There are some things that remain common throughout physics and its application, no matter what is being dealt with. The idea of a system and the idea of a reference frame are among those few prized possessions of physicists that appear to be universal in their reach. Therefore, it is worthwhile to ponder on what they are and how much we understand them.
It is interesting that though most physicists understand that the concept of ‘system’ is of fundamental importance to us, discussions and definitions of it are practically non-existent in major textbooks and sources. Most often, people assume that the readers intuitively understand the meaning of the word ‘system’. It is surprising to note that none out of Goldstein, Landau, Sakurai have a definition or even a description of what constitutes a ‘system’. Further home, Halliday-Resnik-Krane also lacks one and Wikipedia’s definition and the page has no citation rather two extra links one of which is broken. This ought to set us thinking. Why are so many go-to textbooks not willing to define a system?
The Wikipedia (and Encyclopaedia Brittanica) define a ‘system’ as that portion of the universe chosen for analysis or for studying the changes that take place within it in response to varying conditions. In essence, this definition is quite vague and we are helped here by Quora to certain extent. With that in mind, I have come up with this working definition:
My Working Definition
“A system is a part of the universe that is delineated by providing spatial and temporal boundaries and possesses a set of properties/attributes.”
Now to analyse it.
- Does a physical system need to have defined spatial and temporal boundaries? If yes, then the system must always be embedded in space/spacetime. If no, then what kind of physical system would it be? How would it be decided if the phase space of the system is discrete or continuous? Normally, a discrete physical space corresponds to a discrete phase space.
- Practically, we study a system by including it as a subsystem with a measuring apparatus and observing their interactions. Does that mean that for a physicist, the interaction and the system are the same thing, i.e., a system can be represented by enumerating all of its possible interactions?
- Every space is made by a set of points. Are all properties of a system having these points as their parameters? Or can we have some properties that are interdependent? For example – married properties X, Y such that X = f(Y) and Y = g(X) and both are in a stable solution to this set of equations.