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PROBABILITY C.C. Gaither, Alma E Cavazos-Gaither
Published Apr 19, 2016 • 0 citations
Abstract Born, Max As far as I can see, the only foundation of the doctrine of probability, which (though not satisfactory for a mind devoted to the ‘absolute’) seems at least not more mysterious than science as a whole, is the empirical attitude: The laws of probability are valid just as any other physical law in virtue of the agreement of their consequences with experience.
DOI 10.1201/9781420034639-153 Related papers Albert Einstein to Max Born
Albert Einstein
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Born, Max As far as I can see, the only foundation of the doctrine of probability, which (though not satisfactory for a mind devoted to the ‘absolute’) seems at least not more mysterious than science as a whole, is the empirical attitude: The laws of probability are valid just as any other physical law in virtue of the agreement of their consequences with experience.
Some relations between physics and finitary and infinitary mathematics are explored in the context of a many-minds interpretation of quantum theory. The analogy between mathematical ``existence'' and physical ``existence'' is considered from the point of view of philosophical idealism. Some of the ways in which infinitary mathematics arises in modern mathematical physics are discussed. Empirical science has led to the mathematics of quantum theory. This in turn can be taken to suggest a picture of reality involving possible minds and the physical laws which determine their probabilities. In this picture, finitary and infinitary mathematics play separate roles. It is argued that mind, language, and finitary mathematics have similar prerequisites, in that each depends on the possibility of possibilities. The infinite, on the other hand, can be described but never experienced, and yet it seems that sets of possibilities and the physical laws which define their probabilities can be described most simply in terms of infinitary mathematics.
Translated by Irene Born Newton-John In this letter to his old friend, now at Edinburgh University, Einstein first responds to Born’s description of a local physician “who wouldn’t hurt a fly, but [states] that no sacrifice is too great [for] the realization of Marxist ideals, not even the destruction of millions of human lives.” And then it’s back to the old quarrel about quantum mechanics. (See Born’s comment below.) Princeton, 15 September 1950Dear Born,… People such as your Bolshevik doctor come by their fantastic attitude as a result of their objection to the harshness, injustice and absurdity of our own social order (escape from reality). If he happened to be living in Russia, no doubt he would be a rebel there as well, only in that case he would take care not to tell you about it. Nevertheless it seems to me that our own people here [in the US] make an even worse job of their foreign policy than the Russians. And the idiotic public can be talked into anything. And they really are very shortsighted, for technological superiority is transitory, and if it comes to an all-out conflict, the decisive factor is sheer numerical superiority.There is nothing analogous in relativity to what I call incompleteness of description in the quantum theory. Briefly it is because the ψ-function is incapable of describing certain qualities of an individual system, whose “reality” none of us doubt (such as a microscopic parameter). Take a (macroscopic) body that can rotate freely about an axis. Its state is fully determined by an angle. Let the initial conditions (angle and angular momentum) be defined as precisely as the quantum theory allows. The Schrödinger equation then gives the ψ-function for any subsequent time interval. If this is sufficiently large, all angles become (in practice) equally probable. But if an observation is made (e.g. by flashing a torch), a definite angle is found (with sufficient accuracy). This does not prove that the angle had a definite value before it was observed—but we believe this to be the case, because we are committed to the requirements of reality on the macroscopic scale. Thus, the ψ-function does not express the real state of affairs perfectly in this case. This is what I call “incomplete description.”So far, you may not object. But you will probably take the position that a complete description would be useless because there is no mathematical relationship for such a case. I do not say that I am able to disprove this view. But my instinct tells me that a complete formulation of the relationships is tied up with complete description of its factual state. I am convinced of this although, up to now, success is against it. I also believe that the current formulation is true in the same sense as e.g. thermodynamics, i.e. as far as the concepts used are inadequate. I do not expect to convince you, or anybody else. I just want you to understand the way I think.I see from … your letter that you, too, take the quantum theoretical description as incomplete (referring to an ensemble). But you are, after all, convinced that no (complete) laws exist for a complete description, according to the positivistic maxim: esse est percipi [to be is to be perceived]. Well, this is a programmatic attitude, not knowledge. This is where our attitudes really differ. For the time being, I am alone in my views—as Leibniz was with respect to the absolute space of Newton’s theory.… I have not changed my attitude to the Germans, which, by the way, dates not just from the Nazi period. All human beings are more or less the same from birth. The Germans, however, have a far more dangerous tradition than any of the other so-called civilized nations.Kind regards,Yours,A. E. Born’s 1969 comment: 1 1. M. Born, The Born–Einstein Letters 1916–1955: Friendship, Politics and Physics in Uncertain Times, Macmillan, New York (2005), p. 184 Original letter © Hebrew University of Jerusalem. This is probably the clearest presentation of Einstein’s philosophy of reality. … He calls my way of describing the physical world “incomplete.” In his eyes, that is a flaw which he hopes to see removed, while I am prepared to put up with it. I have in fact always regarded it as a step forward, because an exact description of the state of a physical system presupposes that one can make statements of infinite precision about it, and this seems absurd to me. REFERENCESection:ChooseTop of pageREFERENCE <<CITING ARTICLES1. M. Born, The Born–Einstein Letters 1916–1955: Friendship, Politics and Physics in Uncertain Times, Macmillan, New York (2005), p. 184 Original letter © Hebrew University of Jerusalem. Google Scholar© 2005 American Institute of Physics.
Various physical examples are displayed in which the probability distribution can be traced back to its causal origin. It is argued that probability is never irreducible, but is, in principle, always derivable from a deterministic process which determines its numerical value. It is suggested that deterministic and probabilistic theories are interlocked, each presenting a different aspect of reality, yet that no description of the laws of nature in terms of either of these concepts will ever be ultimate.
Translated by Irene Born Newton-John; closing comment by Max Born. 1 1. M. Born, The Born—Einstein Letters 1916-1955: Friendship, Politics and Physics in Uncertain Times, Macmillan, New York (2005), p. 79. Letter © Hebrew University of Jerusalem. This letter antedates by a year or two the “new” quantum mechanics of Werner Heisenberg, Max Born, Pasqual Jordan, and Erwin Schrödinger. Einstein begins with a response to a letter about Japan by Born’s wife, Hedi—a letter that has since been lost. But then, as he would for the next 30 years, Einstein launches into his differences with Max on the interpretation of quantum phenomena. If atomic phenomena are truly random, he grumbles, he’d rather be a croupier. Berlin, 29 April 1924Dear Borns,Your letter, dear Mrs. Born, was really excellent. Indeed, what causes the sense of well-being inspired by Japanese society and art is that the individual is so harmoniously integrated into his wider environment that he derives his experiences not from the self, but mainly from the community. Each of us longed for this when we were young, but we had to resign ourselves to its impossibility. For, of all the communities available to us there is not one I would want to devote myself to, except for the society of the true searchers, which has very few living members at any time.… Bohr’s opinion about radiation is of great interest. But I should not want to be forced into abandoning strict causality without defending it more strongly than I have so far. I find the idea quite intolerable that an electron exposed to radiation should choose, of its own free will, not only its moment to jump off, but also its direction. In that case, I would rather be a cobbler, or even an employee in a gaming house, than a physicist. Certainly my attempts to give tangible form to the quanta have foundered again and again, but I am far from giving up hope. And even if it never works, there is always that consolation that this lack of success is entirely mine. … With best wishes.YoursEinstein… Your pretty remark [Mrs. Born, about subject unknown] makes me want to stroke your head, if that is at all permissible in the case of a married lady. Max Born’s 1969 comments:’ The letter from my wife to which Einstein replied is missing. The basic reason for the dispute between [Einstein and me] on the validity of statistical laws was as follows: Einstein was firmly convinced that physics can supply us with knowledge of the objectively existing world. Together with many other physicists, I have been gradually converted, as a result of experiences in the field of atomic quantum phenomena, to the point of view that this is not so. At any given moment, our knowledge of the objective world is only a crude approximation from which, by applying certain rules such as the probability laws of quantum mechanics, we can predict unknown (e.g. future) conditions. REFERENCESection:ChooseTop of pageREFERENCE <<1. M. Born, The Born—Einstein Letters 1916-1955: Friendship, Politics and Physics in Uncertain Times, Macmillan, New York (2005), p. 79. Letter © Hebrew University of Jerusalem. Google Scholar© 2005 American Institute of Physics.