We first take note of the repeatability of nature, which once one has been brought to notice it becomes so obvious as to be overwhelming. Most things we experience in their ``raw states'' tend to be somewhat complicated, because they arise as combined effects from many sources. Typical of this is the light we see. It tends to be a complex overlay of light produced from the heat of the sun, other light reflected from rocks and the pigments of leaves and other complex chemicals, and yet more light reflected or partially absorbed from the gases in the atmosphere. One of the things we will see in the later chapters on the discovery of quantum mechanics is that these different sources produce light of different ``character''s. But if we are careful, we can isolate light from each of the different kinds of processes, and learn a lot about each kind in isolation. This has been done for the light radiated from or absorbed by gases for several centuries. Because people have known how to use prisms to bend light and produce ``rainbow'' effects since before that, the tools have existed for a long time to characterize light by ``how much of it'' comes from a given color of the rainbow. For the case of natural rainbows, actually created by the bending of sunlight and atmospheric reflections of it in the prisms of raindrops or ice crystals, we see some smoothly bright amount of light in all of the colors we are capable of seeing. If we could see further across the spectrum, we would find that the smooth blended brightness of natural rainbows extents from ``before'' the red that we can see to well ``beyond'' the violet at the other side. (Natural rainbows tend to be more compex than this because of the small size of raindrops, which cause the bent light to contain several ``copies'' of each band of color shining in different directions, so in rainbows with very small water drops, one can see two or even more bands each of red through violet.)
If instead of looking at daylight in real rainbows, though, we look at the light from carefully purified different kinds of gases, bent in a good large prism that creates only one band of each color, we find that the ``rainbow'' that results is totally different from a daylight rainbow. Instead of being smoothly bright across all of the colors we can see, it turns out to be totally dark (no light content at all) across most of the colors, and all of the content of the original light comes from a few very brightly present and very narrowly defined colors. (include diagram and picture of spectra here.) Further, how bright the various inclusions are and more significantly where they appear in the rainbow turn out to be identifying signatures for the kinds of gas used. Once pure samples of different gases have been examined in this way, the resulting knowledge of their ``signature'' spectra enables people to identify which gases are present in complicated mixtures, because the light radiated from the mixtures is made of contributions from each of the components individually.
One thing that we find is that these colors contained in the light are not dependent on how it was created. We can look at a lump of lithium (a soft silvery metal) thrown into a gas fire, which vaporizes it and then makes it burn a bright magenta as it combines with oxygen from the air, or we can look at pure lithium gas in a heated tube, made to glow by passing electric currents through it. In either case, the lines from the lithuim occur in the same place. (Their relative brightness can have something to do with how the light was created, and so can provide a partial identification of that as well as the kind of gas.) Furthermore, and also remarkable, we find that if instead of making the gas glow, we shine some other light like daylight through it, the gas will absorb the daylight and leave missing places, or narrow dark places, in the spectrum of the light that shines through. In this way the gas casts a kind of color-dependent shadow, and the individual shadow regions occur in precisely the same places as the light bands occur if the gas is made to glow instead. It was in fact by casting such shadows that this effect was first abserved, when (Lord Kelvin?) used sodium thrown into a gas flame (to vaporize it) as such a selective shadower of sunlight, and then looked at the spectrum of what was left shining through.
Since everything else can be carefully removed in these
experiments, we come to the conclusion that this effect must
tell us something about whatever internal structure the gas has,
that determines how it interacts with light, either emitting or
absorbing (glowing or casting shadows). We are certain that it
comes from the individual atoms, and not from some property of
the way they interact, firstly because there are few enough
atoms in a gas that they spend most of their time out of contact
with each other (which is what makes it a gas), and secondly
because we can change the number of atoms in a given volume and
thus change the amount of interaction they have, and the
character of the light they emit does not change as a result.
Our concern in the quantum theory will be the details of this
particular interaction. Here we note something simpler and more
blatant. Even a small sample of gas is made of a tremendous
number of individual molecules or atoms (a cubic cm having, for
instance, , or ten billion billion individual atoms).
If these characteristics of their interaction are indeed
telling us something about the structure of individual atoms,
that structure must be increadibly repeatable for all of the
light from so many atoms to always shine in just the same parts
of the spectrum, so that all of the individual contributions
combine to produce clear bright bands or dark shadows, rather
than broad sweeps of light from a lot of atoms all acting
differently.
A repeatability of each of objects, to as fine a
precision as we are capable of measuring, is stunning in a way
that offers little ability to surpass. But there are similar
kinds of effects that can be observed on larger scales that may
serve to re-inforce the point.
Most of the light from any star creates the same kind of broad smooth rainbows as daylight does on earth. Therefore stars directly do not provide very convenient signatures of what may have combined to make them. Much of this is due to the fact that most of the atoms that fall into the body of a star are torn apart, so the structure that was responsible for the characteristic behavior of gases is lost anyway. However, in the empty space between the starts, there are vast clouds of gas of very low density and very little interaction, and because we already know that gases can be identified as well by the shadows they cast as by the light they emit, we can at least make clear identifications of the content of gas clouds by looking at the way they absorb starlight that shines through them. (Actually, because in the outermost layers of the stars themselves, there are atoms that have a cool enough environment not to have been torn apart, we can also partly analyze the content of the stars themselves by the same method, though these atoms are much more hot, dense and in more frequent contact, and the contact and heat complicate the character of the shadows somewhat.)
Not only are all stars ``far'' from the earth (even the order of magnitude of the distance cannot be meaningfully mentioned without giving some idea which stars one is observing), but any light that we see from them, or what is left of it after passing through gas clouds in space, has been traveling for a long time before we see it. Thus when we look at the shadows, we are not only identifying the properties of gas that can be very far away, but we are identifying the way it was a long time ago. And what we find is again that, not only is all of the gas in huge remote regions so much alike that the shadows cast are sharp and narrow, but that it is so identical to the shadows that are cast by gases here (on Earth) and now that everything about the internal structure of the atoms appears to be utterly identical, so much so that we can identify very well how much of what kinds of gases make up the clouds.
So our first case concludes with the observation that, even among increadible numbers of atoms, at any place and at any age we have observed in the universe, all of the structures of any of the atoms of a given kind are reliably just the same.
Having done all the work to detail this slightly non-everyday example to show the effect, we now mention the absolutely most-everyday example of the same thing, one so common and inescapable that it seems ludicrous ever to have overlooked its importance. That example is the whole field of chemistry. We looked first at gases because they are simple, but everything that chemists do, whether with gases or any other forms of chemicals, involves combining lots of individual atoms or molecules with each other so that they ``react'' to produce whatever they produce. The stunning thing to appreciate is that chemistry works at all. There are about a thousand times as many molecules of water in a cubic cm volume as there are of the gases we first mentioned. Yet in all of the reactions that water has with endless other chemicals, no matter which volume of water is used, and no matter which particular molecule of the water encounters which molecule of the other substance, the reaction takes place in just the same way. This is another version of the same testimony that whatever structure atoms and molecules have, it is highly identical and redundant from one such molecule to another.
The reason this example is everywhere is that every living thing on earth is one of the most sophisticated chemists we have ever observed, equalled only by other living things. Everything that lives is immersed in a tremendously complex chemical storm, of air, water and environment, food, toxins and other living things, not to mention the physical complexity of temperatures, light, gravity and various collisions to which it is exposed. From this chaotic and intricate environment, it selectively draws the parts to make more of its own structure and replace what is inevitably destroyed and eroded, and functions as a heat engine to selectively funnel and extract the power necessary to perform all these processes of building and organization. The intricacy of any living thing is a marvel of pre-arrangement, assembling and coordinating bit by bit the various mechanisms that make its living structure stable in this environment whose natural and simplest mechanisms are those which erode and degrade to disorder. No living thing could exist if it had to adjust to incorporate or resist each new chemical it encounters on a case by case basis, all the more so because if individual molecules had even miniscule differences, there would be no sense of a ``structure'' which could be built to perform any function; every combination of chemicals would be a unique and non-repeatable object.
So the whole existence of life hinges on the existence of chemistry, on the premise that a repeatable ``structure'' can be built from chemical blocks, which has a repeatable 'effect'' when it encounters some part of the chemical environment. The fact that clouds of gas far away and long ago cast recognizable shadows gives a sense of the extent in the universe to which atoms and molecules are reliably the same. The increadible sophistication of the chemistry of life, remarkable in that it exists at all, gives a sense of the precision with which the structures are the same. If any observation about nature is basic and should be part of the account of a modern theory of physics, it is this.