Physical objects are not physical systems
TL;DR: What we model in science is not exactly physical objects
In the past few months, I have been clarifying the starting points I need to create a general theory of states and processes. In particular, I finally clarified for myself the difference between a physical object, something that exists in our world, like a ball attached to a piece of string, and a physical system, which is the abstract entity that ends up being modeled, like a pendulum. One big source of confusion is that the same physical object can correspond to multiple physical systems, and that the same physical system can be made of multiple objects. If one confuses objects with systems, then one opens oneself to a crucial category error.
Let’s start with a concrete example. In thermodynamics, a heat engine is a system that transfers heat from a hot source to a cold source to extract work. A heat pump is a heat engine run in reverse, using work to transfer heat from the cold source to the hot source. When we characterize these systems in a theory, we do not care about the physical implementation. Each system, each part of the overall setup, is distinct and characterized by its inputs and its outputs. The theory is general precisely because it does not care about the physical realization, and its generality allows us to understand what the best results conceptually possible are.
Let’s now consider the following concrete setup. We have a big, heavy, insulated cargo container filled with stuff we want to cool off. We connect it to a heat pump that vents the heat into the air. Now, we could take the electricity from the grid, which would be the system that provides work. However, we are going to do the following. We take a dynamo, a device that converts mechanical rotation into electricity, and we connect it to the big insulated cargo container through a pulley. We elevate the container, such that when it is pulled down by gravity, the dynamo converts the gravitational energy into electrical energy and activates the heat pump. Once the cargo reaches the ground, we can pull it back up and repeat.
Now, which physical object corresponds to which physical system? Clearly, the air is the hot source and the heat pump is the heat pump. But what is the cargo? Well, its interior is the cold source, but the whole thing plus the pulley and dynamo is the system providing work. The same physical object can be part of multiple systems. That is, the way we partition systems is not necessarily along the lines of division of physical objects. Biological systems are very complicated to understand precisely because the same object (e.g. bones) provides different interfaces with different functions (e.g. mechanical support, mineral storage and blood cell production).
This difference exists in all physical theories, including quantum theory. A quantum system is simply something that can be described by quantum mechanics. It can be a molecule taken as a whole (e.g. when doing interferometry), or the different parts of the molecule as they interact (e.g. when studying protein folding). Whether the same object is treated as a single quantum system or as a collection of interacting quantum systems depends not just on the level of precision we are interested in, but on whether the processes we are studying are sensitive to that level of precision.
When we measure or prepare some property of an object, we are specifying a mode of interaction: inputs and outputs. If the mode of interaction changes, the physical object stays the same, but the description as a physical system changes. This is, in a nutshell, the root of contextuality in quantum mechanics. If we want to prepare or measure the vertical polarization of an electron, we have to, somewhere, vertically orient some magnet. Attributing states to physical objects, then, is a category error. States are attributed to physical systems.