Is there lower limit to the size of our universe. In other words, how many times can the universe and its mass components be divided up into smaller and smaller chunks until it can divided no farther.
The answer would most likely be found in the two dormant theories, Quantum Mechanics and Einstein’s Theories of Relativity which are used by cosmologists and particle physics to define its evolution.
For example, Einstein’s theories say very little about its origins but it does say a lot about how its components interact to create its observable structures and while doing so tells a lot about how they interact to define the lower limit of its size.
While on the other hand, a few Quantum Mechanical Theories define its evolution and the lower limit to its size in terms of an infinitesimally small point in spacetime. However, it is unable to providing any details about how its components, after its beginnings interact to create the universe, we can observe around us.
For example, one theory called the Big Bang, which is based on the mathematics of Quantum Theory defines its beginnings and the lower limit to its size in terms of the expansion of a point in spacetime called a quantum fluctuation while defining its evolution not in terms of how its component interact but in terms of points in spacetime that represent positions of all of the particles it contains at the time they are observed.
This technique of using a onedimensional point to represent a particle or an objects position is similar to how NASA defines the orbits of planet and its space probes.
For example, they do not use physical size or the volume of a planet to calculate position and interactions with its orbiting components, instead they use a onedimensional point at its center called the center of gravity to represent those interactions.
Similarly, quantum mechanics does not need to use physical size of a particle to define its position because similar to how NASA can use a point at the center of an object to represent it, it can use a point in spacetime that is in the center of a particle to represent its position. In other words, the fact that Quantum mechanics describes the microscopic environment of particles in terms of onedimensional points does not mean that they do not have size.
As was mentioned, earlier Quantum Mechanics assumes the universe began as quantum fluctuation which is a mathematically defined as point in spacetime. In other words, it assumes the size of the universe could be, at its beginning smaller than the period at the end of this sentence.
However, Einstein theories tell us a completely different story of its beginning.
For example, it tells us that matter can only compacted so much before the forces of gravity and time stop it from going any further.
This is true even though in 1915, Karl Schwarzschild proposed based on Einstein theories the gravitational field of a star greater than approximately 2.0 times a solar mass would collapse to form a black hole whose which is a region where time stops and neither light nor particles can escape from it. However, many assumed that the collapse continues until is compacted into a onedimensional point or singularity in spacetime.
One can understand why those that believed that came to the wrong conclusion by analyzing how those forces interact to create a black hole as was done in the previous article "Time is a force more powerful than those of a black hole" published on Aug 31, 2019
Briefly
"In Kip S. Thorne book " Black Holes and Time Warps ", he describes how in the winter of 193839 Robert Oppenheimer and Hartland Snyder computed the details of a stars collapse into a black hole using the concepts of General Relativity. On page 217 he describes what the collapse of a star would look like, form the viewpoint of an external observer who remains at a fixed circumference instead of riding inward with the collapsing stars matter. They realized the collapse of a star as seen from that reference frame would begin just the way every one would expect. "Like a rock dropped from a rooftop the stars surface falls downward slowly at first then more and more rapidly. However, according to the relativistic formulas developed by Oppenheimer and Snyder as the star nears its critical circumference the shrinkage would slow to a crawl to an external observer because of the time dilatation associated with the relative velocity of the star’s surface. The smaller the circumference of a star gets the more slowly it appears to collapse because the time dilation predicted by Einstein increases as the speed of the contraction increases until it becomes frozen at the critical circumference.
However, the time measured by the observer who is riding on the surface of a collapsing star will not be dilated because he or she is moving at the same velocity as its surface.
Therefore, the proponents of singularities say the contraction of a star can continue until it becomes a singularity because time has not stopped on its surface even though it has stopped with respect to an observer who remains at fixed circumference to that star.
But one would have to draw a different conclusion if one viewed time dilation in terms of the gravitational field of a collapsing star.
Einstein showed that time is dilated by a gravitational field. Therefore, the time dilation on the surface of a star will increase relative to an external observer as it collapses because, as mentioned earlier gravitational forces at its surface increase as its circumference decrease.
This means, as it nears its critical circumference its shrinkage slows with respect to an external observer who is outside of the gravitation field because its increasing strength causes a slowing of time on its surface. The smaller the star gets the more slowly it appears to collapse because the gravitational field at its surface increase until time becomes frozen for the external observer at the critical circumference.
Therefore, the observations of an external observer would make using conceptual concepts of Einstein’s theory regarding time dilation caused by the gravitational field of a collapsing star would be identical to those predicted by Robert Oppenheimer and Hartland Snyder in terms of the velocity of its contraction.
However, Einstein developed his Special Theory of Relativity based on the equivalence of all inertial reframes which he defined as frames that move freely under their own inertia neither "pushed not pulled by any force and Therefore, continue to move always onward in the same uniform motion as they began".
This means that one can view the contraction of a star with respect to the inertial reference frame that, according to Einstein exists in the exact center of the gravitational field of a collapsing star.
(Einstein would consider this point an inertial reference frame with respect to the gravitational field of a collapsing star because at that point the gravitational field on one side will be offset by the one on the other side. Therefore, a reference frame that existed at that point would not be pushed or pulled relative to the gravitational field and would move onward with the same motion as that gravitational field.)
(However, some have suggested that a singularity would form in a black hole if the collapse of a star was not symmetrical with respect to its center. In other words, if one portion of its surface moved at a higher velocity that another towards its center it could not be consider an inertial reference frame because it would be pushed or pulled due to the differential gravity force cause be its uneven collapse. But the laws governing time dilation in Einstein’s theory tell us that time would move slower for those sections of the surface that are moving faster allowing the slower ones to catch up. This tells us that every point on the surface of star will be at the event horizon at the exact same time and therefore its center will not experience any pushing or pulling at the time of its formation and therefore could be considered an inertial reference frame.)
The surface of collapsing star from this viewpoint would look according to the field equations developed by Einstein as if the shrinkage slowed to a crawl as the star neared its critical circumference because of the increasing strength of the gravitation field at the star’s surface relative to its center. The smaller it gets the more slowly it appears to collapse because the gravitational field at its surface increases until it becomes frozen at the critical circumference.
Therefore, because time stops or becomes frozen at the critical circumference for all observers who are at the center of the clasping mass the contraction cannot continue from their perspectives.
Yet, Einstein in his general theory showed that a reference frame that was free falling in a gravitational field could also be considered an inertial reference frame.
As mentioned earlier many physicists assume that the mass of a star implodes when it reaches the critical circumference. Therefore, an observer on the surface of that star will be in free fall with respect to the gravitational field of that star when as it passes through its critical circumference.
This indicates that point on the surface of an imploding star, according to Einstein’s theories could also be considered an inertial reference frame because an observer who is on the riding on it will not experience the gravitational forces of the collapsing star.
However, according to the Einstein theory, as a star nears its critical circumference an observer who is on its surface will perceive the differential magnitude of the gravitational field relative to an observer who is in an external reference frame or, as mentioned earlier is at its center to be increasing. Therefore, he or she will perceive time in those reference frames that are not on its surface slowing to a crawl as it approaches the critical circumference. The smaller it gets the more slowly time appears to move with respect to an external reference frame until it becomes frozen at the critical circumference.
Therefore, time would be infinitely dilated or stopped with respect to all reference frames that are not on the surface of a collapsing star from the perspective of someone who was on that surface.
However, the contraction of a star’s surface must be measured with respect to the external reference frames in which it is contracting. But as mentioned earlier Einstein’s theories indicate time in its external environment would become infinitely dilated or stop when the surface of a collapsing star reaches its critical circumference.
Therefore, because time stops or becomes frozen at the critical circumference with respect to the external environment of an observer who riding on its surface the contraction cannot continue because motion cannot occur in an environment where time has stopped.
This means, as was just shown according to Einstein’s concepts time stops on the surface of a collapsing star from the perspective of all observers when viewed in terms of the gravitational forces the collapse of matter must stop at the critical circumference.
This contradicts the assumption made by many that the implosion would continue for an observer who was riding on its surface.
In other words, based on the conceptual principles of Einstein’s theories relating to time dilation caused by a gravitational field of a collapsing star it cannot implode to a singularity or a onedimensional point as many physicists believe because it causes time to freeze at its critical circumference with respect to all observers. Therefore, a universe whose evolution is governed by his theories must maintain a quantifiable minimum volume which is greater than the one defined by Schwarzschild radius because if it were smaller matter could not move through that boundary in space time and it could not evolve any further."
However. the same principle must be applied to the size of the universe at its beginning. In other words, if time stops at the Schwarzschild radius any object or component of a universe smaller than that could not move through it and evolve to form the structures we observed today.
Additionally, Schwarzschild radius also defines the lower limit to size of all subatomic particles because it defines where time would stop at their surface. Therefore, if they were smaller or even equal to that radius they could not interact with the other particles because time would stop as they approached each other and interaction with other particles would never happen.
In other words, in a universe governed by Einstein’s theories the lower limit to the size of both the universe and the particles it contains is defined by Schwarzschild radius.
Yet this would seem to contract the quantum mechanical description of a particle as being represented as point in spacetime without an extended volume.
HOWEVER, THIS IS NOT THE CASE because, as was mentioned earlier the point in spacetime that quantum mechanics defines as the position of a particle could be interpreted as the center of wave component of its duality similar to how NASA uses the point at the center of mass of an extended object to determine its position in spacetime as was shown in the article published on Jan. 1, 2020 "Particles as standing waves in spacetime"
Yet, it is possible that someone with better mathematical skills than me may be able to unify the Quantum universe with Einstein’s by mathematically describing a environment in which the point description of a particle defines the energy center of its wave component of its wave particle duality while showing how that point interacts with their environment based on those properties similar to how NASA uses the center of the energy or gravitational components of planets to how they interact with other each other.
Latter Jeff
Copyright 2020 Jeffrey O’Callaghan
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One question that has yet to be answer regarding Einstein relativistic theories is how time and space interact to create the past, present and future.
Einstein side step this question by assuming, as he put it "there exists in this fourdimensional structure [spacetime] 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 fourdimensional existence, instead of, as hitherto, the evolution of a threedimensional existence."
Marina Cort’s, a cosmologist from the Royal Observatory, Edinburgh defined what has come to be called the block universe to help us understand how Einstein may have viewed the past present and future.
Basically, she asks us to imagine a regular chunk of cement. It has three dimensions but we live in four dimensions: the three spatial dimensions plus one time dimension. A block universe is a fourdimensional block, but instead of being made of cement, it is made of spacetime. And all of the space and time of the Universe are there in that block."
We can’t see this block, we’re not aware of it, as we live inside the cement of spacetime. And we don’t know how big the block universe we live in is: "We don’t know if space is infinite or not. Or time – we don’t know whether it has a beginning or if it will have an end in the future. So, we don’t know if it’s a finite chunk of spacetime or an infinite chunk."
In other words, the past, present, and future exist simultaneously and are locked in a nondynamic, unchanging block of spacetime with the rigidity of cement.
However, to understand why Einstein he had to make this assumption one must first define what space and time are.
For example, some define time only in the abstract saying that is an invention of the human consciousness that gives us a sense of order, a before and after so to speak.Â To physicist’s it is a measure of the relative interval between events which is measured in units of time such as seconds.
While space can be defined as the arena where those events occur. We use the measurements of inch or meter to define the position of those event in that arena.
The problem Einstein with defining how energy causes a dynamic change in a spacetime environment that define "happening and becoming" or the future, may have been due to the fact that he mathematically defined it in terms of a melding of time with space which have different units. Therefore, because, in mathematics if the dimensions or units on the left and righthand sides don’t agree the equation are nonsense it is hard to imagine how the future is created in terms of spacetime. This is why he said "It appears Therefore, more natural to think of physical reality as a fourdimensional existence, instead of, as hitherto, the evolution of a threedimensional existence.
However, the fact he found that definition unsatisfactory is evident when he said that "concepts (or causality) of happening and becoming are indeed not completely suspended, but yet complicated" indicate that he was aware of this.
In other words, Einstein realized that causality of the future in terms of a dynamic process was something that must be considered.
Yet, Einstein gave us an alternative way of understanding "happening and becoming" when he defined the relationship between energy and spacetime in terms of the constant velocity of light and the equation E=mc^2 because in doing so he provided a method of converting a unit of time and energy in a spacetime 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 spacetime universe and one made up of only four *spatial* dimensions.
In other words, Einstein’s mathematics actually defined two mathematically equivalent physical models of the universe one consisting of fourdimensional spacetime and one of only four *spatial* dimensions.
In his spacetime model he mathematically defined all forms of energy including gravity and the kinetic energy of motion in terms of a curvature or displacement in the "surface" of fourdimensional spacetime manifold. However, in his equivalent model consisting of only four *spatial" dimensions he would have defined them in terms of a displacement or curvature in the "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension.
As was mentioned earlier, it was evident Einstein realized the difficulty of deriving the future or happenings in terms of his spacetime model when he said "no longer any sections which represent "now" objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated.
However, the same is not true of the equivalent model mentioned above consisting of only four *spatial* dimensions because defining the causality of change of the future in those terms would eliminate the problem mentioned above with the incompatibility of space and time.
Yet, before we can define the future in terms of the dynamics four *spatial* dimension we must first explain how it interacts with time to cause it to dilate and shorten length of objects when it is in relative motion with respect to an observer.
For example, one can show as was mentioned earlier by using the Einstein mathematics the kinetic energy of motion can be understood in terms of a displacement in a "surface" of a threedimensional space manifold with respect to a fourth spatial dimension as well one in fourdimensional spacetime.
One can understand how this would effect time and the length of objects in relative motion by assuming the perspective of two "2 dimensional creatures are living on the surface of two pieces of paper resting on a desktop.
Also, assume the two creatures can view the surfaces of the other piece of paper, which are separated a pencil.
If the diameter of the pencil is increased, the curvature between the surfaces of the two pieces of paper will increase.
Each of these creatures, when viewing the other piece of paper will only perceive the twodimensional translation of the threedimensional curvature generated by the pencil.
Therefore, each will view the distance between two points on the surface of the other as shorter since they will view that distance as a twodimensional translation of the threedimensional curvature in the surface of the paper.
Similarly, because threedimensional beings could only "view" a threedimensional translation of a "curvature" or displacement in four *spatial* dimension caused by the motion of a reference frame they will measure distance or length in them as being longer than they would be if viewed as an observer who is not in relative motion to it.
The "movement" of time on both surfaces will also be affected.
Each of the twodimensional creatures mentioned earlier will view the others time as moving slower because the threedimensional curvature in the paper makes the distance between events longer than the twodimensional translation of those events. Therefore, it will take longer for events "move" through a curvature in threedimensional space relative to the time it would take for them to move through twodimensional translation on the others surface caused by that curvature.
Similarly, time will become dilated in reference frames that are in motion because the curvature generated on its threedimensional "surface" caused by its relative motion will result the distance between events to be longer than it with respect to the distances measured in reference frames observe on them assumed them to be stationary. Therefore, they will view time in a reference frame that is in motion relative to them as moving slower than if they were in that reference frame.
As show above both of these models, the one based on the physical existence of four dimensions spacetime and the existence of only four spatial dimensions make identical predictions as to the relativistic properties of space and time, therefore which one you chose to define the physical structure of our universe must be based, in part on how you view the future.
However, Einstein spacetime interpretation did not allow him to define the dynamic changes in our environment that we call the future because he mathematically defined them in terms of a melding of time with space which have different units. Therefore, he had to assume that the past present and future was locked in a block of cement.
However, as was shown above the same is not true if one interprets his equation in terms of four *spatial* dimensions because all they all have the same units.
Yet, because as was mentioned earlier both of these models are mathematically equivalent and since we cannot physically observe either a time or a fourth *spatial* dimension, we must look to the affects they would have on the ones we can observe or in this case how we perceive the future to determine which one of these physical models is correct.
In other words, if you view it as something that dictates the past and present you will probably chose his spacetime model. However, if you view the future as a dynamic interaction of the past with the present you will most likely choose the model based on only four *spatial* dimensions.
Latter Jeff
Copyright Jeffrey O’Callaghan 2020
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28
A few years after Albert Einstein unified space and time in his (and by now very well tested!) Theory of General Relativity he applied it to the entire universe and found something remarkable. The theory predicts that the whole universe is either expanding or contracting.
Later in 1929 the astronomer Edwin Hubble measured the velocities of a large selection of galaxies and found that the majority of them were moving away from us. In other words, the universe was expanding.
However, is the universe expanding in space or is it expanding through time?
To answer this one must first define what time and space are.
Some define time only in the abstract saying that is an invention of the human consciousness that gives us a sense of order, a before and after so to speak. To physicist’s it is a measure of the relative interval between events which is measured in units of time such as seconds minutes or hours.
However, space can be defined as the arena where events occur. We use the measurements of inch or meter to define the position of those event in that arena.
As was mentioned earlier, Einstein’s General Theory of Relativity mathematically define the universe in terms of a melding of time with space. However, as was mention above they are they have vastly different properties. For example, one is measure in terms of second while the other is in inches or meters.
Therefore, it is very difficult to understand how time which is measured in seconds can have a dynamic effect on space measured in meters.
To this end Marina Corts, a cosmologist from the Royal Observatory, Edinburgh came up to what has come to be called the block universe.
Basically, it asks us to imagine a regular chunk of cement. It has three dimensions but we live in four dimensions: the three spatial dimensions plus one time dimension. A block universe is a fourdimensional block, but instead of being made of cement, it is made of spacetime. And all of the space and time of the Universe are there in that block."
We can’t see this block, we’re not aware of it, as we live inside the cement of spacetime. And we don’t know how big the block universe we live in is: "We don’t know if space is infinite or not. Or time – we don’t know whether it has a beginning or if it will have an end in the future. So, we don’t know if it’s a finite chunk of spacetime or an infinite chunk."
However, picture this presents a problem for cosmologists because if the merging of space and time causes it to become as ridge as a block of cement how can its spatial component be expanding.
It should be remembered only the spatial component of the universe is expanding not time.
Additionally, because Einstein defined the universe in terms of only four dimensions, one time and three spatial how can we understand its spatial expansion without adding an additional one because a spatial one cannot expand to one made up of time because, as mentioned earlier they have vastly different properties.
Yet, Einstein gave us an alternative 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 spacetime 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 spacetime universe and one made up of four *spatial* dimensions.
In other words, Einstein’s mathematics actually defined two mathematically equivalent physical models of the universe one consisting of fourdimensional spacetime and one of only four spatial dimensions.
Yet, because both of these models are mathematically equivalent and since we cannot physically observe either a time or a fourth *spatial* dimension, we must look to the effects they would have on the ones we can observe to determine which one of these physical models is correct.
For example, if we were a twodimensional creature living on the surface of a balloon that was inflating, we could explain its spatial expansion by assuming we were living in an environment consisting three spatial dimensions because they have the same properties as the two dimension surface of the balloon therefore, it could expand through it. However, we could not explain it by assuming that we were living in an environment consisting of only time and the twodimensional surface of the balloon because time as mentioned earlier it does not have the properties of space and therefore could not expand in it.
Similarly, we can explain why our threedimensional world was undergoing a spatial expansion by assuming we were living in an environment or universe consisting four *spatial* dimensions because it would have the same spatial properties as the three dimension one we live in. However, we could not if we assume our universe consisted of fourdimensional spacetime because time does not have the properties of space and therefore similar to the surface of the balloon it could not expand in it.
As was mentioned earlier "A few years after Albert Einstein unified space and time (and by now very well tested! ) in his theory of General Relativity" and showed it can be "applied to the entire universe ." Therefore, he also showed that because of their mathematical equivalence, a physical model based on one unifying threedimensional space with a fourth *spatial* dimension has also been very well tested and could also be applied it to the entire universe.
However, as was shown above his physical model based on four *spatial* dimensions pass an additional test which his spacetime model cannot, that of explaining the spatial expansion of our threedimension environment.
Later Jeff
Copyright Jeffrey O’Callaghan 2020
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Presently, there is disconnect between our understanding of one of the most mysterious facets of quantum mechanics quantum, that of quantum entanglement and the classical one of separation.
Entanglement occurs when two particles are linked together no matter their separation from one another. Quantum mechanics assumes even though these entangled particles are not physically connected, they still are able to interact or share information with each other instantaneously.
Many believe this means the universe does not live by the law’s classical laws of separation or those derived by Einstein which stated that no information can be transmitted faster than the speed of light.
However, we must be careful not to jump to conclusions because Einstein gave us the definitive answer as to how and why particles are entangled in terms of the physical properties of spacetime.
Quantum mechanics assumes that entanglement occurs when two particles or molecules share on a quantum level one or more properties such as spin, polarization, or momentum. This connection persists even if you move one of the entangled objects far away from the other. Therefore, when an observer interacts with one the other is instantly affected.
There is irrefutable experimental evidence the act of measuring the state of one of a pair of particles can instantaneously effect another even though they are physically separated from each other.
However, before we come to the conclusion it is a result of their quantum mechanical properties, we should first examine the experimental setup and any variables that may allow us to come to a different conclusion.
In quantum physics, it is assumed entangled particles remain connected so that actions performed on one immediately affect the other, even when separated by great distances. The rules of Quantum physics also state that an unobserved photon exists in all possible states simultaneously but, when observed or measured, exhibits only one state.
One of the experiments that many assume verifies that entanglement is a quantum phenomenon uses (This description was obtained from the Live Science web site) a laser beam fired through a certain type of crystal which causes individual photons to be split into pairs of entangled photons. The photons can be separated by a large distance, hundreds of miles or even more. When observed, Photon A takes on an upspin state. Entangled Photon B, though now far away, takes up a state relative to that of Photon A (in this case, a downspin state). The transfer of state (or information) between Photon A and Photon B takes place at a speed of at least 10,000 times the speed of light, possibly even instantaneously, regardless of distance. Scientists have successfully demonstrated quantum entanglement with photos, electrons, molecules of various sizes, and even very small diamonds.
However, Einstein told us there are no preferred reference frames by which one can measure distance.
Therefore he tells the distance between the observational points in a laboratory, can also be defined from the perspective of the photons in the above experiment.
Yet, this tell us (Please see attached graphic) that the separation between the observation points in a laboratory from the perspective of two photons moving at the speed of light would be ZERO no matter how far apart they might be from the perspective of an observer in that laboratory. This is because, as was just mentioned according to the concepts of Relativity one can view the photons as being stationary and the observers as moving at the velocity of light.
Therefore, according to Einstein’s theory all photons which are traveling at the speed of light are entangled no matter how far they may appear to be from the perspective of an observer who is looking at them.
In other words, entanglement of photons can be explained and predicted terms of the relativistic properties of spacetime as defined by Einstein as well as by quantum mechanics.
One way of determining if this is correct would be to determine if particles which were NOT moving at the speed of light experience entanglement over the same distances as photon which are.
This is because, the degree of relativistic shortening of the distance between the end points of the observations of two particle is dependent on their velocity with respect to the laboratory were they are being observed.
Therefore, all photons no matter how far apart they are from the perspective of a lab will be entangled because Einstein tells due to the fact that they are moving at the speed of light that distance will be Zero from their perspective.
However, he also tells us that for particles moving slower than the speed of light the distance between will be greater than zero and how much more would depend on their the relative speed with respect to it. In other words, the slower with respect to the lab they are moving the less that distance will be shortened.
Therefore, if it was found that only photons experience entanglement when the observation points were separated by large distances it would support the idea that it is caused by the relativistic properties of space defined by Einstein.
However, one must remember the wave particle duality of existence as defined by Quantum mechanics tell us that before a particle is observed it has an extended length equal due to its wavelength. Therefore, all particles will be entangled if the reduction in length between the endpoints of the observations when adjusted with respect to their relative velocity is less their wave length as defined by quantum mechanics.
A more conclusive argument could be made for the idea that entanglement is a result of the relativistic properties of space if it was found that entanglement ceased when the relativistic distance between the end points of observation when viewed from the perspective of particle moving slower than the speed of light was greater than its wavelength as defined by quantum mechanics.
Some have suggested that “There are inertial frames for every speed less than light – speaking informally – but there is no inertial frame for light speed itself. Any attempt to generate one actually generates a degenerate frame which can cover only an infinitesimal fraction of spacetime.” However the argument that there are “There are inertial frames for every speed less than light”
because they would create an infinitesimal fraction of spacetime is invalid, because Special Relativity WITHOUT EXCEPTION defines an inertial frame reference as one which is not undergoing acceleration. Therefore, even though using a photon as a reference frame may create infinitesimal 2 dimensional fraction of spacetime the conceptual foundations formulas for length contractions of reference frames in relative motion define by Einstein tells us that one can exist. One reason that all of the mass which is contained in it is not undergoing acceleration.Therefore, the fact that it may define a degenerate frame would be irrelevant to the conclusion draw above because as that post showed it is the distance between the end points of the observation when viewed from a photon that determines whether or not it will be entangled.
Copyright Jeffrey O’Callaghan 2020
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Richard Feynman the farther of Quantum Electrodynamics believed Thomson’s double slit experiment provided a mechanism for understanding the wave particle duality of energy/mass because it clearly demonstrates their inseparability and provides a mechanisms for understanding how it is propagated through space.
The waveparticle duality postulates that all particles exhibit both wave and particle properties. A central concept of quantum mechanics, this duality addresses the inability of classical concepts like "particle" and "wave" to fully describe the behavior of quantumscale objects. Standard interpretations of quantum mechanics explain this paradox as a fundamental property of the Universe, while alternative interpretations explain the duality as an emergent, secondorder consequence of various limitations of the observer.
The reason the abovementioned experiment is so important is because it provides a mechanism for understanding how electromagnetic energy is propagated and why the particle wave dually exists purely in terms of Einstein’s Theory of Relativity.
But before we begin, we must first understand how the electromagnetic wave component of a particle’s duality is propagated through space and time.
One of the difficulties involved in doing so is that we define its movement though space in terms Maxwell’s equations which are based on the interaction between its electric and magnetic components with respect to time not space. This presents a problem because the particle component of its duality must always be defined by its spatial position when observed. Therefore, to understand how they are related we should attempt to define its movement through space and time in term of its spatial properties.
Einstein gave us the ability to do this purely in terms spatial properties of its electromagnetic wave components when he used the constant velocity of light to defined the geometric properties of spacetime because it allows one to convert a unit of time in his spacetime universe to an equivalent unit of space in an environment consisting of only four *spatial* dimensions. Additionally, because the velocity of light is constant it is possible to defined a one to one correspondence between his spacetime universe and one made up of four *spatial* dimensions.
In other words, by mathematically defining the geometric properties of a spacetime universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining his spacetime universe in terms of the geometry of four *spatial* dimensions.
This gives one the ability to derive the properties of an electromagnetic wave and understand its movement in terms of the spatial displacement that would be created by its observed transverse wave characteristics.
For example, a transverse wave on the twodimensional surface of water moves through water because it causes a point on that surface to be become displaced or rise above or below the equilibrium point that existed before the wave was present. A force is developed by the 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. This results in a wave to move on the surface of the water.
Similarly, an energy wave on the "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension would cause a point on that "surface" to become displaced or rise above and below the equilibrium point that existed before the wave was present. This would result a wave moving on the "surface" of threedimensional space.
Therefore, classical wave mechanics, if extrapolated to four *spatial* dimensions tells us a force will be developed by the differential displacements caused by an energy wave moving on a "surface" of threedimensional space with respect to a fourth *spatial* dimension that will result in its elevated and depressed portions moving towards or become "attracted" to each other causing it to move through space.
This defines the causality of the attractive forces of unlike charges associated with the electromagnetic wave component of a photon in terms of a force developed by a differential displacement of a point on a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension.
However, it also provides a classical mechanism for understanding why similar charges repel each other 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 threedimensional space manifold 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 the displacement will be greater for two charges than it would be for a single charge.
One can also define the directionality 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 is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls matter horizontally towards the apex of that displacement.
However, this means that one can define a physical model for the propagation of an electromagnetic field in terms of Einstein’s spacetime theory because, as was shown above when he mathematically defined its geometric properties in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining his theory in terms of the geometry of four *spatial* dimensions.
Yet, viewing it in terms of its spatial components also allows one to understand the mechanism responsible for the wave particle duality of a photon as observed in the Thomson’s double slit experiment and why electromagnetic energy always presents itself as a particle when it strikes the detector in the that experiment.
For example, the article, "Why is energy/mass quantized?" Oct. 4, 2007 showed that one can use the Einsteinâ€™s theories to explain the quantum mechanical properties of an electromagnetic wave by extrapolating the rules of classical resonance in a threedimensional environment to an energy wave moving on â€œsurfaceâ€ of a threedimensional 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 an energy wave moving in four *spatial* dimensions.
The existence of four *spatial* dimensions would give the energy wave associated with a photon 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 would force the "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.
However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established in four *spatial* dimensions.
As was shown in that article these resonant systems in four *spatial* dimensions are responsible for the particle called a photon.
However, one can also use Einstein spacetime theories when viewed in their spatial equivalent to explain how the boundaries of the standing wave responsible for creating the resonant system that article indicated was responsible of a particles formation are created.
In classical physics a standing wave is created when the vibrational frequency of a source causes reflected waves from one end of a confined medium to interfere with incident waves from the source. This interference of the wave energy causes their peaks troughs to be reinforce in the volume they are occupying thereby creating a standing wave.
The confinement required to create a standing wave in spacetime or its equivalent in four *spatial* dimensions can be understood by comparing it to the confinement a point on the twodimensional surface of paper experiences when oscillating with respect to threedimensional space. The energy associated with the wave motion of that point would be confined to its twodimensional surface and would be reflected and interfere with the incident wave when reaches threedimensional space at its edge. Therefore, a standing would be created by its interaction with threedimensional space.
In other words, when a wave on the surface of a piece of paper encounters the third *spatial* dimension at its edge it is reflected back allowing a standing wave to be formed on its surface.
Similarly, an electromagnetic wave moving on the surface of threedimensional space would be confined to it and reflected back to that volume, similar to the surface of the paper if it was prevented from oscillating with respect to a four *spatial* dimensions or fourdimensional spacetime.
In other words, the interference caused by the confinement of an electromagnetic wave to threedimensional space, which is caused by it striking the detection screen in the Thomson’s double slit experiment results in the resonant standing wave to be formed in space called a photon.
That experiment is made up of "A coherent source of photons illuminating a screen after passing through a thin plate with two parallel slits cut in it. The wave nature of light causes it wave component to interfere after passing through both slits, creating an interference pattern of bright and dark bands on the screen. However, at the screen, the light "is always found to be absorbed as discrete particles, called photons".
When only one slit is open, the pattern on the screen is a diffraction pattern however, when both slits are open, the pattern is similar but with much more detail. These facts were elucidated by Thomas Young in a paper entitled "Experiments and Calculations Relative to Physical Optics," published in 1803. To a very high degree of success, these results could be explained by the method of Huygen ‘s Fresnel principle that is based on the hypothesis that light consists of waves propagated through some medium. However, discovery of the photoelectric effect made it necessary to go beyond classical physics and take the quantum nature of light into account.
However, the most baffling part of this experiment comes when only one photon at a time impacts a barrier with two opened slits because an interference pattern forms which is similar to what it was when multiple photons were impacting the barrier. This is a clear implication the particle called a photon has a wave component, which simultaneously passes through both slits and interferes with itself. (The experiment works with electrons, atoms, and even some molecules too.)"
Even more puzzling is why any attempts to measure which slit that electron passed through cause the interference pattern to disappear.
Yet, as mentioned earlier one can derive the outcome of this experiment by assuming that electromagnetic energy is propagated by a wave on the "surface" of a threedimensional space manifold with respect to a fourth spatial dimension instead of fourdimensional spacetime
For example, the reason why the interference patterns remain when only one photon at a time is fired at the barrier with both slits open or "the most baffling part of this experiment" is because, as was just shown it has an extended spatial volume which is directly related to the wavelength.
This means a portion of its energy can simultaneously pass both slits, if the diameter of its volume exceeds the separation of the slits and recombine on the other side to generate an interference pattern.
Additionally, one can also explain why the interference pattern disappears when a detector is added to determine which slit a photon has passed through. The energy required to measure which slit it passes through interacts with it causing the wavelength of that portion to change so that it will not have the same resonant characteristics as one that passed through the other slit Therefore, the energy passing thought that slit will not be able to interact, with the energy passing through the other one to form an interference pattern on the screen.
However, as was shown earlier one can also show the reason the interference pattern appears as a particle when electromagnetic wave contacts a detection screen is because striking it results in it being confined to threedimensional space instead of fourdimensional spacetime or four spatial dimensions, thereby creating a standing wave in either four spatial dimensions or four dimensional spacetime to be created.
In other words, it clearly shows the reason all forms of energy exhibit both wave and particle properties are because they are physically made up of waves in terms of Einstein’s Theory of Relativity.
The above discussion shows that Richard Feynman was right in assuming that Thomson’s double slit experiment provided a mechanism for understanding the wave particle duality of energy/mass because it clearly demonstrates their inseparability.
Additionally, it also provides an explanation how and why energy is propagated through space because it shows the quantum mechanical and wave properties of energy displayed in the double slit experiment can be understood if one assumes they are made up of a resonant system in a moving in a four dimensional spacetime manifold or on a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension in terms Einstein theories.
It should be remembered that Einstein’s genius allows us to choose whether to define an electromagnetic wave either a spacetime environment or one consisting of four *spatial* dimension when he defined its geometry in terms of the constant velocity of light.
Later Jeff
Copyright Jeffrey O’Callaghan 2020
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