I recommend reading the Master: http://bit.ly/2yHQgmk
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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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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.
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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.)
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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.
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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.
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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.
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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.
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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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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.
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As does Unruh's theory, of course, as well.
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