Suppose you take a magnetic compass like the one available at your local stationary shop. That is just a little weak magnet suspended on a joint that lets it move around. Left to itself, the magnet will get affected by the magnetic field of the Earth and the needle will tend to point North.
Now bring this compass near a magnet (the one in a door stop will do). The first thing you notice is that the needle starts moving back and fro oscillating wildly. After a few moments, the friction in the joint causes the oscillations to dampen and slow down. The needle settles to a position pointing wither directly towards or away from the magnet. The time it takes to settle down and the amplitude of the oscillations (how much it swings) depends on the angle at which you bring the magnet.
For instance, if you bring the South Pole of the magnet towards the point of the needle, there is hardly any difference in the initial and final directions of the needle. That is, from before when it was dominated by the Earth’s magnetic field (the Earth’s magnetic South Pole is near the geographic North Pole) and eventually when it is dominated by the field of the magnet we are bringing near, its direction will hardly change. Hence we can expect that there will be very few oscillations.
Conversely, if we bring the South Pole of the magnet near the tail end of the compass needle, the compass will have to swing a full 180 degrees to reach its final resting place. Therefore it will have to swing wildly and the oscillations will be very great.
As you would expect, the case where the oscillations are heavy, more energy is expended by the magnetic field.
Now let us see a quantum analogue of this classical experiment.
A single electron is also a magnet with a very tiny magnetic field of its own. Left to itself, it can orient itself in any direction. Now, if you put an electron in a stronger magnetic field, it will also eventually orient itself in the same way as the compass needle did. That is, its own North Pole will face the South Pole of the external magnetic field and vice versa. But what happens in between is interesting.
Before we look at what the electron actually does, let us consider what we would expect from our intuition about compass needles.
We would expect that initially, the electron will be oriented in any direction. When we apply the magnetic field, it will start oscillating about the direction of the field till it finally comes to rest with its North Pole facing the South Pole of the magnet. To stop oscillating, it will need to give up energy. Electrons give up energy by emitting light particles called photons. So we expect that the electron will emit a photon to stop oscillating and align its moment with the magnetic field it is placed in.
Further, we expect that since the extent of oscillation depends on which direction the electron was initially facing, the energy of the photon will also vary depending on which direction the electron initially faced. So if we take an electron at random and put it in a magnetic field, it will emit a photon with energy that could be any value from 0 (perfect initial alignment) to a maximum (180 degrees alignment change) amount. If we take thousands of electron and repeat this experiment with them one by one, we would find that each of them emit one photon. The energy of the photon always lies between 0 and the maximum value and can have any value in between.
Sounds reasonable? But this does not happen.
What actually happens is that either we get no photon (0 energy) or 1 photon with the maximum energy. That is the energy released when the electron flips 180 degrees. There are no in-between values. What does this mean?
Suppose we turned our magnetic field from East (North magnetic pole) to West (South magnetic pole). Now if we only get photons of 0 or maximum energy then that means that initially all the electrons were facing West (0 energy) or East (maximum energy). No electron could be facing in any other direction (North West, South etc.).
That sounds strange. But it gets stranger.
This same thing is true regardless of whatever direction you choose to set your magnetic field. So you could set the field North (North magnetic pole) to South (South magnetic pole). Again you see the same result. Some electrons don’t emit anything while other emit a single photon of the maximum energy which is released when the electron flips 180 degrees. This would mean that all the electrons either faced South or North.
Here we had assumed we did not know the initial direction of the electron. But what if we started with an electron whose direction we had fixed previously and then measure it later. Lets say we forced an electron so that its North pole is facing up and the South pole is facing down. Now if we put the South Pole of our magnetic field above and North pole below the electron, we see as expected that the electron does not move and there are no photons emitted.
Conversely, if we put the North Pole of our magnetic field above and South pole below the electron, we see as expected that the electron emits 1 electron of the maximum energy.
But what if we bring the magnetic North pole to the right and the South pole to the left? Then there is a 50% chance of seeing the maximum energy photon and 50% chance of seeing no photon. This is the heart of quantum weirdness.
This confounded and perplexed the early pioneers of the field. Some felt that the electron actually exists in a “superposition” of 2 states. When we observe of measure it, it jumps into one of them.
According to some representations of quantum mechanics (such as the Diosi-Penrose model), All quantum systems are supposed to undergo 2 processes. One is unitary evolution (U) which is what they do when they are unobserved in accordance with the rules of Schrodinger’s equation. The other is reduction (R) where they discontinuously shift from a superposition of multiple possible states into a single state upon observation
Note: Actually, the magnetic moment is defined by a quantum mechanical phenomenon called spin and there aren’t any explicit North & South Poles for an electron. But it is fair to approximate them as such for this discussion. The effect is the same.