Observable and interaction

[lalbatros]

Let us consider the http://en.wikipedia.org/wiki/Stern-Gerlach_experiment" experiment.

The inhomogenuous magnetic field produces a drift force that can separate particles according to their spin and offer a possibility for a "measurement". This (very) small magnetic interaction can be embedded in the Hamiltonian of the system as an interaction. If this interaction is active during enough time the separation and also the "measurement" of the spin "observable" are made possible.

This famous experiment illustrates a link between:

an interaction energy
an observable (a "measurement")
a interaction time​

I would be interrested to know more about this link.

Thanks.

Michel

 

[lalbatros]

In other words: how can an observable be "observed".
Are there general rules, or is it enough that this observable in some way appears in the Hamiltonian ? (With some sensibility?)

Michel

 

[denian]

The Stern-Gerlach experiment is a classic example of how the interaction between particles and a magnetic field can lead to the observation of a measurable property, in this case, spin. This interaction energy, which is embedded in the Hamiltonian of the system, allows for the separation of particles based on their spin. By allowing this interaction to occur for a sufficient amount of time, the spin observable can be measured.

The link between the interaction energy, observable, and interaction time is crucial in understanding the results of this experiment. The strength and duration of the interaction will determine the degree of separation and measurement of the spin observable. This link can also be explored further in terms of quantum mechanics and the uncertainty principle, which states that the more precisely one observable is measured, the less precise the measurement of another observable will be.

Overall, the Stern-Gerlach experiment highlights the importance of understanding and controlling interactions between particles and their environment in order to make accurate observations and measurements in science. Further research and study into this link can help us better understand the fundamental principles of quantum mechanics and their applications in various fields of science.