Is defining a "system" something relative or absolute?

Question

I had a quarrel with a friend of mine regarding external/internal forces. He insists that an external force cannot become internal when we change the reference frame, whereas I claim otherwise. For a better perception, assume that a tiny positive charge is detached from the positive plate and set in motion uniformly towards the negative plate inside a parallel plate capacitor by an external force.
If the system is determined by the boundaries which are at rest relative to the capacitor, then the force acting on the tiny charge is external, and those acting on the plates are internal, and, in my friend's view, this is a fixed definition from the viewpoint of all inertial observers. However, I asserted that from the viewpoint of the moving tiny charge, this external force can be considered as internal if the boundary of the system is assumed to be at rest relative to the charge, and on the other hand, the forces acting on the plates are external. Indeed, I want to say that the boundaries of a system cannot be dictated to any observers beforehand, and it can vary from one observer to the other, and all of the calculations regarding the capacitor, say, its internal energy, must have the same result as measured by any observer regardless of how the system is defined by the observer. Who is right? Is defining a system something relative or absolute?

gandalf61 · Answer

A system is a collection of objects that you want to treat as a unified whole. In your example, you could consider the charge on its own to be a system if you were interested in the motion of the charge. Or you could consider the charge and the capacitor plates to be a system if you were interested in the motion of the whole capacitor plus charges.
In other words, you decide which objects you want to include in your system - there is no need to define spatial boundaries or to take account of whether you are moving relative to the objects.
Once you have selected the objects that will form your system then any force exerted by one of these objects on another object in the system is an internal force. Any force exerted by or on an object outside of the system is an external force. Newton’s third law tells us that internal forces will come in equal and opposite pairs.
The distinction between internal and external forces depends only on which objects you choose to be part of your system, and on nothing else.

Bob D · Answer

I don't wish to get into the middle of your argument with your friend, but would like to comment on the title of your post.

Is defining a “system” something relative or absolute?

To borrow a page out of the thermodynamics playbook, a system is anything you define it to be. Once defined, everything not included in the definition of the system becomes the system's surroundings or environment. That which separates the system from its surroundings is the system boundary. Then the combination of the system and the surroundings is the universe. Moreover, once you define the system you need to stick with the definition in order to properly analyze the transfer of energy and mass between the system and its surroundings.
Once you define the system, then the system should be the same in all inertial frames. That is because, according to the theory of special relativity, all physical laws that apply to the defined system in one inertial frame should apply equally in all other inertial frames as long as you don't change the definition of the system. Those physical laws would include all of Newton's laws of motion as they are valid in all inertial frames.
Hope this helps.

Is defining a "system" something relative or absolute?

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