The classical definition of a particle in everyday easily
understandable language is pretty simple: ‘A particle is an object that has
weight and takes up space’. To be more specific, we really should say: ‘A
particle is an object which has

*mass*and*occupies a three-dimensional volume*’, because weight is an ambiguous term, while mass is not. See my video “What is Mass?” on YouTube: https://www.youtube.com/watch?v=gKCN1o6aJuY, and ‘space’ should be specified as three-dimensional. But clearly, modern physics has expanded this definition considerably because the ‘particle zoo’ of the Standard Model includes*massless*particles like gluons, gauge bosons and the Weyl fermion, and*point-like*particles which apparently take up little or no space, and yet have mass, like the electron and up and down quarks.
Just what is a massless particle, or a point-like
particle? An article dated July 23, 2015 starts with the following statement: “Evidence
for the existence of particles called Weyl fermions in two very different solid
materials has been found by three independent groups of physicists.” No
such evidence had been found for more than 85 years, since mathematician
Hermann Weyl found a solution for the equation describing fermions, the particles
that make up ordinary matter, derived by Paul Dirac in 1928. But do massless
and virtually dimensionless particles actually exist? Can something which has
no mass and/or occupies no measureable space be called a particle? What does it
mean to say such ‘particles’

*exist*?
In my last post I made the point that

*existence*is an important concept in the mathematics of a model of a quantized reality. Do sub-atomic particles actually exist? Are they real?
In our search for the meaning of existence and the
nature of reality, we are compelled to lock onto concepts that seem most real and
basic. For example, a major effort has been expended to identify the most basic
building blocks of the universe. And it seems logical to think of them as ‘elementary
particles’, objects that can be considered separate, whole and complete within
themselves, but that are, at the same time, bits of reality bound together in a
variety of ways to form the substance and structure of the reality we
experience. We have established a conceptual model that seems to represent reasonably
well the reality we experience, as objects made up of functional mechanical
and/or organic parts composed of molecules, composed of atoms, composed of
protons and neutrons, composed of quarks, associated with unique elementary
particles known as electrons and photons; and all of these are measurable in
units of mass and energy. But, as nice as this picture is, it doesn’t tell the
whole story; not by a long shot!

It turns out that mass and energy are interchangeable at
the quantum level, in the precise ratio of E/m = c

^{2}where c is the speed of light which has a finite, but very large value that is constant relative to the observer, and the elementary objects that make up the physical universe can become either particles or waves, depending upon choices made by us, the observers. This is easy to say, but infinitely more difficult to understand because, for one thing, it means that photons, whether perceived as particles or waves, always arrive with the exact velocity c relative to the receiving surface or observing eye, regardless of the relative motion of the observer and the source of the light.
The discoveries of Planck (quantum reality) and
Einstein (relativity) tell us that the nature and behavior of reality at the extremes
of scale are counter-intuitive for us as human beings who have physical senses limited
to interpretation of phenomena in the mid-range of the sizes of physical phenomena.
Some aspects of reality on the very large and the very small scales are simply
not detected by our physical senses and most extensions of them. This makes it
very important that we take care that our conceptual models of reality are not
extended beyond their applicability. I have mentioned, e.g., that the
differential calculus of Newton is not applicable to some aspects of our
quantized reality because Newton’s calculus is based on the assumption that the
measureable aspects of reality can be divided indefinitely. In mathematical
terms, this means that the measureable variables of reality can approach zero
as closely as we please. In our quantized reality this simply is not the case. The
actual size of the quantum is the absolute lower limit of divisibility.

If consciousness is not ignored, or passed off as a
dimensionless point of observation, and is included in the equations describing
reality, the calculus of distinctions reveals the fact that reality is not
binary, but triadic, and the solutions to the triadic Diophantine (integer) equations
that describe the combination of elementary particles to form the elements of
the real world apply only to particles that exist. They must exist in the sense
that they have distinct existence with substance and occupy a finite non-zero
volume of space.

Beyond my mystical understanding at present, Ed, but I will follow your ongoing mathematical treatise with interest.

ReplyDeleteThanks Brian. I think you'll find that the mathematics will support your insights.

ReplyDeleteFrom our 'close' connection of a most serendipitous kind, Ed, I guess they will.

ReplyDeleteThank you for sharing this series. Some are over my head, but yet 'particles' of understanding enter my mind. It's always great to learn.

ReplyDeleteThank you for sharing this series. Some are over my head, but yet 'particles' of understanding enter my mind. It's always great to learn.

ReplyDelete