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cccccttttt


Registered: Feb 2006
Posts: 1

NKS version of Maxwell field equations

Looking for NKS model of Maxwell's field equations.


Consider electric charges A and B.

Accelerate A, and according to QED, photons are

emitted which travel over and interact with B, causing

it to accelerate. (QED: The Strange Theory of

Light and Matter by Feynman)


Suppose each particle's position were on a 3D lattice,

and moved at each tick of a clock to a new position.


Someone skilled in NHK must have formulated

an algorithm to describe the motion of B relative to A.


In large particle systems the behavior would approximate

Maxwell's field equations and give the illusion

of smoothness and continuity.


On the very small scale this "grainy" NKS approach


....is simple to visualize and teach

....lends itself to nano simulations

....avoids the machinery of vector calculus

....eliminates the need for the concept of MAGNETISM..


I read this lattice approach has been used for

quark calculations, but have seen no formulation

for electric charges.



Any information appreciated.


Cam Trenor
Bellevue, Wa.

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Old Post 02-20-2006 08:44 PM
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Todd Rowland
Wolfram Research
Maryland

Registered: Oct 2003
Posts: 113

I was talking to Anthony Martin about this problem at the Midwest NKS 2005 conference. It is a good problem, worth pursuing from a NKS perspective.

Let me suggest some ways to get started.

First of all, one might as well start in 2D, (or possibly start in 1D), just as E+M is usually taught. The most obvious thing to try is to borrow from the fluids model, the basic idea that each cell on a hexagonal grid contains at most one particle going in a given direction (not unlike the Pauli principle). One might start by insisting on conservation of momentum and conservation of energy, and enumerate all rules satisfying those properties. The search for a purely particle based system is smaller because noncolliding particles pass through each other, while I'd expect a E+M model to relax this requirement.

One would need a test, and the first might be with a system just consisting of photons. Only later, would one try adding photon-electron interactions and calculating whether the photons were properly scattered by an electron, and so on.

Feynman's book is a nice reference, and one could also consult p.1060. It is worth pointing out that these sorts of particle models don't take into account phase, which is a property which would ideally be a consequence of a model, rather than something built into it.

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