Sunday, July 12, 2015

When Positive Is Negative

I have made a mistake!  The \(x\) axis of a negative particle is the negative \(x\) axis of a positive particle.  The right hand screw rule still gives the direction of the field produced when the particle rotates, but since \(x\) points in the opposite direction we have to reverse the direction of spin.

Equivalently, we can reverse the direction of the generated field.

And that is why, the awkwardness in Earth's Magnetic field,


The magnetic field lines at the North pole go into the ground and the field lines emanate from the south pole.  Earth is a \(g^{-}\) particle.

And we update our particle sign assignment as,


where the \(g^{-}\) particle in spin produces a \(t_T\) field consistent with a spinning \(e^{-}\) particle.  With the sign assignments of these two particles, the corresponding particles of opposite sign are also fixed, because there is only one other particle existing in the same time dimension. Proton, \(p^{+}\) along \(t_c\) and \(g^{+}\) along \(t_g\).  We know that a rotating \(B\) field (\(t_T\) field) generates an EMF, so \(T^{+}\) produces a \(t_c\) field when spin.  And correspondingly, the remaining particle in the same time dimension \(t_T\), is \(T^{-}\).

Morning!