Are Quanta Real?: A Galilean Dialogue – J.M. Jauch

Third Day
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SIMPLICIO’S DREAM I was in a vast, dimly lit hall, like a church, and there were very many people around. Someone was officiating as at a religious service,(¹) but I could not see him at first because the crowd barred the view. The people were all very solemn and they seemed to know what was going on,(²) but I was completely in the dark as to the meaning of it all. Finally I asked somebody next to me what this was all about. He looked at me rather surprised and then he said in a low voice, “Don’t you know that we are here to await our fate?”(3)

This did not make much sense to me, but because of the solemnity of the occasion I did not have the courage to ask further.

Then I noticed that the crowd was slowly moving toward the center of the sanctuary. I moved along with it, and when I finally arrived close enough to see, I perceived a very old man(4) with a silvery beard wearing a long white dress. He was standing near a roulette table throwing a ball made of luminous stone.(5) Many players stood around the table. Each one had only one chance to play. After the play a little Maxwell demon (6) handed each player an envelope containing his fate and escorted him from the room.

When it was my turn I was frightened and wanted to run away. But one of the Maxwell demons had put his crooked hand around my wrist and croaked with a fantastic little giggle: “Come on, buddy, you can’t escape your fate.”

Seeing that there was nothing else to do, I took my chip and put it on number three. A woman who was standing next to me whispered in my ear (7): “You are a fool, you will never unify the opposites on three. You should have chosen four.”

I felt terribly foolish at not having noticed that myself (8) but at this very moment the old man said sharply: “Les jeux sont faits, rien ne va plus.”

The luminous ball was circling around in an erratic manner, tumbling from one number to another, until it finally came to rest on number three. I had won! (9)

A muffled exclamation of wonder broke the silence and everybody looked at me with astonishment and envy. The mean little Maxwell demon became excessively polite, and the croupier handed me a golden(10) envelope, which contained a card with the following inscription:

The Green Man will see you in his chambers; follow your guide.(11)

Immediately my little demon took me gently by the hand and led me through the crowd, which cleared the way respectfully to let us pass. We came to a door and then descended a spiral staircase into a long, dark passage. At its end we entered a chamber lighted with a pleasant, pale green light. At the wall opposite the entrance was a throne, on which sat the “Green Man,” who immediately addressed me with these words: “I have expected you for a long time and you never came, but now that you are here, it is time to begin. You must find the unknown road to truth.”

I was deeply impressed and did not know what to say. Before I could collect my thoughts the “Green Man” continued: “Tell us what you need in your search for truth, it shall be granted. But remember, you can have only one wish, the rest is up to you.”

I was so startled by this sudden revelation that I could scarcely think. Then the meaning of the statement became clear to me, and I said quickly: “Give me a library containing the books with all the wisdom, all the truth, and all the beauty of all time.” (12)

I had barely finished speaking when the light in the room dimmed and a strange transformation took place. When I began to discern the details of my surroundings I discovered that I was in a kind of open spaceship floating through an immense row of book stacks, which extended to infinity in all directions. The spaceship could be moved at any speed up to that of light and could be stopped in an instant without the least feeling of discomfort. Every hundred miles in each direction there was a small platform on which was installed a librarian working at a desk. I went to one of the stacks and opened a beautiful, leather-bound volume. To my astonishment I could not read it, since it seemed to contain only a random series of letters and spaces. Thinking that it might be written in a foreign language I went to the nearest librarian, about 30 miles away, and asked in what language it was. His answer startled me even more. He said:

“These books contain everything that ever was and ever will be written in any language of the past or the future. But together with all the meaningful statements, they also contain all the random sequences of letters up to the longest book that will ever be written. This is the only truly complete library in the world because it contains everything.” (13)

“But such a library must be infinitely large!” I exclaimed. “No,” he replied, “this library has a finite number of volumes. The exact number is unknown but it is finite.”

“But how can I ever find anything in this library?” I asked in despair.

“We have a most efficient electronic retrieval system,” he said, “and anything you want can be instantly commanded by composing on this command console a message to the central memory device.” To show me how it worked, he commanded for me in an instant a letter written by Galileo to his daughter, Sister Maria Celeste, in 1633.

I was deeply impressed, because I knew that this letter, hitherto lost,(14) contains the clue to the unsolved mystery of Galileo’s trial before the Inquisition in 1633.

But before I had time to open the book and read the letter the librarian continued, “Anything that you wish to see is here at your disposal. Try it for yourself.”

I thought quickly what I could command, and after some reflection said, “Let me see the theory of elementary particles which explains all known facts about them.”

“Which one?”

I was a bit surprised at this question and replied, “I did not know there are several. Of course I want the correct one, that is the one which agrees with all the facts known today.”

He smiled and explained, “There are 137 different theories available which satisfy this requirement. You must give me further specifications if I am to select one. Or do you wish to see them all?” (15)

Much surprised that there should be so many different, correct theories, unable to think of any other criterion for selecting one from all this wealth of theories, and lacking the inclination to study them all, I replied, “No, not just now, I just wanted to know what is available.”

As he turned away to resume his work, which no doubt was immense, he said courteously, but a bit dryly, “Any time you need anything, I am at your disposal.”

I left him, and a deep feeling of depression came over me as I moved aimlessly through my immense library in the three dimensions of never-ending space. . . . . .
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Notes:-

1. The semi religious setting, the dim light, and the mystery are all symbols which underscore the ideological involvement in Simplicio’s psychic state.

2. Ideologies are in a sense also social adaptations, and the better they function the less is required of the individual to differentiate himself from the others in the crowd. The process of individuation begins with the awareness of the “other,” who usually seems to the beholder much better adapted than himself.

3. This is it! The fatal word has been pronounced. It is the source of Simplicio’s anxiety, and it represents the existential counterpart of determinism.

4. The “wise old man” is a well-known archetype discovered by C. G. Jung in countless dream sequences. The encounter with the “wise old man” means that the resources of collective racial wisdom are at the disposal of the dreamer if he learns to read and assimilate the symbolic message of the dream.

5. The luminous stone is the “lapis philosophorum” of the alchemists. It symbolizes the integration of the personality.

6. The Maxwell demon was invented by Maxwell in his famous discussion on the irreversibility of thermal systems. It is an imaginary creature (or device) which can control the movements of individual atoms. The demons cannot actually function in physical systems because they are subject to the same fluctuations as the atoms which they are to control. The fact that they can function in the dream means that they are creatures from another level of reality than the dreamer, and thus carry the message of the existence of deeper levels of consciousness which are essential for the psychic processes about to be initiated in Simplicio.

7. The mysterious woman whispering into Simplicio’s ear is the archetype of the “anima.” She is the harbinger of instinctive truths yet to be learned by Simplicio. The passage from the number three to four symbolizes a fundamental problem in individual psychology that is related to the acceptance and unification of opposites. In the context of the dialogue it represents the symbolic acceptance of the principle of complementarity, for which Simplicio is not yet ready.

8. The self-assured intellectual male looks foolish next to the instinctive female, who, with one simple gesture, can upset his entire value system.

9. This is the heart of the dream’s message: What is the good of winning the whole world if one loses one’s own soul? Evidently there are two ways of winning and losing. The first is the one to which the anima was referring just before the game started. The other is the one which we now see occurring. Simplicio is not yet capable of distinguishing the two, hence his surprise at
“winning” when just a moment before he believed the anima that he was going to lose.

10. The gold represents the material gain and also, on a symbolic level, the objective of alchemy.

11. The color green is the symbol of hope and of a new start. It often occurs in dream sequences at a decisive moment in the individual’s history, when options leading to new prospectives become available.

12. This is typical of the materialist’s psychic disposition. He believes that there is no problem which cannot be solved by more or bigger material things.

13. The idea of the “complete” library has been discussed many times before. It occurred to the author from reading “The Library of Babel” by J. L. Borges, in Labyrinths (New York: New Directions, 1961). It poses an interesting paradox. For instance, being complete the library must also contain all its catalogues, including the catalogue of all the catalogues and so on. Evidently such a library cannot be finite. This problem is closely related to Russell’s paradox.

14. We know that the letter referred to here was actually written by Galileo since the replies from his daughter in the convent at Arcetri are preserved. The letters from Galileo to his daughter are unfortunately lost. They would be the most important source of information on Galileo’s trial, since in them he gives a complete account of everything that happened to him when he was questioned by the inquisition in Rome.

15. This is the point where the naked truth is revealed to Simplicio. The ultimate wisdom is not to be found in quantity. There is the other side, so far completely overlooked by Simplicio. There are two criteria of truth as Einstein told us and, as the dream shows, the neglect of the second one leads to absurdity. Cf. A. Einstein, Autobiographical notes, in P.A. Schilpp, ed., Albert Einstein, Philosopher-Scientist (Evanston, Ill.: Library of Living Philosophers, 1949), p. 11.

Fourth Day
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SAGREDO If this is so, may we not try to formulate axiomatically the essential properties of a measuring instrument by saying that such an instrument must permit the choice between classical alternatives and no others. This is the exact translation of your definition of unambiguous and of objective, and means, in the formalism of quantum mechanics, that the only observable quantities which can be measured with a particular apparatus are represented in this formalism by commuting projection operators.

SALVIATI I believe that such a characterization of the measuring instrument is possible, but I must express a warning concerning the absolute precision of such an axiomatic formulation. The word “classical” cannot single out such clear-cut properties as you imply with your axiomatic representation. It should be used only in an approximate sense. Indeed, any concrete model of the measuring process based on the essentially quantal nature of all material bodies shows only that the nonclassical features will be absent with an overwhelming probability in the sense of statistical physics. The axiomatic treatment of the measuring process would thus seem to idealize the situation more than it need be.

SAGREDO I understand exactly what you mean and I am convinced that you are right on this point. But in spite of this, it seemed to me of interest to bring out the ideal classical properties of a measuring apparatus with full precision and clarity which can be furnished only by the axiomatic characterization of such a system. The situation is similar to those which we have noticed several times, when an essential point can be made more easily with idealized elements and concepts in a theory. For instance, this is the case when we use irrational numbers. Strictly speaking, such numbers have no counterpart in reality, yet they are extremely useful.

Of course, I am no doubt presumptuous in trying to contradict you in a matter which you understand so much better than I could ever hope to.

SALVIATI I think your point of view offers no serious inconvenience so long as you keep in mind the limitation of your method. In particular, in such a process one must always remember that no formal rendering can ever be complete, that it must leave undefined a certain number of “primitive” concepts and take for granted, without further analysis, certain relationships between these concepts. The concrete meaning of these primitive concepts and axioms can only be formulated in a “meta language” which is outside the formal scheme of the theory. The particular difficulty in this situation is that the proper choice of these undefined concepts and of their interpretation presupposes a complete knowledge of the entire physical situation. Thus at the outset there is a mutual interdependence of the physical content and its conceptualization which can never result from a simple, logical process.

Once one has understood this point one is necessarily more reluctant to attach a great deal of importance to the axiomatic-deductive organization of a theory such as quantum mechanics, although on a superficial level or for didactic purposes such a procedure might be quite useful.

SAGREDO What you say is certainly most significant and lends credence to the belief that there is much more in science than the mere observation and recording of events and their integration into a conceptual structure.

There are also vision and creative imagination, qualities which alone enable us to abstract from the multitude of possible phenomena those which reveal the true nature of reality. Science reveals structures which are significant or meaningful in some sense and the more meaningful they are, the more real they are.

Is this not the answer to the unresolved task in Simplicio’s dream? Are they not the ingredients needed to bring to light the beauty and perfection of creation, all hidden away in Simplicio’s library, but inaccessible to him because he did not pay attention to what is essential in the search for truth?

Among those principles, that of complementarity is no doubt the sum and substance of our experience with the phenomena of microphysics. Instead of being a principle which expresses the limitation of our ability to know, it expresses the very essence of the objective rendering of the physical phenomena in the unambiguous language pertaining to factual evidence. Once its general character is recognized its operation is seen in many areas where objectivation of experience takes place. In particular, the behavior of quantal systems furnishes us with new points of view concerning the essential properties of composite systems, where it is recognized that the sum of the parts does not at all exhaust the properties of the whole.

SALVIATI I do agree, Sagredo, and I have on several occasions formulated similar ideas. I would go further and add that the understanding of the behavior of individuals interacting within a group is incomprehensible without new structural and dynamical categories which cannot be derived from individual behavior.

Just as the correlations between interacting quantal systems lead to many different kinds of mutations in the behavior of individual systems, which, for want of a better term, we call quantum jumps, so does the person integrated in a group produce spontaneous insights which would have been inaccessible to him in isolation.
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