Dirac: The Rules Mathematicians Find Interesting Are the Ones Nature Chose
The Relation Between Mathematics and Physics by Paul Dirac
In his 1939 James Scott Prize lecture, Paul Dirac traces how physics abandoned the principle of simplicity for mathematical beauty. Relativity and quantum theory pulled vast new domains of pure mathematics into fundamental physics, and Dirac predicts the two will ultimately unify—every branch of pure mathematics gaining its physical application. He proposes a bold method: choose the branch of mathematics that is most beautiful, then look for how it lends itself to physical interpretation.
The mathematician plays a game in which he himself invents the rules while the physicist plays a game in which the rules are provided by Nature, but as time goes on it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen.
- VorpalWay
Shouldn't this have a "(1939)" suffix on the title according to HN rules? ;)
- Xmd5a
> The dominating idea in this application of mathematics to physics is that the equations representing the laws of motion should be of a simple form. The whole success of the scheme is due to the fact that equations of simple form do seem to work. The physicist is thus provided with a principle of simplicity, which he can use as an instrument of research.
https://arxiv.org/abs/math-ph/0009007
> Occam's Razor as a Formal Basis for a Physical Theory
> We introduce the principle of Occam's Razor in a form which can be used as a basis for economical formulations of physics. This allows us to explain the general structure of the Lagrangian for a composite physical system, as well as some other artificial postulates behind the variational formulations of physical laws. As an example, we derive Hamilton's principle of stationary action together with the Lagrangians for the cases of Newtonian mechanics, relativistic mechanics and a relativistic particle in an external gravitational field.
- wolfi1
there is a quote from Pauli about Dirac : 'There is no God and Dirac is his prophet' Heisenberg and Dirac had different opinions on the existence of a god and Pauli, asked for his opinion, had the former to say
- taaha47
"I would like to put forward a suggestion as to how such a scheme might be realized. If we express the present epoch, 2 x 109 years, in terms of a unit of time defined by the atomic constants, we get a number of the order 1039, which characterizes the present in an absolute sense. Might it not be that all present events correspond to properties of this large number, and, more generally, that the whole history of the universe corresponds to properties of the whole sequence of natural numbers? At first sight it would seem that the universe is far too complex for such a correspondence to be possible. But I think this objection cannot be maintained, since a number of the order 1039 is excessively complicated, just because it is so enormous. We have a brief way of writing it down, but this should not blind us to the fact that it must have excessivly complicated properties."
this cannot be an early hint to the result made by chaitin; Chaitin’s Incompleteness Theorem?
- 3lambda
Given its strength in mathematics, it seems likely that AI should be of great help with discovering new physics. We just need to teach it to ask interesting questions.