual the rate of expansion of the universe at each point in its history one must not only take into account the time dilation due to its gravitational density but also the slowing effect that density has on its expansion at each of those point.  In other words, one makes it APPEAR to move slower while the other faster.

Yet, because of the non-linear effects between the time dilation created by its gravitational density and the effects that density has on the universe rate of expansion there will be a point in its history were one will APPEAR to overtake the other. 

The fact that it has been observed that about 4 billion years ago the universe’s expansion change from decelerating to an accelerated phase give us a way to verify the above conclusion

In other words if one calculates the expansion rate of the universe by taking into account the APPARENT speeding up of its evolution resulting from the increase rate at time passes due to the decreasing gravitational density of an expanding universe and finds that it counteracts slowing effect cause by that density about 4 billion years ago it would go a long way to verify the above mechanism.

Some may say that gravitational time dilation would not effect the timing of the expansion because it is  also expanding.   However, Einstein define the time dilation only in terms of the effects a differential gravitational potential has on it therefore an expanding universe will have not effect it.  Some may also say that because the universe is expanding the gravitational density is expanding and weakening at the same rate therefore when we look back the effects it will have on the timing of its expansion will cancel.   However, Einstein tells us the timing of events that cause the universe to expand in the past is locked along with the gravitation density of the universe at the time the expansion took place  Therefore, we must measure the the timing of the events that define the them from the perspective of the gravitational density when those events took place.

Other may say the time dilation effect as discussed in this post is introduced in this calculation, the age of the universe might come down heavily.  This would be true if time was the only factor that must be considered when defining the rate of the universe expansion. For example the gravitational density of the universe would not only effect the passage of time but also it would cause a slowing of expansion due to its attractive forces  Therefore, to define its actual expansion rate one must take into account both slowing effect of gravities attractive forces and the effects it has on time.  The apparent change over to an accelerating universe occurs because of the non-linear relationship that gravity has on time and the expansion rate.  It is possible if one takes both the magnitude of gravity attractive force has on the universe expansion rate and time dilation on its expansion we may discover that it is older than the currently accepted value  of 13 billion years.

Copyright Jeffrey O’Callaghan Nov. 2020

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Quantum mechanics states what the universe is made of while not giving an explanation of why it is that way while Relativity gives us an explanation of why it is what it is but does not tell us what is it made of.  For example, a quantum world is defined in terms of the wave-particle duality of existence while its interactions with that world are defined in terms probabilities and the uncertainty principal which states one cannot precisely measure the properties of Conjugate pairs such as the momentum or position of a particle with complete accuracy.  However, it does not give an explanation of what existence is or how it interacts with its environment to create the universe we live in.  On the other hand, Relativity explains the existence of the universe in terms of an interaction between space and time without telling us what wave-particle duality of existence is or how it interacts with it to create the uncertainty principal.uncertanitys

However, to understand the dynamics of the uncertainty principle in terms of space-time we must first establish a physical connection between the wave function and the properties of the space-time. This can be accomplished because in Relativity the evolution of space-time is defined in terms of an electromagnetic wave while, as was mentioned earlier the wave function represents how the quantum world evolves to the point where it is observed.

This commonality suggests the wave function could be represented by an electromagnetic wave in space-time.  This means to derive the wave particle duality of existence defined by the wave function in terms of space-time one must physically connect the evolution of an electromagnetic wave to its existence.

This is possible because the science of wave mechanics and Relatively tells us an electromagnetic wave moves continuously through space-time unless it is prevented from moving through time by someone or something interacting with it. This would result in it being confined to three-dimensional space. The science of wave mechanics also tells us the three-dimensional "walls" of this confinement will result in its energy being reflected back on itself thereby creating a resonant or standing wave in three-dimensional space. This would cause the energy of an electromagnetic wave to be concentrated at the point in space were a particle would be found.  Additionally, wave mechanics also tells us the energy of a resonant system such as a standing wave can only take on the discrete or quantized values associated with its fundamental or a harmonic of its fundamental frequency.

For example, it explains why if the wave function is prevented from evolving through the probability field that defines a quantum existence by an observation it presents itself as a particle in terms of the properties of an electromagnetic wave in a space-time environment.

Yet, it also tells us, similar to the evolution of an electromagnetic wave in space-time if unobserved the it will continue evolve through the probabilistic universe defined by quantum mechanics.

In other words, it shows how one can understand the evolution of wave-particle duality of a quantum existence by comparing it to the evolution of an electromagnetic wave in space-time

Next, we must explain how quantum mechanics definition of a particle in terms of a one-dimensional point is responsible for the validity of the uncertainty principal.

Relativity and the science of wave mechanics tell us the energy of the standing wave which earlier defined a particle would be distributed over a volume of space-time that corresponds to is wavelength. However, to accurately determine its momentum or position one must be able to determine where those measurement are taken with respect to energy volume those system occupy.

Yet, to measure momentum of a particle in the quantum world one must determine time it takes to move between two points in the probability field.  Therefore, they will be an inherent uncertainty if one cannot determine where with respect to volume of the system those points are.

But because in Relativity the measurement of position is taken with respect to its spatial not its time properties one should define it with respect to space not time

Einstein gave us the ability to do this when he defined the mathematical relationship between space and time in terms of the constant velocity of light because in doing so, he provided a method of converting a unit of time in a space-time environment to its equivalent unit of space 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 only four *spatial* dimensions.

In other words, one can use a displacement in the "surface" of three-dimensional space with respect to a fourth *spatial* dimension to define a particles position while using a displacement with respect to a time dimension to define its momentum.

As was mentioned earlier Einstein defined the energy volume of a system in terms of a displacement in space-time and because energy can neither be created or destroyed it will remain constant therefore the volume of the displacement in space time will also remain constant.

HOWEVER, BECAUSE QUANTUM MECHANICS IS INFORMATION BASED ONE CAN SAY THE INFORMATION VOLUME OF A SYSTEM ALSO REMAINS CONSTANT.

Therefore, because the measurement of monument or position does not change the energy of a system the combined information volume associated with momentum and the displacement associated with position remains constant.

As was also mentioned earlier Quantum mechanics defines both moment and position with respect to a one-dimensional point in a probability field.  However, the accuracy of the information as to where that point is in relation to its information volume is directly related to how much information is taken from the system.  In other words, the more accurate the measurement the more information regarding it must be removed from the system.

However, because, as was mentioned earlier the information volume of a system remains constant the more information taken out of it regarding its momentum will result in there being more space for the point defining its position to occupy. This makes the determination of its position more uncertain because it could be found in anywhere in that larger volume.

This shows how one can define a dynamic relationship between the uncertainty of determining the momentum or position of a particle in terms of interaction between space and time and why it is responsible for the uncertainty principal.  This is because it defines why in terms of the properties of space-time the more information you have about the momentum of a particle the less you can know about it position and the more information you have about its position the less you can know about its momentum.

In other words, it shows how a dynamic interaction between the spatial and time properties of the universe can not only explain the particle wave duality of existence but also the uncertainty principal of quantum mechanics

Copyright Jeffery B O’Callaghan Nov. 2020

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Classical physics is causal; complete knowledge of the past allows for the computation of the future. Likewise, complete knowledge of the future allows precise computation of the past.

Not so in Quantum Physics. Objects are neither particles nor waves; they are a strange combination of both. Given complete knowledge of the past, we can make only probabilistic predictions of the future.past_and_future

In other words, classical mechanics tells us that only one future exists while quantum mechanics tells us that due to its probabilistic interpretation of wave-particle duality of existence, many different ones simultaneously exist and which one become a reality is determined by observation.  Additionally, it states that they are randomly disturbed throughout existence.

On the surface these probabilistic and causal definitions of the future appear to incompatible.

However, that may not be the case.

As mentioned earlier, one of the things that separate the future associated with classical physics from probabilistic one of quantum mechanical is one tell us all of the probable future outcomes of an observation exist while the other which based on causality tells us there in only one.

However, when we role dice in a casino most do not think there are six of them out there waiting for the dice to tell us which one we will occupy after the roll.  This is because the probability of getting a six is related to its physical interaction with properties of the table in the casino where it is rolled. This means the probability of getting a six is determined by the physical properties of the dice and the casino it occupies.  In other words, the probabilities associated with a roll of the dice does not define the future of the casino the casino defines the future of the dice.

Similarly, just because Quantum mechanics defines outcome of an observation in terms of probabilities would not mean all the of the predicted futures exist if the probability of a specific outcome is caused by a physical interaction of the wave-particle duality of existence with the universe it occupies.  In other words, like the dice, it is possible the wave-particle duality of existence does not define the future of the universe the universe defines the future of its wave-particle component.

However, to understand how this is possible one would have to show the probability of a specific outcome of an observation is related to the interaction of the wave-particle duality of existence and the space it occupies.

For example, in the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown the wave-particle duality of existence defined by quantum mechanics can be derived by extrapolating the laws of classical resonance in a three-dimensional environment to an energy wave on a "surface" of a three-dimensional space manifold with respect to a time 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 its natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in an environment consisting of four-dimensional space-time.

The existence of four-dimensional space-time would give an energy wave the ability to oscillate spatially on a "surface" the third spatial dimension with respect to the time dimension thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the "surface" of a three-dimensional space manifold 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-time 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-dimensional space-time would be responsible for particle property of existence in the space-time environment of Einstein.

Yet one can also define the boundary conditions responsible for a creating the resonant system or "structure" that earlier defined a particle.

For example, in our three-dimensional world, 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.

However, the edge of the paper provides a boundary that reflects those oscillation back on itself, thereby creating a resonant wave on the surface of the paper.

Similarly, an energy wave of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate “up” or “down” while moving through time.

However, when it is prevented from moving thought time either by being observed or encountering an object or particle that wave energy will be reflected back on itself, thereby creating a resonant wave on the "surface" three-dimensional space,

In other words, if the wave component of quantum existence is prevented from moving unhindered through time either by an observation or by an interaction with a particle or object it will create a resonant system or structure that defined the quantum properties of existence in the article "Why is energy/mass quantized?".

This shows how, one can derive the wave-particle duality of quantum existence in terms of an interaction of space with time.

The final step in answering the question of why the future is what it is requires one to show how the quantum mechanical wave-particle duality of existence interacts with space to create the future in terms of probabilities.

One can use the analogy of energy of a vibrating or oscillating ball on a rubber diaphragm and how the magnitude of those vibrations would would be greatest at the focal point of those vibrations and decrease as one move away from them.

Similarly, if the assumption that wave properties of a quantum existence represents vibrations or oscillations in a "surface" of three-dimensional space, is correct the magnitude of those oscillations would be greatest at the focal point of and decreases as one moves away from it.

However, as the article, mentioned earlier “Why is energy/mass quantized?” showed the particle property of existence is a result of a resonant structure formed on the "surface" of a three-dimensional space manifold by its interaction with the time 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, the resonant structure that article associated with a particle property of existence 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.

In other words, one can define the future of the quantum mechanical wave-particle duality of existence in terms a causal interaction between it and the universe it occupies.

Additionally, this shows why defining the outcome of an observation of the wave-particle duality of existence as quantum mechanics does in terms of probabilities does not mean all the of those predicted futures exist.  This is because similar to the dice mentioned earlier the probability of a specific future is caused by a physical interaction of it with the universe it occupies.

In other words, the reason why the future is what it is is because the wave-particle duality of existence does not define the future of the universe the universe defines the future of its wave-particle component.

Later Jeff

Copyright Jeffrey O’Callaghan 2020

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There are two ways science attempts to understand or define the behavior of our world. The first is Quantum mechanics or the branch of physics that uses probabilities to define the wave particle duality of existence.  The other is the deterministic universe of Einstein where the interactions of space with time determines the casualty of events in the macroscopic universe we live in. Quantum gravity 

Specifically, the General Theory of Relativity tells us that gravity is a result of a curvature in space-time whose magnitude is directly related to the amount of matter or number of particles contained in given volume of space-time.

While quantum mechanics use probabilistic properties of the wave particle duality of existence to define the position of particles such as protons and elections in a given volume of space.

Since we all live in the same world you would expect the probabilistic approach of quantum mechanics to be compatible with the deterministic one of Einstein.  Unfortunately, they define two different worlds that on the surface appear to be incompatible.  One defines existence in terms of the probabilities associated with the wave particle duality of existence mentioned earlier while the other defines it in terms the deterministic of properties the continuous field of space and time.

Therefore, one could argue the Physicist of Quantum Gravity is the science of explaining the how the probabilities associated the wave particle duality of a quantum existence controls the deterministic universe of gravity as defined by Einstein or show how that universe is responsible for those probabilities in terms of the interaction of space and time.

For example, one can derive the probability of getting a six on a role of dice based on the fact that dice physically has six sides with only one having a six on it.  This is true even though one cannot predict when a six will occur.  In other words. one can show that probability getting a six on the role of a dice is determined by the physical properties of the dice and not that the probably of six occurring is the reason one rolls a six.

Similarly, if one can show the position of a particle is not caused by the probability of finding it there but is caused by a property of space-time one could understand how to connect gravity with the probabilistic world of quantum mechanics.  This is because, as mentioned earlier Einstein defined gravity in terms of the number of particles in given volume of space-time.

For example, in the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown the wave particle duality of existence define by quantum mechanics can be understood by extrapolating the laws of classical resonance in a three-dimensional environment to an energy wave on a "surface" of a three-dimensional space manifold with respect to a time 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 its natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in an environment consisting of four-dimensional space-time.

The existence of four-dimensional space-time would give an energy wave the ability to oscillate spatially on a "surface" the third spatial dimension with respect to the time dimension thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the "surface" of a three-dimensional space manifold 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-time 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-dimensional space-time would be responsible for particle property of existence in the space-time environment of Einstein.

Yet one can also define the boundary conditions responsible for a creating the resonant system or "structure" that earlier defined a particle.

For example, in our three-dimensional world, 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.

However, the edge of the paper provides a boundary that reflects those oscillation back on itself, thereby creating a resonant wave on the surface of the paper.

Similarly, an energy wave of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate “up” or “down” while moving through time.

However, when it is prevented from moving thought time either by being observed or encountering an object or particle that wave energy will be reflected back on itself, thereby creating a resonant wave on the "surface" three-dimensional space,

In other words, if the wave component of quantum existence is prevented from moving unhindered through time either by an observation or by an interaction with a particle or object it will create a resonant system or structure that defined the quantum properties of existence in the article "Why is energy/mass quantized?".

This shows how, one can explain the wave particle duality quantum existence in terms of an interaction of space with time.

The final step in integrating quantum mechanics with Einstein gravitational theories is to physical connect its probabilistic interoperation of a particles position with the physical properties of space-time as defined by him.

The physics of wave mechanics tells us, due to the continuous properties the energy wave of a quantum system  means it would be distributed throughout "surface" a three-dimensional space manifold with respect to time.

For example, the energy of a vibrating or oscillating ball on a rubber diaphragm would be disturbed over its 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 wave properties of a quantum existence represents vibrations or oscillations in a "surface" of three-dimensional space, is correct these oscillations would be distributed over the "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.

However as the article, mentioned earlier  “Why is energy/mass quantized?” showed the particle property of existence is a result of a resonant structure formed on the "surface" of a three-dimensional space manifold by its interaction with the time 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, the resonant structure that article associated with a particle properties of existence 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 explains why in terms of the physical properties of four-dimensional space-time why one must use the probabilities associate with quantum mechanics to determine the exact the position a single particle in space.  However, it allows one integrate the probabilities associated with the quantum mechanical definition of existence with the physical properties gravity because as was mentioned earlier gravity can be defined in terms of the quantity of particles in a given volume of space-time.

In other words, the gravitational force in a given region of space-time will be greater where the probability density of particles as define by quantum mechanics is the greatest.

As was mentioned earlier one can show that probability getting a six on the role of a dice is determined by the physical properties of the dice and not that the probably of six occurring is the reason one rolls a six.

In other word, the Physicists of Quantum Gravity may not be related to the quantum probability of finding a particle in a given region of space-time but to determining reasons why those probabilities are what they are.

Later Jeff

Copyright Jeffrey O’Callaghan 2020

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There is no one realty because each individual creates one that is unique to him or her in an attempt to organize the physical or classical world through information gathered by the senses.  However, physicists have been given the task of defining a universal explanation of it obtained through, in a large part instrumentation and mathematics. One could say one say "The Physics of Reality" is the science that attempts to define a universal reality or one that most can agree on by integrating the information provided by instrumentation and mathematics to that provided by the senses.

For example, cosmologists use telescopes to determine how our universe came to be because it allows them to observe an environment that is too far away to stimulate our sense of sight. They then attempt, in most cases to use mathematics to organized and provide an explanation of how both, the one that directly available to the sense and the one seen through telescopes appear the way they do. The reasons mathematics is the primary tool use by physicists is because many feel it is the only tool that can accurately describe the physical steps involved in defining what we see through both the senses and telescopes.

However, even though mathematics can be used to provide an explanation for the physical reality of the universe it can never replace the reality is it defining. This is because, as was mentioned earlier each person defines his or her reality in terms of the information he or she receive about physical world through the senses.  However, all mathematics is abstract in nature, therefore, it does not have a presence in the physical world and because of that it cannot be part of the one that interacts with the senses.

Some may disagree and try to tell you that the mathematics is the reality because they feel it is the only way to describe what the senses tell them about how the world is organized.  This belief is widely held by the proponents of quantum mechanics because they believe that it is the only way to describe the observations of a quantum environment

For example, many feel the entanglement of some particles which the mathematics of quantum mechanics predicts and observations have confirmed is at the heart of the disparity between classical reality and the quantum one because it is one of the features that is lacking in a classical world.

In the classical environment the one that encompass our senses we only observe objects interacting when they make physical contact. However, quantum mechanics predicts that particles which are entanglement can interact with each other regardless of how far apart they are.

Yet, the fact that many experiments have verified that two particles that are not in physical contact can interact with each other have led some to say that we must replace the classical reality of our senses with the mathematical one of quantum mechanics because they both cannot be right.  However, because entanglement has been observed the mathematics of quantum mechanics many bel should replace the physical reality of our sensory environment.

However, Einstein provided an alternative by giving a us explanation in terms his Special Theory Relativity for the how and why two particles become entangled that is also supported by the classical or physical world of the senses.

As was mentioned earlier many experiments have verified, most using polarized photons that entanglement does occur.  However, Einstein showed us that this is not because some mathematical equation defines its properties but because his theories tell us that photons which are moving at the speed of light can never be separated with respect to an external observer no matter how far apart he or she perceives them to be.

This is because he tells that that there are no preferred reference frames by which one can measure distance. Therefore, one must not only view the separation of a photon with respect to an observer who was external to them but must also look at that separation from a photon’s perspective.

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

Specifically, he told us that it would be defined by

However, because according to the concepts of relativity, one can view the photons as being stationary and the observers as moving at the velocity of light the distance or length between the two points use to take the measurement confirm entanglement from the perspective of photons moving at the speed of will be zero in the observer’s reference frame. Therefore, according to Einstein’s theory the entanglement of photon’s is not due to the mathematics of quantum mechanics but due to the relativistic properties of the classical world of the senses.  In other words, from the perspective of two entangle photons they are still are still connected even though they appear to an observer to be physical separated.

However, coming to that conclusion does not require us to deny the existence of the physicality of the reality encompassed by our sense.

As was mentioned earlier, each individual creates his or her own reality based on the information he or she receive from physical world through the senses.  Therefore, because the information regarding the relationship between velocity and length is readily available to the senses is would be integral part of their reality.  However, the abreact properties of the equations of quantum mechanics that predict entanglement are not and therefore are not part of the reality available to the senses.

For example, the effect velocity has on time and length has been confirmed by atomic clocks placed in airplanes as well as orbiting satellites by comparing them to those on the ground.  Therefore, the explanation given above of the causality of entanglement in terms of Einstein theories is observable part of the physical world that the senses use to define reality.

Therefore, one could say difference between the reality defined by the mathematics of Einstein and those of quantum mechanics is that his theories gives each individual a way of integrating his explanation of entanglement with their sensory information obtained through the use of atomic clocks in airplanes whereas the purely abstract mathematical explanation of it that quantum mechanics does not.

As was mentioned earlier "The Physics of Reality" is the science that attempts to define a universal explanation of it or one that most can agree on by integrating the information provided instrumentation and mathematics to that provided by the senses.  Therefore, because Einstein’s mathematics provides an explanation of entanglement in part by using the senses to directly observe instruments such as an atomic clock along with the mathematics of his theory shouldn’t we consider his explanation more creditable or real that the one provided by quantum mechanics.

Later Jeff

Copyright Jeffrey O’Callaghan 2020

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But not simpler.

For example, one of the simplest ways to define mass and its inertia can be found in Einstein General and Special Theories of Relativity and in the formula E=mc^2 that defines its relationship to energy.

However, some researchers have chosen to ignore its simplicity by proposing that something called the Higgs mechanism is responsible mass and its inertia or its resistance to a change in velocity.

Briefly they have tried to show that the conditions for electroweak symmetry would be "broken" if an unusual type of field existed throughout the universe, and indeed, some fundamental particles would acquire mass. The field required for this to happen (which was purely hypothetical at the time) became known as the Higgs field (after Peter Higgs, one of the researchers) and the mechanism by which it led to symmetry breaking, known as the Higgs mechanism. A key feature of the necessary field is that it would take less energy for the field to have a non-zero value than a zero value, unlike all other known fields, therefore, the Higgs field has a non-zero value (or vacuum expectation) everywhere. This non-zero value could in theory break electroweak symmetry. It was the first proposal capable of showing how the weak force gauge bosons could have mass despite their governing symmetry, within a gauge invariant theory.

However, as was mentioned earlier the General Theory of Relativity provides a much simpler explanation as to what mass and inertia is.

This is because that theory defines gravitational energy in terms of a curved displacement in space-time which concentrates its energy in the apex of that curvature.  However, in doing so it essentially tells us that rest mass is a concentrated form of energy because that is the only thing that exists at the apex of that curvature.  Additionally, the experimentally confirmed of the equation E=mc^2 supports that assumption by defining relative concentrations of mass of all objects and particles to energy in a space-time environment in terms of the velocity of light squared.

However, in defining how mass is accelerated in terms of a curved displacement in the "surface" of space-time he also defines constant motion in terms of a linear displacement of the two-dimensional space-time plane it was moving through because if it was curved or nonlinear it would be accelerated.  This also defines the reason constant motion is relative because each observer will view the linear displacement in space-time associated with its motion from perspective of his own linear baseline in space-time.

On the other hand, accelerated motion is not relative because it is caused by a nonlinear curvature in space-time therefore each observer will have a different baseline for determining its energy depending on where he is in relation to the focal point of that curvature.  For example, the force of gravity increases as an observer approaches a mass because he is observing it form a different energy point on the curvature in space-time responsible for energy force.

This also provides another way of understanding the causality of inertia because the linear displacement in the two-dimensional plane of space-time associated with its velocity consist of two components. The first is the energy associated with apex of the curvature in space-time that defines rest mass mentioned earlier and the second is the energy required to shift the linear displacement associated with its relative velocity. However, this means the inertia or energy required to make changes in relative velocity or, as was shown earlier the linear displacement in space-time that is responsible for it would be proportional to the energy associated with its mass.  In other words, it provides the reason why the inertia of all objects and particles is directly proportion to their mass and energy.

To put it another way,  because Einstein defined mass in terms of the concentration of energy in space-time one must add the energy of the linear displacement he associated with relative velocity to derive the mass of all objects and particles.

This tells us the reason the mass and inertia of particles in particle accelerators increase as their velocity does is because one must add the energy associated with the linear displacement in space time caused by their velocity to their rest mass.

This definition of mass and inertia gives us a much simpler explanation than the one mentioned above which uses the Higgs boson for why one particle or object has a different mass from another and why it resists changes in its motion.   However it is not too simple because as was shown above it can explain all aspects of mass and inertia while having the advantage of being supported by a definable mechanism in terms of Einstein theories whereas I do not believe that as of today there is a fundamental explanation for the precise manner in which each of the known particle species interacts with the Higgs boson.

Later Jeff

Copyright Jeffrey O’Callaghan 2020

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What makes gravitational force different from those of electromagnetism is that gravity acts along the perpendicular axis of space-time while electromagnetic forces acts in the two-dimensional plane that is perpendicular to gravity.  This is the reason why gravity only acts in one direction attractive while that of electromagnetic can act in two directions, attractive and repulsive because it has the freedom to move along that two dimensional plane.

Einstein had difficulty in understanding how derive to the forces of electromagnetic as they moved through space in terms of his space-time model as was documented by the American Institute of Physics.

From before 1920 until his death in 1955, Einstein struggled to find laws of physics far more general than any known before. In his theory of relativity, the force of gravity had become an expression of the geometry of space and time. The other forces in nature, above all the force of electromagnetism, had not been described in such terms. But it seemed likely to Einstein that electromagnetism and gravity could both be explaneed as aspects of some broader mathematical structure. The quest for such an explanation — for a unified field theory that would unite electromagnetism and gravity, space and time, all together — occupied more of Einstein’s years than any other activity.

However, the reason is NOT that his theories could not support electromagnetism but more likely because time moves only one direction forward similar to how gravity only moves in one direction attractive.  However, electromagnetism "moves" in two direction attractive and repulsive therefore it is difficult to understand how one directional properties of time could be responsible for it.

Yet Einstein gave us an easier way to see how and why his space time model can be linked to the positive and negative forces associated with electromagnetism when he used the constant velocity of light to define geometric properties of forces in a space-time environment  This is because that would allow one to convert a unit of time in his four-dimensional space-time universe to a unit of space in a universe consisting of only four *spatial* dimensions.  Additionally, because the velocity of light is constant it is possible to define a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words, by mathematically defining the geometric properties of time in his space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of define the time-based components in terms of its equivalent in only four spatial dimensions.

The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the displacement associated energy in a space-time environment 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 including gravitational and electromagnetism can be derived in terms of a spatial displacement in any "surface" or plane of three-dimensional space with respect to a fourth *spatial* dimension.

This allows one to form a physical image of how electromagnetic forces can be both attractive and repulsive in terms of the differential force caused by the "peaks" and "toughs" of an energy wave moving in the three-dimensional plane with respect to a fourth *spatial* dimension that is perpendicular to gravity’s.

For example, Classical wave mechanics tells us a wave on the two-dimensional surface of water causes a point on that surface to become displaced or rise above or below the equilibrium point that existed before the wave was present.  A force is developed by that differential displacement of the surfaces, which will result in the elevated and depressed portions of the water moving towards or become "attracted" to each other and the surface of the water.

Similarly, it tells us an energy wave on the three-dimensional plane with respect to a fourth *spatial* dimension that is perpendicular to gravity would cause a point on that plane to become displaced or "elevated and depressed" with respect to the equilibrium point that existed before that wave was present.

However, it also tells us a force will be developed by those differential displacements in the plane that was perpendicular to gravity that will result in its "elevated and depressed" portions moving towards or become "attracted" to each other as the wave moves through space.

This defines the causality of the attractive forces of unlike charges associated with the electromagnetic field in terms of the force developed by the differential displacements of a point on the three-dimensional plane that is perpendicular to gravity.

However, it also provides a classical mechanism for understanding repelling forces of electromagnetism because observations of water show that there is a direct relationship between the magnitude of a displacement in its surface to the magnitude of the force resisting that displacement.

Similarly, the magnitude of a displacement on a three-dimensional plane with respect to a fourth *spatial* dimension caused by two similar charges will be greater than that caused by a single one.  Therefore, similar charges will repel each other because the magnitude of the force resisting that displacement will be greater for two charges than it would be for a single charge.

One can also derive the magnetic component of an electromagnetic wave in terms of the horizontal force developed by the horizontal displacement caused by its peaks and troughs.  This would be analogous to how the perpendicular displacement of a mountain generates a horizontal force on the surface of the earth, which pulls matter horizontally towards the apex of that displacement.

Additionally, one can derive the causality of electrical component of electromagnetic energy in terms of the energy associated with its "peaks" and "troughs" that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement because classical Mechanics tells us a horizontal force will be developed by that displacement which will always be 90 degrees out of phase with it.  This force is called magnetism.

This shows that one can use Einstein’s General theory of Relativity to derive the physical properties of both electromagnetism and gravity.  Additionally it defines the reason why the force of gravity only acts only by attracting objects is because it is confined to the perpendicular axis of space-time or its equivalent in four *spatial* dimensions while electromagnetism can both, attract and repulse objects because it has the freedom to move objects or particles two directions in the two dimensional plane that is perpendicular to gravity’s .

It should be remembered that Einstein’s genius allows us to choose whether to define an electromagnetic wave 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.

Later Jeff 

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As was mentioned in the Scientific American article "Is Gravity Quantum?"

"All the fundamental forces of the universe are known to follow the laws of quantum mechanics, save one: gravity. However, finding a way to fit gravity into quantum mechanics would bring scientists a giant leap closer to a “theory of everything” that could entirely explain the workings of the cosmos from first principles. A crucial first step in this quest to know whether gravity is quantum is to detect the long-postulated elementary particle of gravity, the gravitron. In search of the graviton, physicists are now turning to experiments involving microscopic superconductors, free-falling crystals and the afterglow of the big bang."

When Einstein was asked about the consequences of not being able to observe the graviton he replied "It seems as though we must sometimes use 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"

However, there is a way of fitting gravity into quantum mechanics that does on involve observing the gravitron.

Quantum mechanics assumes all forces are defined by a particle wave dichotomy while Einstein General Theory of Relativity tells us that gravity causes ripples or waves in the fabric of space-time.  However, if one can use the concepts developed by Einstein to show that those gravity waves also exists as a particle wave dichotomy similar to the particle wave dichotomy of quantum mechanics one may be able define a physical connection between his theories and quantum mechanics.

But before we begin, we must first define the relationship between how that particle wave dichotomy manifests itself in the quantum world.

The physicist John Wheeler said the best answer was given by Aatish Bhatia “Don’t look: waves. Look: particles.” That’s quantum mechanics in a nutshell."

In other words, quantum mechanics tells us when a force is observed to interact with an object such as a proton or electron the particle component of its dichotomy becomes predominate while its wave properties only present themselves as it moves unhindered through space.

As was mentioned earlier one may be able to bridge the gap between Quantum Mechanics and General Relativity if one can define how and why the wave in space-time Einstein associated with gravity exist as a particle wave dichotomy similar to the other forces that quantum mechanics defines in those terms.

One of the problems we face in doing this is that his theory defines the force of gravity with respect to time while Quantum theory defines all forces in terms of the spatial properties of position when interacting with objects.

However, Einstein gave us a way to transform his time based definition of gravity into a spatial one which is more consistent with Quantum Mechanics spatially oriented definition of a particle when he defined gravities geometric properties in terms of the constant velocity of light.  This is because it allows one to convert a unit of time in his four-dimensional space-time universe to a unit of a space in one consisting of only four *spatial* dimensions which would be more consistent with quantum mechanics position orient definition of a particle.  Additionally, because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words, he provided a qualitative and quantitative means of redefining his space-time universe in terms of an equivalent one in only four *spatial* dimensions.

However, redefining the time based geometry of gravity in terms of its equivalent in four *spatial* dimensions also allows one to not only understand why all forces, including gravity exist as a particle wave dichotomy but also, as mentioned earlier the interaction or non-interaction of a force with anything determines which of those "realities" becomes predominate.

For example the article “Why is energy/mass quantized?” Oct. 4, 2007 showed one can derive particle properties of the wave component of gravities dichotomy 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 its wave component 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 collision of two black holes. 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 quantum mechanics associates with the particle component of its particle wave dichotomy.

Yet, it also allowed one to derive the physical boundaries of the particle component of its dichotomy 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 by the interaction of forces with "things" in three-dimensional space is what defines the spatial boundaries of the resonant system of the particle component of it particle wave dichotomy defined in the article “Why is energy/mass quantized?” Oct. 4, 2007.

In other words, Einstein theories tell us the particle component of the particle wave dichotomy of gravity would appear or become reality when it confined to three-dimensional space by its interaction with "something" in three-dimensional space.

This is similar to the particle wave dichotomy quantum mechanics associates with all forces in that they manifest themselves as waves until the interact with another quantum system.

Not only that but it allows one to form a direct connection between the General Theory of Relativity and Quantum Mechanic’s assumption that reality is defined in terms of a particle wave dichotomy because the same logic used above can be applied to all forces to explain why, if a force is allowed to move uninhibited through space the wave reality of its dichotomy will be predominate and why if it interacts with anything its particle ones will be predominate.

In other words, we do not have to observe the Gravitron to bring quantum mechanics and its particle wave dichotomy into the Theoretical environment of General Relativity because the physical reasons for that dichotomy are inherent in its theoretical structure.

Additionally, it gives consistent explanation of why one can sum up quantum mechanics in these words "Don’t look: waves. Look: particles" by extrapolating the "single" physical picture provided by the General Theory of Relativity to all quantum systems.

It should be remembered that Einstein’s genius and the symmetry of his mathematics 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.

Later Jeff

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