28 March 2012

Einstein-Schrödinger, Summer of 1935

Letters exchanged between Einstein and Schrödinger in the summer of 1935 had a lot to do with Schrödinger 's article published later that year introducing his quantum cat problem to the world. I've taken the quotes below from The Shaky Game: Einstein, Realism and the Quantum Theory, (C) 1986 by Arthur Fine, who, in this book, was the first to point out  how much Einstein influenced Schrödinger's invention of the simultaneously-alive -and-dead cat in the box.  

Google Books has at least some of Fine's book avaiable for viewing online

"During the summer of 1935," says Fine, "Schrödinger was in residence at Oxford, while Einstein was spending the summer at Old Lyme, Connecticut.  The Einstein, Rosen, Podolsky (EPR) paper. .. came out in the May 15, 1935, issue of The Physical Review. Schrödinger wrote about it to Einstein on June 7, and his part of the correspondence continued with letters to Einstein on July 13, August 19, and October 4. Before receiving the letter of June 7, Einstein had written to Schrödinger on June 17 and then wrote again, responsively, on June 19, August 8, and September 4."

Schrödinger to Einstein, June 7:

I am very pleased that in the work that just appeared in Physical Review you have publicly called the dogmatic quantum mechanics to account over those things that we used to discuss so much in Berlin. Can I say something about it? It appears at first as objections, but they are only points that I would like to have formulated yet more clearly.
Einstein, on June 17, before he'd received Schrödinger's June 7th letter, wrote to him and mentioned, among other things, the possibility of Schrödinger's appointment to the Institute for Advanced Study, in Princeton, New Jersey, where Einstein found employment soon after Hitler rose to power and Einstein gave up his professorship in Berlin. The Nazi's wanted to fire Einstein anyway (they labeled relativity "Jewish physics" and wouldn't allow it to be taught in Germany) but he pre-empted them by quitting. 

Einstein to Schrödinger, June 17:

From the point of view of principles, I absolutely do not believe in a statistical basis for physics in the sense of quantum mechanics, despite the singular success of the formalism of which I am well aware. I do not believe such a theory can be made general relativistic. Aside from that, I consider the renunciation of the spatio-temporal setting for real events to be idealistic-spiritualistic. This epistemology-soaked orgy ought to come to an end. No doubt, however, you smile at me and think that, after all, many a young whore turns into an old praying sister, and many a young revolutionary becomes an old reactionary.
"Einstein wrote again just two days later," Fine writes, "expressing his pleasure at  Schrödinger's 'detailed letter.' . . .  Recall that Einstein uses the analogy of finding a ball after opening one of two covered boxes in order to explain the idea of completeness and to motivate the intuitive concept of local causality (his 'separation principle'). It is in the context of this ball-in-the-box analogy, I believe, that Schrödinger's cat begins.  It has to do with the idea of completeness, concerning which Einstein writes this:"

Einstein to Schrödinger, June 17:

Now I describe a state of affairs as follows:  The probability is 1/2 that the ball is in the first box. Is this a complete description?

NO:  A complete statement is: The ball is (or is not) in the first box.  That is how the characterization of the state of affairs must appear in a complete description.

YES:  Before I open them, the ball is by no means in one of the two boxes. Being in a definite box only comes about when I lift the covers. This is what brings about the statistical character of the world of experience, or its empirical lawfulness. Before lifting the covers the state [of the two boxes] is completely characterized by the number 1/2, whose significance as statistical findings, to be sure, is only attested to when carrying out observations. Statistics only arise because observation involves insufficiently known factors, foreign to the system being described.

We face similar alternatives when we want to explain the relation of quantum mechanics to reality. With regard to the ball-system, naturally, the second "spiritualist" or Schrödinger interpretation is absurd, and the man on the street would only take the first, "Bornian" interpretation seriously. But the Talmudic philosopher dismisses "reality" as a frightening creature of the naive mind, and declares that the two conceptions differ only in their mode of expression.


Schrödinger to Einstein, July 13:

You have made me extremely happy with your two lovely letters of June 17 and 19, and the very detailed discussion of very personal things in the one and very impersonal things in the other. I am very grateful. But I am happiest of all about the Physical Review piece itself, because it works as well as pike in a goldfish pond and has stirred everyone up. . .
I am now having fun and taking your note to its source to provoke the most diverse, clever people: London, Teller, Born, Pauli, Szilard, Weyl. The best response so far is from Pauli who at least admits that the use of the word "state" ["Zustand"] for the psi-function is quite disreputable. What I have so far seen by way of published reactions is less witty. ... It is as if one person said, "It is bitter cold in Chicago"; and another answered, "That is a fallacy, it is very hot in Florida." . . .
My great difficulty in even understanding the orthodoxy over this matter has prompted me, in a lengthy piece, to make the attempt to analyze the current interpretation situation once and for all from scratch. I do not know yet what and whether I will publish on it, but this is always the best way for me to make matters really clear to myself. Besides, a few things in the present foundation strike me as very strange.

Einstein to Schrödinger, August 8:

The system is a substance in chemically unstable equilibrium, perhaps a charge of gunpowder that, by means of intrinsic forces, can spontaneously combust, and where the average lifespan of the whole setup is a year.  In principle this can quite easily be represented quantum-mechanically.  In the beginning the psi-function characterizes a reasonably well-defined macroscopic state.  But, according to your equation, after the course of a year this is no longer the case at all. Rather, the psi-function then describes a sort of blend of not-yet and of already-exploded systems.  Through no art of interpretation can this psi-function be turned into an adequate description of a real state of affairs; in reality there is just no intermediary between exploded and not-exploded.
. . .
My solution of the paradox presented in our work is this.  The  ψ function does not describe a state of one system, rather (statistically) an ensemble of systems. For a given
ψ1 wavefunction a linear combination c1ψ c2ψsignifies an expansion of the totality of systems.  In our example of the system composed of two parts A, B, the change that the ψ function suffers if I make an observation on A signifies, conversely, the reduction to a subensemble from the whole ensemble; the reduction simply occurs in accord with a varying point of view, depending on the choice of the quantity that I measure on A.  The result is then an ensemble for B, that likewise depends on this choice.

 Schrödinger to Einstein, August 19:

Many thanks for your lovely letter of 8 August.  I believe it doesn't work [das geht nicht] that one relates the psi-function to an ensemble of systems and thereby solves the antinomy or paradox.  To be sure I do not like the idiom "das geht nicht" at all, for it expresses the prejudice of the people with blinders who take certain computational devices as permanently established because otherwise they could not advance their own [ideas].

By the way, The Hebrew University's Einstein website is putting or has put about 80,000 Einstein documents online, as announced last year on Einstein's birthday