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michael_nielsen's profile
michael_nielsen
michael_nielsen
michael_nielsen
@michael_nielsen

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michael_nielsen

@michael_nielsen

Searching for the numinous. Co-purveyor of https://quantum.country/ 

San Francisco, CA
michaelnielsen.org
Joined July 2008

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    1. michael_nielsen‏ @michael_nielsen Nov 3
      • Report Tweet

      On the oddly pervasive notion of the conservation of energypic.twitter.com/j0iWw1sbTY

      21 replies 23 retweets 225 likes
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    2. michael_nielsen‏ @michael_nielsen Nov 3
      • Report Tweet

      michael_nielsen Retweeted John Carlos Baez

      Well, I goofed. Energy conservation in GR turns out to be subtle, and it's certainly not right to flatly say energy is conserved. Quite a few people pointed this out. Here's a couple of samples, at different levels of explanation:https://twitter.com/johncarlosbaez/status/1191164917597917184 …

      michael_nielsen added,

      John Carlos Baez @johncarlosbaez
      Replying to @michael_nielsen
      Energy is conserved in theories where 1) symmetries give conservation laws and 2) time translation is a symmetry. It's not conserved in the Big Bang cosmology, where 2) fails.
      1 reply 1 retweet 26 likes
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    3. michael_nielsen‏ @michael_nielsen Nov 3
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      michael_nielsen Retweeted Claudio Paganini

      And a nice discussion here (and in followups):https://twitter.com/the_happyproton/status/1191107133628207106 …

      michael_nielsen added,

      Claudio Paganini @the_happyproton
      Replying to @seanmcarroll @michael_nielsen @QiaochuYuan
      The fact that energy is not conserved in an expanding universe is actually what makes the ground state (GS) special. In a fix cavity a system would go forth and back between an excited state and a GS + photon state. The redshift prevents this on universal scales.
      1 reply 0 retweets 6 likes
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    4. michael_nielsen‏ @michael_nielsen Nov 3
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      It is, nonetheless, possible to make some sense of the notion of energy conservation in GR. Here's an overview: http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html … (also by @johncarlosbaez and collaborator).

      1 reply 1 retweet 10 likes
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    5. michael_nielsen‏ @michael_nielsen Nov 3
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      There's also a set of ideas known as the ADM formalism, a so-called Hamiltonian formulation of GR. (The Hamiltonian is a sort of energy function). https://en.wikipedia.org/wiki/ADM_formalism …

      1 reply 0 retweets 6 likes
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    6. michael_nielsen‏ @michael_nielsen Nov 3
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      These caveats don't make my original statement correct! But they are useful context, a sense in which the notion of energy (or a Hamiltonian) is correct in general relativity.

      1 reply 0 retweets 1 like
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    7. michael_nielsen‏ @michael_nielsen Nov 3
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      Another topic: some people are replying "Isn't this Noether's theorem?" But that misses the the point. Of course, once you're in Lagrangian mechanics & have time-translation invariance, conservation follows. And there's an analogous quantum argument...

      1 reply 0 retweets 4 likes
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      michael_nielsen‏ @michael_nielsen Nov 3
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      ... but assuming all that structure begs the question.

      6:00 PM - 3 Nov 2019
      • 5 Likes
      • The Trouble With Economics Victoria Watson Claudio Paganini Tiago Souza Federico Vaggi
      3 replies 0 retweets 5 likes
        1. Ruvi Lecamwasam‏ @RLecamwasam Nov 3
          • Report Tweet
          Replying to @michael_nielsen

          Does that mean this question reduces to "why can all these theories be recast in a Lagrangian form, despite the fact that they are radically different mathematically?" Or is there another subtlety?

          0 replies 0 retweets 1 like
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        1. Jonathan Oppenheim‏ @postquantum Nov 4
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          Replying to @michael_nielsen

          Jonathan Oppenheim Retweeted Jonathan Oppenheim

          Does this (partly) answer it? https://twitter.com/postquantum/status/1191101333874651136 … (time translation invariance + information conservation in QM). In classical (Lagrangian) mechanics we assume evolution is determined by q,\dot{q} & I've wondered if this could be motivated. In QM this seems more baked in.

          Jonathan Oppenheim added,

          Jonathan Oppenheim @postquantum
          Replying to @postquantum @michael_nielsen @QiaochuYuan
          You might like that in quantum mechanics, energy conservation follows from information conservation (that time-evolution is unitary). If evolution is unitary then by the Stone-von-Neumann theorem it is e^{-iHt}. and then energy H is conserved since H commutes with e^{-iHt}.
          0 replies 0 retweets 1 like
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        1. Matthew Cory‏ @TricksterDoesIt Nov 3
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          Replying to @michael_nielsen

          Symmetries in NATURE lead directly to conservation laws.

          0 replies 0 retweets 0 likes
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