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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. Laurens Gunnarsen‏ @MathPrinceps 31 Oct 2018
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      Replying to @j_bertolotti

      But there is no "the" inhomogeneous solution, and indeed there cannot be. That is the whole point. One can only distinguish between inhomogeneous solutions by the imposition of boundary conditions. This is a fundamental mathematical inevitability.

      1 reply 0 retweets 0 likes
    2. Jacopo Bertolotti‏ @j_bertolotti 31 Oct 2018
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      Replying to @MathPrinceps

      There is privileged inhomogeneous solution: the one that describes the sources that are actually there. And those sources are perfectly local.

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

      What physical law are you invoking here? Certainly not the laws of electricity and magnetism, for these are fully expressed by Maxwell's equations -- which, as a matter of mathematical fact, cannot prefer any inhomogeneous solution without the imposition of boundary conditions.

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

      You seem tacitly to be assuming that "the" solution of Maxwell's equations for the field of a point charge is that given by the so-called "retarded potential Green function." But to make this (admittedly common) assumption is to impose a boundary condition (at null infinity.)

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

      No other consideration can privilege this particular Green function (and the inhomogeneous solutions to which it leads.) Boundary conditions alone can distinguish it. One may argue that certain boundary conditions are physically appropriate. But they're inevitably non-local.

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

      My point is that you are tacitly augmenting the laws of Nature here. Local physics gives differential equations. By privileging a particular solution to those differential equations, you are going beyond local physics. And you must, too, to speak about radiation intelligibly.

      1 reply 0 retweets 0 likes
    7. Jacopo Bertolotti‏ @j_bertolotti 31 Oct 2018
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      Replying to @MathPrinceps

      Yes, I am assuming a "retarded Green's function" solution. But the "zero at infinity" boundary is only relevant after an infinite amount of time, i.e. is not physically relevant.

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

      You are assuming, then, that the field of your point source is very nearly zero very far away, at very early times. But this is obviously a non-local condition. Whether it is satisfied cannot be determined by inspecting only the immediate (spacetime) vicinity of your source.

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

      To this I add, by the way, that Dirac and others have noted that a classical theory of point electrons -- even when augmented by suitable non-local boundary conditions -- is essentially untenable. A consistent classical theory of radiating charges has yet to be formulated.

      1 reply 0 retweets 0 likes
    10. 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)

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      Laurens Gunnarsen‏ @MathPrinceps 31 Oct 2018
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      Replying to @j_bertolotti

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

      5:59 PM - 31 Oct 2018
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        1. New conversation
        2. 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.

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        3. 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
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