Einstein was able to define the origins of gravity and potential energy associated with rest mass in terms of curvature or the changing geometry of a space-time manifold but he did not tell us anything about the causality of kinetic energy.

For example he told us that gravity is caused by curvature or distortion in a space-time manifold however he did not due the same for kinetic energy associated with constant relative motion.

Yet its casualty is central to our understand of our universe because it along with gravity and Dark Energy are assumed to be responsible for evolution of the universe.

However one reason may be because kinetic energy of relative motion is constant with respect to both distance and time.  In other words the energy of an object in constant motion always moves the same distance in a given time interval.

As was just mentioned one of the difficulties in defining the kinetic energy in terms of the space-time environment defined by Einstein is that its magnitude is determined only by the distance an object moves through space within a constant time interval.  In other words it is only dependent on the spatial not on time parameters of its movement.

However redefining Einstein’s space-time universe in terms of its spatial properties would allow one to define the energy of constant motion in terms of those spatial properties.

Einstein gave us the ability to do this when he define the displacement or curvature he associated with the potential energy of rest mass in terms of the equation E=mc^2 and the constant velocity of light because that gave us the ability to redefine a unit of time in his space-time universe to an equivalent unit of space in a universe consisting of only four *spatial* dimensions.

This fact is the bases for assuming as was done in the article “Defining energy” Nov. 26, 2007 that all forms of energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Using those concepts one could define the energy of rest mass in terms of magnitude of a physical displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension cause by a objects mass while defining the kinetic energy of two masses in relative motion in terms of the spatial displacements cause by that motion. 

In other words the “surface” of three dimensional space associated with objects in relative motion would exist on different three dimensional plains with respect to a fourth *spatial* dimension.

For example magnitude of kinetic energy of two masses would be defined the relative magnitude of their displacement in “surface’ of three dimensional space with respect to a fourth *spatial* dimension 

In other words it allows one to mathematically derive the causality of relativistic motion in terms of the geometry of either four *spatial* dimensions or four dimensional space-time space because when Einsteinâ€s defined his space-time universe in terms of energy/mass and the constant velocity of light he allow to chose one or the other and get the same end results.

Einstein in his General Theory of Relativity derived the causality of gravity in terms of a curvature or displacement in a space-time manifold however in his Special Theory of Relativity he only told us the effects of relative motion has on an environment not what caused the energy of that motion.  However as was shown above one can use his theoretical concepts to mathematically define its casual in terms physical displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension thereby give a more complete understanding of the relativistic environment encompassed by his theories.

This is significant because understanding the spatial properties of relative motion is the first step in understanding how Newton’s laws of motion are physically connected to Einstein’s space-time environment.

Later Jeff

Copyright 2018 Jeffrey Oâ€Callaghan

The post What is the origin of kinetic energy and why should we care? appeared first on Unifying Quantum and Relativistic Theories.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Later Jeff

Copyright 2015 Jeffrey O’Callaghan

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

For example, if the walls of an above ground pool filled with water collapse the elevated two-dimensional surface of the water will flow or expand and accelerate outward towards the three-dimensional environment surrounding it while the force associated with that expansion decreases as it expands.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Later Jeff

Copyright 2015 Jeffrey O’Callaghan

The post Why the “Big Rip” cannot happen appeared first on Unifying Quantum and Relativistic Theories.

We think so.

The Big Bang theory postulates the universe emerged from a singularity and is presently expanding from the tremendously hot dense environment associated with it.  Additionally it assumes the momentum generated by the heat of that environment is sustaining its expansion.

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

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

However the proponents of the big bang model would like us to believe that it was created out of nothing which would be a violation of that law.

Granted some physicist’s have devised a cleaver and what some believe to be a contrived or “adhoc” mathematical solution to this problem by postulating the existence of an inflation field even though there is absolutely no experimental or observational evidence to support its existence.

However there is another explanation for origin of the energy powering the expansion of our universe which does not violate any of the accepted physical laws, makes a great deal more sense than assuming its expansive energy originated out nothing and would give us the ability to understand what came before the beginnings of our present universe.

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

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

As mentioned earlier the law of conservation of energy/mass tells us that the kinetic energy of the universeâ€s energy/mass cannot exceed its gravitational contractive properties.  Therefore, at some point in time the gravitation contractive potential of its energy/mass must exceed the kinetic energy of its expansion because as mentioned earlier not all of that energy is directed towards its expansion. Therefore at that point, in time the universe will have to enter a contractive phase.

(Many physicists would disagree because recent observations suggest that a force called Dark energy is causing the expansion of the universe accelerate.  Therefore they believe that its expansion will continue forever.  However, as was shown in the article “Dark Energy and the evolution of the universe” Oct. 1 2012 if one assumes the law of conservation of mass / energy is valid, as we have done here than the gravitational contractive properties of its mass equivalent will eventually have to exceed its expansive energy and therefore the universe must at some time in the future enter a contractive phase.)

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

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

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

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

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

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

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

Many cosmologists do not accept the cyclical scenario of expansion and contractions because they believe a collapsing universe would end in the formation of a singularity similar to the ones found in a black hole and therefore, it could not re-expand.

However, according to the first law of thermodynamic the universe would have to begin expanding before it reached a singularity because that law states that energy in an isolated system can neither be created nor destroyed

Therefore because the universe is by definition an isolated system; the energy generated by its gravitational collapse cannot be radiated to another volume but must remain within it. This means the radiation pressure exerted by its collapse must eventually exceed momentum of its contraction and therefore it would have to enter an expansion phase because its momentum will carry it beyond the equilibrium point were the radiation pressure is greater that the momentum of its mass. This will cause the mass/energy of our three-dimensional universe to oscillate around a point in the fourth *spatial* dimension.

This would be analogous to the how momentum of a mass on a spring causes it spring to stretch beyond its equilibrium point resulting it osculating around it.

There can be no other interoperation if one assumes the validity of the first law of thermodynamics which states that the total energy of our three dimensional universe is defined its mass and the momentum of its components. Therefore, when one decreases the other must increase and therefore it must oscillate around a point in four spatial dimensions.

The reason a singularity can form in black hole is because it is not an isolate system therefore the thermal radiation associated with its collapse can be radiated into the surrounding space. Therefore, its collapse can continue because momentum of its mass can exceed the radiation pressure cause by its collapse in the volume surrounding a black hole.

If this theoretical model is valid the heat generated by the collapse of the universe must raise the temperature to a point where protons and neutrons would become dissociated into their component parts and electrons would be strip off all matter thereby making the universe opaque to radiation.  It would remain that way until it entered the expansion phase and cooled enough to allow matter to recapture and hold on to them.  This Age of Recombination, as cosmologists like to call it is when the Cosmic Background Radiation was emitted.

One could quantify this theories model by using the first law of thermodynamics to calculate the temperature of the universe when the radiation pressure generated by its gravitational collapse exceeds the momentum of that collapse and see if it if it great enough to cause the complete disassociation of the proton and neutron into their quark components as it must to account for their observed properties and that of the Cosmic back ground radiation.

However this provides physical connection to the previous cycle because of the feedback loop that would be an integrals part of the system describe above.

For example the mechanism outlined above would provide a negative feedback loop in terms of universeâ€s total mass because if it is too great the speed of its collapse will be faster due to its greater gravitational potential thereby causing the next cycle to begin at a higher temperature.  This will result in a faster expansion rate and therefore less time for mass to clump together to form stars and galaxies. While if its mass component is too small it would expand to a larger volume resulting a slower contraction resulting in the next cycle beginning at a lower temperature which means its expansion will be slower allowing for the creation of more mass.

In other words it gives us a way of determining what came before the beginning of our universe because it shows that some of its physical properties such as the ratio of its total mass to its expansion rate can be understood in terms of what it was before it began.

Later Jeff

Copyright Jeffrey O’Callaghan 2013

The post What came before the Big Bang appeared first on Unifying Quantum and Relativistic Theories.

One of them is that it would give explanation of why time is dilated in bodies that are in relative motion or a gravitational field that is more consistent with its observed properties than is provided by the space-time concepts of Albert Einstein’s Special and General Theories of Relativity. 

For example observations made by both physicists and non physicists alike suggests that time is only a non-physical measure of when in relation to other events a physical, chemical, and biological change take place similar to how a unit of length is a non-physical measure of the where in relation to other objects one is located in a three dimensional environment. This is because similar to time, length is not perceived as having the physical properties of matter or space but only as measurement of where one object is located relative to another. 

In other words observations regarding time suggest that it only has the non-physical properties associated with a measurement and not the physical properties of Einstein’s time or space-time dimension.
Additionally our perception of irreversibly of time or that it always moves in one direction, forward also appears to contradict the concept that it has physical properties because it is possible to reverse the position of an object in a spatial dimension whereas one cannot in a time or space-time dimensions.  For example, one can move an object to a different position with respect to where it was and then reverse the process and move it back to its original position three-dimensional space whereas one cannot in a move an object forward in a space-time dimension time and then move it back to its original position with respect to time.  Therefore observations suggest that a time or a space-time dimension does not share the physical properties associated with the spatial dimensions.

Therefore, defining a space-time dimension in terms of its physical properties as Einstein did does not appear to be consistent with the observation that time is irreversible.

However, this same observation, as was shown in the earlier article “Defining time” Sept 20, 2007 suggest that time may only be a non-physical a measure of the sequential ordering of the casualty of events because one cannot reverse the causality of an event without creating a new event thereby making it consistent with the perception of its irreversibility.

That article also showed why assuming time only has the non-physical properties of a measurement would provide an unambiguous definition of it that is more consistent with both physical and mathematical observations of time than defining it in terms of the physical properties of a dimension as Einstein had done.

It also points out one of the most obvious observational flaws with Einstein’s assumption of the physicality of time or a space-time dimension is that no one has ever observed any of its physical properties and therefore it is difficult to explain or understand how it can interact with the physicality of three-dimensional space to cause gravity. 

Yet Einstein gave us a way of translating the non observable physical properties of time to the physically observable properties of a spatial dimension when he defined its geometry in terms of the constancy of the velocity of light.

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

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

Observations of our environment tell us that all forms of mass have a spatial component or volume and because of the equivalence defined by Einstein’s one must assume that energy also must have spatial properties.

As mentioned earlier Einstein equation E=mc^2 tell us there is a dynamic relationship between the geometric properties of our universe and mass/energy in that when one coverts mass to energy in a closed three-dimensional *spatial* environment, the space it is made up of expands while if one coverts energy to mass that environment contracts.  Yet it is difficult to understand how three-dimensional space can both expand and contract in a space-time universe because our experiences tell with time tells us that it only moves in one direction forward.  However it is easy to understand how it could in one consisting of four *spatial* dimension because our experiences it tell us that we can move in two direction in a spatial environment up down forwards of backwards.

The fact that one can use the equation E=mc^2 to qualitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is one the bases of assuming as was done in the article “Defining potential and kinetic energy?” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  In other words one can use Einstein’s equations to quantitatively and conceptually define energy in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimensions.

However, as was shown in the article “Gravity in four spatial dimensions” Dec. 01, 2007 one can use the same technique to derive a one to one qualitative and quantitative correspondence between the space-time curvature Einstein postulated was responsible for gravity and the curvature in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension that article postulated was responsible for it.  Additionally because they are both based on constancy of the velocity of light the relative magnitude of the “curvature” caused by given quantity of energy/mass in a space-time universe and one consisting of fourth *spatial* dimensions will be identical.  In other word the magnitude of a gravitational field in both a space-time environment and one of four *spatial* dimensions would be dependent on the quantity of energy/mass that environment contained.

However as was mentioned earlier a worldview based on the existence of four *spatial* dimension instead of four dimensional space-time has an advantage in that it also allows one to explain time dilation and predict relativistic properties of space, time, mass, and energy in terms of the observable spatial properties of a three-dimensional environment instead of as Einstein did of using the unobservable ones of a time or a space-time dimension.

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

It is difficult to understand why in terms of four dimensional space-time because as mentioned earlier all forms of energy in a space-time environment are defined in terms of a curvature in its geometry. However because time is observed to only move in one direction this curvature for both kinetic and gravitational energy must always be in the same direction thereby making it difficult to explain why they oppose each other.

However this is not a problem if one defines energy as was done in the article “Defining potential and kinetic energy?” in terms of the geometry of four *spatial* dimensions because we observe that we can move in two direction upwards and downwards or backwards and forwards in a *spatial* dimension.

Therefore one can explain and understand why kinetic and gravitational energy oppose each other by deriving them in terms of oppositely directed curvatures in “surface’ of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However this means according the concepts outlined above the total energy/mass of an object would be equal to the sum of the absolute value of the displacements in a “surface” of a three-dimensional space manifold caused by the rest mass of an object and that caused by its relative velocities.  This is because the total curvature associated the kinetic and gravitational energy in a given volume of space would be equal to sum of the difference between their magnitudes and because there are opposite or negatively directed with respect to the each other one would have to add their absolute magnitudes to get the total energy/mass in a given volume space.

Therefore, the total energy/mass of an object would be dependent on its relative motion because one must add the energy/mass associated with its motion to its rest energy/mass.

However defining the gravity and kinetic energy in terms of oppositely directed curvatures in four *spatial* dimensions not only defines the reason for the mass increases associated with relative velocities that is more consistent with observations but it also provides an more consistent explanation for the casualty of time dilation and the length foreshortening observed in gravitational and moving reference frames based on physical observations made in a three-dimensional environment.

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

Assume that two “2 dimensional 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 two-dimensional translation of the three-dimensional curvature generated by the pencil.

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

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

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

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

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

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

Therefore, according to that definition time will become dilated in reference frames that are in relative motion because the curvature generated in three-dimensional space by its motion will cause three-dimensional beings in that reference frame to view the distance between events to be longer in than it would be for an observer who is outside of it.  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 mentioned earlier article “Defining potential and kinetic energy?” showed both “gravity” and kinetic energy can be define in terms of a curvature in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension as well as a curvature in a space-time manifold.

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

However it would also provide a mechanism for why time dilated with gravitational field that is consistent with our observations of three-dimensional space.

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

This shows one can theoretically define a mechanism responsible for both the time dilation and foreshortening of the length associated with objects in relative motion or in a gravitational field based on physical observations of a three-dimensional environment that is fully consistent with the qualitative and quantitative predictions of relativity by assuming space is composed of four *spatial* dimensions.

However as was mentioned earlier a worldview based on the existence of four *spatial* dimension instead of four dimensional space-time has an advantage in that it also allows one to derive them by extrapolating the observable spatial properties of a three-dimensional environment to a fourth *spatial* dimension instead of as Einstein did by extrapolating the unobservable property of time to a space-time dimension.

Later Jeff

Copyright 2012 Jeffrey O’Callaghan

The post Time dilation in four *spatial* dimensions appeared first on Unifying Quantum and Relativistic Theories.

Unfortunately there is absolutely no direct observational or experiment evidence supporting its physicality. 

In fact one of the most persistent observations regarding time is that it is not directly perceived in terms of a physical entity such as matter or space but only as a measure of an irreversible physical, chemical, or biological change in a physical system.

However this suggests as was shown in the article “Defining what time is.” Sept 20, 2007 time may only be a non-physical measurement of the sequential ordering of a physical, chemical, or biological change in space similar how a unit of length is a non-physical measure of a change in the ordering of the position of an object in space. This is because similar to time, length is not perceived as matter or space but only as a non-physical measure of where an object is located with respect to a given point in space.

Yet this appears to contradict the assumption that time or a space-time dimension is or has the properties of a physical entity because as mentioned earlier most of us do not perceived it as having the physical properties of matter or space.

However, what is even more damaging to the concept that it has physical properties is that they are not required to define relativistic properties of our universe as many physics seem to think.

This is because Einstein gave us a way of converting a unit of time in a space-time dimension to unit of space in four *spatial* dimensions when he used the constant velocity of light to define its geometric properties.  Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

However using Einstein’s equations as is suggested above to redefine the universe in terms of four *spatial* dimensions instead of four dimension space-time would allow one to understand its relativistic properties in terms of the observable properties of the spatial dimensions while maintaining the same quantitative predictive powers as those associated with a space-time dimension because as mentioned earlier there is a one to one correspondence between them.

For example  the article “Embedded dimensions” Oct 22, 2007 showed that one can derived all forms of energy including gravitational and kinetic in terms of a displacement or curvature in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension and why one must assume that kinetic energy is a result of an oppositely directed displacement in its “surface” than the one associated with gravity.

The conclusion that the causality of kinetic energy is a result of an oppositely directed displacement in a “surface” of three-dimensional space with respect to the one associated with gravity is based on the observation that they are oppositely directed.  For example, the kinetic energy of an orbiting satellite is oppositely directed with respect to the gravitational energy associated with the planet it is orbiting.  Therefore, if one defines gravity in terms of a “depression” in a “surface” of a three-dimensional space manifold with respect to fourth *spatial* dimension one should define kinetic energy in terms of a oppositely directed “elevation” in that “surface”.

However this means according the definitions given in the article “Embedded dimensions” the total energy/mass of an object would be equal to the sum of the displacements of a “surface” of a three-dimensional space manifold caused by the rest mass of an object and that caused by its relative velocity.

Therefore, the energy/mass of an object would be dependent on its relative motion because one must add the energy of its motion to its rest energy/mass.

This defines the mechanism responsible for why the energy/mass of an object increases when viewed by an observer who is in relative motion to it in terms of the geometry of four *spatial* dimensions.

The following analogy can be used to understand and define the relativistic properties length and time

Assume that 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 two-dimensional translation of the three-dimensional curvature generated by the pencil.

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

Similarly, because three-dimensional beings could only “view” a three-dimensional translation of a “curvature” or displacement in four *spatial* dimension caused by the 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 two dimensional creatures mentioned earlier will view the others “time” as moving slower because the three-dimensional curvature in the paper makes the distance between events longer than the two dimensional translation of those events.  Therefore, it will take longer for events “move” through the curvature in three-dimensional space relative to the time it would take for them to move along two dimension translation of that surface.

Earlier it was mentioned that the magnitude of the displacement or “curvature” an object generates in a fourth *spatial* dimension is dependent on its velocity.

However as mentioned earlier, we have defined time as only being the measure or the “distance between” the sequential ordering of the causality of an event.

Therefore time will become dilated in reference frames that are in motion because of the curvature generated in three-dimensional space by its relative motion, three-dimensional beings in that reference frame will view the distance between events to be longer in it than it would if they were in motion relative to it.  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 because events in those reference frames will have a greater separation.

The velocity of light is constant despite the relative motion of an observer because the foreshortening or shortening of the length or distance the light travels is proportional to the motion of the observer.  Therefore, the velocity of light will be constant in all reference frames despite the relative velocities of the observers to those reference frames because velocity is defined in terms of distance divided by time.

It should be remember this scenario applies to all forms of energy including gravitational because, as the article “Embedded dimensions” Oct. 22, 2007 showed, three-dimensional beings perceive energy in terms of the magnitude of a “curvature” in “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

The Lorentz transformations derived from this theoretical model will take on the same form as the Lorentz transformations derived from Relativity.

This is because this theoretical model postulates that a displacement or curvature in “surface” of a three-dimensional space manifold, with respect to a fourth *spatial* dimension caused by the gravitational or kinetic energy of an object is proportional to the velocity of light.

Therefore, because both Relativity and the above mechanism predict a physical shortening of length and a slowing of time are related to the geometry of space, the form of the Lorentz transformations associated with the foreshortening length and slowing of time will be identical for both of these models.

However, this theoretical model differs from that of Relativity’s in that it defines the magnitude of a foreshortening of length and a slowing or dilation of time in terms of a “curvature” in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension instead of curvature in four dimensional space-time manifold.

As mentioned earlier the article “Defining energy” derived the mechanism responsible for gravity in terms of a “curvature” in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, it was shown earlier that a curvature in a “surface” of a three-dimension space manifold with respect to a four *spatial* dimension was responsible for length foreshortening and time dilation.

Therefore, because both gravitational and the kinetic energy of relative motion are derived from a common “curvature” in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension they will have a similar effect on physical properties of length and time.

This means both Relativity and this paper predict an observer in a gravitational field will measure the length of an object to be shorter and passage of time to be slower with respect to an observer who is located outside of a gravitational field.

However, as mentioned earlier this paper defines this shortening of length and slowing of time in a gravitational field in terms of four *spatial* dimension instead of four-dimensional space-time manifold.

The “relative” characteristics of a “curvature” in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension associated with kinetic and gravitational energy would also make it impossible for an observer to determine if an acceleration is caused by gravitational or kinetic energy such as that from an exhaust of a rockets engine.

This is because the mechanism defined above indicates the magnitude of a force associated with both gravitational and kinetic energy is related to the absolute magnitude of a “curvature” a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, because a three-dimensional observer can only observe the three-dimensional effects of a curvature in four *spatial* dimensions he or she could not determine whether he or she is in a gravitational field or an accelerated reference frame.

This means the concepts contained in this article would make identical qualitative and quantitative and predictions with respect to the relativistic properties of space and time and the inability to determine the casualty of acceleration in terms of the physical properties of four *spatial* dimensions instead of four dimensional space-time because they are based on the analytical and qualitative properties of Einstein’s experimentally verified equation E=mc^2.

As mentioned earlier the primary reason why most scientist assume the physicality of time or a space-time dimension is because the foundation of modern cosmology is based on the physical existence of time or Einstein’s space-time dimension.

Yet as this article shows one can make the same quantitative and qualitative predictions regarding them by assuming they are caused by a physical interaction between the third and fourth *spatial* dimension and not one made up of time.

However this article also suggests the reason why scientists are unable physically observe time or a space-time dimension is because its existence is based on the illusion that it is responsible for the relativistic properties of space, time and energy/mass.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

The post The illusion that is time. appeared first on Unifying Quantum and Relativistic Theories.

One is that it would allow for the theoretical derivation of the relativistic of properties of three-dimensional space and the inertial properties of energy/mass in terms of a four dimensional Newtonian universe.
In the article “Defining energy” Nov 27, 2007 is was showed all forms of energy including kinetic and gravitational can be derived in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension while the article “Defining time?” Sept. 20, 2007 showed defining it only in terms of a measure of distance between the sequential ordering of the causality of events would provide an unambiguous definition that is consistent with both physical and mathematical observations of it. 

However, as was shown in the article “Embedded dimension” Oct. 22, 2007 we as three-dimensional beings can only perceive the cord of an arc generated by a displacement in a “surface” of three-dimensional space with respect to a four *spatial* dimension. 

This means the Newtonian concept of absolute three-dimensional space would not exist in a universe consisting of four *spatial* dimensions because, as that article showed three-dimensional beings are only able to observe cord of the arc generated in a “surface” of three-dimensional space by gravity or the kinetic energy of a moving reference frame. Therefore because the cord of an arc is shorter than the arc itself, three-dimensional beings will view the distance between two points or events in those reference frames to be shorter than would be if they were not in relative motion or in a gravitational field.  Hence, the Newton concept of absolute length would not exist because length in all reference frames would be influenced by gravity or their relative velocities in a four dimensional environment.

However, the passage of time will also be affected in reference frames that are in relative motion or in a gravitational field if one defines it in terms of measure of the “distance between” the sequential ordering of the causality of an event as was done in the article “Defining time?” because the distance between events in them will be greater due to the curvature in three-dimensional space caused by their gravitational field or relative motion.

Therefore, time will become dilated in reference frames that are in motion or in a gravitation field because the curvature generated in three-dimensional space by the displacements those article associated with gravity and relative motion will cause the distance between events to be longer in it than it would be for an observer who is outside of it.  Therefore external observers will view time in each other’s reference frame to be moving slower with respect to their time because of the greater distance those events must travel.

Therefore, the Newtonian concept of absolute time would not exist in a universe consisting in a four *spatial* dimensions.

This shows how one can derive the relativistic properties of three-dimensional space in terms of a universe consisting four dimensional Newtonian space.

Yet one can also derive the causality of the classical concepts of inertia, mass and momentum by extrapolating the Newtonian laws of three-dimensional space to a fourth.

Isaac Newton defined inertia as being responsible for why an object at rest will remain at rest, and one in motion will remain in motion in a straight line at a constant speed.

In the article “Why Space-time?” Sept. 27, 2007 it was shown that one can derive the energy associated with the rest mass of an object or particle in terms of the “depth” of a displacement caused by a curvature in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Additionally it was shown one can derive the causality of all forces including gravitational in terms of an interaction of mass with the slope of a curvature in a “surface” of a three-dimensional space caused by the displacement.

(This curvature is analogous to a curvature in a four-dimensional space-time manifold Einstein theorized was the causality of accelerations.)

As mentioned earlier the article “Defining energy” derived the energy associated with the velocity of an object in terms of the displacement with respect to a fourth “spatial” dimension of a volume of three-dimensional space containing it.

Therefore, the inertia or momentum of an object would, according to the concepts presented in those articles be defined by the sum of the displacements in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension associated with its rest mass and its relative velocity.

The first component would be the displacement in a “surface” of a three-dimensional space associated with the rest mass of an object, whose magnitude as the article “Why Space-time?” showed is defined by the magnitude of its mass.  While second would be the momentum or the magnitude of a displacement that the article “Defining energy” showed was the casualty of the energy or momentum of its relative motion. (The momentum of an object at rest with respect to other objects is zero so the displacement of three-dimensional space with respect to those objects would also be zero.)

Therefore to define the total energy of an object or particle one would have to add the displacements in a “surface” of a three-dimensional space manifold associated with the energy of its rest mass to that associated with its relative motion.

However, as mentioned earlier the article “Why Space-time?” showed that all accelerations are caused by an object or particle interacting with a curved “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore, if the causality of the momentum inertia of a reference frame is a displacement of a “surface” of a three-dimension space manifold it would tent to stay rest or ones in motion would tend to stay in motion unless it interacted with a force or as the article “Why Space-time?showed a three-dimensional “surface” that was curved with respect to a fourth *spatial* dimension or a force.

This defines a causal link between the inertia, mass, momentum and force in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Additionally it allows one to understand the casualty of Isaac Newton law of inertia or why an object at rest will remain at rest, and an object in motion will remain in motion in a straight line at a constant speed by extrapolating his laws of three-dimensional space to a fourth.

Einstein could define the casualty of gravity but not inertia in terms of a four-dimensional space-time manifold because the “surface” of three-dimensional space can be curved but not displaced with respect to a space-time or a time dimension.

This shows how one can derive the relativistic and inertial properties of energy/mass in terms of a four dimensional Newtonian universe

Later Jeff

Copyright Jeffrey O’Callaghan 2011

The post The “Relativity” of a four dimensional Newtonian universe appeared first on Unifying Quantum and Relativistic Theories.