For centuries knowledge meant proven knowledge — proven either by the power of the intellect or by the evidence of the senses. Wisdom and intellectual integrity demanded that one must desist from unproven utterances and minimize, even in thought, the gap between speculation and established knowledge. The proving power of the intellect or the senses was questioned by the sceptics more than two thousand years ago; but they were browbeaten into confusion by the glory of Newtonian physics. Einstein’s results again turned the tables and now very few philosophers or scientists still think that scientific knowledge is, or can be, proven knowledge. But few realize that with this the whole classical structure of intellectual values falls in ruins and has to be replaced: one cannot simply water down the ideal of proven truth - as some logical empiricists do — to the ideal of’probable truth’1 or — as some sociologists of knowledge do — to ‘truth by [changing] consensus’.2

Sources of Quantum Mechanics

Falsification and the Methodology of Scientific Research Programmes

“Philosophy of science without history of science is empty; history of science without philosophy of science is blind”. Taking its cue from this paraphrase of Kant’s famous dictum, this paper intends to explain how the historiography of science should learn from the philosophy of science and vice versa. It will be argued that (a) philosophy of science provides normative methodologies in terms of which the historian reconstructs ‘internal history’ and thereby provides a rational explanation of the growth of objective knowledge; (b) two competing methodologies can be evaluated with the help of (normatively interpreted) history; (c) any rational reconstruction of history needs to be supplemented by an empirical (socio-psychological) ‘external history’.

History of Science and Its Rational Reconstructions

La metodología de los programas de investigación científica

General relativity is a deterministic theory with non-fixed causal structure. Quantum theory is a probabilistic theory with fixed causal structure. In this paper, we build a framework for probabilistic theories with non-fixed causal structure. This combines the radical elements of general relativity and quantum theory. We adopt an operational methodology for the purposes of theory construction (though without committing to operationalism as a fundamental philosophy). The key idea in the construction is physical compression. A physical theory relates quantities. Thus, if we specify a sufficiently large set of quantities (this is the compressed set), we can calculate all the others. We apply three levels of physical compression. First, we apply it locally to quantities (actually probabilities) that might be measured in a particular region of spacetime. Then we consider composite regions. We find that there is a second level of physical compression for a composite region over and above the first level physical compression for the component regions. Each application of first and second level physical compression is quantified by a matrix. We find that these matrices themselves are related by the physical theory and can therefore be subject to compression. This is the third level of physical compression. The third level of physical compression gives rise to a new mathematical object which we call the causaloid. From the causaloid for a particular physical theory we can calculate everything the physical theory can calculate. This approach allows us to set up a framework for calculating probabilistic correlations in data without imposing a fixed causal structure (such as a background time). We show how to put quantum theory in this framework (thus providing a new formulation of this theory). We indicate how general relativity might be put into this framework and how the framework might be used to construct a theory of quantum gravity.

https://iopscience.iop.org/article/10.1088/1751-8113/40/12/S12/pdf

Towards quantum gravity: a framework for probabilistic theories with non-fixed causal structure

For pt.I see ibid., vol.12 (1979). The quantum mechanical Coulomb and isotropic oscillator problems in an N-dimensional spherical geometry, which were shown in the previous paper to possess the dynamical symmetry groups SO(N+1) and SU(N) respectively as classical systems, are analysed by the method used by Pauli to find the energy eigenvalues of the hydrogen atom. This analysis is carried through completely for N=3 to obtain energy eigenvalues and recurrence relations among energy eigenfunctions. It is shown that Pauli's method is equivalent to Schrodinger's method of solving the radial Schrodinger equation by factorisation of the second order differential operator. The latter method is used to find the energy eigenvalues in N dimensions, and the corresponding eigenfunctions are obtained in closed form.

http://iopscience.iop.org/article/10.1088/0305-4470/12/4/009/pdf

Sources of Quantum Mechanics

Citations

Falsification and the Methodology of Scientific Research Programmes

History of Science and Its Rational Reconstructions

La metodología de los programas de investigación científica

Towards quantum gravity: a framework for probabilistic theories with non-fixed causal structure

Dynamical symmetries in a spherical geometry. II

Related Papers (5)

Quantum Mechanics

The Principles of Quantum Mechanics

The quantum theory of radiation

Classical Mechanics

Quantum theory and measurement