Tuesday, November 4, 2014

The Stern-Gerlach Experiment

What if in the Stern-Gerlach experiment, the electrons are not travelling in a straight path but an helical path.  The following diagram shows the deflection of a electron in its helical path by a magnetic field orientated vertically upwards.  Basically, the electron in its helical path has a magnetic moment, the direction of which is given by the right hand screw rule considering the sign of the charge.  The magnetic North due to the spinning charge is repulsed away from the magnetic North of the deflecting B field.


A helical path has a clockwise or anti-clockwise sense, the resulting magnetic moment from this spin is opposite of each other.  This results in deflections in two opposite directions.  If the electrons emerge from their source with circular velocities within a narrow band, not including zero, and that their spin is evenly distributed, half to half, then the resulting deflections will form two bands, up and down, along the direction of the B field.

In a similar way, deflection in the lateral direction is shown below.


Such deflections are summarized below,


What happens when a ray of a particular sense of spin is subjected to two B fields consecutively but in opposite directions?

When only one of the up/down rays is allowed to pass beyond the B field, only half  the ray intensity will emerge from the B field.  Obviously, a ray that has been deflected in one direction will not pass if that direction is blocked in a subsequent B field pointing in the same direction as the first.  But flipping the subsequent B field will still allow the same ray to pass when in both B fields the same deflection is allowed to pass.


The diagram shows a up-pass followed by a down-pass that results in no output, and a up-pass followed by a flipped up-pass that has output.  So, blocking one of the deflection consistently results in a rotational sense filter.  Deflection in the direction of the B field corresponds to a clockwise rotation in the circular part of the helix.

The electron is in a helical path because it has attained terminal velocity.  The post "To Light Speed and Beyond" has shown that it takes very little distance for an electron to attain light speed when subjected to an accelerating field (B or E).

The deflection of silver atoms however is a different issue.