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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. Jacopo Bertolotti‏ @j_bertolotti 31 Oct 2018
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      Replying to @MathPrinceps

      Why should I need to assume anything about the field at a distance greater than c t? (You seem more concerned about the mathematical structure of the theory than about the Physics the theory strives to describe. I am not)

      1 reply 0 retweets 0 likes
    2. Laurens Gunnarsen‏ @MathPrinceps 31 Oct 2018
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      Replying to @j_bertolotti

      I recommend reading the Master: http://bit.ly/2yHQgmk 

      1 reply 0 retweets 0 likes
    3. Jacopo Bertolotti‏ @j_bertolotti 1 Nov 2018
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      Replying to @MathPrinceps

      Interesting, but irrelevant to our discussion. In that paper Dirac tries to solve the problem of the field singularity for a point electron within the Maxwell eqs framework, but it never claims (like you do) that classical electrodynamics is nonlocal.

      1 reply 0 retweets 0 likes
    4. Laurens Gunnarsen‏ @MathPrinceps 1 Nov 2018
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      Replying to @j_bertolotti

      Sigh. Did you read the paper? All of its conclusions depend upon choices of Green functions, which in turn depend upon boundary conditions. Physical laws do not determine boundary conditions. Imposing them in general, which you are doing, is adding a non-local law to physics.

      1 reply 0 retweets 0 likes
    5. Laurens Gunnarsen‏ @MathPrinceps 1 Nov 2018
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      Replying to @MathPrinceps @j_bertolotti

      Consider the simpler case of Newtonian gravity. This may be formulated in two ways: via action at a distance (which is non-local), and via a gravitational potential function subject to a Poisson equation (which is local) AND a boundary condition at infinity (which is non-local.)

      1 reply 0 retweets 0 likes
    6. Laurens Gunnarsen‏ @MathPrinceps 1 Nov 2018
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      Replying to @MathPrinceps @j_bertolotti

      If you drop the boundary condition on the Newtonian potential function, then an arbitrary homogeneous solution may be added to it. And this arbitrariness makes the gradient of the Newtonian potential -- i.e., the gravitational "force" -- arbitrary. It can be annulled at a point.

      1 reply 0 retweets 0 likes
    7. Laurens Gunnarsen‏ @MathPrinceps 1 Nov 2018
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      Replying to @MathPrinceps @j_bertolotti

      A purely local formulation of Newtonian gravity theory, then, leads naturally and inevitably to the Equivalence Principle. In such a theory, the notion of gravitational "force" is meaningless. This notion can only be recovered by adding a non-local "law" to the theory.

      2 replies 0 retweets 0 likes
    8. Laurens Gunnarsen‏ @MathPrinceps 1 Nov 2018
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      Replying to @MathPrinceps @j_bertolotti

      The same situation obtains in Maxwell theory. It is a purely local theory, whose laws take the form of partial differential equations. In this theory, no meaningful statements can be made about the "radiation" emitted by a source, until and unless boundary conditions are imposed.

      2 replies 0 retweets 0 likes
    9. Jacopo Bertolotti‏ @j_bertolotti 1 Nov 2018
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      Replying to @MathPrinceps

      Take a charge. Not a theoretical one, take a real one. Now accelerate it. It will emit radiation that can be measured. And what happens at a distance L (e.g. the walls of my lab) only influence it after a time of order L/c. The walls of my lab matter, but not immediately.

      1 reply 0 retweets 0 likes
    10. Laurens Gunnarsen‏ @MathPrinceps 1 Nov 2018
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      Replying to @j_bertolotti

      As an empirical matter, a uniformly accelerated charge does not radiate. Dirac calculates the radiation field in the vicinity of an accelerating point electron, and finds that it vanishes when the acceleration is constant. The question is: why? That's where this discussion began.

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      Laurens Gunnarsen‏ @MathPrinceps 1 Nov 2018
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      Replying to @MathPrinceps @j_bertolotti

      Dirac, of course, supplies an answer. It has nothing to do with the Unruh effect. It does, however, depend crucially on non-local conditions, added to Maxwell theory.

      9:54 AM - 1 Nov 2018
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        1. Laurens Gunnarsen‏ @MathPrinceps 1 Nov 2018
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          Replying to @MathPrinceps @j_bertolotti

          As does Unruh's theory, of course, as well.

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