We have shown throughout "The Imagineer’s Chronicles" 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 the microscopic mass of a particle in terms that is consistent with those of planets and stars.

A two-dimensional animation showing how three-dimensional space can be compressed with respect to a fourth *spatial* dimension

Credit: John Eden

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 properties 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 book Alpha & 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."

However, one of the most observable properties of particles is that they have mass.  Therefore, if the Standard Model is the ultimate theory of particles, as many physicists believe you would think that it should be able to define or at least incorporate that observation into its theoretical structure.  The fact it cannot, as mentioned in Charles book, is a reason to look beyond it for a deeper understand of our universe.

In the article "The “gravity” of four *spatial* dimensions" Jun. 1, 2009 it was shown a gravitational potential can be derived in terms of curvature in a "surface" of a three-dimensional space manifold with respect to a fourth "spatial" dimension and its rest mass in terms of a geometric compression 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 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 "The Imagineer’s Chronicles" regarding the relativistic properties of space, time, mass, and energy.

However, one advantage to defining mass in this way is that it permits the microscopic mass of a particle to be derived in a manner that is consistent with those of planets and stars.

In 1924, Louis de Broglie theorized that all particles have a transverse 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 mass quantized?" May 1 2008 one can derive both the probabilistic interpretation of a particle made by Born, Bohr, and Heisenberg and its transverse wave properties theorized by Louis de Broglie in terms of a resonant system formed by a wave moving on a continuous "surface" of a three-dimensional space manifold respect to a fourth *spatial* dimension.

However, defining the quantum characteristics of a particle in terms of a resonant system generated by a transverse wave also allows one to derive its mass in terms of a mechanism similar to the one that defined the mass of star or planet in the article mentioned earlier "The “gravity” of four *spatial* dimensions"

This is because a transverse wave on a "surface" of a three-dimensional space manifold would compress or shorten the three-dimensional distance between two points on that manifold. 

This would be analogous to the how a transverse wave on the "surface" of water shortens or compress the two-dimensional distance between two water molecules on its surface.

However, as was shown in the article "The “gravity” of four *spatial* dimensions" a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension associated the rest mass of an object such as a star or planet also would cause space to be compressed.

Therefore, one could derive the rest mass of both macroscopic objects and microscopic particles terms 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 .

This concept of deriving gravitational potential and the quantum properties of mass can also can 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.

This suggests if one assumes mass is result of the geometric properties of four *spatial* dimensions instead of four-dimensional space-time it may be possible to incorporate the observation that particles have mass into the theoretical structure of the Standard Model and define a quantum gravity.

Later Jeff

The "Shadows" of four spatial dimensions

Copyright 2009 Jeffrey O’Callaghan

(In a PDF format)

2 Comments to “The Geometry of mass”

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2. mcdonalds coupon — 09/13/2009 @ 9:01 pm
   

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