Re: a question about non-locality
From: Bruce Scott TOK (Use-Author-Supplied-Address-Header_at_[127.1)
Date: 03/23/05
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Date: Wed, 23 Mar 2005 19:23:15 +0100 (MET)
Kevin Blake wrote:
|> In Bjorken and Drell - QED part 1 I read a statement that one doesnt
|> use a square rooted Hamiltonian (H= SQRT/m*2.c*4+m*2.p*2/) in a wave
|> equation of the Schoedinger type
|> (–ih.dpsi/dt=H.psi) because after expanding the root in Taylor series
|> one gets all powers to infinity of the space derivatives. This makes
|> the theory non-local.
|>
|> 1.Now I don't inderstand how the n+1 derivative is more non- local
|> than the n-th derivative – in the end all is taken to the limit of the
|> local point)
It is not n+1 versus n but N_large versus n = 1 here. Think of finite
differences. With n = 1 you communicate with neighboring grid points.
With n = 1 applied N times you communicate with grid points a count N
away. Now let N --> \infty.
|> 2.Then in the quantum theory based on Schroedinger equation there are
|> only second order derivatives over space but nevertheless one is left
|> at the end with a non-local theory (EPR type paradoxes).
Here, think about elliptic equations.
-- cu, Bruce drift wave turbulence: http://www.rzg.mpg.de/~bds/
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