In the center of quantum mechanics, the base of all physics at the subatomic level, lies a profound, unsolved problem called the measurement problem. So far, all we have are theories that try to guess why this problem exists and what it means or represents.
The problem goes like this:
Imagine you have a subatomic particle, say a photon, in a box that is completely sealed from the outside world so that no information can come in and out. This photon has a property called spin. Spin, if you have not heard of it, is like angular momentum, but for subatomic particles (the particles are not actually spinning but act like they do, the full explanation requires a different post). A photon can spin in one of two ways, either spin up or spin down, analogous to clockwise and counterclockwise respectively.
Before we continue, you must first understand that all subatomic particles have a wave-function, which is a function that describes all the possible states of the particle (due to the wave-particle like nature of subatomic particles). All these states combined and their relative probabilities (this will make more sense later) is what comprises the superposition, which is the particle in all these possible positions at the same time.
In this situation, the photon has been created in such a way that the photon is in superposition between the spin up and spin down state, meaning that the photon is both equally in a spin up and spin down state at the same time. Now that this photon is in the box, say you wanted to take a measurement of it. You open the box and suddenly you find that the photon has collapsed to be either spin down or spin up, and that if you keep doing it over and over, that the collapse is 50/50. In the same way that an object cannot be in two places, it appears that upon measurement, the superposition of the particle probabilistically collapses depending on the values of each state assigned by the wave-function (technically wave-function squared), into one of the states within the superposition. Why and how the wave-function collapses upon any measurement is what is called the measurement problem.
The collapse of a superposition due to a measurement that was just described is typically called the collapse of the wave-function, due to the superposition being governed by the underlying wave-function. Both terms will be used throughout the rest of the article.
The first question that you may ask here is whether the particle was actually in only one state to begin with, or whether it knew which state it was going to collapse into. But that is not the case. A series of experiments called the Bell experiments were performed to test this theory (originally theorized by Einstein’s EPR paper), but found it to be wrong.
This leads us to the question of what constitutes a measurement, as perhaps that would give us a clue as to why and how the superposition collapses only when we measure it.
The first logical answer to this question is that a measurement is (in this scenario) an interaction with an object that can upon interaction calculate the spin of the particle. Let us call this object a spin detector (it is actually called a Stern-Gerlach device). What would differentiate this from a “normal object” like an electron or a rock? To figure this out, we can theorize that the photon interact with the electron in 2 possible ways since the electron does not tell us what is actually going on.
The photon can interact with the electron in one state, due to the electron collapsing the wave-function of the photon. In this case, as observers, we have no idea in which state it interacted with, so it appears to be the case that the electron has simply entered the superposition of the photon, since the photon is still in superposition and the electron is now part of the photon’s system.
The photon interacts in superposition, meaning that the electron also enters into the superposition. This theorized situation is not possible though, as we will soon figure out.
In both scenarios, the electron enters superposition and the observer appears to not have collapsed the wave-function of the system.
Let us now try the same two options with the detector.
We already know that the detector interacts with the photon in one state based on the detector’s information, so the second option is immediately eliminated.
In the first case, the detector calculates the spin of the particle. This information though, is in the detector, and if as observers we do not interact with the information, just the detector, the photon can also be considered still in superposition just like the electron, as we have no idea which state it interacted with.
The electron and detector in this situation are almost identical.
The only difference that appears to exist (but does not exist) is that with the detector, we can learn the state of the particle if we interact with it correctly. This collapses the wave-function of the photon-detector system from our perspective and pulls us into the superposition (relative to a distant observer who still does not know which state the photon is in).
But in reality, the exact same thing happens with the electron if we interact with it in any way, as we interact with it in the state that results from the photon interaction, collapsing the wave-function of the photon-electron system. It is just that in the detector’s case, the state clearly indicates the photon’s state while in the electron’s case, it is almost impossible to deduce the photon’s state, though the information is still there. The important thing though, is that there was interaction, and with interaction comes information, resulting in a wave-function collapse.
This logic extends to all matter interaction with a superposition, including interacting with a detector without observing the detected information, as was described earlier.
*side note: since the electron and detector collapse the wave-function in the same way, the elimination of the second option (an object interacting with a photon while keeping it in superposition from the object’s perspective) also applies to the electron and all other matter particles.
Therefore, what we have learned here is that any matter interaction with a superposition, no matter what the interaction is, collapses the superposition from the matter’s perspective, while pulling the matter into the superposition from an outside observer’s perspective. Notice what we previously considered measurement is referred to as matter interaction, as we have now learned that in this problem, any matter interaction collapses the wave-function in the same way that a measurement by a detector does.
Possible solutions of the Measurement Problem
The wave-function and its collapse applies to all subatomic particles all the time, but what its collapse upon measurement represents and how it happens, aka. the measurement problem, is still a mystery.
Nevertheless, there are several theories that try to explain what the collapse represents, here are two of them:
The most common theory is called the Copenhagen Interpretation, due to being built only on what we can measure, and is the one that I have been using the whole time. It simply states that any measurement collapses the wave-function for that observer, and that all the other possible positions in the superposition do not exist anymore. For an outside observer, the matter performing the measurement has simply entered or become part of the original wave-function. One interesting thing is that according to this theory, everything in the universe is part of one wave function.
The other popular but controversial theory is called the many worlds theory. This theorizes that instead of superposition, the universe splits into many universes, with each possible state of the superposition occurring in a different one. In this theory, the only uncertainty is simply not knowing which universe you are in, meaning that in your specific universe, there are no superpositions and no probabilistic wave-function collapses, simply a fixed state. This is one of the features that many scientists find appealing about this theory.
Bonus: Here is a funny shirt I made specifically about wave-function collapse.
