Weak quantization

Quantization is called weak when a motion apparently allowed by the equation ∫pdq=nh, has less than the normal a-priori weight. It is believed that the deficiency in a-priori weight is taken over, either by neighboring classically allowed motions, or by neighboring strongly quantized motions when such are present in the region of the phase-space considered. Weak quantization is to be expected when uncertainties arise as to the period that should be used in determining the limits of the phase integral ∫pdq. Several cases are considered; (a) when the period is so long that there is considerable chance of interruption by a quantum transition; (b) when a system has two apparent periods, a long true period T and a short quasi-period θ; (c) when the periodicity is disturbed frequently in a fortuitous manner as by molecular collisions. In case (b), the tendency towards quantization with respect to T may be gradually replaced by quantization with respect to θ as T is lengthened, and then the probability of quantum transitions which correspond to quantization with respect to T is weakened while that of transitions related to θ is strengthened. This suggests the possibility that the strengthening of the probability of transitions related to a period θ may be accompanied by a strengthening of quantization with respect to that period

Temperature equilibrium in a static gravitational field

In the case of a gravitating mass of perfect fluid which has come to thermodynamic equilibrium, it has previously been shown that the proper temperature T0 as measured by a local observer would depend in a definite manner on the gravitational potential at the point where the measurement is made. In the present article the conditions of thermal equilibrium are investigated in the case of a general static gravitational field which could correspond to a system containing solid as well as fluid parts. Writing the line element for the general static field in the form ds2=gijdxidxj+g44dt2 i,j=1,2,3, where the gij and g44 are independent of the time t it is shown that the dependence of proper temperature on position at thermal equilibrium is such as to make the quantity T0sqrt[g44] a constant throughout the system

Compte rendu de : Louis Couturat, L’Algèbre de la logique

Pour l’exposé de la logique formelle, voici les circonstances qui sont données : la classification extraordinairement subtile des différentes formes de jugements et de conclusions, qui se produit déjà dans la conscience, ne trouve dans la langue qu’un instrument trop lourd et grossier. Pour cette raison, il est de pratique courante, depuis longtemps dans l’étude des jugements et des conclusions, de représenter cette classification par des symboles conventionnels. À cela se rapporte surtout le..

Compte rendu de : Louis Couturat, L’Algèbre de la logique

Pour l’exposé de la logique formelle, voici les circonstances qui sont données : la classification extraordinairement subtile des différentes formes de jugements et de conclusions, qui se produit déjà dans la conscience, ne trouve dans la langue qu’un instrument trop lourd et grossier. Pour cette raison, il est de pratique courante, depuis longtemps dans l’étude des jugements et des conclusions, de représenter cette classification par des symboles conventionnels. À cela se rapporte surtout le..

On the Gravitational Field Produced by Light

Expressions are obtained, in accordance with Einstein's approximate solution of the equations of general relativity valid in weak fields, for the effect of steady pencils and passing pulses of light on the line element in their neighborhood. The gravitational fields implied by these line elements are then studied by examining the velocity of test rays of light and the acceleration of test particles in such fields. Test rays moving parallel to the pencil or pulse do so with uniform unit velocity the same as that in the pencil or pulse itself. Test rays moving in other directions experience a gravitational action. A test particle placed at a point equally distant from the two ends of a pencil experiences no acceleration parallel to the pencil, but is accelerated towards the pencil by twice the amount which would be calculated from a simple application of the Newtonian theory. The result is satisfactory from the point of view of the conservation of momentum. A test particle placed at a point equally distant from the two ends of the track of a pulse experiences no net integrated acceleration parallel to the track, but experiences a net acceleration towards the track which is satisfactory from the point of view of the conservation of momentum

The conceptual foundations of the statistical approach in mechanics

Classic 1912 article reformulated the foundations of the statistical approach in mechanics. Largely still valid; essential reading for serious student. Covers older formulation of statistico-mechanical investigations (kineto-statistics of the molecule); modern formulation of kineto-statistics of gas model; work of W. Gibbs, and more. Extensive notes and prefatory material. Bibliography.In this concise classic, Paul Ehrenfest ― one of the twentieth century's greatest physicists ― reformulated the foundations of the statistical approach in mechanics. Originally published in 1912, this classic has lost little of its scientific and didactic value, and is suitable for advanced undergraduate and graduate students of physics and historians of science.Part One describes the older formulation of statistico-mechanical investigations (kineto-statistics of the molecule). Part Two takes up the modern formulation of kineto-statistics of the gas model, and Part Three explores W. B. Gibbs'

Pauli letter collection: letter to Wolfgang Pauli

Ehrenfest discusses the disappearance of the "zeroth-order spectrum" for X-ray diffraction in liquids (Zernike-Prins, in: Z. Phys. : 41 (1972), pp.190). He asks Pauli to calculate it

Pauli letter collection: letter to Wolfgang Pauli

Ehrenfest sends his daughter's notes on Pauli's work in the early twenties for comments. He also asks about a action-at-a-distance in the Schrödinger theory

Pauli letter collection: letter to Wolfgang Pauli

Ehrenfest sends a short note in which he expresses his doubts as to the separability of the operator-function M representing the spin interaction of the two He-electron

Pauli letter collection: letter to Wolfgang Pauli

Ehrenfest gives some personnal remarks on Oppenheimer and sends him to pauli. He also makes a comment on rutgers