The Infinite Divisibility of Matter

By David Pratt

If we take a material object, such as a loaf of bread, and keep cutting it in half, again and again, will we ever arrive at a fundamental building block of matter that cannot be divided further? This question has exercised the minds of scientists and philosophers for thousands of years. In the fifth century BC the Greek philosopher Leucippus and his pupil Democritus used the word atomos (lit. "uncuttable") to designate the smallest individual piece of matter, and proposed that the world consists of nothing but atoms in motion. This early atomic theory differed from later versions in that it included the idea of a human soul made up of a more refined kind of atom distributed throughout the body.

Atomic theory fell into decline in the Middle Ages, but was revived at the start of the scientific revolution in the seventeenth century. Isaac Newton, for example, believed that matter consisted of "solid, massy, hard, impenetrable, movable particles." Atomic theory came into its own in the nineteenth century, with the idea that each chemical element consisted of its own unique kind of atom, and that everything else was made from combinations of these atoms. By the end of the century all ninety-two naturally occurring elements had been discovered, and progress in the various branches of physics produced a feeling that there would soon be nothing much left for physicists to do.

This illusion was shattered in 1897, with the discovery of the electron, the first subatomic particle: the "uncuttable" had been cut. This was followed by the discovery of the proton in 1911 and the neutron in 1932, the two particles that make up the atomic nucleus. In the decades that followed, subatomic particles began to proliferate like bacteria, and today over 200 are known. Most of them are created from the energies released in collision experiments in particle accelerators, and decay into more stable particles after a fraction of a second.

To try to inject some order into this particle zoo, the "standard model" was developed. According to this model there are twelve fundamental particles of matter: six leptons, the most important of which are the electron and its neutrino; and six quarks (since quarks are said to come in three "colors," there are really 18 of them). [The announcement in April 1994 that promising evidence of the elusive "top quark" had finally been found was greeted by physicists with cries of joy. But the discovery of further evidence for a particle known as the "pomeron" at another particle accelerator the following month met with almost total disinterest, because this embarrassing particle does not fit into any existing theory.] Individual quarks have never been detected, and it is believed that they can exist only in groups of two or three -- as in the neutron and proton. There are also said to be at least 12 force-carrying particles (of which only three have been directly observed), which bind quarks and leptons together into more complex forms.

Leptons and quarks are supposed to be structureless, infinitely small particles, the fundamental building blocks of matter. But since infinitesimal points are abstractions and the objects we see around us are obviously not composed of abstractions, the standard model is clearly unsatisfactory. It is hard to understand how a proton, with a measurable radius of 10 to the negative 13th cm, can be composed of three quarks of zero dimension. And if the electron were infinitely small, the electromagnetic force surrounding it would have an infinitely high energy, and the electron would therefore have an infinite mass. This is nonsense, for an electron has a mass of 10 to the negative 27th gram. To get round this embarrassing situation, physicists use a mathematical trick: they simply subtract the infinities from their equations and substitute the empirically known values! As physicist Paul Davies remarks: "To make this still somewhat dubious procedure look respectable, it is dignified with a fine-sounding name -- renormalization." (P. Davies & J. Gribbin, The Matter Myth, 1992, p. 244.) If this is done, the equations can be used to make extremely accurate predictions, and most physicists are therefore happy to ignore the obviously flawed concept of point particles.

The latest theoretical fashion in particle physics is known as string theory (or superstring theory). According to this model, the fundamental constituents of matter are really one-dimensional loops -- a billion-trillion-trillionth of a centimeter (10 to the negative 33rd cm) long but with no thickness -- which vibrate and wriggle about in 10 dimensions of spacetime, with different modes of vibration corresponding to different species of particles. It is said that the reason we see only three dimensions of space in the real world is because the other dimensions have for some unknown reason undergone "spontaneous compactification" and are now curled up so tightly that they are undetectable. Because strings are believed to be so minute, they are utterly beyond experimental verification; to produce the enormous energies required to detect them would require a particle accelerator 100 million million kilometers long.

String theorists have now discovered a peculiar abstract symmetry (or mathematical trick), known as duality. This has helped to unify some of the many variants of the theory, and has led to the view that strings are both elementary and yet composite; they are supposedly made of the very particles they create! As one theorist exclaimed: "It feels like magic." (See Scientific American, January 1996, pp. 72-8.) While some physicists believe that string theory could lead to a Theory of Everything in the not-too-distant future, others have expressed their opposition to it in no uncertain terms. For instance, Nobel Prize winner Sheldon Glashow has likened it to medieval theology, based on faith and pure thought rather than observation and experiment, and another Nobel laureate, the late Richard Feynman, bluntly dismissed it as "nonsense." (P. C. W. Davies & J. Brown (eds.), Superstrings, A Theory of Everything?, 1988, pp. 180-4, 191, 192-8.)

An alternative approach which is currently being investigated by a small number of physicists is that subatomic particles are vortices in an underlying medium -- a primitive fluid or ether. (See E. Lerner, The Big Bang Never Happened, 1992, pp. 369-72; M. B. Cooke, Einstein Doesn't Work Here Anymore, 1983, pp. 1-39; C. F. Krafft, Glimpses of the Unseen World (1956), BSRF reprint, 1986; C. E. Krafft, The Ether and its Vortices (1955), BSRF reprint, 1987.) Physicist David Bohm regarded "elementary" particles as complex, relatively constant forms produced by patterns of motion at some deeper, implicate, level of reality. He adds:

One may suppose that this deeper level of movement may be analysable into yet finer particles which will perhaps turn out to be the ultimate substance of the whole of reality. However, the notion that all is flux . . . denies such a supposition. Rather, it implies that any describable event, object, entity, etc., is an abstraction from an unknown and undefinable totality of flowing movement. -- Wholeness and the Implicate Order, 1980, p. 49

Recent evidence from particle collision experiments suggests that quarks do have internal structure and are not in fact elementary. (See New Scientist, February 17, 1996, p. 17.) No internal structure has yet been detected in electrons, but this proves only that they must be smaller than can currently be measured, not that they have no size at all. As Bohm points out, between the shortest distance now measurable in physics (10 to the negative 16th cm) and the shortest distance in which current notions of spacetime are believed to have meaning (10 to the negative 33rd cm), there is a vast range of scale in which an immense amount of yet undiscovered structure could be contained. This range is roughly equal to that which exists between our own size and the known "elementary" particles. (D. Bohm & F. D. Peat, Science, Order & Creativity, 1987, p. 94.) 10 to the negative 33rd cm is called the Planck length, and physicists believe that on this scale the fabric of space becomes an effervescing froth of spacetime bubbles. But while this may be the smallest distance that has any meaning for us, there is no reason to assume that the concept of space has absolutely no meaning beyond it. As Bohm says, the Planck length is only a limit on the applicability of our ordinary notions of space and time, and it is quite arbitrary to suppose that there is nothing beyond this limit at all. (Wholeness and the Implicate Order, p. 193) Instead of bringing us to a "rock bottom" level of reality, 10 to the negative 33rd cm may merely bring us to the bottom level of our own physical world.

In The Secret Doctrine, published in 1888, H. P. Blavatsky writes:

It is on the doctrine of the illusive nature of matter, and the infinite divisibility of the atom, that the whole science of Occultism is built. It opens limitless horizons to substance informed by the divine breath of its soul in every possible state of tenuity, states still undreamt of by the most spiritually disposed chemists and physicists. -- 1:520

This implies that there is an infinite number of states of matter, all but a few of which have rates of vibration beyond our range of perception. And all the infinite grades of matter can be regarded as different phases of one universal divine essence of consciousness-life-substance.

Blavatsky provides a compelling argument for the infinite divisibility of matter. She quotes Alexander Butlerov, a renowned Russian chemist, who also took a serious interest in spiritualistic phenomena. He attacked as contradictory the orthodox scientific opinion of the time that an atom was indivisible and yet elastic:

Without any elasticity, the atoms could not manifest their energy . . . [But] what are the conditions requisite for the manifestation of elasticity? An elastic ball, when striking against an obstacle, is flattened and contracts, which it would be impossible for it to do, were not that ball to consist of particles, the relative position of which experiences at the time of the blow a temporary change. This may be said of elasticity in general; no elasticity is possible without change with respect to the position of the compound particles of an elastic body. This means that the elastic body is changeful and consists of particles, or, in other words, that elasticity can pertain only to those bodies that are divisible.

Blavatsky comments:

This is sufficient to show how absurd are the simultaneous admissions of the non-divisibility and elasticity of the atom. The atom is elastic, ergo, the atom is divisible, and must consist of particles, or of sub-atoms. And these sub-atoms? They are either non-elastic, and in such case they represent no dynamic importance, or, they are elastic also; and in that case, they, too, are subject to divisibility. And thus ad infinitum. But infinite divisibility of atoms resolves matter into simple centres of force, i.e., precludes the possibility of conceiving matter as an objective substance. This vicious circle is fatal to materialism. -- SD 1:519

In other words, anything which is absolutely indivisible -- whether we call it a particle of matter or a quantum of energy -- would be entirely homogeneous and inflexible. But how can something of this nature take part in interactions with other physical entities? If we apply a force to it, the force must cause deformation and be transmitted through the internal structure of the entity. But if it was truly homogeneous it would have no internal structure, there would be no deformation, and the force applied would have to pass instantaneously (infinitely fast) to the other side. Since this is impossible, everything must be composite and divisible. It might be countered that the concept of elasticity does not apply to particles as understood by modern physics, which are described as fuzzy and indistinct, a "ghostly melee of half-forms," which can be understood only in terms of mathematical abstractions. (The Matter Myth, p. 141.) But this is merely an evasion. Either these ghostly entities are entirely homogeneous and undeformable, in which case they are pure abstractions and exist only on paper, or they are inhomogeneous and deformable, in which case they must be divisible.

Bohm points out that arguments on whether matter is fundamentally discrete or continuous go back to the ancient Greeks, and at first sight the two points of view appear to be incompatible.

However, on closer investigation it would appear that any theory of the continuous nature of matter can in fact be based upon an opposing theory involving discrete matter that is so fine as to have never manifested its nature up to the present time. Conversely, any theory of the discontinuous structure of matter can be explained as arising through the localization and concentration of a continuous background. -- Science, Order & Creativity, pp. 72-3

Physical particles can therefore be thought of as concentrations of an underlying, continuous ether. But the ether is only relatively continuous. Further analysis would show that it, too, is discontinuous, and these particle-like discontinuities would be concentrations of a deeper, subtler ether, which in turn is relatively continuous, but actually consists of even finer particles, which are in turn concentrations of an even subtler ether, and so on, ad infinitum. Thus as we move from our own distance scale beyond the Planck scale towards the infinitesimal, there is no reason to suppose that an absolutely bottom level of matter, consisting of absolutely homogeneous particles, will ever be reached. Between the two abstract limits of the infinite and the infinitesimal, there is a limitless number of concrete, finite systems -- atoms, planets, stars, galaxies, etc. -- each existing on a hierarchy of planes, from spiritual to material, and all their constituent grades of substance are composite, divisible, and inhomogeneous, though the substances on higher planes or subplanes are relatively more homogeneous than those on lower planes or subplanes.

At the start of the century, the atom was pictured as a miniature solar system, with the nucleus corresponding to the sun, and the orbiting electrons to the planets. This view was later rejected when it was found that electrons did not follow well-defined orbits but seemed to be "smeared out" around the nucleus in an electron cloud. Many physicists have concluded that the microscopic world is completely different from the macroscopic world: the subatomic realm is blurred, indeterministic and, according to some, even nonobjective when we are not observing or measuring it; in short, it is completely alien to ordinary experience and cannot be understood by reason and logic.

But perhaps this conclusion was overhasty, and there is a simple explanation for the apparently weird nature of the quantum realm, an explanation connected with the much smaller time and distance scales on which things happen at the subatomic level. An electron is said to move at 600 miles per second, or 0.3% of the speed of light, just 30 times faster than the speed at which the earth revolves around the sun. However, the orbit of an electron is so tiny that an electron revolves around the atomic nucleus an incredible 4 million billion times every second! An earth year is equal to one revolution around the sun, and an electron "year" to one revolution around the nucleus. According to ancient Hindu chronology, the manvantara or active lifetime of the earth lasts 4,320,000,000 years, and is followed by a pralaya or rest period of the same length, with periods of manvantara and pralaya alternating endlessly. If we apply the same figures to an electron, it would mean that an electron's manvantara (life cycle) lasts about one millionth of a second, following which it disappears from our plane for another millionth of a second before reimbodying again. In one of our seconds it would reimbody nearly half a million times!

For the earth to reimbody the same number of times as the electron in one second, it would have to orbit the sun over 100 billion trillion times faster than it does at present -- things would certainly appear rather blurred, fuzzy, and "smeared out"! As G. de Purucker says, the forces at work in the microscopic realm "are so minute and operate with such smallness of field and rapidity of function that the details are bewilderingly confusing." (The Esoteric Tradition, 1973 (1935), p. 854n.) All particle properties, motions, and interactions are in a sense stroboscopic illusions produced by the way our own time frame or rate of consciousness meshes with the flickering reimbodiments of the subatomic world; yet the overall effect is orderly and lawful because it is an expression of the fundamental karmic law of harmony. In a sense, it is not even the same electron orbiting the nucleus from one instant to the next, since its own myriad constituents will also be constantly disembodying and reimbodying, and pursuing their own evolutionary journeys. Clearly, any model of subatomic particles can only ever be an approximation to the inexhaustible complexity of reality.

The analogy between an atom and a solar system may therefore be valid after all. Perhaps there are beings on an electron for whom the electron appears just as solid, stable, and sedate as our own earth does to us. And these beings may be composed of subatomic particles which seem to behave just as weirdly as our own subatomic world. The earth itself may be a mere electron in the body of some supercosmic entity for whom a second is equivalent to a million reimbodiments of the earth, with the solar system corresponding to an atom, a galaxy to a molecule, and sheets of galaxies to macromolecules. Such analogies may be extended endlessly towards the infinitely small at one end of the scale and the infinitely large at the other. This underlines the sheer relativity of space and time. In infinite nature there are no absolutes, and no limitations -- except those stemming from our own limited understanding.

Although the details of each level of reality differ, the fundamental structural, geometrical, and evolutionary principles are the same. This is expressed in the law of analogy: as above, so below; every microcosm mirrors the larger macrocosm of which it forms part and is the macrocosm of its own constituent microcosms. In the words of H. P. Blavatsky:

Analogy is the guiding law in Nature, the only true Ariadne's thread that can lead us, through the inextricable paths of her domain, toward her primal and final mysteries. -- SD 2:153

(From Sunrise magazine, June/July 1996. Copyright © 1996 by Theosophical University Press)

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