We have shown throughout this blog that there would be several theoretical advantages to defining the universe in terms of four *spatial* dimensions instead of four-dimensional space-time.
One is that it would allow physicists to derive a particles mass by extrapolating the laws of a three-dimensional environment to a fourth *spatial* dimension.
For the past 25 years, the Standard Model of particle physics has given us a complete mathematical description of the particles and forces that shape our world. It predicts with so much accuracy the microscopic properties of particles and the macroscopic ones of stars and galaxies that many physicists feel that it is the ultimate theory of matter and energy.
But as Charles Seife mentions on page 142 of his bookAlpha & Omega “Taken literally the plain vanilla form of the Standard model of particle physics does not say anything about particle mass at all: in fact if theorists try to put mass in to the equations of that model the equations blowup and become meaningless.”
In 1964 a British physicist Peter Higgs tried to resolve this issue by expanding on the ideas of American theoretical physicist Phillip Anderson and postulated that something called a Higgs field, which is mediated by the Higgs boson is responsible for endowing particles with mass.Â
However, since then considerable time and money have been spent looking for it without success even though physicists know where to look for it and the energy levels required to find it.
For example the Large Hardon Collider, the most expensive scientific instrument ever built was designed to reach those energy levels and yet even though it has been operating there for some time now it has not been found. This leaves physicists with the problem of deciding if they should keep looking for it or move beyond The Standard Model of Particle Physics to define “New Physics” that can incorporated mass into its theoretical structure.
As mentioned earlier one of the theoretical advantages to defining the universe in terms of four *spatial* dimensions instead of four-dimensional space-time is that it would allow one to derive a particles mass by extrapolating the laws of a three-dimensional environment to a fourth *spatial* dimension..
In the article “The “gravity†of four *spatial* dimensions” Dec. 15, 2007 it was shown it can be derived in terms of curvature in a “surface” of a three-dimensional space manifold with respect to a fourth “spatial” dimension and the rest mass objects such as particles, stars, or planets in terms of a geometric compression of three-dimensional space caused by a curvature in that “surface”.
This concept is similar to one presented in the General Theory of Relativity which defines a gravitational potential and mass in terms of a geometric curvature or compression in a four-dimensional space-time manifold.
But even though they are based on different geometries, they make identical predictions, as we have shown throughout this blog regarding the relativistic properties of space, time, mass, and energy and the equivalence between gravity and accelerated reference frames.
However, as mentioned earlier, one advantage to deriving the mass of a particle in terms of four *spatial* dimensions is that allows one to define it by extrapolating the laws of a three-dimensional environment to one consisting of four.
In 1924, Louis de Broglie theorized that all particles have a wave component. (His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.) But he abandon the attempt made in his paper “The Theory of the double solution” to interpret their wave properties in terms of classical space and time because of the almost universal adherence of physicists to the purely probabilistic interpretation of Born, Bohr, and Heisenberg.
This was unfortunate because, as was shown in the article “Why is energy/mass quantized?” May 1 2008 and “Heisenberg uncertainty principal: A Classical interpretation†Sept. 1, 2010 one can derive both the probabilistic interpretation of a particle made by Born, Bohr, and Heisenberg and its wave properties theorized by Louis de Broglie by extrapolating the laws of classical resonance in a three-dimensional environment to a matter wave moving on a “surface” of a three-dimensional space manifold respect to a fourth *spatial* dimension.
Briefly they showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet by a matter wave in four *spatial* dimensions.
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* dimensions thereby fulfilling one of the requirements for classical resonance to occur.
These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. 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 in a continuous form of energy/mass.Â
These resonant systems are responsible for the quantum mechanical properties energy/mass.
This cannot be done if one assumes as Einstein did that space is composed of four-dimensional space-time because time is only observed to move in one direction forward and therefore could not support the bi-directional spatial movements required to define a resonant system.
However, defining the quantum mechanical characteristics of a particle in terms of a resonant system generated by a matter wave would allow one to derive its mass in terms of a compression in a three-dimensional volume as was done in the article mentioned earlier “The “gravity†of four *spatial* dimensions“.
This is because a wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension would compress or shorten the three-dimensional distance between two points on that manifold analogous to the how a wave on the “surface” of water shortens or compress the two-dimensional distance between two water molecules on its surface.
Therefore, unlike the Standard Model of Particle Physics one could incorporate the mass of both macroscopic objects and microscopic particles in one theoretical construct by assuming it is result of a common mechanism related to a geometric compression in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension .
The idea of deriving mass and its quantum mechanical properties in terms of a compression in a three-dimensional space can also serve as the basis for defining a theory of quantum gravitation as will be shown in a later article “Discovering quantum gravity†Jun. 15, 2010.
Later Jeff
Copyright 2007 Jeffrey O’Callaghan