... because they [messrs Stern and Gerlach] set up the apparatus that way.how come the gradient has no x or y parts?
The Stern Gerlach Experiment is a physics experiment conducted by Otto Stern and Walther Gerlach in 1922 to study the properties of atoms and their angular momentum.
The Stern Gerlach Experiment was significant because it provided evidence for the existence of electron spin and confirmed the quantum mechanical theory of angular momentum.
In the Stern Gerlach Experiment, a beam of silver atoms is passed through an inhomogeneous magnetic field. The magnetic field causes the atoms to split into two beams, each with a different spin orientation.
The results of the Stern Gerlach Experiment showed that the silver atoms had a quantized angular momentum, meaning that their spin could only take on certain discrete values rather than a continuous range of values.
The Stern Gerlach Experiment provided strong evidence for the existence of quantum properties, such as electron spin, and helped to confirm the principles of quantum mechanics. It also opened the door for further research and experiments in this field.