[Physics] Is time subjective

observersreference framesspacetimespecial-relativitytime

In Minkowski spacetime time is subjective [or more precisely: time is different for every particle/ reference frame]. It is the coordinate time of an observer whose reference frame travels up the $ct$-axis. Before Minkowski, we thought that time was the same for everybody, but now we know that the slightest movement of an observer destroys synchronization with regard to the other observers. Each bus driver lives slower than a prisoner because he is moving, even if the difference is not perceivable. Time is an accumulation of a huge number of relative Minkowski diagrams.

Does that mean that there is no generally applying physical definition of time dimension left? Or is there an absolute dimension of time of the universe in which we are living, and which is independent from the observer?

Best Answer

You shouldn't use the "subjective/objective" distinction for a place where "relative/absolute" is much more appropriate, because they mean different things. For something to be subjective, it must be dependent on the knowledge or state of mind of an observer.

As an example, suppose we define "depth" as "length along the direction an observer is facing". This direction can be used to define a "depth axis", and measurements of depth would depend on projections to that axis. Then how deep an object is depends on the circumstances of the observers, and so is relative. But it is not subjective: it doesn't matter is the observer is delusional about they're facing, etc.

In special relativity, time is rather analogous to this. In spacetime, your four-velocity is kind of like 'direction you're facing' would be in ordinary space. It defines the temporal axis of your inertial frame, and time measurements would be projections to that axis, similarly to the previous case.

Related Question