Ockham’s razor is the idea that, in trying to understand something, getting unnecessary information out of the way is the fastest way to the truth or to the best explanation.
For example Einstein’s General Theory of Relativity is based on the relative simple concept of a curvature in a spacetime metric. Granted the math required to determine the gravitational forces on an object can be very complicated and not easy for many to understand however understanding or visualizing how a curvature in spacetime can cause objects to accelerate is relative easy to do. This is because one can form a relatively simple physical image of it based on how objects such as a ball is accelerated on a curved two dimensional surface on the earth and them extrapolating that to a curvature in a spacetime metric.
However, even though in 1917, he added a cosmological constant to his equations which some fell would provide one of simplest mathematical explanations for Dark energy it is difficult for many to conceptually integrate it with the physical imagery that is provided by his theory.
Yet, this may be due to the fact that Einstein chose to define gravity in terms of time or a spacetime dimension while the accelerative forces of Dark Energy are related to the spatial properties of an expanding universe.
In other words, as Ockham pointed out the best way to understand it would be to eliminate time or the spacetime dimension from his general theory of gravity and replace it with spatial one because as was just mentioned our universe is not expanding through time dimension therefore it is not necessary to our understanding of its spatial expansion.
Einstein gave us the ability to do this he derived the physical properties of a gravity in a spacetime environment in terms mass and energy and the constant velocity of light because that provided a method of converting a unit of time in a spacetime environment with unit of space in four *spatial* dimensions. Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his spacetime universe and one made up of four *spatial* dimensions.
A Discussion on General Relativity by Students of John Wheeler and Bob Dicke 
This fact that one can use Einstein’s theories to qualitatively and quantitatively derive the spatial properties of energy in a spacetime 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 threedimensional space manifold with respect to a fourth *spatial* dimension.
In other words one can not only use Einstein’s equations to quantitatively and qualitatively derive how energy interacts with time in a spacetime dimension but also how it would interact with its spatial equivalent in four spatial dimensions.
We know from the study of thermodynamics that energy flows from areas of high to ones with 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 twodimensional surface of the water will flow or expand and accelerate outward towards the threedimensional environment sounding it.
Yet we know from observations of the cosmic background radiation that presently our threedimensional 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 threedimensional "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.
Similarly if the "surface" of a threedimensional manifold was elevated with respect to a fourth *spatial* dimension as Einstein tell us as it would be if one redefined his spacetime universe in terms of four spatial dimension then it would be accelerated outward for the same reason as how the water in a pool whose sides had collapsed.
In other words one qualitatively understand the casually of the accelerated expansion of our universe in term of the physical image of water accelerating out of collapsed pool.
Some may feel that this is an over simplification of what appears on the surface to be a rather complex phenomena such as Dark Energy but is no more simplistic that the one use to help us understand how gravity works in a spacetime environment. Granted the math behind this concept may be complex and difficult to understand as it is with the gravitational curvature in spacetime however that does not mean that we cannot use it to understand its causality.
It should be remember that Einstein’s genius and the symmetry of his mathematics allows us to choose whether to define the forces associated with gravity and dark energy in either four *spatial* dimensions or four dimensional spacetime.
Later Jeff
Copyright 2016 Jeffrey O’Callaghan
31
In 1928 Paul Dirac developed through complex mathematical calculations a theory that integrated quantum mechanics, used to describe the subatomic world, with Einstein’s Special Relativity, which says nothing travels faster than light.
However, he soon realized his equations not only worked for an electron with negative charge. It also worked for a particle that behaves like an electron with positive charge.
In other words, they predicted something entirely new to science – antiparticles.
In 1932, Carl Anderson a professor at California Tech experimental confirmed their existence when he observed cosmic rays in a cloud chamber leaving a track which could have only been created by something with a positively charged, and with the same mass as an electron."
However, even though the environment containing antimatter is defined only in terms of the abstract prosperities of mathematics its existence can tell us a great deal about the physical geometry of our universe.
For example, Einstein’s theories make very specific predictions based on the existence of a single spacetime environment that if found not to occur would invalidate it.
For example, his theory tells us that light should bend as it passes by a massive object.
If this was not observed his theory would have to be discarded.
However, 1919 Arthur Eddington lead an expedition to photograph the total eclipse of the Sun. The photographs revealed stars whose light had passed near sun had been bent exactly as Einstein had predicted. The experiment was repeated in 1922 with another eclipse with the same confirmation.
Additionally in past century, since he proposed his theory there has not been any observations of our macroscopic universe that disagree with any of its predictions.
Even so this does not mean that we should assume that our universe is physically made up of four dimensional spacetime because, as with all multidimensional theories when Einstein derived the geometric properties of a spacetime universe in terms of the constant velocity of light he also define another one with identical properties in terms of four *spatial* dimensions.
In other words, by defining the geometric properties of spacetime in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining its time related properties in terms of only four *spatial* dimensions.
As was mentioned earlier the fact that light bends as it passes by massive objects does not mean our universe is made up of four dimensional spacetime because the symmetry of equations used to make that prediction also predicts one made up of only four *spatial* dimensions will do the same.
Therefore, the fact that light bends as it passes by a mass cannot be used to eliminate that possibility.
However, there is an experiment very similar to the one Arthur Eddington preformed that would resolve this ambiguity.
Einstein’s Theory of General Relativity tells us that objects that create gravitational field cause time to "move" slower. However, due to the symmetry of his equations one could also say that time slowing down results in the formation of a gravitational field. Therefore, one must assume that a gravitational field must always be attractive because observations indicate that the passage of time can only be slowed not accelerated.
However, the fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the energy he associated with gravity in terms of four *spatial* dimensions means as was done in the article “Defining energy?” Nov 27, 2007 that it can be derived in terms of a spatial displacement in a "surface" of a threedimensional space manifold with respect to a fourth *spatial* dimension as well as one in a spacetime dimension.
However, unlike time, which is observed to only move in one direction forward observations tell us that we can move in spatially in two directions up down or backwards and forwards.
Therefore, if and only if the universe was made up of four *spatial* dimensions could there exist a form of mass that posses a negative gravitational potential.
One candidate for such a mass is antimatter. We know from observations that in it has an electrical charge that is oppositely directed from its matter counterpart. Therefore, it is possible that it has a gravitational field that is oppositely directed from that of ordinary matter.
An experiment has been proposed that could determine if this is indeed true.
As describe in the New Scientist article "Antimatter mysteries 3: Does antimatter fall up?" Apr 29, 2009, it involves using uncharged particles to prevent electromagnetic forces from drowning out gravitational effects. It will first build highly unstable pairings of electrons and positrons, known as positronium, then excite them with lasers to prevent them annihilating too quickly. Clouds of antiprotons will rip these pairs apart, stealing their positrons to create neutral antihydrogen atoms.
Pulses of these antiatoms shot horizontally through two grids of slits will create a fine pattern of impact and shadow on a detector screen. By measuring how the position of this pattern is displaced, the strength – and direction – of the gravitational force on antimatter can be measured.
In other words, there is an experiment that could determine if our universe is physically composed of four dimensional spacetime or four *spatial* dimensions because as was mentioned earlier a universe physically composed of four dimensional spacetime cannot support a negative gravitational potential while one made up of four *spatial* dimensions can.
Yet if found to be true it does not mean that Einstein’s theories are invalid because his theories and predictions were based on pure mathematics and as mentioned earlier a universe consisting of four dimensional spacetime and four *spatial* dimensional are mathematically are equivalent in every respect.
However, it would require us to rethink our understanding of the physical geometry of our universe and the causality of gravitational forces.
Later Jeff
Copyright Jeffrey O’Callaghan 2016
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