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August 10, 2018

The Philosophy and Physics of Noether’s Theorems

Posted by David Corfield

Nicholas Teh tells me that there is to be a conference held in London, UK, on October 5-6, 2018, celebrating the centenary of Emmy Noether’s work in mathematical physics.

2018 brings with it the centenary of a major milestone in mathematical physics: the publication of Amalie (“Emmy”) Noether’s theorems relating symmetry and physical quantities, which continue to be a font of inspiration for “symmetry arguments” in physics, and for the interpretation of symmetry within philosophy.

In order to celebrate Noether’s legacy, the University of Notre Dame and the LSE Centre for Philosophy of Natural and Social Sciences are co-organizing a conference that will bring together leading mathematicians, physicists, and philosophers of physics in order to discuss the enduring impact of Noether’s work.

Speakers include our very own John Baez.

We have the entry nLab: Noether’s theorem. Since this (the first theorem) concerns group symmetries and conserved quantities, and since we are at the nn-Category Café, naturally we’re interested in higher Noetherian constructions, involving actions by higher groups. For an example of this you can turn to Urs Schreiber’s Higher prequantum geometry and its talk of ‘higher Noether currents’ as a L L_{\infty}-algebra extension (p. 21).

Here are all the conference speakers:

Posted at August 10, 2018 10:05 AM UTC

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Re: The Philosophy and Physics of Noether’s Theorems

Just to point out that the conference is at Notre Dame’s Fischer Hall which is in London, UK, as opposed to at the University of Notre Dame itself!

Posted by: Scott Balchin on August 10, 2018 10:53 AM | Permalink | Reply to this

Re: The Philosophy and Physics of Noether’s Theorems

Thanks! I hadn’t even noticed that. In fact, I’d better modify the post as it’s rather essential information.

Posted by: David Corfield on August 10, 2018 10:58 AM | Permalink | Reply to this

Re: The Philosophy and Physics of Noether’s Theorems

This isn’t strictly related to higher categories per se, but has there been any attempt to formalise Noether’s theorem in a type-theoretic framework?

The closest I can find is this paper by Atkey, but it seems to be just a minor extension of System Fω (and hence, non-HoTT) and it can only describe classical Lagrangians whose symmetries are already apparent even without the type system. What I’d like to see is a mechanical way of deriving all the invariants of a Lagrangian-formulated physical system that works for both QM and GR, and such that it is immediately implementable in a suitable subset of Coq.

Posted by: Clark Urzo on August 12, 2018 5:20 AM | Permalink | Reply to this

Re: The Philosophy and Physics of Noether’s Theorems

Close to the end of Noether’s theorem is a remark about where it is formalised in cohesive HoTT. I was asking Urs about this here.

You could ask anything specific at the end of that discussion thread.

Posted by: David Corfield on August 12, 2018 9:19 AM | Permalink | Reply to this

Re: The Philosophy and Physics of Noether’s Theorems

For anyone who can’t make this meeting, there are still a few places left at the LMS-IMA Joint Meeting: Noether Celebration, next Tuesday 11 September at De Morgan House, London. Register here

Posted by: Richard Pinch on September 5, 2018 5:45 PM | Permalink | Reply to this

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