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MathPrinceps's profile
Laurens Gunnarsen
Laurens Gunnarsen
Laurens Gunnarsen
@MathPrinceps

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Laurens Gunnarsen

@MathPrinceps

Mathematical physicist and mentor to mathematically talented youth. Talent is that which bridges the gap between what can be taught and what must be learned.

Joined June 2012

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    1. Robert McNees‏ @mcnees 23 Mar 2019
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      The mathematician Emmy Noether was born #OTD in 1882. She made groundbreaking advances in abstract algebra, and her eponymous theorems articulated the deep connection between symmetries and conserved quantities in physics. Image: Public domain (photographer unknown)pic.twitter.com/BBGd3K0En9

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    2. Robert McNees‏ @mcnees 23 Mar 2019
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      While at Göttingen, Noether proved the two theorems that bear her name. It is the first theorem, often just called “Noether’s Theorem,” that associates conserved quantities with symmetries of physical systems http://cwp.library.ucla.edu/articles/noether.trans/german/emmy235.html …pic.twitter.com/sR6tlg9sIL

      2 replies 7 retweets 38 likes
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    3. Robert McNees‏ @mcnees 23 Mar 2019
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      A symmetry is something you can do to a system that doesn’t change its physics. For example, all other things being equal, a collision between two masses works out the same way in your office and in the lab down the hall. A translation down the hall is a symmetry of the physics.

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    4. Robert McNees‏ @mcnees 23 Mar 2019
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      Likewise, if you collide the two masses in exactly the same way, you’ll get the same result in a minute or an hour or a year that you got earlier today. So a translation in time can be a symmetry. You might also rotate the experiment and find that the physics is unchanged.

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    5. Robert McNees‏ @mcnees 23 Mar 2019
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      Noether’s Theorem states that for every symmetry of a physical system there is a property of the system that does not change over time — a “conserved quantity.” For translations in space it's momentum, for translating in time it’s energy, and for rotations it's angular momentum.

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      Laurens Gunnarsen‏ @MathPrinceps 23 Mar 2019
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      Replying to @mcnees

      Actually, this misstates the theorem slightly, in a way that makes it seem less impressive than it really is. The quantities Noether associated with (infinitesimal) symmetries are not in general conserved, but rather Ad*-equivariant. (They're also integrals of local densities.)

      5:25 PM - 23 Mar 2019
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        2. Laurens Gunnarsen‏ @MathPrinceps 23 Mar 2019
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          Replying to @MathPrinceps @mcnees

          For example, "boosts" (i.e., velocity transformations) are symmetries of special-relativistic systems, to which Noether's theorem associates non-conserved quantities

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        3. Robert McNees‏ @mcnees 23 Mar 2019
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          Replying to @MathPrinceps

          I don’t think I understand. Given a Lorentz invariant theory, Noether’s theorem associates a constant of the motion with boosts. It may depend on t, but it is still a constant of the motion.

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