Concepts required to define a "system"?

[Stephen Tashi]

What concepts are required to define a "system" in physics ? - as in the phrase "In a closed system ... " or "If two systems are isolated from each other ..."?

Is "system" always used as a term of common speech, or can it be defined more precisely?

For example, in the thread https://www.physicsforums.com/threa...nd-Newtons-2nd-law.891171/page-3#post-5616570 we consider the physical system defined by "the rocket" and it seems we have to resort to common speech to clarify the details of exactly what we wish to include in that system.

The problem of specifying a "system" would be simple if we could specify it as a set of "objects". It is common to use the word "mass" to indicate an object, but "mass" is a property of an object, not the object itself.

We think of an "object" has having some existence that persists in time. An object like a coffee cup has various non-persistent properties. It can have a variable position, velocity etc. and still be considered "the same" object - even though those properties have changed. In Newtonian physics, we could define an object as something that has a persistent total mass, but an object like a rubber ball need not have a fixed distribution of mass. Perhaps a particular object could be defined by a particular time-varying spatial distribution of mass.

We can refer to particular kinds of objects such as "an electron", "a particle" etc. Are there physical models that define such objects completely ? - or do physical models give some of the properties of such objects without claiming to completely define the objects themselves?

 

[CWatters]

What concepts are required to define a "system" in physics ? - as in the phrase "In a closed system ... " or "If two systems are isolated from each other ..."?

Is "system" always used as a term of common speech, or can it be defined more precisely?

Have you seen..

https://en.wikipedia.org/wiki/Closed_system

The problem of specifying a "system" would be simple if we could specify it as a set of "objects". It is common to use the word "mass" to indicate an object, but "mass" is a property of an object, not the object itself.

Defining a system boundary by objects physically inside it would be wrong. It's usually important to consider what is crossing the boundary. For example you can't apply conservation of energy to the system if energy crosses the system boundary. In that case the system wouldn't be "closed" and the law of conservation of energy only applies to closed systems.

The system boundary isn't always a physical place. Things that cross the system boundary don't necessarily leave the physical system. For example consider a ball of clay hitting wall with an inelastic collision. You can't usually apply conservation of energy to this problem because you don't know how much energy is converted to heat. We say the system isn't "closed" even if most of the heat stays in the clay.

 

[Stephen Tashi]

Have you seen..

https://en.wikipedia.org/wiki/Closed_system

I glanced at that article. It takes for granted that the concepts of "in" and "out" are defined for a "system". It doesn't say whether "in" and "out" have some geometric interpretation or whether they have the meaning of membership in a set (i.e. "in" = "a member of the set").

Likewise https://en.wikipedia.org/wiki/Physical_system speaks of "portion of the physical universe" without specifying whether "portion of" is a geometric concept or the mathematical concept of "subset".

Defining a system boundary by objects physically inside it would be wrong.

Are you implying that a "system" has a "boundary" in the sense of a boundary in 3D space? - or some more abstract mathematical space? As I mentioned in the OP, defining a system in terms of "objects" transfers the problem of defining a "system" to the problem of defining an "object".

It seems to me that it is difficult and perhaps impossible to define an "object" in terms of specific physical quantities.

 

[DrClaude]

For me, the system is what you are considering explicitly/in detail, by contrast to the environment, a reservoir, an external field, the universe... The boundary of the system can change depending on how big you want to make it, and sometime will encompass a reservoir or the EM field, for instance.

I guess that the idea behind considering a system and was is outside that system allows to get a grasp on what is conserved and what is not (energy, momentum, mass, etc.), especially depending on the possible exchanges with the outside world (closed system, isolated system, ...).

 

[Stephen Tashi]

For me, the system is what you are considering explicitly/in detail, by contrast to the environment, a reservoir, an external field, the universe...

I agree and I don't have any problem understanding the definition of a physical system as it is described using common language. My question is more technical. Is there a way to define a "system" precisely in term of its physical properties? - or must we always use the notions of common speech to define a "system" and any particular "object" that is part of a system?

 

[CWatters]

I suspect you could prove that something must be part of a system in certain cases. For example something might have to be part of the system or the system would appear not to conserve momentum.