The first Stern-Gerlach experiment was in 1922, long before the discovery of electron spin with which it is now associated.
It was an attempt to prove the existence of "space quantization," the limitation of the direction of angular momentum to a few space directions, as hypothesized by Niels Bohr
and Arnold Sommerfeld.
Even today, Stern-Gerlach is one of the experiments that most directly shows the quantization at the core of quantum mechanics. Understanding how it works sheds light on the problem of measurement
The Stern-Gerlach apparatus consists of an oven that heats a gas of neutral silver atoms. The rapidly moving atoms escaping from the oven are collimated (limited in the vertical dimension) and sent between two magnets, one of which has a sharp point that concentrates the magnetic field. If the field were homogeneous, there would be no effect of the atoms' trajectories. The inhomogeneous magnetic fields bends the trajectories proportional to the amount of spin.
If the particles' spins had a range of classical values, the trajectories would be smeared out vertically. Because the spins are quantized, half the spins are deflected up, the other half deflected down, by a discrete amount.
The quantization of spin is clearly visible as two distinct spots. The Stern-Gerlach experiment allows us to visualize the quantization, to see it directly, perhaps better than most quantum experiments.
We can also study the superposition of probability amplitudes and their deterministic evolution according to the Schrödinger
equation of motion as the components of the superposition are pulled apart into two different parts of space, then directly see the collapse of the wave-function
when one component encounters a detector in its path.
Designing a Quantum Measurement Apparatus
The first step in quantum measurement is to build an apparatus that separates a quantum system physically into distinguishable paths or regions of space, where the different regions correspond to (are correlated with) the physical properties we want to measure.
We do not actually distinguish the atoms as following one of the paths at this first step. That would cause the probability amplitude wave function to collapse. This first step is reversible
, at least in principle. It is deterministic and an example of John von Neumann
's process 2
, evolution of the system according to the Schrödinger
equation of motion.
We need a beam of atoms (and the ability to reduce the intensity to one atom at a time). Spin-up atoms are deflected upward (shown in blue). Spin-down atoms go down (shown in red in a schematic diagram adapted from photons passing through birefringent filters as going straight). Any given atom has the possibility of being deflected up or down by the inhomogeneous magnetic field in the Stern-Gerlach apparatus. Quantum mechanics describes the single atom as being in a superposition of up and down states.
Note that this first part of our apparatus accomplishes the separation of our two states into distinct physical regions.
We have not actually measured yet, so a single atom passing through our measurement apparatus is described as in a linear combination (a superposition) of spin-up and spin-down states,
| ψ > = ( 1/√2) | up > + ( 1/√2) | down > (1)
This does not mean that there are two atoms, one on each path. It is a statement about probabilities. There is an equal probability that the atom will be found (at random) with its spin up or its spin down.
This is a superposition of probability amplitudes, which can interfere with one another, not a superposition of particles, which cannot. Whenever we measure, we do not find a fraction of a particle, but the whole particle. Nor does it become two particles, one spin-up and one spin-down, as in the popular but mistaken interpretation of the Schrödinger Cat
as in a superposition of live and dead cats.
An Information-Preserving, Reversible Example of Process 2
To show that Von Neumann's process 2
is reversible, we can add a second Stern-Gerlach apparatus, in line with the superposition of the physically separated states,
Since we have not made a measurement and do not know the path of the photon, the phase information in the (generally complex) coefficients of equation (1) has been preserved, so when they combine in the second apparatus, they emerge in a state identical to that before entering the first apparatus (black arrow).
An Information-Creating, Irreversible Example of Process 1
But now suppose we insert something between the two apparatuses that is capable of a measurement to produce observable information. We need a detector that locates the atom in one of the two paths.
Let's consider an ideal photographic plate capable of precipitating visible silver grains upon the receipt of a single particle (and subsequent development). Today photography cannot detect single particles, but detectors using charge coupled devices (CCDs) are approaching this sensitivity. We could also use a simple Geiger counter
Note that we do not literally "see" a spin-up atom. All that we really see is a black spot on a photographic plate or an increment in the numeric display of a Geiger counter.
We infer that what we see was caused by a spin-up atom, since our detector is located in the path such a particle would travel.
We can write a quantum description of the plate as containing two sensitive collection areas, the part of the apparatus measuring spin-up atoms, | Aup
> (shown as the blue spot), and the part of the apparatus measuring spin-down atoms, | Adown
> (shown as the red spot)
We treat the detection systems quantum mechanically, and say that each detector has two eigenstates, e.g., | Aup0
>, corresponding to its initial state and correlated with no atoms, and the final state | Aup1
>, in which it has detected a spin-up atom.
When we actually detect the atom, say in a spin-up state with statistical probability 1/2, two "collapses" or "jumps" occur.
The first is the jump of the probability amplitude wave function | ψ
> of the atom in equation (1) into the state | up
The second is the quantum jump of the spin-up detector from | Aup0
> to | Aup1
These two happen together, as the microscopic quantum states of individual atoms have become correlated with the states of the sensitive detectors in the macroscopic Stern-Gerlach apparatus.
One can say that the atom has become entangled with the sensitive spin-up detector area, so that the wave function describing their interaction is a superposition of atom and apparatus states that cannot be observed independently.
| ψ > + | Aup0 > => | ψ, Aup0 > => | up, Aup1 >
These jumps destroy (unobservable) phase information (between the possible spin-up and spin-down states), raise the (Boltzmann) entropy of the apparatus, and increase information (Shannon entropy) in the form of the visible spot. The entropy increase takes the form of a large chemical energy release when a photographic spot is developed (or a cascade of electrons in a CCD or Geiger counter).
We can animate these irreversible and reversible processes, here shown as polarized photons in a birefringent filter, but equally applicable to spin-up and spin-down atoms in the Stern-Gerlach apparatus.
We see that our example agrees with Von Neumann. A measurement which finds the atom in a specific state spin-up
is thermodynamically irreversible, whereas the deterministic evolution described by Schrödinger's equation up to the moment of detection is reversible.
We thus establish a clear connection between a measurement, which increases the information
by some number of bits (Shannon entropy), and the necessary compensating increase in the (Boltzmann) entropy of the macroscopic apparatus, and the cosmic creation process
, where new particles form, reducing the entropy locally, and the energy of formation is radiated or conducted away as Boltzmann entropy.
Note that the Boltzmann entropy can only be radiated away (ultimately into the night sky to the cosmic microwave background) because the expansion of the universe provides a sink for the entropy, as pointed out by David Layzer
. Note also that this cosmic information-creating process requires no conscious observer. The universe is its own observer.
All quantum measurements that become observations have a three-step character, which begins when the wave function describing a quantum system, evolving deterministically according to the Schrödinger
equation, encounters (perhaps becomes entangled with) a measuring apparatus.
- In standard quantum theory, the first required element is the collapse of the wave-function. This is the Dirac projection postulate, which John von Neumann called Process 1 in any measurement.
Note that the collapse might not leave a determinate record. If nothing in the environment is macroscopically affected so as to leave an indelible record of the collapse, we can say that no information about the collapse is created. The overwhelming fraction of collapses are of this kind. Moreover, information might actually be destroyed. For example, collisions between atoms or molecules in a gas that erase past information about their paths.
- If the collapse occurs when the quantum system is entangled with a macroscopic measurement apparatus, a well-designed apparatus will also "collapse" into a correlated "pointer" state that can be seen by an observer as new information.
This is the second required element - a determinate record of the event. Note this is impossible without an irreversible thermodynamic process that involves: a) the creation of at least one bit of new information (negative entropy) and b) the transfer away from the measuring apparatus of an amount of positive entropy (generally much, much) greater than the information created.
Notice that no conscious observer need be involved. We can generalize this second step to an event in the physical world that was not designed as a measurement apparatus by a physical scientist, but nevertheless leaves an indelible record of the collapse of a quantum state. This might be a highly specific single event, or the macroscopic consequence of billions of atomic-molecular level of events.
- Finally, the third required element is that the indelible determinate record is looked at by an observer, presumably conscious, although the consciousness itself has nothing to do with the measurement (despite von Neumann's puzzling about some kind of "psycho-physical parallelism").
When we have all three of these essential elements, we have what we normally mean by a measurement and an observation, both involving a human being.
When we have only the first two, we can say metaphorically that the "universe is measuring itself," creating an information record of quantum collapse events. For example, every hydrogen atom formed in the early recombination era is a record of the time period when macroscopic bodies could begin to form. A certain pattern of photons records the explosion of a supernova billions of light years away. When detected by the CCD in a telescope, it becomes a potential observation. Craters on the back side of the moon recorded collisions with solar system debris that could become observations only when the first NASA mission circled the moon.