More generally, the hidden variable account of a given system becomes entirely different when we remember that it has undoubtedly interacted with numerous other systems in the past and that the total wave function will certainly not be factorable. The same effect complicates the hidden variable account of the theory of measurement, when it is desired to include part of the 'apparatus' in the system. Bohm of course was well aware of these features of his scheme, and has given them much attention. However, it must be stressed that, to the present writer's knowledge, there is no proof that any hidden variable account of quantum mechanics must have this extraordinary character. It would therefore be interesting, perhaps, to pursue some further 'impossibility proofs,' replacing the arbitrary axioms objected to above by some condition of locality, or of separability of distant systems.
John Stewart BellRelated topics
above account apparatus arbitrary attention character condition course different given hide knowledge locality measurement mechanics past perhaps present proof quantum variable well replacingRelated quotes
Had it merely called to our attention the existence and exact nature of certain fundamental gaps in economic theory, the Theory of Economic Behavior by von Neumann and Morgenstern would have been a book of outstanding importance. But it does more than that. It is essentially constructive: where existing theory is considered to be inadequate, the authors put in its place a highly novel analytical apparatus designed to cope with the problem.
It would be doing the authors an injustice to say that theirs is a contribution to economics only. The scope of the book is much broader. The techniques applied by the authors in tackling economic problems are of sufficient generality to be valid in political science, sociology, or even military strategy. The applicability to games proper (chess and poker) is obvious from the title. Moreover, the book is of considerable interest from a purely mathematical point of view.
Leonid Hurwicz
It is quite easy to include a weight for empty space in the equations of gravity. Einstein did so in 1917, introducing what came to be known as the cosmological constant into his equations. His motivation was to construct a static model of the universe. To achieve this, he had to introduce a negative mass density for empty space, which just canceled the average positive density due to matter. With zero total density, gravitational forces can be in static equilibrium. Hubble's subsequent discovery of the expansion of the universe, of course, made Einstein's static model universe obsolete. ...The fact is that to this day we do not understand in a deep way why the vacuum doesn't weigh, or (to say the same thing in another way) why the cosmological constant vanishes, or (to say it in yet another way) why Einstein's greatest blunder was a mistake.
Frank Wilczek
Third Theory.-According to this theory, there is nothing in the whole Universe... that is due to chance; everything is the result of will, intention, and rule. It is a matter of course that he who rules must know. The Mohametan Ashariyah adhere to this theory, notwithstanding evident absurdities implied in it. ...The Ashariyah were therefore compelled to assume that motion and rest of living beings are predestined, and that it is not in the power of a man to do a certain thing or to leave it undone. ...It follows also from this theory, that precepts are perfectly useless, since the people to whom any law is given... can neither do what they are commanded nor abstain from what they are forbidden. ...According to this theory, it must also be assumed that the actions of God have no final cause. All these absurdities are admitted by the Ashariyah for the purpose of saving this theory.
Maimonides
The city is very different from the country, girl. It is a kind of shared consciousness that begins its work on you as soon as you enter it, if not well before, a consciousness that begins to separate you from the country possibly even before you decide to journey toward it. It encircles you with forces much greater than the walls and gates which imitate tinier villages or towns. People who come to it come seeking the future, not realizing all that will finally affect them in it is their own, only more or less aware, involvement with the past. The way we do things here-really, that's all there is to be learned in our precincts. But in the paving of every wide, clear avenue, in the turnings of every dark, overhung alley, in the ornaments on every cornice, in the salt-stained stones of each neighborhood cistern, there are traces of the way things once were done-which is the key to why they are done as they are today.
Samuel R. Delany
When [Born and Heisenberg and the Göttingen theoretical physicists] first discovered matrix mechanics they were having, of course, the same kind of trouble that everybody else had in trying to solve problems and to manipulate and to really do things with matrices. So they had gone to Hilbert for help and Hilbert said the only time he had ever had anything to do with matrices was when they came up as a sort of by-product of the eigenvalues of the boundary-value problem of a differential equation. So if you look for the differential equation which has these matrices you can probably do more with that. They had thought it was a goofy idea and that Hilbert didn't know what he was talking about. So he was having a lot of fun pointing out to them that they could have discovered Schrödinger's wave mechanics six month earlier if they had paid a little more attention to him.
Edward Condon