The unfolding of time is typically described as a sequence of spatial regions: one region of space gets realized, and then another, and then another.
For example: consider a region of space in which Harold is crowned king. As events transpire, a number of further regions of space get realized. Finally, a region of space arrives in which Harold is slain by William. The unfolding of time here is described by a sequence spatial regions leading from Harold’s crowning to Harold’s death.
Although there does not seem to be any one-true-description of unfolding, it happens that intertial observers do agree about the order in which (time-like separated) events unfold.
In particular, in the weak-gravitational regime of Harold and William, spacetime is approximately Minkowski. So, William will identify one possible sequence of spatial regions leading up to the death of Harold. An astronaut moving away from William with velocity v = c/2 will identify a different sequence of spatial regions. However, William and the astronaut will agree about the order in which time-like separated events occur: first Harold is crowned, and then Harold is slain.
On the other hand, an accelerating observer will not generally agree about the order in which these events unfold.
Imagine that at the moment of Harold’s death, there is a second astronaut at rest relative to William, who begins to accelerate away at a constant rate. As the astronaut accelerates ever closer to the speed of light, her simultaneity hypersurfaces (the spatial regions that she uses to foliate spacetime) will tilt ever closer to 45 degrees, as dictated by the geometry of Minkowski spacetime. All these surfaces will intersect on some 2D surface I. Moreover, on the other side of the surface of I, the astronaut will judge the order of events to be the reverse of what William judges: first Harold is slain by William, and then Harold is crowned king. The astronaut will describe some events as unfolding in the wrong direction.
So, the order in which time unfolds is not a fact that all observers agree about.
According to one common definition of objectivity, a claim is objectively true or false if and only if all observers agree about that claim. But in our example, the claim, ‘time unfolds from Harold’s crowning towards Harold’s death’ can only be valuated according to the subjective judgement of one observer. Other observers, such as the accelerating astronaut, are equally correct to valuate the claim differently.
Thus, in this sense, there is no objective fact of the matter as to the order in which time unfolds.
Soul Physics is authored by Bryan W. Roberts. Thanks for subscribing.
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