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THE CONSTANT h/

The reduction of all of the repeatable, scalable properties of chemistry to properties of relatively few (for practical purposes, well fewer than 100) absolutely repeatable but mutually different kinds of ``atoms'' was the turning point that made possible the modern advances in chemistry, which gave it methods to raise it beyond a practice of enlightened trial and error. As such, it casts a powerful precedent as a paradigm for understanding other kinds of repeatability. But the repeatability of chemistry is uncharacteristically simple, because in some sense atoms have nearly ``sharp'' boundaries. While this description is not quite literal, atoms are much like little hard balls that effectively ignore each other when they are farther apart than a moderate fraction of their individual diameters, and interact in a very narrow range of ways when they are closer than that. As such, they lend themselves to a very literal building block description in which each of the blocks has relatively few and relatively simple properties.

At the level of chemistry we are left with the atom as a basic, if repeatable structure. That leaves us still in need of an explanation of why individual atoms are repeatable, and why they can have only such a narrow range of properties. The existence of electric currents in metals was the first strong evidence that atoms are not indeed indivisible, but rather have some kind of ``parts'' that can be exchanged from one to another. This is because while the metals themselves are very chemically suited to a description as being composed of atoms, there is no sense in which whatever it is that we experience as an ``electric current'' is something ``additional'' that has to be added to the metals in order to flow through them. At the same time, there is nothing in the chemistry of metals that leads us to believe from their properties that there is any ``other'' substance in them besides what has already been accounted for by the atoms. Thus is seemed likely that whatever appeared as an ``electric current'' was not something additional to the atomic content of metals, nor something that had to be added to it from a different source, but rather some ``part'' of the metal atoms themselves, which could be ``pulled out'' or ``separated'' from ``the rest'' of the atom, or that at least in some way could hop from one atom to another down a long string, and even be taken from the metals altogether. (Examples?) At the same time it was not obvious that whatever ``part'' of atoms might account for electric currents was necessarily a ``building block'' per se. (For instance, some of the early language on this topic refers to these currents as some kind of ``fluid'', with the implication that this fluid was not necessarily made of a collection of little grains of anything.)

The idea that whatever constitutes electric current is, though, some sort of ``substance'' in its own right, and not simply a collective property of that atoms that display it, became necessary when (who?) showed that it was possible to make electric currents flow through empty space. These are the famous ``cathode rays'' that shine up behind the glass of television sets and make the special paints on them glow to form the picture. These cathode rays had all the properties of all other electric currents, and they were released from and absorbed into metals and other chemicals, after which they were no more chemically ``present'' as additional parts of the metals than were any other electric currents. But still the fact that something can be a substance in its own right is a weaker proposition than that it consists of proper little ``building blocks'', much less a description of how those might interact.

The most potent evidence for the building block picture of atoms came from the experiments of Ernst Rutherford with natural radioactivity. Though at the time no-one knew what this ``radioactivity'' was, people knew that there were certain materials that could be found on earth that gave off ``something'' that could turn photographic film black just like light could, but that ``the something'' was not itself visible, also like light. But unlike light, we cannot directly see whatever makes up this radioactivity, even if it bounces off the things it ``shines on'', so it doesn't make them ``light up'' in the same way that light does. Thus, while some of its effects are much like those of the light we know, they are harder to see and therefore somewhat more difficult make familiar. Also like light, this radioactivity can be blocked, or shadowed, with a thick block of ``solid material'' (like a thick lead wall for some kinds of radioactivity, or as little as a sheet of paper or skin for other kinds), though different kinds of radioactivity are more successful at shining ``through'' materials than is light.

So the first observation that came from radioactivity was simply that whatever it is, at least some kinds of it could shine ``through'' a certain amoung of ``solid'' atomic matter just as if the matter were not there. The surprise for Rutherford, when he carefully made the apparatus necessary to ``see'' this radioactivity in ways that his eyes could not, was that while most of it did indeed shine through a thin leaf of gold foil, every once in a while a ``part'' of the radioactivity would bounce violently back toward the direction whence it came, as if it had struck a very heavy and immovable wall and recoiled. From the great rarety with which such backward bounces occurred, but the fact that they were on some occasions exactly what would be expected from bounces off very heavy objects, Rutherford formed the first definite description of the ``internal structure'' of an atom, as an object that was mostly very empty and transparent (which is how radioactivity could shine through it, as through empty space), but with a very tiny core that contained almost all of its mass in very little size. Similarly the ``substance'' of the radioactivity was behaving very much like little balls of some kind, that most of the time simply passed through the ``empty space'' that ``filled'' most of the atom, because the core, named the nucleus, was a small and seldom-hit target. But, also just like little balls hitting much bigger and heavier ones, on those rare occasions when, just by chance, the ``balls'' of the radioactivity did hit the very small nucleus, they bounced off it violently because it was so much heavier.

Something was needed to account for the fact that all of that empty space around the nucleus was held vacant, because otherwise there would be nothing to hold the nuclei apart as they are observed to be. Through a sequence of steps (which distract from the main point here, so I would like not to go into them), it was decided that the same ``substance'' that could flow either in metals or through empty space as electric currents was diffusely filling the large vacant region that accounted for most of the volume, and that the nucleus was something else. As a brief digression, we note here that it had already been understood that the same stuff that makes up electric currents in space could be accumulated on pith balls (or balloons, or cat fur) and make the resulting objects attract or cling to each other in various ways. In this way was discovered the notion that there is another ``something'', denoted an electric charge, that somehow represents the accumulation of an electric current. From long before Rutherford it had been surmised that since even though some metals can always carry currents, they do not always ``cling'', so if indeed whatever made up the current were also ``accumulated'' as part of the internal structure of atoms, there must also be an ``opposite charge'' present in the atoms, which had a corresponding ``anti-cling'' effect on any particular other object. In that way the accumulation of what carried the current could be a part of atoms, while not necessarily causing them to be ``charged''. In this language the actual observation of those cases in which things did cling was accounted to too much of one or the other kind of accumulated ``electric charge'' as the accumulated current came to be called, and that the slight deviation from balance was responsible for the overall cling.

From the fact that all whole atoms do not have an overall charge, or ``cling'', even when exceedingly many of them are grouped together, it became necessary to suppose that every atom has a precisely balanced and equal amount of both kinds of charge. Rutherford concluded from his experiments that the kind of ``charge'' that was commonly made to flow through metals or empty space was purely associated with whatever filled the almost-empty space of most of the atoms, and that the balancing other-sign ``charge'' was a property completely confined to the nucleus itself. By this time the picture of little ball-like constituents was becoming more compelling, so the thing that flows in currents, which had been called an ``electron'' (etymology, if desired), was thought about as a tiny ball that flew through otherwise empty space around a very heavy and oppositely electrically charged nucleus. Just as the macroscopic clinging of oppositely charged objects had been observed to hold them together, the opposite charge of electrons from the nucleus was what was assumed to keep them whirling around, rather than flying away into space. (diagram of rutherford description of atom).

In this langauge, the picture of an atom as a composite structure, with many little ``parts'' is very convincing, but as a ``building block'' picture it is rather different from the picture of atoms in chemistry, that only interact when they touch each other, and thus directly account for the repeatability of what they make as long as they themselves are always the same. Rutherford's picture of atoms looks more like the picture astronomers had already been able to assemble of the solar system, with a big heavy ``sun'' at the center surrounded by mostly empty space, with much lighter ``planets'' whirling around it and held in place by some kind of attraction for the sun at the center. In the case of the solar system, the attraction was first appreciated by Newton to be the same gravity that attracts people toward the center of the earth (they stop because its surface gets in the way), and in the case of Rutherford's atoms it was the attraction of opposite ``electric charges''. (In some sense, the fact that little better understanding of these ``attractions'' existed than names for them is unimportant, because as long as they always behave the same way they enable predictions to be made, which is the real essence of understanding).

But here Rutherford's atom, while wonderful in accounting for his other experiments, fails very badly if what we want from it is some explanation of how atoms can so reliably be the same. That is because, if Rutherford's model is really like little solar systems, it predicts that atoms must be like little solar systems, which are not at all the same. Even if we go out on a limb because of our success with chemistry and propose that, within atoms, each nucleus and all of the electrons are ``the same'' as each other, thus postponing our accounting for sameness to a finer level of discrimination, we don't gain the advantage from this assumption that we did in chemistry. That is because the identical ``atoms'' in chemistry are something like bricks in a house, which can be laid one atop another in a repeatable way as long as they are the same. But Rutherford's atom has the new complication of all that ``empty space''. If the electrons in it are were really like planets, even if they were all alike, it should be possible to combine them to make endlessly different kinds of ``solar systems'', just by setting them in motion differently. After all, we can look at the planets going around the sun, and at the various moons going around the planets, and even to the extent that they are all just lumps of rock, their combinations can vary completely. All of our experience and understanding of gravity since then has reinforced the confidence that this endless non-repeatability is indeed possible to solar systems.

But the real atoms are repeatable, so we must have missed something important in assuming that atoms are very much like solar systems. Certainly it would not be surprising if atoms were different, if their constituents were different, so for now we will just make the assumption that each nucleus and each electron is ``identical'' as a building block, just as atoms were (actually, in some ways they are even moreso). This does indeed leave us with the later problem of explaining this new form of repeatability (about which maybe more later), but if we are willing to use it as a starting point, it allows us to focus on the simpler problem of what causes the arrangement itself of these simple identical parts in empty space to be always the same?

Thus the problem of the identicalness of atoms, which was our most obvious clue, turns out to be something of a composite problem, with many different parts that must be explained. The identicalness of the building block themselves, the electrons and nuclei, turns out to be a more difficult problem to be left for later. The other problem, to account only for the repeatability of their arrangement, though not the most obvious one from everyday experiences with chemistry and starlight, turns out to be the one on which it was first possible to make some progress.




Next: Repeated angular momenta Up: THE FUNDAMENTAL DIMENSIONFUL Previous: DIMENSIONS AND SCALING


desmith@
Thu Aug 31 12:01:42 CDT 1995