Zilch (electromagnetism)
In physics, zilch is a conserved quantity of the electromagnetic field.
Daniel M. Lipkin observed that if he defined the quantities
then the Maxwell equations imply that
which implies that the total "zilch" is constant. Generalising the result, Lipkin found nine related conservation laws, all unrelated to the stress-energy tensor. He named the quantity zilch because of the apparent lack of physical significance.
Zilch can also be expressed using the dual electromagnetic tensor as
It was later demonstrated that zilch is part of an infinite number of zilch-like conserved quantities, a general property of free fields.
Zilch has occasionally been rediscovered. It has been called "optical chirality", since it determines the degree of chiral asymmetry in the rate of excitation of a small chiral molecule by an incident electromagnetic field. A physical interpretation of zilch was offered in 2012; zilch is to the curl or time derivative of the electromagnetic field what helicity, spin and related quantities are to the electromagnetic field itself. The conservation of zilch is not associated with duality transformations, but instead with a more subtle symmetry transformation, which has no special name.
