Tuesday, June 23, 2015

Negative Energy, Screw It

There is no need to define negative energy nor negative time,


just opposing spins, given the right hand screw rule.  The sign in the expression,

\(i\cfrac{\partial\,\psi_{t_g}}{\partial\,x_1}\)

for the diagram on the left changes to,

\(-i\cfrac{\partial\,\psi_{t_g}}{\partial\,x_1}\)

with opposite spin, as the diagram on the right.

In both cases, \(x_1\) serve as the radius of the cross section circle perpendicular to \(x_2\), the direction of travel of the particle.  \(i\) rotates \(x_1\), \(\pi/2\) anti-clockwise into the perpendicular direction and the expression denotes the change in \(\psi_{t_g}\) in the direction perpendicular to \(x_1\), in the plane containing the circle that defines the spin.

The diagram on the left with a anti-clockwise spin is a photon, as we know them.