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 = c2 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.