----------------------------------
S11c. The Stern-Gerlach experiment
----------------------------------
Another basic quantum experiment is the Stern-Gerlach experiment.
An input beam of silver atoms is passed through an inhomogeneous
magnetic field in a fixed direction, which produces a sideways
classical force on each silver atom proportional to the atom's
magnetic moment. The magnetic field is said to split the input beam
into two separate beams corresponding to atoms of spin up and down,
respectively, which shows in the experiment as silver spots where
the beams hit a screen. If the beam of silver atoms is replaced by
a beam of electrons with very low intensity and the screen is replaced
by a more sensitive detector, one observes single detection events,
each randomly at one of the two spots. Each such event is generally
interpreted as a spin measurement (up or down), which makes sense
only if the wave function actually collapses to |up> or |down>.
(Though this is very questionable since the electron stops existing
as an object separable from the screen.)
If a blocker is put in the way of one of the beams, the corresponding
spot on the screen disappears, but if the blocker is sensitive as well,
single observations are found to occur at the blocker as well.
According to strictly orthodox but purely unitary quantum mechanics,
the situation is the following:
If a single particle leaves the magnetic area, it is in an entangled
state consisting of a bilocal superposition of wave packets somewhere
along the two beams. When it encounters the blocker,
this single electron turns into a still bilocal superposition of wave
packets: One remains stuck where the blocked beam meets the block
and the other continues its motion along the unblocked beam.
A little later, this second wave packet meets the screen, and we end up
with a still bilocal superposition of wave packets, now both sitting
at the end points of the respective beam. Without the blocker,
essentially the same happens, except that the electron ends up
in a superposition of two spots on the screen.
More precisely, what happens is that if one starts with a pure
state |x,p> |left>, where |x,p> denotes an approximately coherent
state with position x and momentum p, and
|left>=1/sqrt(2)(|up>+|down>),
one gets approximately a superposition
1/sqrt(2)(|x^+(t),p^+(t)>|up> +|x^-(t),p^-(t)>|down>),
where the parameters in the approximately coherent states follow
classical paths in phase space determined by approximately classical
motion due to the magnetic field, the blocker and the screen -
After hitting blocker and screen. respectively, positions are constant
and momenta vanish, and the particle is in a superpostion of two spots.
All this follows without difficulty from the superposition principle,
i.e., from the linearity of the Schroedinger equation.
To match observations in an objective interpretation of the wave
function, one needs a mechanism for changing the unobserved
superposition of spots into the observed definite spot. In an
observer-independent interpretation this has to happen in the split
moment between the particle feeling the presence of blocker or screen
and hitting or passing it. This is the so-called collapse of the wave
function.
According to the old school (von Neumann, London and Bauer, Wigner),
in a purely unitary setting it requires a conscious look at what
really happened to change the superposition of spots into a definite
spot, which gives quantum mechanics an uncomfortable subjective,
human-centered touch.
----------------------------------
S11c. The Stern-Gerlach experiment
----------------------------------
Another basic quantum experiment is the Stern-Gerlach experiment.
An input beam of silver atoms is passed through an inhomogeneous
magnetic field in a fixed direction, which produces a sideways
classical force on each silver atom proportional to the atom's
magnetic moment. The magnetic field is said to split the input beam
into two separate beams corresponding to atoms of spin up and down,
respectively, which shows in the experiment as silver spots where
the beams hit a screen. If the beam of silver atoms is replaced by
a beam of electrons with very low intensity and the screen is replaced
by a more sensitive detector, one observes single detection events,
each randomly at one of the two spots. Each such event is generally
interpreted as a spin measurement (up or down), which makes sense
only if the wave function actually collapses to |up> or |down>.
(Though this is very questionable since the electron stops existing
as an object separable from the screen.)
If a blocker is put in the way of one of the beams, the corresponding
spot on the screen disappears, but if the blocker is sensitive as well,
single observations are found to occur at the blocker as well.
According to strictly orthodox but purely unitary quantum mechanics,
the situation is the following:
If a single particle leaves the magnetic area, it is in an entangled
state consisting of a bilocal superposition of wave packets somewhere
along the two beams. When it encounters the blocker,
this single electron turns into a still bilocal superposition of wave
packets: One remains stuck where the blocked beam meets the block
and the other continues its motion along the unblocked beam.
A little later, this second wave packet meets the screen, and we end up
with a still bilocal superposition of wave packets, now both sitting
at the end points of the respective beam. Without the blocker,
essentially the same happens, except that the electron ends up
in a superposition of two spots on the screen.
More precisely, what happens is that if one starts with a pure
state |x,p> |left>, where |x,p> denotes an approximately coherent
state with position x and momentum p, and
|left>=1/sqrt(2)(|up>+|down>),
one gets approximately a superposition
1/sqrt(2)(|x^+(t),p^+(t)>|up> +|x^-(t),p^-(t)>|down>),
where the parameters in the approximately coherent states follow
classical paths in phase space determined by approximately classical
motion due to the magnetic field, the blocker and the screen -
After hitting blocker and screen. respectively, positions are constant
and momenta vanish, and the particle is in a superpostion of two spots.
All this follows without difficulty from the superposition principle,
i.e., from the linearity of the Schroedinger equation.
To match observations in an objective interpretation of the wave
function, one needs a mechanism for changing the unobserved
superposition of spots into the observed definite spot. In an
observer-independent interpretation this has to happen in the split
moment between the particle feeling the presence of blocker or screen
and hitting or passing it. This is the so-called collapse of the wave
function.
According to the old school (von Neumann, London and Bauer, Wigner),
in a purely unitary setting it requires a conscious look at what
really happened to change the superposition of spots into a definite
spot, which gives quantum mechanics an uncomfortable subjective,
human-centered touch.