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 c₁ψ₁  +  c₂ψ₂  signifies 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. 

Get on the wave train...

I still have almost all the math and physics textbooks I bought for classes during my undergrad and graduate school careers, and one of my favorite texts is simply called Optics.  My copy of the book is a first edition (1974) and third printing (December 1976), and was the chosen textbook for an undergraduate class I took in the spring of 1978 at the University of Arkansas at Little Rock called Optics and Wave Motion.

(Bill Clinton was elected governor of Arkansas for the first time in 1978.  In '77 and '78, I worked as a nightwatchman at the Old State House while attending UALR.  Clinton gave a fundraising party at the Old State House in early 1978, at night.  Making one of my hourly rounds through the building, I crossed paths with him.  He shook my hand and said, "I'm Bill Clinton.  I'm running for governor."  I said, "I'm David Trulock.  I work here."  That was it, as far as I recall.)

The authors of this particular text on optics are Eugene Hecht and Alfred Zajac, professors of physics at the time at Adelphi University.  I think they did a good job writing the book, which is not the general rule with textbooks. Here's a quote from their book, one of several I'll be discussing related to the concept of coherent superpostion and polarization. This is from the section titled "Natural Light" in the chapter on polarization:

An ordinary light source consists of  a very large number of  randomly oriented atomic emitters. Each excited atom radiates a polarized wave train for roughly 10^-8 seconds.  All of the emissions having the same frequency will combine to form a single resultant polarized wave which persists for no longer than 10^-8 sec.  New wave trains are constantly emitted and the overall polarization changes in a completely unpredictable fashion. If these changes take place at so rapid a rate as to render any single resultant polarization state indiscernable, the wave is referred to as natural light. It is also known as unpolarized light, but this is a bit of a misnomer since in actuality the light is composed of a rapidly varying succession of the different polarization states.

 We can mathematically represent natural light in terms of two arbitrary, incoherent, orthogonal, linearly polarized waves of equal amplitude (i.e. waves for which the relative phase difference varies rapidly and randomly).

Okay. So natural light, say sunlight such as that streaming in the library window right now (11:27 am CST) onto my keyboard, involves a bunch of little bitsy wave trains, which is what I meant when I said light is produced by random atomic electromagnetic expectorations.  The often-depicted sine wave (single frequency) light wave is quite different:

Keep in mind that an idealized monochromatic plane wave must be depicted as an infinite wave train. If this disturbance is resolved into two orthogonal components perpendicular to the direction of propagation, they, in turn, must have the same frequency and be infinite in extent, and therefore be mutually coherent (ε = constant).  In other words, a perfectly monochromatic plane wave is always polarized. …

What I really want to get to is Hecht & Zajac's discussion of representing a linearly polarized beam of light as consisting of identical photons which themselves must be considered individually as coherent superpositions of left and right circularly polarized states.  This relates to Gordon Baym's discussion of delicate phase relationships, and is the same idea of the superposition of live and dead cat states in the dilemma of Schroedinger's cat:

We have already seen that an electromagnetic wave can impart both energy and linear momentum. Moreover, if a plane wave incident upon some material is circularly polarized we expect electrons within the material to be set into circular motion in response to the force generated by the rotating E-field.  Alternatively we might picture the field to be composed of two orthogonal P-states which are 90° out of phase.  These simultaneously drive the electron in two perpendicular directions with a π/2 phase difference.  The resulting motion is again circular.  In effect the torque exerted by the B-field averages to zero over an orbit and the E-field drives the electron with an angular velocity ω equal to the frequency of the electromagnetic wave.  Angular momentum will thus be imparted by the wave to the substance in which the electrons are imbedded and to which they are bound. …

Thus far we’ve had no difficulty in describing purely right- and left-circularly polarized light in the photon picture; but what is linearly or elliptically polarized light? Classically, light in a linear polarized state can be synthesized by the coherent superposition of equal amounts of light in right and left circularly polarized states (with an appropriate phase difference).  Any single photon whose angular momentum is somehow measured will be found to have its spin totally either parallel or anti-parallel to its direction of propagation.  A beam of linearly polarized light will interact with matter as if it were composed, at that instant, of equal numbers of right- and left-handed photons.

There is a subtle point that has to be made here. We cannot say that the beam is actually made up of precisely equal amounts of well-defined right- and left-handed photons; the photons are all identical. Rather, each individual photon exists simultaneously in both possible spin states with equal likelihood. On measuring the angular momentum of the constituent photons, -ћ would result equally as often as +ћ.  This is all we can observe. We are not privy to what the photon is doing prior to the measurement (if indeed it exists prior  to the measurement).  As a whole, the beam will therefore impart no total angular momentum to the target.

In contrast, if each photon does not occupy both spin states with the same probability, one angular momentum, say  +ћ, will be measured to occur somewhat more often than the other, - ћ.  In this instance, a net positive angular momentum will therefore be imparted to the target.  The result en masse is elliptically polarized light, i.e. a superposition of unequal amounts of right- and left-handed light bearing a particular phase relationship.

(For the uninitiated, E(t) = Asin(ωt + ε) is an equation for a sine wave, or single frequency wave, with amplitude A, frequency ω, phase difference ε relative to some other sine wave, and t representing time; E and B are the standard letters designating the electric and magnetic fields, respectively;  P-states are linearly polarized states,  π/2 is a different way of saying 90°, and  ћ is Planck's constant divided by 2π.)

So I hope you all can see again that even for describing a single photon, the same existential language and quantum superposition model as in the Schroedinger cat problem are necessary.  But are they sufficient?  That's the big question in the debate on the EPR problem, which Einstein and Niels Bohr continued to disagree on until they died (E. in 1955, B. in 1962).  Next time: The Shaky Game: Einstein, Realism & Quantum Theory, by Arthur Fine.