# Why is it said that magnetism breaks time reversal symmetry?

• fluidistic

#### fluidistic

Gold Member
It is known that Maxwell equations have the time reversal symmetry. I.e. by changing t by -t, J by -J (which can be understood as the charges going in the opposite direction when time is reversed, which makes sense), E to E and B to -B, the equations are still satisfied.

However, it is also claimed in several places (condensed matter when dealing with ferromagnetism or topological insulators when dealing with magnetic materials, just to name a few.) that magnetism breaks the time reversal symmetry.

How is that even possible? Wouldn't that imply that Maxwell equations lack the T-symmetry? If not, what's going on?

it is also claimed in several places (condensed matter when dealing with ferromagnetism or topological insulators when dealing with magnetic materials, just to name a few.)
Can you link to a specific citation?

Wouldn't that imply that Maxwell equations lack the T-symmetry?

No, they just show that the solutions of an equation (which, btw, is probably not Maxwell's Equations in the examples you cite, since they are talking about quantum phenomena, not classical electromagnetism) do not have to have the same symmetries as the equation itself does. The latter two references talk about spontaneous symmetry breaking, which is the term commonly used for this phenomenon.

A simple example of the phenomenon would be a pencil balanced on its point. The equations describing what happens to the pencil if it tips over are rotationally symmetric; but once the pencil tips over, it will fall in one particular direction, not all of them at once. So the single solution that describes what the pencil actually does is not rotationally symmetric, even though the underlying equations are. The papers you reference are talking about cases where phenomena involving magnetism have the same property: the individual solutions that get realized in experiments do not have time reversal symmetry, even though the underlying equations do.

• Dale
A nice practical example of this is the microwave circulator which is extremely common in microwave systems. It is basically a three-port device which consists of a PCB with microwave transmission lines with a ferrite "puck" glued on top of it. The ferrite gives the circuit directionallity which means that nearly all (about 98-99%) of the signal will only travel in one direction.
If you terminate the third port with a matched load you get an isolator; which is a component will passes signals in one direction but isolated in the other.