The effectiveness of mathematics in physics of the unknown

Abstract

If physics is a science that unveils the fundamental laws of nature, then the appearance of mathematical formulae in its language can be surprising or even mysterious. This was Eugene Wigner's argument in 1960. I show that another approach to physical theory accommodates mathematics in a perfectly reasonable way. To explore unknown processes or phenomena, one builds a theory by employing fundamental principles as constraints within a general mathematical framework. Such studies of the unknown, or blackbox models, demonstrate the unsurprising effectiveness of mathematics on the example of Einstein's principle theories, the S-matrix approach in quantum field theory, effective field theories, and device-independent approaches in quantum information.

Résidus phytosanitaires dans les vins : état des lieux, analyses et expertise

“…Les teneurs maximales (jusqu'à 50 mg/L mesurés) sont observées dans des parcelles ayant reçu le plus grand nombre d'applications (6à 1800 g/ha soit plus de 10000 g/ha/an cumulés). Mais cela n'est pas toujours vérifié [7,9].…”

“…Dans les vins issus de raisins traités avec des phosphites, les teneurs sont généralement observées au-dessus de 3 mg/L [9].…”

“…Dans les vins issus de raisins traités au folpel, les teneursévoluent généralement au-dessus de 0.03à 0.05 mg/L [8,9,12]. L'hypothèse d'un apport autre que phytosanitaire en phtalimide dans les vins n'est pasàécarter car c'est une molécule qui sert aussià fabriquer du caoutchouc ou stabiliser du polychlorure de vinyle (PVC) Les dérivés de phtalimide peuventégalementêtre utilisés comme agents de polymérisation de certaines résinesépoxy.…”

Philosophical foundations of effective field theories

“…One of the best known answers was to be found in the S-matrix approach, which had already been impulsed in the 1940s through the work of Heisenberg. The S-matrix only aimed at asking questions about physical observables: it avoided the need to have knowledge about the fundamental structure of interactions between elementary particles [26].…”

“…Current high-energy physics also uses an alternative 'bottom-up' strategy: the underlying high-energy theory is unknown and the lowenergy EFT is constructed by formulating the most general Lagrangian compatible with a given set of degrees of freedom and symmetries. Theoretic constructs that employ fundamental principles tasked with limiting the possibilities in a description of unknown facts have been called "blackbox models" [26]. Although blackbox models appear in many fields of physics, from Einstein's "principle theories" to deviceindependent methods in quantum information [25], in the case of EFTs they take on a universal and fundamental character: it is common among physicists to think of all current physical theories, including the Standard Model, as low-energy EFTs of some unknown fundamental theory.…”