The interest of research workers has frequently been focused on the phenomenon of regularly shaped crystals suddenly forming from a liquid, e.g. a supersaturated salt solution. According to the atomic theory the forming force in this process is to a certain extent the symmetry characteristic of the solution to Schrödinger's wave equation, and to that extent crystallization is explained by the atomic theory. Nevertheless this process retains a statistical and - one might almost say - historical element which cannot be further reduced: even when the state of the liquid is completely known before crystallization, the shape of the crystal is not determined by the laws of quantum mechanics. The formation of regular shapes is just far more probable than that of a shapeless lump. But the ultimate shape owes its genesis partly to an element of chance which in principle cannot be analysed further.
Werner HeisenbergRelated topics
almost atomic certain chance characteristic crystallization element salt equation far force forming formation genesis historical interest known liquid might mechanics quantum research state symmetry ultimate Laws owesRelated quotes
An essential element in forming a single electorate is the sense that in the last resort all parts of it stand, or fall, survive or perish, together. This sense the British do not share with the inhabitants of the continent of Western Europe. Of all the nations of Europe Britain and Russia alone, though for opposite reasons, have this in common: they can be defeated in the decisive land battle and still survive. This characteristic Russia owes to her immensity. Britain owes it to her ditch. The British feel – and I believe that instinct corresponds with sound military reason – that the ditch is as significant in what we call the nuclear age as it proved to be in the air age and had been in the age of the Grande Armée of Napoleon or the Spanish infantry of Philip II. Error or truth, myth or reality, the belief itself is a habit of mind which has helped to form the national identity of the British and cannot be divorced from it.
Enoch Powell
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
Science Of Energetics. Although the mechanical hypothesis just mentioned may be useful and interesting as a means of anticipating laws, and connecting the science of thermodynamics with that of ordinary mechanics, still it is to be remembered that the science of thermodynamics is by no means dependent for its certainty on that or any other hypothesis, having been now reduced, to a system of principles, or general facts, expressing strictly the results of experiment as to the relations between heat and motive power. In this point of view the laws of thermodynamics may be regarded as particular cases of more general laws, applicable to all such states of matter as constitute Energy, or the capacity to perform work, which more general laws form the basis of the science of energetics, - a science comprehending, as special branches, the theories of motion, heat, light, electricity, and all other physical phenomena.
William John Macquorn Rankine
First of all I want to remind you of the essential features of models. In my opinion they are: (i) drawing up a list of the variables to be considered; (ii) drawing up a list of the equations or relations the variables have to obey and (iii) testing the validity of the equations, which implies the estimation of their coefficients, if any. As a consequence of especially (iii) we may have to revise (i) and (ii) so as to arrive at a satisfactory degree of realism of the theory embodied in the model. Then, the model may be used for various purposes, that is, for the solution of various problems. The advantages of models are, on one hand, that they force us to present a "complete" theory by which I mean a theory taking into account all relevant phenomena and relations and, on the other hand, the confrontation with observation, that is, reality. Of course these remarks are far from new.
Jan Tinbergen
Take a moment to remember the times on your own spiritual quest when you felt most enthusiastic. We want to pinpoint the times in which we felt more God conscious and devotional than ever before. Conversely, look at the times when you felt unenthused and do a similar analysis. These questions might help stimulate your thought process: Are you enthusiastic about your existence as a servant of the Lord? Are you enthusiastic to follow the basic principles that will help elevate your consciousness? Are you enthusiastic in the association of saintly people? Are you enthusiastic about what you can experience in your purest state? We must examine our spiritual life on a daily, weekly, and even yearly basis. This examination will help us recognize how various activities and thoughts affect us. We should note how the quality of our experiences varies according to our absorption in the process of bhakti.
Bhakti Tirtha Swami