"If physicists were for once to talk sense,
they would not produce speculations about atoms...."
— Rudolf Steiner
What are atoms, according to Rudolf Steiner? Well, for one thing, they don’t really exist.  But no, wait, they do. 
If they do exist, what are they? Well, “[T]he atom is nothing else than congealed electricity.”  What in the world can this mean? This is tough...
But don’t worry about it — atoms are, in a sense, something else altogether. And what is that? “[A]toms are really tiny little caricatures of demons....” 
OK? You may think this "clarification" takes us a long step away from clarity, but that's what the man said.
But wait again. “[T]hose thought-out atoms have no existence ... [T]his old atomic theory has no longer any validity whatsoever. We think it out — and yet feel it has nothing to do with reality.” 
OK? Got it? Atoms are this or that, but in any event the atomic theory (or at least the "old" atomic theory) is invalid. Atoms (or at least atoms that we think out) have no existence. This is what we "feel," anyway.
Figuring this out may take a little more thought (or feeling)...
I’ll get back to you.
— Roger Rawlings
TO BE SERIOUS
FOR A MOMENT
Joking aside, we can understand Steiner, heaven help us. He didn't hold with any atomic theory, new or old (except his own). Things don't fundamentally consist of atoms, he argued; they fundamentally consist of spirit.
What he was getting at is that atoms are empty bubbles.  And by this (he always had trouble explaining himself) he meant that thinking about atoms gets us just about nowhere since atoms (if they "exist") are mere physical constituents. Atoms would be meaningful phenomena only if they were understood to be filled with spirit, specifically the Christ Impulse. "[T]he old atomic theory...has nothing to do with reality. [paragraph break] But things are quite different when we permeate our ideas, our abstract laws, with what in truth is the Christ Impulse; and when I speak of the Christ Impulse I do not mean anything that the orthodox creeds look to...." 
The Christ Impulse is nothing you can learn about in churches — regular religions, even regular forms of Christianity, are wrong. And the Christ Impulse is nothing you can learn about through science — because science (except for Steiner's own "spiritual science") is wrong. The only way to learn the true Truth, gentle reader, is to heed Steiner. The Christ Impulse, according to Steiner, is the spiritual impetus that Christ (the Sun God) enabled, which — if we enact it ourselves — will carry us forward in our Steiner-foreseen stupendous spiritual evolution.
Now, you may or may not like the sound of any of this (some people do like the notion that material phenomena are meaningless unless imbued by spirit — they intuit that this must be the case) — but whether or not you like it, it suffers from the slight drawback that it cannot be confirmed in any way except subjectively, in our feelings, our intuitions, our clairvoyance. And to have reliable, high-grade clairvoyance, we need to develop organs of clairvoyance. (I've been over this before. I hope you were paying attention.)
And here Steinerism falls to the ground, cracks open, and blows away as tiny grains of dust (or, might I suggest, atoms?). Organs of clairvoyance do not exist. Clairvoyance does not exist. Our intuitions can often be dead wrong. And our emotions are very, very often dead wrong. They are subjective, meaning that they are disconnected from objective reality — they are the stuff of preference and dream and fantasy and neurosis and subconsciousness and misunderstanding.
In brief, gentle reader, Steinerism is null and void. It has no real contents. The empty bubble is not the atom, it is Anthroposophy.
Steiner also spoke of "atoms," in rather a different sense, as kernels or seeds: During evolution, gods and other high beings create a plan that we must follow, if we are wise. Each stage of evolution is created within an "atom" that later expands, becoming that stage. For example, we are now in the "Earth" stage of our evolution (that is, we now live on "Earth," having formerly lived on "Saturn," "Sun," and "Moon"). Each stage emerged from an "atom" created in the previous stage.
We will next go on to "Jupiter", which will spring from the appropriate "atom" being created for us now: "[D]uring the evolution of each planet a specific plan is worked out by the guiding powers. While the earth is evolving, plans for the atom for the evolution of Jupiter — which succeeds the earth — are drawn up." 
Such atoms would not be empty bubbles if they existed. Just one small problem: They don't.
"If physicists were for once to talk sense, they would not produce speculations about atoms and molecules, but they would say: The visible world consists of the past, and carries in it not molecules and atoms, but the future. And you would be right in saying of the world that the past appears to us in the present, and the past wraps up everywhere the future, for the present is only the total effect of past and future. The future is what lies in the strength of matter. The past is what shines in the beauty of light, which includes, of course, sound and warmth." 
"[T]he rationally-minded scientists of the present day are all occultists of materialism, for they talk of 'atoms'. But if they are not irrational it will never occur to them to declare that with any kind of 'method' one can never come to the atom. The atom remains in the occult. It is only that they do not like to be called 'Occultists', but they are so in the fullest sense of the word." 
"The physicist imagines that each body consists of an infinite number of immeasurable small parts, like atoms. They are not in contact with each other, but they are separated by small interstices. They, in the turn, unite to larger forms, the molecules, which still cannot be discerned by the eye. Only when an infinite number of molecules unite, we get what our senses perceived as bodies ... The physicist explains all sense-perceivable, all sense-perceptible qualities by motion. So, what moves cannot yet have qualities. But what has no qualities cannot move at all. Therefore, the atom assumed by physicists is a thing that dissolves into nothing if judged sharply. So, the whole way of explanation falls. We must ascribe to color, warmth, sounds, etc., the same reality as to motion. With this, we have refuted the physicists, and have proved the objective reality of the world of phenomena and of ideas." 
Anthroposophists are convinced by Steiner's arguments on such points; virtually no one else is.
This will clarify everything:
"[T]hrough the electrification of the atoms we transform them into carriers of evil ...
[W]hen we imagine matter in the form of atoms, we transform these atoms into carriers of death;
but when we electrify matter, Nature is conceived as something evil. For electric atoms are little demons of Evil."
— Rudolf Steiner, "Concerning Electricity", ANTHROPOSOPHIC NEWS SHEET, No. 23/24, June 9, 1940 —
from a lecture delivered January 28, 1923.
with thanks to Crayola.]
“How can one, as an occultist, now know anything about the atom?
Now just imagine it to be possible to make an atom grow continually bigger and bigger until it was as big as the earth;
one would then discover a very complicated world ...
Only the occultist is in a position to enlarge the atom so much and to contemplate its interior.”
— Rudolf Steiner, THE TEMPLE LEGEND (Rudolf Steiner Press, 1997), p. 185.
Should I laugh about Steiner's teachings? Perhaps not.
Yet I find laughter better than wailing or grumping.
And, after all, absurdity is usually laughable.
And Steiner's teachings were generally, marvelously, absurd.
 Rudolf Steiner, SCIENCE (Rudolf Steiner Press, 2003), p. 192.
 Ibid., p. 192.
 Rudolf Steiner, THE TEMPLE LEGEND (Rudolf Steiner Press, 1985), p. 114.
"We are going forward to an age when, as I indicated recently, men will understand what the atom is, in reality. It will be realised — by the public mind too — that the atom is nothing but coagulated electricity. — The thought itself is composed of the same substance. Before the end of the fifth epoch of culture, science will have reached the stage where man will be able to penetrate into the atom itself. When the similarity of substance between the thought and the atom is once comprehended, the way to get hold of the forces contained in the atom will soon be discovered and then nothing will be inaccessible to certain methods of working." — Rudolf Steiner, "The Work of Secret Societies in the World - The Atom as Congealed Electricity" (transcript, Rudolf Steiner Archive), a lecture, GA 93.
 Rudolf Steiner, RHYTHMS OF LEARNING (Rudolf Steiner Press, 1998), p. 161.
 Rudolf Steiner, WONDERS OF THE WORLD, ORDEALS OF THE SOUL, REVELATIONS OF THE SPIRIT (Rudolf Steiner Press, 1963), p. 184.
 SCIENCE, p. 192.
 WONDERS OF THE WORLD, ORDEALS OF THE SOUL, REVELATIONS OF THE SPIRIT, p. 184.
 Rudolf Steiner. THE TEMPLE LEGEND AND THE GOLDEN LEGEND (Rudolf Steiner Press, 1997), p. 190.
For more on this, see "The White Lodge."
 Rudolf Steiner, COLOUR (Rudolf Steiner Publishing Company, 1935), lecture 1, GA 291.
 Rudolf Steiner, HUMAN AND COSMIC THOUGHT (Rudolf Steiner Press, 1991), p. 49.
 Rudolf Steiner, ATOMISM AND ITS REFUTATION (Mercury Press, 1975), a letter and an essay, GA 38.
"[A]ll atoms are holes or empty bubbles in the spiritual world. All physical things are composed of countless numbers of such holes. When we touch things we bump into these holes, this nothing." — Rudolf Steiner, FROM THE CONTENT OF THE ESOTERIC CLASSES (transcript), 3-31-1914, GA 266.