How Small Is Small?

By: Dharmbir Sharma
Submitted: 2007-01-17 11:22:49
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It may not be quite obvious but the word small is indeterminate. It is relative not only because it has to refer to some physical attribute but also it has a ‘large’ range to it. There are small stars and there are small insects. It is even difficult to define the range, especially its lower end.

It had been clear even to the ‘ancients’ that if you keep dividing something into smaller and smaller parts, ultimately it ceases to be a physical thing. It becomes an idea or a concept. The philosophers believed that all the multiplicity of things in the universe could be traced back to a single entity. Leucippus and Democritus thought that this entity was the atom, which was eternal, indivisible, and indestructible. Much earlier a school of ancient Indian philosophy (vaisheshik) had stated the same idea that the atom (Sanskrit word kana) was the elementary unit from which everything in the universe was made. Vedanta went a step further and did not even bother about the smallest entity. It proclaimed that the ultimate reality behind all existence was ‘smaller than the smallest’, thus making it formless and nonmaterial.

Not too long ago the atom was considered indivisible even in science. We now know that the atom is divisible. It consists of electrons, protons, and neutrons. Even protons and neutrons are composed of other particles known as quarks. In fact there are no elementary particles now; they all result from different configurations of vibrations (energy). Even though these particles (energy packets) combine in different ways to form matter in diverse forms, they are not objects in the usual sense of the word. They are merely concepts. Yet all physical phenomena can be correctly explained through these. The behavior of concepts cannot be described by everyday language and that is why the language of mathematics is needed for their exact description.

When we talk of division the first thing that comes to mind is a set of numbers. The simplest division is division into two parts and the process can be repeated indefinitely. Take any number and performing this continued division you keep getting smaller and smaller numbers; thus you can get as close to zero as you want but can never actually get there. At some point therefore it becomes meaningless to continue the process.

This is exactly what happened in particle physics. When it got to electrons, photons, and quarks there was no further splitting. Since everything is ultimately described in terms of wave functions, waves (or energy) must be the end point. The string theory in different versions simply leads to the conclusion that energy is the prime entity which gives rise to everything in the universe. Energy is all pervading and cannot be divided. In that sense it is also infinite. It is both the beginning and the end.

The equivalence of matter and energy is an established fact. The transformation of matter into energy is well understood. The challenge to science now is to find how energy is transformed into matter. Ancient philosophies (Vedanta, Sankhya) have suggested ways in which this transformation occurs. These are, of course, qualitative suggestions and as yet there is no way to test them. But in physics also this is only a concept and the process of production of particles from string vibrations is yet to be demonstrated.

Dharmbir Rai Sharma is a retired professor with electrical engineering and physics background. He obtained his M.S. degree in physics in India and Ph.D. in electrical engineering at Cornell University. He has taught in universities here and also in Brazil, where he spent sometime. He maintains a website http://www.cosmosebooks.com devoted mainly to philosophy and science.

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