In 1907 a book was published, entitled Two New Worlds, which made serious, sober workers in the field of natural science rub their eyes incredulously.
The author, an Irishman, Fournier d'Albe, had already made important scientific-technical investigations, inter alia into the properties of that strange, photo-sensitive metal, selenium.
But the remarkable fact is that in the first part of his book he makes a profound study of what he calls the "infra-world," that is, the world in which atoms and electrons take the place of solar systems and planets. In the second part of his book he attempts to visualize the difference in proportions, considering our earth as an electron, our solar system as an atom of a "supra world." Fantasy? No doubt; but fantasy based on thorough knowledge. His views and calculations are partly founded on the results of scientific investigations into the structure of matter, partly guided by an excellent understanding of the laws of analogy, which he applied with masterly skill. Fantasy? Yes, but fantasy largely due to a keen intuition of that which cannot be grasped with mere knowledge of facts, and which is virtually veiled by the latter — and certainly not with the knowledge of scientific facts, which, naturally, is incomplete knowledge.
Thus, if we must at present revise Fournier d'Albe's results, it is because of our growing knowledge of the structure of matter.
Fournier d'Albe's intuitive basic idea is that there are various interpenetrating worlds, the denizens of one being yet utterly incognisant of the existence of other similar worlds, also inhabited by living beings, only on a scale many million times larger or smaller than their own; this really Theosophical conception holds equally well at present as when Fournier d'Albe surprised and amused the world by the "fantasies" referred to above.
To what issues did mathematics and analogy lead Fournier d'Albe? This may be made clear with reference to a few points discussed in his book.
First of all he showed what relation the units of length, time, force, and density of the infra-world bear to those applicable to our own world, arriving at the following conclusions.
In the infra-world the unit of length, like that of time, is 1022 times smaller than that of the "ordinary" world. The unit of force is even 1033 times smaller, the unit of density 1011 times larger than our own. A few examples will illustrate the immense significance of these seemingly simple facts.
Before proceeding any further, however, we would direct attention to the following observations.
Fournier d'Albe is convinced that each of the millions of infra-worlds of which the minutest speck of dust, or the smallest bacterium of our earth, is built up, is a world which, in outline, resembles our own. On this point he says:
No life remotely resembling our own is possible on any scale intermediate between us and the infra-world But if the main thesis of this essay is true, and the infra-world is a habitable universe not essentially different from our own, then there is no valid argument, either in physiology or psychology, to show the impossibility of our having been inhabitants of the infra-world previous to our birth into this world. A life of "seventy years" into the infra-world might be crowded with events, and yet it would add but an altogether inappreciable fraction to our earthly span of life. The facts of embryology are far from being accounted for, and the phenomena of ontogenetic development are so obscure that a reasonable hypothesis like the above can only tend towards their elucidation. It certainly removes the difficulty experienced in conceiving the boundless possibilities of life as being contained in an invisibly small germ.
In the latter part of this reasoning the unit of time plays an important role. Let us, for a better understanding, try to realize how long the "70 years" of the infra-world would appear to us. A simple calculation shows that the 2 X 109 (1) seconds of the infra-world (which practically form the seventy years in question) last shorter than a fifth of a billionth (Am. trillionth) part of a second in our world. A single wink of the eye takes longer in the infra-world than terrestrial geology accepts for the formation of the earth's crust. And yet, the infra-creatures live their lives, are born, grow and die, without any knowledge of the — in our eyes — tearing pace of their world.
Also infra-astronomy exists!
It will have taken the astronomers of the infra-world (i. e. an electron revolving about, say, an oxygen nucleus) many centuries to discover the laws in accordance with which the planets of this solar system — the remaining electrons of the atom — travel round their sun. If their attempts have finally been successful, they will have discovered . . . Kepler's laws, while their perturbation theory — though it may be different from ours in some respects — will also use the methods which the earth astronomers constantly apply.
Also the following example, which has been literally taken from Fournier d'Albe, may be useful to gain some understanding of the difference in time-scale. It shows how differently identical facts are interpreted by a terrestrial observer and an astronomer of the infra-world who lives on the planet "Talav" of the solar system "Grean." This solar system — an atom — consists, in addition to its sun and "Talav," of two other planets — electrons — called "Secunda" and "Tertia." A fourth electron has just joined this atom, but it is expelled from the system under the influence of ultra-violet radiation — a process which occurs countless times in every gas that is acted upon by ultra-violet light, and which process takes an unimaginably short period of time.
These events are described in the astronomical reports of the "Talav" observatory as follows:
"From the Records of the Talav Observatory" Year 5280, July 1. — This year's conjunction of Prima, Secunda, and Tertia is looked forward to with considerable interest. Tertia will certainly be lost to our system if she undergoes any additional outward perturbation.
Oct. 5. — Last night's observations show that the conjunction has not expelled Tertia. She is therefore safe for another 72 years, unless something extraordinary happens.
Year 5283, Feb. 5. — An unknown comet has been sighted in the orbital plane of Secunda. Approaching with a speed of 108 cm. per second, and will pass Grean at half Talav's distance. Will probably join our system.
March 1. — New comet turns out to be a planet of the size and mass of Talav, and same charge. Has joined our system, and will have an orbit of great eccentricity, extending considerably beyond that of Tertia.
Year 5285, March 15. — New planet is approaching apo-Grean, but is showing decided perturbations, which are shared by all other planets. These are cosmic and periodic. Period estimated at three months.
April 4. — New planet's orbit has become parabolic under influence of cosmic perturbations, and the planet will be lost to our system. (Terrestrial Note. — The above entries represent a case of ionisation by ultra-violet light.)
However interesting these speculations of Fournier d'Albe's may be, it is not to be denied that at the present moment they are no longer in perfect agreement with our scientific knowledge about the structure of matter. Although his reasonings and calculations have by no means become obsolete, present-day knowledge of facts — in so far as scientific facts exist — is different from what was known in 1907. Then, atoms and electrons were not yet the immaterial wave-structures which they may nowadays be conceived of without a risk of conflict with established facts.
However, this implies that even if the basis of Fournier d'Albe's reasonings (viz., his insight into the power of analogy) remains valid, his conceptions will nevertheless have to be modified so that his original ideas will hardly be recognised. His central idea, however, the one basis of his investigation, holds true now as well as it did then. Summarizing we may perhaps formulate this basis as follows: the great is repeated in the small. An atom is a solar system, just as we may look upon a solar system as an atom of gigantic dimensions. These ideas, it need scarcely be said, are purely Theosophical, and that is just why we want to reflect on them again, asking ourselves to what conceptions the Hermetic fundamental idea "as above, so below" may lead if it is applied in Fournier d'Albe's manner to what we at present know about the building stones of matter: the atoms. This is of particular importance since our Theosophical literature concerning these comparisons is still based on Bohr's model, although this model has long been superseded by the modern conceptions of matter-waves and the quantum-theory. The atom is no longer a system with a nucleus about which revolve spatially well defined electrons, nor is it off-hand comparable any longer with a material sun round which material planets are moving. It is this too — from a particular point of view — but it is much more, and this seems quite worthy of attention, because it may make for clarity of profound Theosophical doctrines. Moreover, such speculations might have a fructifying effect on the opinion of science about certain astronomical problems.
On the whole, scientists do not care for speculations such as Fournier d'Albe's. The reason again lies in the conflict between science — always searching for facts and their mutual relations — and philosophy — constantly attempting to penetrate behind the facts and undergo their realization, and this, we hold, should be the primary object of each investigation, and especially in the field of natural science.
However, we are not concerned here with the question whether or not science cares for the above speculation, but whether it disagrees with the findings of modern science; for if this should prove to be the case, science would rightly point to the field of perhaps attractive, but deceptive fantasies.
Now, the far-reaching analogy between a solar system and an atom cannot in a single detail be contradicted scientifically. Indeed, it is remarkable how, after first having exercised a fructifying influence on Bohr's conception of the atom — present-day astronomy itself shows a tendency to consult the atom-physicist and wants to be informed on certain details regarding the solar system which are puzzling it.
A case in point is the article by St. Mohorovicic, entitled: "Ein neues Gesetz fur die Entfernungen im Sonnensystem," which was published recently in the classical journal of astronomy: Astro-nomische Nachrichten, where the author says: "Our law, which probably indicates the most stable orbits, also applies to the atom-theory. Consequently, quite new conceptions will have to be introduced in theoretical astronomy, as has already been the case in the atom-theory."
It is easy to understand why in this article the atom-theory is taken as an example, for this theory treats of the regularity that is detectable in the distances between the various planets and the sun, and which greatly resemble the succession of the so-called "stable" orbits of the electrons round a nucleus. As these latter may be satisfactorily explained by the modern quantum theory as a result of the interference of matter-waves, it is obvious that the astronomer is looking for similar explanations of the succession of the planets" orbits. He may find them, if, reasoning along the same lines as Fournier d'Albe and Theosophy, he will look upon the solar system as a kind of atom on a gigantic scale, although he should bear in mind that analogy is not quite the same as identity. The solar system differs from the atom in many details. The laws that hold true for the atom cannot off-hand be applied to the solar system, but have to be formulated anew according to the prevailing conditions, though on the basis of the same principle. Thus also in astronomy the fundamental principle of the law of gravitation leads to quite different laws according as it is applied to the movements in a system consisting of the sun and a number of planets, or to the movements of a planet that is subject to the attraction of a binary star. The key of analogy is capable of opening many doors, but the entrant will perceive that there is a variety of rooms behind these doors, and that, to be able to live there, he will have to adapt himself to the prevailing conditions — which will often require his utmost exertions.
There does exist an analogy between a solar system and an atom. No scientific investigator can reasonably deny it in the light of our modern conceptions about the structure of the atom. For the analogy is so evident that the study of Bohr's model was facilitated by the fact that a large number of mathematical problems which presented themselves, proved to be closely related to problems astronomers had encountered in the perturbation-theory. As to the formal resemblance between the two systems — and science, especially mathematics, is silent where non-formality is concerned — not a single well-founded objection can possibly be raised to making an attempt to ascertain in how far the speculations of a Fournier d'Albe may be adapted to our present knowledge of facts.
In the following pages we shall try to give an outline of the consequences to which speculations as mentioned above may lead.
However, since a line of thought is something dynamic, and as such always of greater importance than any result obtained, which is therefore static, we shall especially try to explain in detail the trend of thought pursued, and hardly pay any attention to the provisional results found by this method.
This involves a difficulty, namely the unfeasibility of indulging in technical-mathematical speculations, while it is nevertheless just the short, symbolic notation of higher mathematics which is capable of throwing a vivid light on the scientific foundations of theoretical physics, for on this science our investigations are based as far as actual facts are concerned. This difficulty cannot be overcome. The best thing we can do is to steer between the Charybdis of these far-reaching theoretical speculations and the Scylla of superficial popularization.
First of all, we have to state more clearly the difference between Bohr's atom and the atom as conceived of in wave-mechanics.
In 1913 Bohr enunciated the idea that an atom is a solar system in miniature, consisting of a "nucleus" with a positive electric charge — the sun — about which particles with a negative electric charge — electrons — are revolving in circular or elliptical orbits. The electrons move under the influence of the electrostatic forces of the atomic system, and these movements are perfectly analogous to those of the planets of classical astronomy, which, inter alia, appears from the fact that, to a first approximation, Kepler's laws are also applicable to the atom. However, Bohr's hypothesis made it necessary to accept an atomic model that was quite different from all that theoretical astronomy tells us about the proportions of a solar system. For, Newton's law of gravitation, which in theoretical astronomy governs all the movements in a planetary system, does not in any way impose limitations on the magnitude of a planet's orbit about the sun. Nor does this law in the least interfere with the possibility of a certain planet following its course between the orbits of Venus and the Earth. However, it does not apply — according to Bohr — to the miniature solar system of the nucleus with its electrons. Here, the electrons are only capable of moving in orbits of sharply defined dimensions, each electron having the choice between a number of orbits of different lengths, but it cannot remain revolving in an intermediate orbit. If an electron is thrown out of its course somehow (by collision, release or absorption of energy) it cannot possibly change over to another differing but slightly from its previous orbit. Causes, which were quite obscure to Bohr — but which at any rate do not flow from the law of gravitation — compel the electron to take one of the other so-called "stable" orbits. The transition from one orbit to another takes place in such an infinitesimally short period of time that Bohr speaks of a "jump."
Bohr's new and daring hypothesis may therefore be summarized as follows: Sometimes the electron "jumps" — compelled by external causes — from one stable orbit to another. This jump (and this is the second new feature of Bohr's atomic model) involves the release or absorption of light by the atom, the characteristics of the light (color, wave-length) only depending on the jump in question.
The longer we reflect on this model, the more questions arise. What made Bohr introduce conditions that are not accepted in classical physics? What remains of the resemblance between the solar system and the atom, where the electron-planets are obliged to follow accurately prescribed courses, with the only possibility of "jumping" from one orbit to another? What is the analogy between the orbits of the planets and the stable orbits of the electrons? Is there something analogous to the "jump," something comparable with the emission or absorption of light during the jump?
It looks as if the beautiful analogy which first attracted us so much was a very superficial one, and that the scientific thinker — just on the strength of Bohr's atomic model — has to reject all speculations such as Fournier d'Albe's.
It indeed seems to be so — but is it true?
We would first of all state that Bohr's model has led to such great triumphs for theoretical as well as experimental physics and that it proved so capable of correlating such a large number of seemingly quite allied facts, that it must be largely based on reality.
However, as Bohr did not understand the proper background of his hypothesis — and could only point to their confirmations — it is clear that his model need by no means imbody the whole truth.
In the years following 1913, investigators tried to penetrate deeper and deeper into the essence of Bohr's representation. Men like de Broglie, Schrodinger, Heisenberg, Dirac, and others, obtained very elucidating results in this respect. Bohr's atom proved to be only a very rough picture of the much more complicated events that together form what we call an atom of matter.
The greatest progress that our knowledge about the structure of matter has made is, philosophically speaking, the fact that science has come to the conclusion that matter has to be described in terms that do no longer indicate any material property. Science begins to understand that the essentials of matter can only be approximated by the de-materialization of matter.
It is true, the Theosophical standpoint that spirit and matter are two aspects of one and the same "substance" (i. e., "that which stands firm') has not yet been altogether accepted. Science has but just started to leave its materialistic line of thought for a more spiritual one. But: la verite est en marche.
At this juncture it may be justly asked to what results the above investigations have given rise. In agreement with the more or less materialistic basic tendencies predominating in modern science, two directions have been followed, both of which lead to the same mathematical basic equation. This equation, as far as we are able to see it at present, governs all the problems of atom-physics; technically it is called "wave-equation." However, the opinions about the interpretation of this equation vary considerably. One group of scientists adhere to the existence of the smallest particles of which matter is said to be built up. But if this is true, they will have to give up the notion of causality as applicable to the behavior of these smallest particles. The natural laws are then no longer causal laws, but statistical laws of probability.
The other view, which at present has perhaps fewer adherents in the scientific world, definitely breaks with the conception of smallest particles as realities. It considers the separate particles, electrons, nuclei, or whatever they may be called, as more or less an illusion of the underlying reality. However, this reality itself cannot be understood in terms of time and space, for it transcends them altogether. Reality is one and indivisible, and its manifestations may be conceived of as a vast, universal vibration-process. If we direct our attention to definite, local areas — such as we may observe in the individual waves in looking at the sea — the causal laws operate with respect to the actions of these several parts among themselves. But as soon as we want to delimit a particular area more sharply, it becomes blurred and no longer possesses any well-defined boundaries, any more than a sea-wave is an isolated thing. However, this does by no means interfere with the notion of causality, which, strictly speaking, is applicable only to the actions of entities sharply separated by time and space, but rather expands it to universal interaction. Everything is related to everything else, because the entire multiplicity that we perceive with the senses or postulate with our mind behind the objects observed, is but an illusion of what is in reality One Whole. This thought, although science does not express it, is the basis of the "wave-structure" of matter. This is a purely Theosophical conception, for it is but the modern way of expressing that the world in which we live is a world of maya.
As said before, the two opinions about the significance of the wave-equation are still contending for priority. Direct observation — which is the only criterion acknowledged by science — has so far not been able to find anything that might turn the scale. But as soon as we reject the scientific line of thought and inquire after the sense of what has been found, then, at least as far as the Theosophist is concerned, there need be no doubt which of the two viewpoints approaches the occult truth more closely.
As we are, moreover, perfectly justified scientifically in considering matter as a wave-structure, we shall now return to the investigation in question, and try to find out whether a modification of Bohr's atom in accordance with the wave-theory, will clear up the difficulties mentioned above.
In view of the limited space available, we shall not enter into details on this point, but nevertheless we would establish the following fact: all the difficulties which Bohr's peculiar conceptions present disappear completely, while the points that attracted us in the above atomic model remain unchanged. For, so long as we continue to focus our attention on a small area, which, for convenience, might be called an atom, we indeed see something which, in outline, corresponds perfectly to Bohr's model: a "nucleus" surrounded by "stable" orbits in which an "electron" moves in the manner described above (in accordance with Kepler's laws, etc.). But this picture suggests itself only so long as we do not look attentively. As soon as we direct our attention to the electron, say, to find out its actual size, or to ascertain where it is at a given moment, then it resolves itself into what, for lack of a better expression, is frequently called a "wave-packet." It is not sharply defined spatially. It cannot be considered as an isolated part distinct from the other electrons and the nucleus. The atom, which seemed to consist of discrete components — the nucleus, the electron, the stable orbits, etc. — appears to be one indivisible unit, which cannot be split up into its constituents except artificially.
It is not possible to explain these results in more detail or make them acceptable. Nor is this necessary, for any more elaborate treatise on wave-mechanics or atom-structure will inform the reader of these technical questions as fully as he likes — if he wants to take the trouble to indulge in scientific investigations. For us, the principal question is: Is our solar system still comparable with an atom if we accept the views about the structure of matter and in particular those about the structure of the atom based on the wave-theory developed by de Broglie; or have Fournier d'Albe's speculations to be rejected altogether as being unfounded and not in agreement with actual facts?
Let us not give our answer too rashly. What are the facts that have to be considered?
First there is the atomic model of wave-mechanics, which shows us a solar system in which Kepler's laws hold good, but in which we have also to reckon with the existence of "stable" orbits, the "jumps" of electrons, and the radiation-phenomena to which they give rise. In addition, we know at present that this picture was founded on superficial observations. We also know that things are different in reality, that the sphere of action of each of these electrons extends through the whole atom; yes, in the last analysis, there are no isolated electrons, but only the one reality, which, as an atom, was separated from a still vaster reality beyond it, with which it forms one whole, just as the electron is one with the reality we have called "Atom."
The same line of thought has to be followed in regard to the solar system. There, we see the sun about which the planets travel in their orbits in accordance with the laws of gravitation, of which Kepler's laws are special cases.
Do stable orbits exist?
The majority of astronomers will be inclined to answer this question in the negative — and yet: there is the "law" of Bode and Titius, pointing to a remarkable grouping which is so strikingly regular that "fortuity" seems out of the question — although science has so far not quite succeeded in finding an "explanation" for this regularity; yes, even the correct mathematical expression for regularity is still a moot point.
Nor of this subject shall we give the technical details; suffice it to say that probably not all the orbits which are conceivable on the basis of the law of gravitation really exist — on the contrary, it is only very definite orbits that seem to be available for the planets. This inference permits the assumption that the atom possesses stable orbits, although finality has not by any means been reached in this matter; however, the orbits of different planets should not be confused with the different orbits in which one and the same electron may revolve.
"But," the opponents of the Fournier d'Albe theory will no doubt put forward, "even if we should admit the possibility of the existence of "stable" orbits in a planetary system, even then the fact remains that we have never yet observed a "jump" from one orbit to another." Quite true, of course. But the argument is not a sound one, since these opponents probably lose sight of the difference in time-scale. The "jump" of an electron takes an almost incomputably short time, we wrote — certainly, but measured with our standards! If we should describe this event in the language of the Talav astronomers, the word "jump" would not suggest itself at all. We should learn that, owing to a certain cosmic disturbance which it either would be or would not be possible to specify any further, the orbit of a particular planet slowly shifted altogether over a period of many thousands of centuries. And as to the chance of such an event occurring, it should be borne in mind that between every two "jumps" of the same electron, milliards of "electron centuries" elapse; and when a new "jump" begins to take place, even the remembrance of the preceding "jump" will therefore have been obliterated.
The same consideration might be applied to our solar system if we should like to maintain the analogy in question. Not a single argument based on actual facts is capable of contradicting the possibility of the existence of "stable" orbits and "jumps" in our planetary system. Nor can we point to events that argue for this assumption. However, as facts are lacking and Fournier d'Albe's views seem plausible, it is permissible to adopt them and to posit a far- reaching analogy between the atom and the solar system — as this is in perfect agreement with the Gupta-Vidya.
But if we do this seriously, we have to go a considerable step further. For then we can no longer look upon the sun and the planets as spatially limited and isolated bodies. Just as the electron as an isolated particle proved to be an illusion, we shall have to give up the idea of the planets and the sun being separate units.
On the face of it, this seems to be an unrealizable demand. But if we reflect on it and make ourselves familiar with the idea, the truth begins to dawn upon us with the conviction that such a view is perfectly tenable.
Our opinion about the limitation and separateness of each several planet is in the last analysis based on our deep-rooted materialistic views, which make a fundamental difference between "matter "and the "force" exerted by that "matter." But it is just the most recent atomic theories that are beginning to doubt the validity of such a distinction. Matter and force — on a higher plane: pro-matter and spirit — are aspects of the one Substance. This novel truth — which has been known to the Keepers of the holy Occult Wisdom or Gupta-Vidya from time immemorial, but which became lost for the bulk of humanity — cannot be repeated too often. The discoveries of science will prove the correctness of the Old Wisdom at the same rate as science will succeed in understanding the profound meaning of the latter.
As already said before: In the light of wave-mechanics there is no essential difference between an electron and the field of force of that electron. But does not exactly the same apply to a planet? Also a planet makes itself felt far beyond its immediate vicinity by the action it exercises, surrounded as it is by its own field of gravitation, by an electric and a magnetic field. If we pay attention to its sphere of action and identify the planet with it — as we dissolved an electron into a system of interpenetrating waves interfering with each other — then each planet occupies the whole space of the solar system, and a planetary system can no longer be considered as a unit made up of the sun and a number of relatively small, delimited orbs traveling about the sun, but as a com-plex conglomerate of interpenetrating spheres, which are moving in and through each other and interacting most intimately.
Thus, the old idea that the different planets influence each other, which the modern pseudo-science of astrology has taken from the true Astrology of the Ancients, also called the Science of the Gods, regains its true significance. And in this connexion it should be especially noted that the interaction of the planets is not restricted to the physically perceptible actions of gravitation or magnetic and electrical influence, but that this action and penetration also include astral and spiritual influences — which science has so far remained utterly ignorant of.
This far-reaching conclusion suggests itself at once if we revise Fournier d'Albe's speculations and bring them into line with the modern scientific conception about the structure of the atom.
Is it saying too much to maintain that modern science perfectly agrees with the teachings of the Old Wisdom, thus confirming H. P. Blavatsky's Message?
1. The reader need not look askance at this probably queer notation. We chose it to be able to write in a simple form otherwise inconveniently large and unmanageably long figures. For instance, 109 (read: ten to the ninth power). (return to text)
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