The Principles of Quantum Mechanics, by P.A.M. Dirac (Oxford University Press, 1958)
[The important things in the world appear as the invarlants (or more generally the nearly invariants, or quantities with simple tranformation properties) of these transformations.]: Leaving out the parenthesis and the word 'important' this statement is more or less correct. It must not be forgotten that the things that undergo transformation are themselves invariants of transformations. (A 'nearly invariant' is a hopelessly illegitimate creature—to be 'nearly invariant' is to be 'almost a thing'.)
: The ingenious system, depending on the principle that black is white, that is set before us in the pages that follow, may well deal with those practical problems for the solution of which it was expressly devised. But to expect that it will be found philosophically satisfying is the height of presumption. We do not ask for common sense—it is not common sense that we are looking for—but we cannot accept dishonesty.
A physical experiment is essentially public: it must, in theory at least, be observable by more than one person. If, then, you start by assuming the validity of the experimental method, which does not admit that there is such a thing as a point of view, you cannot thereafter introduce an observer without falling into contradiction. If there is no such thing as an 'observer' occurring in the physical experiment, we are entitled, or rather obliged, to ask what is meant by the word. Is it something that occurs only in quantum mechanics?
: Classical theory assumes the statistical nature of matter; this is a confusion. Quantum theory assumes the classical assumption, and then assumes an ultimate structure of matter: this is a double confusion. [so long as big and small are merely relative concepts, it is no help to explain the big in terms of the small. Ii is therefore necessary to modify classical ideas in such a way as to give an absolute meaning to size.] last sentence u/l: If there is absolute smallness, how is magnification possible? When one inch is magnified to two inches (with a lens) is each unit of absolute smallness in the (finite) row of such units that make up the inch, doubled in length? Or are the units doubled in number? Or is there simply more space between them?
[...Causality applies only to a system which is left undisturbed. If a system is small, we cannot observe it without producing a serious disturbance....]: How does one discover that causality (or anything else, for that matter) applies to what causes be observed?
: The principle of superposition is of the greatest importance in phenomenology; but precisely on that account it cannot be introduced into a scientific theory without at once violating the principles of identity and contradiction. In consequence of this, Quantum theory is obliged to fall back, in the last resort, on the principle of analogy. See p. 53.
[The justification for the whole scheme depends, apart from internal consistency, on the agreement of the final results with experiment.]: This puts the proposed axioms in a queer light. See p. 310.
p. 20/27-p. 21/5
[...we shall use the words 'conjugate complex' to refer to numbers and other complex quantities which can be split up into real and pure imaginary parts, and the words 'conjugate imaginary' for bra and ket vectors, which cannot...]: Kierkegaard: 'to think a contradiction is... not an easy matter, it is always connected with great difficulties. See p. 57.
: How can one introduce the Infinitesimal Calculus into a theory that assumes absolute smallness?
[However, for some purposes it is more convenient to replace the abstract quantities by sets of numbers with analogous mathematical properties and to work in terms of these sets of numbers.]: What is the mathematical definition of analogy?
[The difficulties, being of a profound character, can be removed only by some drastic change in the foundations of the theory, probably a change as drastic as the passage from Bohr's orbit theory to the present quantum mechanics.]: ...it is ridiculous to treat everything as if the System were complete, and then to say at the end, that the conclusion is lacking. If the conclusion is lacking at the end, it is also lacking in the beginning, and this should therefore have been said in the beginning. A house may be spoken of as finished even if it lacks s minor detail, s bell-pull or the like; but in s scientific structure the absence of the conclusion has retroactive power to make the beginning doubtful and hypothetical, which is to say: unsystematic.—S. Kierkegaard, C.U.P., pp. 16-17