The Stern-Gerlach experiment is probably the pithiest experiment showing the failure of classical physical ideas, and the necessity of less intuitive but more exciting and mysterious quantum mechanical ideas. This writeup requires no background knowledge! While I will mention esoteric concepts like magnetic moments, the results of the Stern-Gerlach experiment are the important things. The results, and the field of quantum mechanics developed to predict them, are among the foundations of physics.
Background concepts
I stress that none of these concepts need to be understood in any detail. I have to introduce them so we can discuss the experiment. It is well-known that electrons have an intrinsic negative electrical charge. Less familiar to most of us is that electrons have an analogous intrinsic magnetic moment. Basically, every electron behaves like a tiny permanent magnet--in one direction of space is its north pole and in the other its south pole.
When a permanent magnet is put in a non-uniform magnetic field (e.g. placed near another permanent magnet, which as you know, produces stronger magnetic fields near it than away from it), it feels a force. Usually we think of this force snapping magnets together, but we know that it repels magnets also. The reason that magnets tend to snap together despite the fact that the force can be both repulsive and attractive is that one magnet tends to rotate the other, flipping it by 180 degrees and creating an attractive force. Since an electron is a particle, it doesn't rotate in the magnetic field--it simply moves "up" or "down". Imagine an electron as a permanent magnent without the possibility of applied torque--rotational force. It is important to be able to visualize that, depending on the orientation of the electron's magnetic moment, it could feel attraction or repulsion, or if rotated by 90 degrees from those orientations, nothing at all. Intermediate orientation angles would correspond to a continuous variation of the magnitude of attractive or repulsive force.
Understand? Let me know!
The Stern-Gerlach experiment
The Stern-Gerlach experiment used a beam of silver atoms made by heating silver in an oven with a small hole through which some exited. The beam was collimated (made basically unidirectional) by placing a small slit beyond the hole. After passing through the slit, the atoms were exposed to a nonuniform magnetic field, which in the diagram below, moves them up or down. The deflection up or down is measured by a detector.
| South |
| pole | |
Collimated ---------- |
silver atoms Nonuniform |
--------------> magnetic |Detector
field |
---------- |
| North | |
| pole |
So what should we expect to see on the detector? It turns out that only the final, 47th electron of a silver atom contributes to its total magnetic moment. All the other magnetic moments cancel eachother out. Intuitively, we expect that since a silver atom was randomly shot out of an oven, its magnetic moment--its north pole and south pole--should be oriented randomly. Depending on the orientation of the magnetic moment, each atom could deflect up, down, or not at all. There should be a continuous distribution measured on the detector. This is not what was measured in the experiment. Below is the distribution measured by the detector (a ** indicates detection).
| South |
| pole | |
Collimated ---------- **|
silver atoms Nonuniform |
--------------> magnetic |Detector
field |
---------- **|
| North | |
| pole |
This is a remarkable result. It seems to suggest that atoms randomly shot from an oven can only have two orientations of magnetic moment (which are called "spin up" and "spin down")! But wait--this doesn't make sense. The orientation of the magnetic field was random. What if we rotate it? What if we have the north pole located outside the screen and the south pole located inside the screen (and rotated the detector correspondingly)? The experiment showed we get the same result! No matter how we rotate the magnetic field and detector, the measurement pattern is the same. It's important to really understand this, so I will summarize. The magnetic moment of a silver atom can have any direction in space. However, the component of this magnetic moment along any axis, when measured, always has the same magnitude (called a Bohr magneton), and is either positive or negative (i.e. it points up or down).
The situation is a bit ridiculous, and indeed our universe seems to be inherently ridiculous. But the situation gets even weirder.
Physicists were, of course, very interested in the above result and did some followup experiments. One result is not too surprising (but perhaps expected results should be surprising in the strange quantum world). Suppose that an identical magnetic-field setup, with similarly-oriented north and south poles, is placed after the initial setup in a location such that only spin-up atoms enter it (assume spin-up atoms would move down in the nonuniform magnetic field). In other words, what happens when we perform exactly the same measurement on atoms that have already been measured to have one orientation? Please ignore the practical difficulties of setting up this experiment. The detector pattern looks like this:
| South |
| pole | |
"Spin-up" ---------- |
atoms Nonuniform |
--------------> magnetic |Detector
field |
---------- **|
| North | |
| pole |
So the spin-up atoms are still spin-up after a second measurement. In a sense, the first measurement was the positioning of the second magnetic-field setup and the second measurement is observing the pattern on the detector. A general physical principle is this:
When a physical quantity (aka observable) is initially measured, its value is probabilistic and, in cases like spin, quantized (into spin up and spin down). A subsequent measurement of the same observable performed immediately afterward will yield a non-probabilistic result.
Physicists thought of other experiments. Suppose that again a second magnetic-field setup is positioned such that only spin-up atoms enter it, but the second setup and detector are rotated by 90 degrees (so the north pole is out of our screens and the south pole is into our screens). The result isn't too shocking now--we get our familiar split spin up/spin down (perhaps after rotation these could be called "spin into" and "spin out of" the screen) pattern on the detector. A block diagram looks like this:
---- ------- spin-down
|Oven|--|Measure|--beam blocked
| | |spin up|
---- |or down|--spin ---------
------- up--|Measure | split
beam |spin into|--beam
|or out of|
---------
But there's one last experiment that is very shocking. Suppose we add one more measurement to the block diagram above. Suppose that after measuring spin into or out of, we block one of those beams and measure spin up or down on the other. Of course, we expect to measure only spin up since we allowed only spin-up atoms into the second detector. You might have already guessed the measured detector pattern.
|
**|
|
|
|
**|
|
In other words, measuring spin out of/spin into destroys all information about spin up/spin down! Again, this is a fundamental concept of quantum physics.
Measurement of one physical observable can make a previously-measured different observable probabilistic again.
Since we're being general, we might wonder exactly what measurement means, since it changes the universe. Sometimes measurement converts observables from probabilistic to deterministic, and sometimes it does the opposite. Nobody is certain exactly what constitutes measurement, but invariably one is forced into a definition like this: Measurement is conscious observation of a physical quantity. Perhaps I (and others) am not seeing things clearly, but this seems to imply that there is a link between consciousness and physics. I find this implied link to be the most fascinating aspect of our universe, but I can't make heads or tails of it. Sorry for the self-indulgent aside!
In the case of spin, measuring orientation of spin in one direction destroys all information about the spin in a perpendicular direction. Similarly, when the position of a particle is measured, all information about its momentum is lost and vice versa (see Heisenberg uncertainty principle).
So you want an explanation for all of this? Well, there really isn't one! Many have come up with philosophical interpretations of these strange experimental results, and a mathematical framework based on probability, called quantum mechanics, was developed to describe the results of such experiments. Still, physicists are not very comfortable with a scientific theory in which they must resort to philosophy instead of mathematics to explain the universe. Perhaps it would be acceptable to say It appears that this is just the way the universe is constructed, and nothing more can be learned. But then, people have proposed all sorts of puzzles and paradoxes, like Schrodinger's cat, that we should be able to explain, but cannot. The only way to advance is through more experiments, but the million dollar question is What experiments?