Clueless layman question: How does one determine that a particle is in superposition since measuring it causes the “collapse” into one state or the other?
Ask me about chemistry or the life sciences. I have just as many questions as anybody else about quantum mechanics.
A particle can be described as also being a wave. When that's done, the particle is represented by a wavefunction. In short, the wavefunction squared gives the probability that the particle will be in some particular state. So, the calculation, which represents the behavior of reality, involves probabilities and not certainties regarding the values particular to the possible state of the particle. That means before each look at a particle, the particle is considered to be in a superposition of all the possible values it can have. That includes when one takes a second look at the same particle.
In cases like the one in the article though, the state is a single many particle state of a system that involves the values of 2 particles and the vaue of the state of the system. That means the values are limited and certainties and distinguishability enter the picture. So if one has information about one, or more of the particles that are linked by being in the same system state, they have information about the value(s) of other particle(s) by virtue of knowing the value(s) for the state of the system.
In the first case, the particles were free and even if they were not and there was a common state, no initial info was known. Since the laws of physics must be consistent, each measurement of a free particle will be consistent with a probability and not certainty. That applies even if it's the same particle and a measurement that indicated it was "up" was obtained. That behavior, or peculiarity of reality makes it appear as if the particle "collapses" back to a state that consists of a superposition of values. ...like an exposed card that's shoved back into the a deck that's subsequently reshuffled.
The details begin to be understood when one considers that "particles" arise out of fields and the particles are described by superimposed, time varying sinusoids. In general, it's the phase of the representative waves that change, that causes the "collapse" type description. Phase velocities can be faster than light, but all that obtains from that is a slower than light speed, wave envelope shape change. The particles represented by the amplitudes of the field(s) never move faster than light, nor do they communicate(exchange energy) faster than light, but the phases of the sinusiods that make up the field(s) envelopes do.
If one has 2 particles in a particular system, the state is known and a relavant pair value for one of the particles is known, the other must be fixed to the opposite, or some other value that maintains the overall fixed the system value(s). In general, that's because the particle's wave components are phased to accomodate their membership in the system with a particular state. System membership in the article is called entanglement. The particles in any such system can not be in a collapsed state, because they're constantly being looked at by the other particles in the system. ie. the phases of the sinusoids that represent the particles are locked so that the system's value(s) remain fixed.