There are many theories that attempt to explain what we observed in our three dimensional environment in terms of higher dimensions. However they all suffer from the same problem in that the existence of those higher dimensions are primarily based on abstract on mathematical models. The reason is because we as three dimensional beings are only able to observe objects in the three-dimensional environments we occupy. Therefore we must rely on mathematics to guide us in understanding how their existence influences what we observe in our world.
Many feel the most promising is called string theory, which attempts to define all of the observed properties of our universe in as many as ten dimensions.
However, as is pointed out on page 51 of Lee Smolin book "The Trouble with Physics" all attempts at unifying physics through extra dimensions suffer from the same problem. There are a few solutions that lead to the world we observe but there are many which do not. One has to set the initial conditions, which are found by observing our world to determine which solutions define what we observe. The use of this circular methodology means its validity is not based on its theoretical structure but on its flexibility.
In other words its validity is not based on connecting the observed properties of our environment to it but the randomly picking which the ones do the best job.
Einstein’s theories are very different in that they make specific predictions based on the existence of a single space-time 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 space-time because as with all multidimensional theories when Einstein derived the geometric properties of a space-time 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 space-time 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 doers not mean our universe is made up of four dimensional space-time 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 a experiment very similar to the one Arthur Eddington preformed that would resolve this ambiguity.
Einstein’s Theory of General Relativity tells 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 time only moves in one direction forward.
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 is one bases for assuming 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 three-dimensional space manifold with respect to a fourth *spatial* dimension as well as one in a space-time 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 backwards and forwards.
Therefore if the universe was made up of four *spatial* dimensions there should 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 posses an opposite electrical charge than its matter counterpart. Therefore it is logical to assume that it posses a gravitational field that is oppositely directed from that of matter.
An experiment has be 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 anti-atoms 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 space time or four *spatial* dimensions because as was mentioned earlier a universe physically composed of four dimensional space-time 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 space-time 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.
Copyright 2015 Jeffrey O’Callaghan
Vol. 3 — 2012
Quantum mechanics defines our observable environment only in terms of the probabilistic values associated with Schrödinger’s wave equation.
However it is extremely difficult to define a set of statements which explains how those probabilities are physically connected to it even though it has held up to rigorous and thorough experimental testing.
This may be the reason most physicists consider quantum mechanics only in terms of its mathematical formalization instead trying to understand the meaning of it in terms of the space-time environment we occupy.
For example in 1924 Louis de Broglie was the first to realize all particles are physically composed of a matter wave as the discovery of electron diffraction by crystals in 1927 by Davisson and Germer) verified. However in his paper, “Theory of the double solution“ he unsuccessfully attempted to define a physical interpretation of Schrödinger equation in classical terms of space and time.
As is pointed at his biography on the nobleprize.org web site in "1951, he together with some of his younger colleagues made another attempt, one which he abandoned in the face of the almost universal adherence of physicists to the purely probabilistic mathematical interpretation of, Bohr, and Heisenberg."
However the fact that no has been able to physically connect those probabilities to our environment does not change the fact that there must be one because if there wasn’t they could not interact with it to create the physicality of observable world upon which those probabilities are based.
As mentioned earlier Louis de Broglie and his colleagues tried unsuccessfully to find a physical interpretation of Schrödinger equation in classical terms of space and time.
However the reason for their failure may be due to the fact that it is related to the spatial not time dependent properties of the wave function.
If so one may be able to establish the connection by looking at it in terms of its spatial properties instead of the space-time one Louis de Broglie and his colleagues used.
Einstein gave us the ability to do this defined the geometric properties of space-time in terms of the constant velocity of light and a dynamic balance between mass and energy because that provided a method of converting a unit of time in a space-time environment of unit of space in four *spatial* dimensions. Additionally because the velocity of light is constant he also defined a one to one quantitative and qualitative correspondence between his space-time universe and one made up of four *spatial* dimensions.
The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions is one bases for assuming as was done in the article “Defining energy?” Nov 27, 2007 that all forms of energy 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.
This would have allowed Louis de Broglie to physically connect the probabilities associated Schrödinger equation to the quantum properties of a matter wave in terms of a physical or spatial displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension as was done in the article "Why is energy/mass quantized?" Oct. 4, 2007.
Briefly that article showed that one can do this by assuming they are caused by the formation of a resonant system on a "surface" of a three-dimensional space manifold with respect to fourth "spatial" dimension. This is because it showed the four conditions required for resonance to occur in a three-dimensional environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in one made up of four.
The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimension thereby fulfilling one of the requirements for classical resonance to occur.
These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.
However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or "structure" to be established on a surface of a three-dimensional space manifold.
Yet the classical laws of three-dimensional space tell us the energy of resonant systems can only take on the discontinuous or discreet energies associated with their fundamental or harmonic of their fundamental frequency.
However, these are the similar to the quantum mechanical properties of energy/mass in that they can only take on the discontinuous or discreet energies associated with the formula E=hv where "E" equals the energy of a particle "h" equal Planck’s constant "v" equals the frequency of its wave component.
In other words Louis de Broglie would have been able to physicality connect the the quantum mechanical properties of his particle waves to Schrödinger equation in terms of the discrete incremental energies associated with a resonant system in four *spatial* dimensions if he had assume space was composed of it instead of four dimensional space-time.
Yet it also would have allowed him to define the physical boundaries of a quantum system in terms of the geometric properties of four *spatial* dimensions.
For example in classical physics, a point on the two-dimensional surface of a piece of paper is confined to that surface. However, that surface can oscillate up or down with respect to three-dimensional space.
Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate “up” or “down” with respect to a fourth *spatial* dimension.
The confinement of the “upward” and “downward” oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries associated with a particle in the article "Why is energy/mass quantized?" Oct. 4, 2007
As mentioned earlier in the article “Defining energy?” Nov 27, 2007 showed 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.
However assuming the energy associated with Louis de Broglie particle wave is result of a displacement in four *spatial* dimension instead of four dimensional space-time as was done earlier would allows one to connect the probabilities associated with Schrödinger equation to the physicality of our observable environment we all live in.
Classical mechanics tell us that due to the continuous properties of waves the energy the article "Why is energy/mass quantized?" Oct. 4, 2007 associated with a quantum system would be distributed throughout the entire "surface" a three-dimensional space manifold with respect to a fourth *spatial* dimension.
For example Classical mechanics tells us that the energy of a vibrating or oscillating ball on a rubber diaphragm would be disturbed over its entire surface while the magnitude of those vibrations would decease as one move away from the focal point of the oscillations.
Similarly if the assumption that quantum properties of energy/mass are a result of vibrations or oscillations in a "surface" of three-dimensional space is correct then classical mechanics tell us that those oscillations would be distributed over the entire "surface" three-dimensional space while the magnitude of those vibrations would be greatest at the focal point of the oscillations and decreases as one moves away from it.
As mentioned earlier the article “Why is energy/mass quantized?” shown a quantum particle is a result of a resonant structure formed on the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
Yet Classical Wave Mechanics tells us resonance would most probably occur on the surface of the rubber sheet were the magnitude of the vibrations is greatest and would diminish as one move away from that point,
Similarly a particle would most probably be found were the magnitude of the vibrations in a "surface" of a three-dimensional space manifold is greatest and would diminish as one move away from that point.
This shows how one can physically connect the probabilities associated Schrödinger wave equation to our observable environment by redefining it in terms of four *spatial* dimensions.
It should be remember Einstein’s genius allows us to choose to define a quantum system in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories thereby giving us a new perspective on the probabilistic properties of a quantum environment and how they physically connected to our observable universe.
Copyright Jeffrey O’Callaghan 2015
Vol. 3 — 2012