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1kWe have shown through this blog and its companion book “The Reality of the Fourth spatial dimension” there are would be many 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 define a particles mass and inertia by using one’s imagination to extrapolate observations made in a three-dimensional environment to a fourth *spatial* dimension.
For the past 50 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 does not say anything about particle mass at all: in fact if theorists try to put mass in to its equations they blowup and become meaningless.”
In 1964 Peter Higgsshowed that one can solve this problem and explain why particles have inertial or rest mass if one assumes space is permeated by what is called a Higgs field.
He was able to show that if a particle changes its velocity or accelerates, then the Higgs field should exert a certain amount of resistance or drag which according to his theory is the origin of mass. In a slightly more precise terminology, the origin of mass is an interaction between a particle and the (nonzero) Higgs field. It also assumes the disturbance created by mass as it moves through this field would have to generate the particle called the Higgs boson.
The only problem is that the Higgs boson has never been observed.
This is problematic for its proponents primarily because The Large Hadron Collider (LHC) the world’s most expensive and highest-energy particle accelerator has been able to attain the energy levels which most believe should make it observable.
However, if it cannot be observed in the high energy environment presently generated by the LCH, scientists are going to have to make a decision as to whether or not to continue to expend the resources looking for something that may not exist or expend even more to create a more powerful accelerator.
This is especially relevant because as mentioned earlier there is an alternative explanation for mass that is based on the observable and therefore verifiable properties of three-dimensional space which does not require the large expenditures in time and money as would be required for verifying the existence of the Higgs boson.
Observations of our three-dimensional environment tell us the total potential energy of an object or particle is related to the magnitude of its relative displacement. For example the potential energy of water in a bucket is determined by the height or displacement of its surface relative to the surface of the table it is resting on. However, its potential energy is greater if one measure it with respect to the relative to the floor on which the table is resting.
In the following discussion the potential energy of the water in the bucket relative to the table top will represent the rest mass of an object or particle while its energy with respect to the floor will correspond to the energy associated with its relative motion or velocity.
In the article “Why Space-time?” Sept. 27, 2007 it was showed one can derive the rest or inertial mass of an object or particle in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Additionally it was shown one can derive the causality of all accelerations including gravitational in terms of an interaction of its mass with the slope of a curvature in a “surface” of a three-dimensional space caused by that displacement.
(This curvature is analogous to a curvature in a four-dimensional space-time manifold Einstein theorized was responsible for gravitational accelerations)
This means that one could define the potential, inertial or rest energy of mass by extrapolating the observations of the potential energy of the water in a bucket resting on the surface of a table to a displacement in a “surface” of a three-dimensional manifold with respect to a fourth *spatial* dimension. In other words one could define the potential energy associated with inertial mass in terms of the displacement of a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension for the same reason as one can define the potential energy of the water in the bucket as being related to its displacement with respect to the table top.
However the article “Defining energy” Nov 26, 2007 derived the energy associated with the relative velocities in terms of a differential displacement of a volume of an object or particle with respect to a fourth “spatial” dimension. In other words it was able to show the energy associated with velocities are a result of a differential displacement in a “surface” of a three-dimensional space manifold with respect to a fourth “spatial” dimension.
(The energy associated with relative velocities would be associated with the displacement of the surface of the table with respect to the floor in the example mentioned earlier.)
Isaac Newton defined inertia as being responsible for why an object at rest will remain at rest, and an object in motion will remain in motion in a straight line at a constant speed.
This means, one could define the potential energy associated with the velocity or momentum of an object or particle in terms of the displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension associated with its rest mass plus that associated with its relative velocity because according to the concepts presented in those articles it would be defined by the sum of those components.
The first would be magnitude of the displacement in a “surface” of a three-dimensional space associated with the rest mass of an object. The second would be the magnitude of the displacement of that “surface” with respect to a fourth *spatial* dimension caused by the energy of its relative motion. (The momentum of an object at rest with respect to other objects is zero so the displacement of three-dimensional space with respect to those objects would also be zero.)Â
This also defines why the “relativistic” mass or inertia of an object or particle increase as its velocity approaches that of light because its total energy/mass would, according to the concepts presented here be related to the relative magnitude of the total displacement in a “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension which in turn would be related to their relative velocities.
Yet, as mentioned earlier the article “Why Space-time?” showed that accelerations are caused by an object or particle interacting with a curved “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
Therefore, if as mentioned earlier the momentum of a particle or object is caused by a displacement of a “surface” of a three-dimension space manifold it would tent to stay rest or ones in motion would tend to stay in motion unless it interacted with a “surface” that was curved with respect to a fourth *spatial* dimension.
This means that one does not have to assume the existence of the Higgs Boson to explain why particles have both mass and inertia because it shows how one can use his or her imagination to explain it by extrapolating observations of a three-dimensional environment to a fourth *spatial* dimension.
Later Jeff
Copyright Jeffrey O’Callaghan 2011
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