Light

[drufae]

Light exist without any matter, charge or anything else for that matter.It consists of 2 fields ( a magnetic and an electric) which oscillate.Both of them sustain each other.

The thing which amazes me is that the the existence of the fields is independent of any causing 'thing' along with it.The wave representation of light can clearly be explained as a solution of maxwell's equations in a vacuum .I was wondering are e.m. waves the only solution to these equations.If not what are the others and how would one go about creating other such stable configurations of fields.

(please note I intended for this thread to be a general discussion and do not mind even if it drifts slightly away from the topic .. thought not too much )

[swansont]

The uniqueness theorem tells you that once you have found the solution to that differential equation, that's the only one.

[drufae]

The Uniqueness theorem states that if a solution of the Poisson's eq. is found to satisfy the boundary conditions then it will be the only solution.However in order to apply the theorem the scenario must have no varying magnetic fields thereby making [math] \nabla \times E [/math] zero.This allows us to describe E in terms of a scalar field and thus allows us to use an eq expressible as the Poisson's eq(Helmholtz decomposition).

In the case of light (and perhaps other solutions) there clearly exist a varying magnetic field ([math] \nabla \times E = - \frac{\partial B}{\partial t} \neq 0

[/math])hence Poisson's eq cannot be used to describe it.

Edited July 25, 2010 by drufae

[Bignose]

A freely-available paper on the uniqueness of Maxwell's equations: http://ceta.mit.edu/PIER/pier64/08.06061302.Zhou.pdf

[drufae]

Thanks ,I'll go through the paper asap.