How I learned to stop worrying and embrace contextuality
TL;DR: Quantum contextuality is just about boundary conditions
Quantum mechanics is contextual: not all properties of a system are defined at all times. The confusion stems from a common misconception: things are what they are only because of their intrinsic features. A chair is a chair because it is a chair. Unfortunately, things are not that simple. A chair is a chair because we are on the surface of the earth. A chair would not be a chair for long on the surface of the sun. The fact that we have a chair, and not a small amount of plasma, depends not just on the chair, but on its surroundings and their interaction. Chairs are context dependent. Everything in physics is context dependent.
The typical reaction to this problem is to look for entities and interactions that remain the same in every context. Yes, whether we have water, water vapor or ice depends on the external temperature and pressure, phase of matter is context dependent, but there are always water molecules and electromagnetic forces between them. In fact, this explains why we have the different phases of water in different conditions. Yes, we may have water molecules or molecular oxygen/hydrogen depending on external conditions, but there are always oxygen and hydrogen atoms mediated by electromagnetic forces. In fact, this explains in which context we have the different configurations. What we need to do, then, is simply to find the “true” intrinsic object that the universe is made of, and we are done. The theory of everything. But will this work?
The first hint of a problem is that the issue of contextuality is never really solved at any level, it is just handed off to the next one. Yes, water molecules exist in a bigger context than ice or water vapor, but they too have a limited context and can transform into molecular oxygen/hydrogen. Even what we call fundamental particles can transform into one another: a magnetically trapped positron will remain a positron indefinitely, but it will not remain so for long if it is surrounded by standard matter. In this case, there is no underlying level: we do not understand positron-electron annihilation as the rearrangement of some other well-defined objects that are left unchanged within the transition.
The second, much deeper problem lies in quantum contextuality. This tells us that it is not just the objects that are contextual, but also the properties that they possess. If we prepare the spin of an electron along the vertical direction, the spin along the horizontal direction is not well defined. If want to define the spin along the horizontal direction, we change context and now the spin along the vertical direction will not be well defined. It is not just that the electron is context dependent, what properties are defined is also context dependent.
Note that by context here we mean a very concrete thing: the set of processes, of operational requirements, for which the object can exist in that state. If I say “I have a Kg of ice”, I am implicitly saying that its surroundings are within a specific range of pressure and temperature. If I say “I have a positron with its spin prepared along the vertical position”, I am implicitly saying that it is magnetically trapped, with its spin oriented accordingly. The statement “the same positron is prepared with its spin along the horizontal position” is incompatible with the previous one because it requires a different system-environment setting: it belongs to a different context.
It is therefore not inconceivable that the search for the “true” intrinsic objects with the “true” intrinsic properties is an altogether futile endeavor, one that distracts us from asking the real fundamental questions. What is the relationship between contexts and states? What are the operational requirements that are necessary to be able to define objects with their states? What are the minimum assumptions we need to make about the system-environment interactions to be able to do physics?
If one starts to think along these lines, numerous interesting insights are brought to light. We can talk about an object if we can, potentially, interact with it separately from all other objects. For example, if whenever we moved a particular chair, the table would also move, we would not be talking about a separate chair and table, but a chair-table system. Similarly, the internal dynamics of the system should not be relevant to the description of the object as a whole. If the motion of each chair molecule were such that it significantly affected macroscopic properties, we would not be talking about a chair, but of a collection of molecules. Therefore to be able to define an object, we must have at our disposal processes for which the dynamics of the overall object is, in some sense, independent from the dynamics of its substructure, of other objects and of the environment. The dynamics of the system is decoupled from the dynamics of the environment and its internal dynamics. The assumption of system independence, then, is a constitutive requirement for an object, and it will be valid only within a specific context.
Contextuality is not some weird quantum phenomenon. It is a common feature of experimental science, part of its foundations.