Mechanics Quotes - page 5
![This fallacious result is not... a peculiarity of classical mechanics; it is given also by a very wide class of possible systems of mechanics. This being so, no minor modification of the classical mechanics can possibly put things right. Something far more drastic is needed; we are called upon to surrender either the [1] continuity or the [2] causality of classical mechanics, or else the possibility of [3] representing changes by motions in time and space. (James Jeans)](https://cdn.quotesdtb.com/img/quotes_images_webp/89/james-jeans-causality-class-293489.webp)
Heisenberg finds that facts of observation lead uniquely and inevitably to the theoretical structure known as matrix mechanics. This shows that the total radiation in any region of empty space can change only by a single complete quantum at a time. Thus not only in the photo-electric phenomenon, but in all other transfers of energy through space, energy is always transferred by complete quanta; fractions of a quantum can never occur. This brings atomicity into our picture of radiation just as definitely as the discovery of the electron and its standard charge brought atomicity into our picture of matter and of electricity.
James Jeans
Precisely similar ideas are applicable to the molecules that form the air in a room. ...The classical mechanics now predicts that the whole energy of motion will be changed into radiation [heat], so that the molecules will shortly be found lying at rest on the floor... In actual fact they continue to move with undiminished energy, forming a perpetual-motion machine in defiance of classical mechanics. ...We have passed from one to another of three worlds... from the man-sized world to the world of the electron.
James Jeans
A similar situation occurred in astronomy, where the Newtonian law of gravitation had been found to predict the orbits of the outer planets with great accuracy, but had failed with the orbits of Mercury and Venus. The relativity theory of gravitation had provided the necessary modification of Newton's law, and in working out the details of the new theory, Einstein had utilized the fact that Newtonian law gave the right result at great distances from the sun. Heisenberg, confronted with a similar problem, was able to avail himself of the fact that the classical mechanics gave the right result at great distances from the atomic nucleus. Here, and here alone Heisenberg's theory made contact with the world of the older physics.
James Jeans
In the interior of the atom, Bohr had tried the plan of retaining the particle-electron and modifying the classical mechanics. Heisenberg took the opposite course, his procedure amounting in effect to retaining the classical mechanics, at least in form, and modifying the electron. Actually, the electron dropped out all together, because it exists only as a matter of inference and not of direct observation. For the same reason, the new theory contains no mention of atoms, nuclei, protons, or of electricity in any shape or form. The existences of all these are matters of inference, and Heisenberg's purely mathematical theory could no more make contact with them than with the efficiency of a turbine or with the price of wheat.
James Jeans
Another conspicuous failure of classical mechanics was with one aspect of the problem of radiation. ...Imagine a crowd of steel balls rolling about on a steel floor. ...There must... be a steady leakage of energy from... causes, such as air resistance and the friction of the floor, so the balls will eventually lose energy, and, after no great length of time, will be found standing at rest on the floor. The energy of their motion seems to have been lost... most of it has been transformed into heat. The classical mechanics predicts that this must happen; it shows that all energy of motion, except possibly a minute fraction of the whole, must be transformed into heat whenever such a transformation is physically possible. It is because of this that perpetual-motion machines are a practical impossibility.
James Jeans
The main result reached by the new theory was that the classical mechanics can be made to account for the whole range of spectral phenomena, provided entirely new meanings are given to such symbols as p and q which had hitherto been taken to describe the position and motion of the electron. ...The most significant of the new properties is that the product pq is no longer the same as the product qp - in other words the order in which the two factors are multiplied together is no longer a matter of indifference. The difference between pq and qp is found to be always the same, being Planck's constant h multiplied by a numerical multiplier.
James Jeans
The need for a fundamentally different approach to the study of physical processes at the molecular level motivated the development of relevant statistical methods, which turned out to be applicable not only to the study of molecular processes (statistical mechanics), but to a host of other areas such as the actuarial profession, design of large telephone exchanges, and the like. In statistical methods, specific manifestations of microscopic entities (molecules, individual telephone sites, etc.) are replaced with their statistical averages, which are connected with appropriate macroscopic variables. The role played in Newtonian mechanics by the calculus, which involves no uncertainty, is replaced in statistical mechanics by probability theory, a theory whose very purpose is to capture uncertainty of a certain type.
George Klir
In spite of all the foregoing, there is a science of economics, a true, and even exact, science, which reaches laws as universal as those of mathematics and mechanics. The greatest need for the development of economics as a growing body of thought and practice is an adequate appreciation of the meaning, and the limitations, of this body of accurate premises and rigorously established conclusions. It comes about in the same general way as all science, except perhaps in a higher degree, i. e., through abstraction. There are no laws regarding the content of economic behavior, but there are laws universally valid as to its form. There is an abstract rationale of all conduct which is rational at alt, and a rationale of all social relations arising through the organization of rational activity.
Frank Knight
As a witness of that period, I am also deeply convinced that John Bell indirectly played a crucial role in the progress of the application of quantum mechanics to individual objects, microscopic and mesoscopic. The example of his intellectual freedom, that had led to the recognition of the importance of entanglement, was no doubt an encouragement to those who were contemplating the possibility of developing new approaches, beyond the so-efficient paradigm developed decades earlier. His example opened the gate for new quantum explorations.
Alain Aspect
Surely, after 62 years, we should have an exact formulation of some serious part of quantum mechanics? By 'exact' I do not of course mean 'exactly true'. I mean only that the theory should be fully formulated in mathematical terms, with nothing left to the discretion of the theoretical physicist... until workable approximations are needed in applications. By 'serious' I mean that some substantial fragment of physics should be covered. Nonrelativistic 'particle' quantum mechanics, perhaps with the inclusion of the electromagnetic field and a cut-off interaction, is serious enough.
John Stewart Bell
It can be argued that in trying to see behind the formal predictions of quantum theory we are just making trouble for ourselves. Was not precisely this the lesson that had to be learned before quantum mechanics could be constructed, that it is futile to try to see behind the observed phenomena?
John Stewart Bell
I expect that mathematicians have classified such fuzzy logics. Certainly they have been much used by physicists. But is there not something to be said for the approach of Euclid? Even now that we know that Euclidean geometry is (in some sense) not quite true? Is it not good to know what follows from what, even if it is not necessarily FAPP? Suppose for example that quantum mechanics were found to resist precise formulation. Suppose that when formulation beyond FAPP was attempted, we find an unmovable finger obstinately pointing outside the subject, to the mind of the observer, to the Hindu scriptures, to God, or even only Gravitation? Would that not be very, very interesting?
John Stewart Bell
The first charge against 'measurement', in the fundamental axioms of quantum mechanics, is that it anchors there the shifty split of the world into 'system' and 'apparatus'. A second charge is that the word comes loaded with meaning from everyday life, meaning which is entirely inappropriate in the quantum context.
John Stewart Bell
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 Bell
In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that such a theory could not be Lorentz invariant. Of course, the situation is different if the quantum mechanical predictions are of limited validity. Conceivably they might apply only to experiments in which the settings of the instruments are made sufficiently in advance to allow them to reach some mutual rapport by exchange of signals with velocity less than or equal to that of light. In that connection, experiments of the type proposed by Bohm and Aharonov, in which the settings are changed during the flight of the particles, are crucial.
John Stewart Bell
