Quantum Theory of Lotteries

Авторский перевод здесь: http://www.proza.ru/2003/05/30-159

ABSTRACT: Honest random lotteries offering prizes of order 10,000,000.00 or greater are considered. It is argued that such lotteries have no winners in the classical sense.

Immense lottery winnings have gained attention of the national press. The subject is also of considerable interest to members of the scientific community. Many a physicist would prefer to continue his or her professional pursuit of truth and its applications backed by a $10,000,000.00 windfall from a state lottery. Nevertheless, there is a conspicuous absence in the ledger of big lottery winners of any reputable scientist who would have had prior publications in a refereed journal. Until recently I thought this absence could be fully explained by a reluctance of scientists to purchase lottery tickets. Indeed, even a casual consideration of the odds often discourages a seasoned researcher from getting involved. And without a ticket the chance of winning big in a lottery is commonly believed to be identically zero (this belief, shared by the author, is rooted in solid empirical evidence).

However, the opposite side of the same belief has no empirical basis and is disputed in the present work.

One often hears that by the mere act of buying a lottery ticket one somehow becomes exposed to a finite, albeit small, probability of becoming a winner. Having given the matter a deep thought, I came to the conclusion that this view was not satisfactory. I realized with a chilling clarity that should I ever buy a ticket it would not be the winning ticket, at least certainly not for anything of order $10,000,000. In what follows, I shall argue that this conclusion applies to anybody I know, and, furthermore, to anybody anybody knows. It rests on firmly established experimental facts, and calls for a thorough re-examination of our intuitive notion of probability.

In its classical Laplacean form, the Theory of Probability tends to assign a finite value to all kinds of improbable events. Mathematicians tell us that there is a non-zero chance that a monkey seated in front of a typewriter would produce all the Oeuvres of Shakespeare in a chronological order, or that a beginner would win a chess match against grandmaster Kasparov.

Needless to say, such things never happen. Most physicists would agree that no observable (verifiable) fact should change if a probability of exactly zero were ascribed to all improbable events, instead of the currently accepted intangible values. It would only spare us a few false expectations.

A 10,000,000.00 lottery surely falls into the same category as a match against Kasparov. Our certainty of not winning in both cases exceeds our certainty in any Natural Law. Indeed, are there many fundamental constants that we know to better than 0.1 ppm? Or that we care to know for that matter?

On purely theoretical grounds, it therefore makes sense to assume that the probability of winning big in a state lottery is exactly 0. As an eminently sane person, Laplace would have nothing against this proposition. After all, he had only considered turns of pitch and toss and never played hazardous games against sovereign states. The absurd idea that a free citizen could win 10 megabucks was totally foreign to Laplace. There was no room for such hypotheses in his Universe, even accounting for inflation.

A trivial though practical corollary is that one should be advised to refrain from buying lottery tickets, unless, of course, one is driven by a higher purpose - like, for example, redressing the inequities of taxation, which is probably what motivates politicians who run the game. There is, however, a much more fundamental consequence.

Having made the above assumption - which I maintain is the only reasonable assignment of the probability - one must address the problem of Mrs. Thompson who, as we all know, had recently won $41,560,423.53. She could be observed on television smiling appropriately.

The crux of the matter is that Mrs. Thomson became observable only AFTER she had won the money. There is no shred of evidence that she had existed before. No scientist had made a proper observation of her before the drawing day. A testimony of her relatives would not be convincing. Some people claim to have traveled in a UFO. It is much more logical to state unequivocally that Mrs. Thomson had materialized during the lottery drawing, along with her supporters, dependents and witnesses.

Quite generally, we must treat people as observables, like it befits a scientific community. Distinctly, they all fall into two classes: those who, like Mrs. Thompson, have won their $10,000,000.00 or more, and those, like the rest of us, who never had nor, rest assured, will ever have done anything like that. Transition between these two groups is as impossible as is a process whose sole consequence would be transmission of heat from a colder body. Each of us is born into one of the two classes and has the appropriate class consciousness. Those from Mrs. Thomson's category usually come into being at a mature age, and are replete with what might be called memories of the past. Of course, these are merely harmless illusions.

One need not be alarmed at the rate with which human materializations occur in the USA (and to a lesser extent abroad). Speaking of Laplace, I have already mentioned the Inflationary Universe. Modern theory, which goes by that name, seriously speculates that the whole Thing had one day materialized by tunneling out of the vacuum. This should give solace to Mrs. Thompson in that she is not really different from everybody else; for the physicists this may contain the clue to the underlying mechanism of big lotteries. One day we may be able to control it, and possibly harness its obviously enormous power.