We humans are poor creatures. We are bound by our genetics, imprisoned within three spatial dimensions, residing on a beautiful but otherwise insignificant planet in the vast Cosmos—a planet periodically bombarded by comets that wipe out most of its life.
And yet, we strive to understand as much of the world—outside and inside us—as it is possible for us to grasp. What we perceive with our senses at any given moment is just one side of a multifaceted reality. Plato's allegory of the cave reveals only a small part of the whole truth.
Since today is May 1st, it is more than appropriate to quote from Mario Bunge’s 1950 paper, “The Inexhaustible Electron” (Science & Society, Vol. 14, No. 2, Spring 1950, pp. 115–121):
“The electron is as inexhaustible as the atom; nature is infinite, but it exists infinitely.”
—Lenin, Materialism and Empirio-Criticism (1908)
Lenin wrote this during the crisis of modern physics, at a time when the classical theory of the electron had been given a consistent form, mainly through the work of H. A. Lorentz (1853–1928). The central problem of this theory—which was then expected to explain all the properties of matter—was the structure of the electron.
What is the nature of the electron’s mass: mechanical, electromagnetic, or both? What is the nature of the field within the electron? What is its radius? These were some of the questions that intrigued physicists forty years earlier.
Physicist and philosopher Mario Bunge wrote those words 75 years ago. Today, the situation is not much better. In 1995, J. Keller and Z. Oziewicz organized an international conference, Theory of the Electron, in Mexico City. A group photo shows 37 participants, and the conference proceedings span 500 pages. In 2002, J. Keller published a 275-page monograph, The Theory of the Electron (Kluwer, 2002), summarizing just one such theory.
Why would the electron be considered inexhaustible? Clearly, it is more than just a point. But if it is not a point, then what is it? What “shape” does it have?
I think a better approximation would be to imagine the electron as a sphere. But what lies inside this sphere? Perhaps it contains a window. A window to where? To other dimensions—what else could it be?
And how many of these other dimensions are there? Well, that depends on how you choose to look at them. Which face of the multidimensional universe do you want to observe? One face might have a finite number of dimensions; another might well be infinite-dimensional.
This should not be surprising. We need to get used to it. One face of a quantum object may appear as a “particle,” another as a “wave.” We can see only one face at a time. Sometimes it will be sharp, sometimes it will be blurry.
Anyway, we are discussing spheres—in fact, we are discussing their geometry. We treat oriented spheres as “objects.” We are learning how to navigate in the space of these objects.
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| Object Oriented Programming |
Lie sphere geometry reminds me of "object-oriented programming," which caught my attention in the past. We will return to the math in the next post.
"I think a better approximation would be to imagine the electron as a sphere."
ReplyDeleteToroidal models of the electron are also widespread.
https://www.zitter-institute.org/p/zitter-repository.html
There is also a model of the electron in the form of a torus stretched over a sphere without poles.
Some like to use black hole equations for fermions in which case you get Compton radius vortices with the volume inside the Compton radius as complex space.
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