The Oxymoron of Quantum Coin-Flipping

Is the thought experiment of Schrodinger's cat similar to the experiment of coin flipping? Is it quantum physics or a simple probability problem? (original Quora question)

The question makes a good point. There's a problem in interpreting QM as something separate from simple probability relationships, and thereby attempting to wrangle reality into QM’s various mathematical and experimental boxes.

A take-away question would be, If reality is not a coin flip exercise (or playing dice with God, as Einstein once quipped), how does QM relate to reality?

I copied and pasted a few related passages from Letters on Wave Mechanics (1967).

Einstein to Schrodinger (1928)

Dear Schrodinger,

I think that you have hit the nail on the head. It is true that the evasion using the arbitrarily large domain of cyclic variables to limit the value of p is very ingenious. But an uncertainty relation interpreted that way does not appear to be very illuminating. The thing was invented for free particles, and it fits only that case in a natural way. Your claim that the concepts p,q will have to be given up, if they can only claim such a "shaky" meaning, seems to me to be fully justified. The Heisenberg-Bohr - tranquilizing philos­ophy-or religion? -is so delicately contrived that, for the time being, it provides a gentle pillow for the true believer from which he cannot very easily be aroused. So let him lie there.

Einstein to Schrodinger (1939)

There is also the mystic, who forbids, as being unscientific, an inquiry about something that exists independently of whether or not it is observed, i.e. the question as to whe­ther or not the cat is alive at a particular instant before an observation is made (Bohr). Then both interpretations fuse into a gentle fog, in which I feel no better than I do in either of the previously mentioned interpretations, which do take a position with respect to the concept of reality.

I am as convinced as ever that this most remarkable situa­tion has come about because we have not yet achieved a complete description of the actual state of affairs.

Of course I admit that such a complete description would not be observable in its entirety in the individual case, but from a rational point of view one also could not require this.

Schrodinger to Einstein (1950)

Dear Einstein,

It seems to me that the concept of probability is terribly mishandled these days. Probability surely has as its sub­stance a statement as to whether something is or is not the case-an uncertain statement, to be sure. But nevertheless it has meaning only if one is indeed convinced that the some­thing in question quite definitely either is or is not the case. A probabilistic assertion presupposes the full reality of its subject. No reasonable person would express a conjecture as to whether Caesar rolled a five with his dice at the Rubi­con. But the quantum mechanics people sometimes act as if probabilistic statements were to be applied just to events whose reality is vague.

The conception of a world that really exists is based on there being a far-reaching common experience of many in­dividuals, in fact of all individuals who come into the same or a similar situation with respect to the object concerned. Perhaps instead of "common experience" one should say "experiences that can be transformed into each other in a simple way". This proper basis of reality is set aside as trivial by the positivists when they always want to speak only in the form: if 'T' make a measurement then "I" "find" this or that. ( And that is to be the only reality.)

It seems to me that what I call the construction of an ex­ternal world that really exists is identical with what you call the describability of the individual situation that occurs only once-different as the phrasing may be. For it is just because they prohibit our asking what really "is", that is, which state of affairs really occurs in the individual case, that the posi­tivists succeed in making us settle for a kind of collective description. They accuse us of metaphysical heresy if we want to adhere to this "reality". That should be countered by saying that the metaphysical significance of this reality does not matter to us at all. It comes about for us as, so to speak, the intersection pattern of the determinations of many-indeed of all conceivable-individual observers. It is a condensation of their findings for economy of thought, which would fall apart without any connections if we wanted to give up this mode of thought before we have found an equivalent that at least yields the same thing. The present quantum mechanics supplies no equivalent. It is not con­scious of the problem at all; it passes it by with blithe disin­terest.

Einstein to Schrodinger (1950)

But it seems certain to me that the fundamentally statis­tical character of the theory is simply a consequence of the incompleteness of the description. This says nothing about the deterministic character of the theory; that is a thorough­ly nebulous concept anyway, so long as one does not know h,ow much has to be given in order to determine the initial stiate ("cut'').

It is rather rough to see that we are still in the stage of our swaddling clothes, and it is not surprising that the fel­lows struggle against admitting it ( even to themselves).

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