In conclusion, then, no satisfactory interpretation of quantum mechanics exists today. The questions posed by the confrontation between the Copenhagen interpretation and the hidden variable theorists go to the very foundations of microphysics, but the answers given by hidden variable theorists and Copenhagenists are alike unsatisfactory. Human curiosity will not rest until those questions are answered, but whether they will be answered by conceptual innovations within the framework of the present theory or only within the framework of an as yet unforeseen theory is unknown. The first step toward answering them has been attempted here. It is the modest but essential step of becoming clear on the nature and magnitude of the difficulties.
Hilary PutnamRelated topics
answering becoming clear conclusion confrontation curiosity difficulties essential framework given hide human interpretation magnitude mechanics nature present quantum rest satisfactory step theory unknown variable yet unforeseen today copenhagen microphysics questionsRelated quotes
The difficulties which Arkwright encountered in organizing his factory system, were much greater than is commonly imagined. In the first place, he had to train his work-people to a precision in assiduity altogether unknown before, against which their listless and restive habits rose in continual rebellion; in the second place, he had to form a body of accurate mechanics, very different from the rude hands which then satisfied the manufacturer; in the third, he had to seek a market for his yarns; and in the fourth, he had to resist competition in its most odious forms. From the concurrence of these circumstances, we find that so late as the year 1779, ten years after the date of his first patent, his enterprise was regarded by many as a doubtful novelty.
Andrew Ure
That classical theory had catastrophic implications for the constitution of matter was barely appreciated by Planck and others at the turn of the century, and played no substantial role in the development of quantum theory until Bohr's work 13 years later.
The lesson that could be drawn from this, and also from the development of general relativity, is that a crisis will only become creative if it is formulated in a mathematically precise manner. This conclusion has an echo in Bell's insistence on having quantum mechanics "fully formulated in mathematical terms, with nothing left to the discretion of the theoretical physicist", but what it really calls for is a critique of the "orthodox" theory fully formulated in mathematical terms with nothing left to the discretion of the critic.
Kurt Gottfried
...nor have I found occasion to depart from the plan... the rejection of the whole doctrine of series in the establishment of the fundamental parts both of the Differential and Integral Calculus. The method of Lagrange... had taken deep root in elementary works; it was the sacrifice of the clear and indubitable principle of limits to a phantom, the idea that an algebra without limits was purer than one in which that notion was introduced. But, independently of the idea of limits being absolutely necessary even to the proper conception of a convergent series, it must have been obvious enough to Lagrange himself, that all application of the science to concrete magnitude, even in his own system, required the theory of limits.
Augustus De Morgan
The present life of man, O king, seems to me, in comparison of that time which is unknown to us, like to the swift flight of a sparrow through the room wherein you sit at supper in winter, with your commanders and ministers, and a good fire in the midst, whilst the storms of rain and snow prevail abroad; the sparrow, I say, flying in at one door, and immediately out at another, whilst he is within, is safe from the wintry storm; but after a short space of fair weather, he immediately vanishes out of your sight, into the dark winter from which he had emerged. So this life of man appears for a short space, but of what went before, or what is to follow, we are utterly ignorant. If, therefore, this new doctrine contains something more certain, it seems justly to deserve to be followed.
Bede
The very name of my subject, economics, suggests economizing or maximizing. But Political Economy has gone a long way beyond home economics. Indeed, it is only in the last third of the century, within my own lifetime as a scholar, that economic theory has had many pretensions to being itself useful to the practical businessman or bureaucrat. I seem to recall that a great economist of the last generation, A. C. Pigou of Cambridge University, once asked the rhetorical question, "Who would ever think of employing an economist to run a brewery?” Well, today, under the guise of operational research and managerial economics, the fanciest of our economic tools are being utilized in enterprises both public and private.
Paul Samuelson
