Crisis

Is science going through a critical stage?

Solvey Conference

This is an old paper by Luigi Foschini about the problem of interpretation of quantum physics which has raised a discussion about the effectiveness of science and its limits;

Is Science going through a critical stage?

The unexpected discoveries at the beginning of the century, particularly thanks to Heisenberg, Bohr, and Godel, has driven the science to drastic changes, opening new, extraordinary, and infinite research fields. After this, many scientists saw, and still today see, a crisis, with dreadful meaning, in the science. However, this crisis is only present in that type of science, driven by determinism, which is strictly linked to the common sense.

In this paper the author answers the question of the title negatively; Science and specifically physics is not in crisis,what happens is that for the first time quantum physics forces us to face the “hypotheses of effectiveness” of every theory in physics that consists of excluding factors of the problem in order to make it simpler and thus available to study;

How many times one has supposed it ideal (rigid bodies, geometrical bodies, material points). How many times one supposes that the resistance of an electric device is negligible? How many times is friction considered negligible? And taking into consideration the two-bodies problem, one forgets the interactions among the bodies of the universe, isn’t it? Physics and engineering are permeated with hypothesis of this kind, without which we could not adventure in building models or formulating theories. The more or less indirect consequences for engineering are constituted by the introduction of the safety factor, by the concept of reliability of devices; in physics we speak about the experimental errors, the domain of validity of a theory and so on.With all these hypotheses, how could one say what is the nature? This is nota mere philosophical speculation, a sophism, a formal problem.

What is in crisis is the old deterministic view that we can complete science in the way that it can describe everything. That is has not happened in physics (” the unified theory of everything”) but -most important-  cannot  happen with the formal language of physics; mathematics.

However, one is not allowed to think that mathematics is the last hope for Determinism. As a matter of fact the analogous of the principles of indeterminacy for mathematics was expressed by Kurt G ̈del in 1931 [7]. In his article, he stated the impossibility to realize the hilbertian program: in 1900, during the Second International  Congress of Mathematicians in Paris, David Hilbert introduced a list of 23 problems which covered the most different fields of mathematics [10]. Among these, point 2, relative to the demonstration of non-contradiction of arithmetics, deserves a particular attention. From Hilbert’s viewpoint all mathematical theories should have been reduced to formal systems: then this would have been enough to demonstrate the non-contradiction. In 1930, G ̈del wrote an article, which was published one year later where he demonstrated that this was not possible. As a matter of facts, within a sytem like that expressed by Bertrand Russell and Alfred N. Whitehead in the Principia Mathematica it is possible to express propositions which are not decidable within the system’s axioms. One can view this as the impossibility of defining each concept through a unique and defined linguistic universe.

Crisis is not something to fear of -as the title of the blog you are reading suggests also;

Using the term ‘crisis’ they suggest something dreadful, that will lead to the very end of science. Some scientists think that this crisis is already operating and it is the result of the principles up to now discussed, others think it will come along with the Great Unified Theory. Nevertheless, the word ‘crisis’ shows no dreadful meanings: it derives from the Greek κρισις, which in turn is linked to κρινω, which means ‘to divide’ and metaphorically ‘to decide’ 2 . It were the Greeks the first to introduce the process of analysis as a division of a thesis in propositions, leading more easily to truth. If, within a theory, we separate or, better, underline, some essential laws we could then consider them as principles for a new theory.

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Further reading