David Corfield
Determinism and Indeterminism in Modern Physics

Bois-Reymond uses Laplace for unintended ends. Laplace only drawing the distinction between causality and probability.

Physicists disagree on definition of principle of physical explanation, yet physics advances, displaying “a peculiar inner constancy, an immanent methodological coherence, which finally always asserts itself, even when judgments concerning this practice are widely divergent. We must therefore start with this practice and examine it directly.” p. 30

p. 30 No small part of the difficulty with which current discussions of the causal problem in physics has to contend rests, I am convinced, on the fact that epistemology in general has not yet distinguished sharply and clearly between different types of physical statements.

p. 35 …all the statements of physics are determined through one another, they mutually condition and support one another, and their specific “truth” is due precisely to this mutual interconnection. The reciprocal interweaving and bonding constitutes one of the basic features of the system of physics. Within it therefore there is no proper substantial carrier, nothing that per se est et per se concipitur. There is only a functional coordination in which all the elements, all the determining factors of physical truth, uniformly participate. At the “lower” levels according the “higher” levels are already implied and in a definite sense are presupposed. If we choose a spatial analogy for the structure of phyics, we must not liken this structure to a pyramid resting on a broad base of immediately given and independent “facts,” rising gradually from this and ending in a highest point, perhaps in a single “cosmic formula.” For this would involve overlooking the mutual interconnection and forgetting that “everything significantly factual is already theory.” There would always be the possibility of imagining the higher layers removed without destroying the bottom layer or even altering it essentially…This cannot and must not prevent us, to be sure, from ascribing to it a determinate structure, a higher and lower order of elements; but this logical distinction of the elements must not be interpreted as suggesting the possibility of their actual separation, their independent existence.

p. 50 At first glance the universality of the action principle seems by no means beyond question. This universality could be attained only at the cost of a circumstance which, from the purely physical point of view, led again and again to difficulties and doubts. For the more universally the principle was conceived, the more difficult it became to specify clearly its proper concrete content. It becomes finally a kind of Proteus, displaying a new aspect on each new level of scientific knowledge. If we ask what precisely that “something” might be to which the property of a maximum or a minimum is ascribed, we receive no definite and unambiguous answer.

Physical principles, such as the Principle of Least Action:

p. 52-53: Here in fact we find a basic methodological characteristic common to all genuine statements of principles. Principles do not stand on the same level as laws, for the latter are statements concerning specific concrete phenomena. Principles are not themselves laws, but rules for seeking and finding laws. This heuristic point of view applies to all principles. They set out from the presupposition of certain common determinations valid for all natural phenomena and ask whether in the specialized disciplines one finds something corresponding to these determinations, and how this “something” is to be defined in particular cases.

The power and value of physical principles consists in this capacity for “synopsis,” for a comprehensive view of whole domains of reality…Principles are invariably bold anticipations that justify themselves in what they accomplish by way of construction and inner organization of our total knowledge. They refer not directly to phenomena but to the form of the laws according to which we order these phenomena. A genuine principle, therefore, is not equivalent to a natural law. It is rather the birthplace of natural laws, a matrix as it were, out of which new natural laws may be born again and again.

pp. 53-54 The principles of physics are basically nothing but such means of orientation, means for surveying and gaining perspective. At first they are only valid as hypotheses. They cannot stipulate dogmatically from the beginning a particular result of investigation. But they teach us how to find the direction in which we have to advance. We must raise ourselves again and again above the level of immediate perceptions, and also above the level of experimental data and of particular laws, in order to gain once more a sure footing within all these levels. The outward and upward movement that is here demanded therefore serves the purpose not of any kind of transcendence but only those of a pure immanence–the inner construction and securing of experience.

p. 60 What is the significance of the causal principle and what new insight does it add to what we have learned from the ongoing epistemological analysis? What further step is still to be taken and what new insight concerning scientific knowledge is yet to be expected after we have traversed the earlier levels, after we have progressed from statements of the results of measurements to those of the laws, and from these to statements of principles?

I would like to give an answer to this question, which at first sight will perhaps seem paradoxical. There is in fact nothing left over, nothing new in principle to be added to the description of the process of cognition and of the epistemological structure of science. What the causal principle signifies–and this is the thesis I want to explain and establish in the sequel–is not a new insight concerning content, but solely one concerning method. It does not add a single factor homogeneous with the foregoin, which could be placed alongside it as a material supplement. With regard to content it does not go beyond what has already been observed; it only confirms it and confers upon it as it were the epistemological imprimatur. In this sense it belongs, using the language of Kant, to the modal principles; it is a postulate of empirical thought. And this postulate specifies fundamentally nothing more than that the process, which we have sought to describe in detail, is possible without limitation. It does not maintain that the process of translating data of observation into exact statements of the results of measurements, or the process of gathering together the results of measurements into functional equations by means of general principles, is ever complete. What it demands and what it axiomatically presupposes, is only this: that the completion can and must be sought, that the phenomena of nature are not such as to elude or to withstand in principle the possibility of being ordered by the process we have described. We should understand the causal principle in this sense, and in this sense we will submit it to critical examination in the following pages. For us the causal principle belongs to a new type of physical statement, insofar as it is a statement about measurements, laws, and principles. It says that all these can be so related and combined with one another that from this combination there results a system of physical knowledge and not a mere aggregate of isolated observations.

p. 188 The essence of the causal concept remains untouched as long as this essence is grasped in its true universality–that is, defined only by the demand for strict functional dependence. If the individual elements of determination available to quantum mechanics are used in accordance with the general principles of the theory and in keeping with the limits fixed by the uncertainty relations, a functional relationship, precisely definable, will always exist between them. Then the “causal law of quantum mechanics” is valid–that is, the thesis that if at any time certain physical quantities are measured as exactly as possible in principle, quantities will also exist at any other time whose magnitude on being measured can be predicted with precision. (See page 127)

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