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.

Eventually theorists came up with three sorts of explanations for what has come to be called Dark Energy.  Maybe it was a result of a long-discarded version of Einstein’s theory of gravity, one that contained what was called a “cosmological constant.” Maybe there was some strange kind of energy-fluid that filled space. Maybe there is something wrong with Einstein’s theory of gravity and a new theory could include some kind of field that creates this cosmic acceleration. Theorists still don’t know what the correct explanation is, but they have given the solution a name. It is called dark energy.

However it can be shown that the currently accepted version of Einstein’s General Theory of Relative not a discarded one can explain why the universe expansion is accelerating.

However one of the difficulties in integrating the expansive force called Dark Energy into Einstein’s space-time universe is that observations tell us that three-dimensional space is expanding towards a higher spatial dimension not a time or space-time dimension.  

Therefore to explain the observed spatial expansion of the universe one would have to assume the existence of a fourth *spatial* dimension in addition to the three spatial dimensions and one time dimension that Einstein’s theories contain.

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

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 that equation  he provided a method of converting a unit of energy he associated with time in a space-time universe to a unit of space in one consisting of only four *spatial* dimensions.  Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a quantitative 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 quantitatively derive the spatial properties of energy in a space-time universe in terms of four *spatial* dimensions is one the bases of assuming as was done in the article “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.  In other words one can use Einstein’s equations to quantitatively define energy in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimensions.

We know from the study of thermodynamic that energy flows from areas of high density to area 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 sounding it and that the force associated with that expansion will decline as its surface spread out.

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

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

Yet this means similar to the two dimensional surface of the water in the pool three-dimensional space will accelerate and flow or expand outward in the four dimensional environment surround it and that the force associated with that it will decline as it surface increases. 

This shows one can explain what the force called dark energy is and why it is causing the accelerated expansion of the universe in terms of the geometry of four *spatial* dimension.

However it should be remembered this solution was derived directly from Einstein’s current General Theory of Relativity not a discarded one.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

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One is it that it allows one to understand why the universe must be flat in terms of our everyday experiences.

Einstein gave us this ability when he used the velocity of light to define the geometric properties of space-time because it allows one to convert a unit of time associated with energy in his four dimensional space-time universe to a unit of a space identical to those of our three-dimensional space.  Additionally because the velocity of light is constant it is possible to defined a universe made up of four *spatial* dimensions that makes predictions identical to those he had attributed to four dimensional space-time

For example a four dimensional space-time universe or one made up of only four *spatial* dimension can be geometrically open, closed, or “flat” and its shape is dependent on the quantity mass and energy within it.
In an opened universe, there is insufficient matter to halt the expansion initiated by the big bang.  This will result in a saddle shape or open universe, which will continue to expand forever.

In a closed universe, the gravitational potential of its mass is large enough to overcome the expansive forces of the big bang.  This will result in the universe having a spherical shape, which would be destined to collapse.

A universe will be flat if the attractive gravitational potential of matter just equals the expansive energy of the big bang.  This will result in the expansion slowing and only stop after an infinite amount of time has passed.

However, a recent observation by NASA’s WMAP satellite has shown the universe is flat to within a 2% margin of error.

But why the universe appears to be flat even after 14 billion years of expansion is still a mystery because a flat universe is like the top of a hill.  If you are a little away from it – a bit open or a bit closed – the expansion of the universe soon drives you far away from this value, just as a ball that is a short distance from a hilltop will roll down to the bottom.  Therefore, when the Universe was one second old, it must have deviated from flatness by less than one part in ten-thousand-trillion (10¹⁶).  This is a problem because it is hard to understand how the amount of mass and the energy associated with the expansion could have been adjusted to such precision.

To resolve this issue physicist Alan Guth proposed the universe underwent a very rapid period of expansion increasing its size by more than a trillion in the first few nano-seconds after its birth.  This resolves the flatness problem because its size is magnified by the inflation factor so much that locally it appears flat.

The reason for this can be understood by imagining what a two-dimensional creature who was living on a surface of a balloon would observe regarding the curvature of its surface.  If the size of the balloon were small compared to his field of vision he would notice that it surface was curved.  However, if its size was very large compared to his field of vision it would appear to him to be flat.

Inflation solves the flatness problem because it predicts the size of the universe increased so much in the initial expansion that the portion we can observe appears to flat.

However, another reason why the universe appears to be flat is because if the universe is a closed system, the first law of thermodynamics tells us the sum of the gravitational potential of its energy/mass and its kinetic or thermal energy is constant.

As was mentioned earlier Einstein’s genius allow us to defined a universe made up of four *spatial* dimensions that makes predictions identical to those he had attributed to one made up four dimensional space-time.

Therefore instead of deriving kinetic and gravitational energy in terms of unidirectional curvature or depression in a “surface” of a space-time manifold one can as was done in the in the article  “Defining potential and kinetic energy?” Nov. 26, 2007 one can derive both in terms of oppositely directed curvatures in “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  In other words if one defines gravity in terms of a depression in its “surface” one can derive kinetic energy as an in terms of elevation in it.

This differs from Einstein’s theoretical definition of energy in that he defines both gravitational and kinetic in terms of in terms of a unidirectional displacement in a four dimensional space-time manifold.

However, unlike Einstein’s definition: defining gravity and kinetic energy in terms of oppositely directed curvatures in space is not based entirely on theory because observations tell us that kinetic energy is oppositely directed from gravitational energy.  For example, the kinetic energy of an orbiting satellite is oppositely directed from its gravitational energy.

This difference is significant to our understanding of the shape or flatness of our universe because as mentioned earlier its curvature is related to the ratio of total gravitational potential of its energy/mass to the total kinetic energy of its expansion.

This is because the universe is a closed system with respect to its energy/mass the first law of thermodynamics tells us there must exist a 1 to 1 correspondence between the gravitational potential of the universeâ€s energy/mass and the oppositely directed kinetic energy associated with its expansion because all of its expansive energy must originate from within its energy/mass.  This 1 to 1 ratio between gravitational potential and kinetic energy will be maintained throughout the entire history of the universe because kinetic energy also posse gravitational potential that is equivalent to its energy content. 

However, as was shown in the article “Defining potential and kinetic energy?” this means there must be a 1 to 1 correspondence between the downward directed curvature associated with its gravitational potential and the upward directed one associated with its Kinetic energy.  Therefore, on a large scale the universe will appear to be flat because these oppositely directed curvatures will cancel each other.

This means one does not have to assume the universe underwent an inflationary period to explain why it is flat now and has remained that way if one assumes as is done here that the gravitational energy of energy/mass and its kinetic energy are related to oppositely directed curvatures in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This cannot be done in terms of four-dimensional space-time because time or a space-time dimension is observed to move only in one direction forward and therefore could not support the bi-directional movement required to define the asymmetry between gravitational potential and kinetic energy.

This concept of a zero energy universe may sound strange to many, but it is rather simple to understand.  A ball thrown up in the air has two forms of energy: kinetic and gravitational potential.  If kinetic energy were considered as positive, the potential energy, due to the gravitational pull of the Earth, would be negative.  If the positive portion of the energy beats the negative portion, the ball will escape from Earth.  If the negative energy is greater, it will return.  If the total energy is precisely zero the ball will barely escape – slowing to a stop when it is infinitely far away.

Another way of understanding this concept compare it to the effect crumpling a piece of paper has on its overall flatness. 

Our experiences with a  piece of paper shows us that if one crumples one that was original flat and views its entire surface the overall magnitude of the displacement caused by that crumpling would be zero because the height of it above its surface would be offset by an oppositely directed one below its surface.  Therefore, if one views its overall surface only with respect to its height its curvature would appear to be flat.

Similarly, if the gravitational potential of the universe’s energy/mass is oppositely directed form that of its kinetic energy the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension would appear to be flat because, similar to a crumpled piece of paper the “depth” of the displacement below its “surface” caused by it would offset by the “height” of the displacement caused by its kinetic energy.

Therefore, due to the asymmetry between the gravitational potential of energy/mass and its kinetic energy in a closed system we call the universe one can understand why it will appear to be “flat” throughout its entire history based on the first law of thermodynamics and our experiences.

Later Jeff

Copyright 2008 Jeffrey O’Callaghan

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