Preparing a spin state and measurements

[MagicalMayhem]

Hey guys,

I'm very new to quantum mechanics and have purchased 'Quantum Mechanics: The Theoretical Minimum. I'm still a bit confused by a fairly fundamental idea.

In the book, it states that you first prepare a spin state (say the σz = +1) in the initial measurement. If you rotate the apparatus by 90 degrees then measure again, a +1 or -1 measurement will be produced (with a statistical average of repeated measurements being 0, I'm happy with that). Let's say the apparatus produced σ = -1. My question is, is the system now 'prepared' in this new direction? If you simply measured the spin again without resetting the spin or apparatus, would you produce the same measurement of σ = -1 again and again?

In the book, it says 'The intermediate measurement along the x-axis will leave the spin in a completely random configuration as far as the next measurement is concerned.' If someone could clarify this for me please, I would greatly appreciate it!

Thanks!

 

[Simon Bridge]

Welcome to PF,

Hey guys,

I'm very new to quantum mechanics and have purchased 'Quantum Mechanics: The Theoretical Minimum. I'm still a bit confused by a fairly fundamental idea.

In the book, it states that you first prepare a spin state (say the σz = +1) in the initial measurement. If you rotate the apparatus by 90 degrees then measure again, a +1 or -1 measurement will be produced (with a statistical average of repeated measurements being 0, I'm happy with that). Let's say the apparatus produced σ = -1. My question is, is the system now 'prepared' in this new direction? If you simply measured the spin again without resetting the spin or apparatus, would you produce the same measurement of σ = -1 again and again?

yes.

In the book, it says 'The intermediate measurement along the x-axis will leave the spin in a completely random configuration as far as the next measurement is concerned.' If someone could clarify this for me please, I would greatly appreciate it!

you send a beam of particles through a zspin-meter, if you measure spin to be +1 for all particles in the beam (say) then a second zspin-meter, further away, will also get +1.
But, if you put an xspin-meter between these two, the second z spin will now be 50:50 +1 or -1 and the meter will record half the beam one way and half the other way.

 

[MagicalMayhem]

Thank you very much! That greatly clarifies things.

 

[Simon Bridge]

No worries - it can help to get a feel if you know the real-world setup as well as the somewhat abstract QM description.

The definitive experiment was presented by Otto Stern and Walther Gerlach in 1922. They used a shaped magnet which deflects a particle according to how much spin was pointing along the orientation of the magnet (particles with spin act like magnets). Since the initial beam had random-spin atoms in it, the classical prediction was that the beam fan out in some way and they would be able to learn stuff by measuring how the beam spread out. The actual experiment resulted in only two beams coming out the other side, suggesting only two spin states somehow aligned completely with or against the magnet.

When I tell people this, they all seem to think of using more magnets on the resulting beams and these guys did too.

Intercepting one of the beams with another magnet-rig resulted in two more beams, unless the second rig was oriented the same way as the first - in which case there was only one beam - deflected the same way as the first one.

The rig they used is now called the Sterg-Gerlach apparatus, and the experiment is named after them.
Students of quantum mechanics study it early on in their education.
http://en.wikipedia.org/wiki/Stern–Gerlach_experiment

Since then pretty much every possible trick has been tried with different combinations of magnets and other things.