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The solution of the Sixth Hilbert Problem: the Ultimate Galilean Revolution

D'Ariano, Giacomo (2018) The solution of the Sixth Hilbert Problem: the Ultimate Galilean Revolution. Philosophical Transactions of the Royal Society A.

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Abstract

I argue for a full mathematisation of the physical theory, including its axioms, which must contain no physical primitives. In provocative words: "physics from no physics". Although this may seem an oxymoron, it is the royal road to keep complete logical coherence, hence falsifiability of the theory. For such a purely mathematical theory the physical connotation must pertain only the interpretation of the mathematics, ranging from the axioms to the final theorems. On the contrary, the postulates of the two current major physical theories either don't have physical interpretation (as for von Neumann's axioms for quantum theory), or contain physical primitives as "clock", "rigid rod ", "force", "inertial mass" (as for special relativity and mechanics). A purely mathematical theory as proposed here, though with limited (but relentlessly growing) domain of applicability, will have the eternal validity of mathematical truth. It will be a theory on which natural sciences can firmly rely. Such kind of theory is what I consider to be the solution of the Sixth Hilbert's Problem. I argue that a prototype example of such a mathematical theory is provided by the novel algorithmic paradigm for physics, as in the recent information-theoretical derivation of quantum theory and free quantum field theory.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
D'Ariano, Giacomogiacomo.dariano@unipv.it0000-0003-0602-5519
Keywords: algorithmic paradigm, VI Hilbert problem, quantum automata
Subjects: Specific Sciences > Physics > Fields and Particles
Specific Sciences > Physics
Depositing User: Prof. Giacomo Mauro D'Ariano
Date Deposited: 07 May 2018 14:15
Last Modified: 07 May 2018 14:15
Item ID: 14652
Journal or Publication Title: Philosophical Transactions of the Royal Society A
Publisher: rsta.royalsocietypublishing.org
Official URL: http://rsta.royalsocietypublishing.org/content/376...
DOI or Unique Handle: https://doi.org/10.1098/rsta.2017.0224
Subjects: Specific Sciences > Physics > Fields and Particles
Specific Sciences > Physics
Date: 29 January 2018
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/14652

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