Identifying System Equality Across Observers

[Logic Cloud]

Say we have two separated observers which have a velocity relative to each other and are both looking at a system. By a system, I mean simple systems as encountered in mechanics. They want to determine if they are looking at the same system or not. They can perform measurements on the system without disturbing it and they can communicate their results with each other. Is there a way for the observers to determine whether the systems they are looking at are in fact the same system or not?

Of course, they could compare measurements for time and position and see if the results are linked by a Galilean or Lorentz transformation. However, it seems to me you shouldn't have to have knowledge of some transformation law before you can determine if you are seeing the same system or not. In other words: which properties determine a system, taking into account different observers?

 

[mfb]

They can always see a copy of a system instead of the same system, with no way to figure that out unless they are allowed to manipulate the system.

However, it seems to me you shouldn't have to have knowledge of some transformation law before you can determine if you are seeing the same system or not.

You need this knowledge, otherwise you don't understand (fast) moving objects.