Tuesday, June 19, 2018

Absolute relativistic simultaneity

If we accept relativity theory as providing a metaphysically correct theory of time, the folk concept of temporal simultaneity needs revision. The standard way to revise it has been to relativize it to a reference frame. Instead of simultaneity being a binary relation between events (A is simultaneous with B) it becomes a ternary relation between events and a frame (A is simultaneous with B in F).

But another revision of the folk concept is possible: We keep simultaneity a binary relation, and specify that two events are simultaneous if and only if they are colocated in spacetime (this is roughly the same as saying that they are simultaneous according to every frame). Spatially distant events, on this revision, are never simultaneous.

The downside of the absolute simultaneity revision is that a lot of first-order
simultaneity judgments become false. Leibniz and Newton were not developing calculus simultaneously. I am not typing this at the same time as my daughter is playing a game on another laptop. Etc.

The upside is that colocation is a much more fundamental concept given relativity theory than the concept of a reference frame.

So we have a choice: We can keep our ordinary first-order judgments as to what events are in fact simultaneous or we can preserve the arity of the simultaneity relation and the judgment about the fundamentality of simultaneity. I think cases of revision of ordinary concepts, preserving ordinary first-order judgments tends to trump other things. So I am inclined to think the standard revision is superior as a way of doing justice to the language.

But the absolute revision may be better as a philosophical heuristic. For we might think that fundamental philosophical concepts should be frame-invariant, like fundamental physical concepts are.


Brian Cutter said...

A third option would be to say that two events are simultaneous iff they are space-like separated. This would require us to abandon reject certain intuitive "structural" principles about simultaneity, e.g. that it's an equivalence relation. But on the plus side, it allows us to preserve most of our ordinary first-order judgments about simultaneity, and it allows us to preserve the idea that simultaneity is a binary relation.

James Goetz said...

I accept that relativity provides a metaphysically and physically correct theory of time when we consider teleportative wormhole theory predicted by general relativity. For example, my 2016 "Semiclassical Theism and the Passage of Planck Times" (https://doi.org/10.1080/14746700.2016.1191881) describes that an observer in a hypothetical omnicluster of teleportative wormholes detects a universal chronology that is unaffected by relativity's predictions for time dilation and the relativity of simultaneity.

Martin Cooke said...

Is it not an unjustified leap of faith in contemporary physics to assume that relativity theory provides a metaphysically correct theory of time? Physics has seemed to have a comprehensive and yet very simple explanation, and then been proved to be metaphysically incorrect, before; and we already know of a few temporal things that physics has yet to explain. Furthermore, the appearance of the theory is suspicious: it appeared from nowhere a hundred years ago, when the employers of scientists were worried about rebellious scientists, and it can only be verified with expensive laboratories.

Alexander R Pruss said...


I can't wrap my mind around a non-transitive simultaneity. And any event that is simultaneous with my present is happening presently. But then there are events that are happening presently one of which is earlier than the other. (For if on a planet orbiting alpha Centauri lightning strikes and causes a fire, the lightning is earlier than the fire. Yet both could be spacelike separated from my present.)

Alexander R Pruss said...

How about this move? Most of the time when we talk of simultaneity in ordinary language, we mean approximate simultaneity. The precision of that approximate simultaneity is at best 10 milliseconds. So we go for my suggestion that true simultaneity is coincidence in spacetime, but we allow approximate simultaneity to involve a spatial distance of about 10 light milliseconds, about 3000 km, and a temporal distance of about 10 milliseconds. In which frame do we measure these two distances? Our own: for approximation is relative to one's own interests.

Alexander R Pruss said...


I just wrapped my mind around non-transitive simultaneity. We almost never talk of instantaneous events in ordinary life (exception: "the ball that was thrown upwards achieving maximum height"). So bracket the rare case of instantaneous events.

Normally we talk of temporally extended events. But when we say two such events are simultaneous, we surely don't mean that they both begin and end at exactly the same time. For that just doesn't happen in nature. Rather, I think we mean something like this: "The two events substantially temporally overlap." But even apart from relativity theory, substantial temporal overlap isn't transitive.

However, it's still weird to think that there can be two events one of which ends a year before the other begins and yet both of them are simultaneous with my writing this comment.

IanS said...

For extended events you could define ‘practical’ simultaneity like this: events A and B are ‘practically simultaneous’ if most of A is in the forward light cone of most of B and vice versa. (‘Most of’ is deliberately vague to match the vagueness of ‘practically’, but you could make it more precise.) Note that this practical simultaneity is relativistically invariant and intransitive.

The definition maintains folk simultaneity: events lasting 100 milliseconds, simultaneous in the usual sense, and less than (say) 100 km apart would count as practically simultaneous. So would events lasting 1 second, occurring at the same time (UTC) anywhere on earth.

Events of shorter duration (perhaps measurable by instruments) would have to be spatially closer to count as practically simultaneous. In the extreme case, instantaneous events would have to be coincident. So this approach can accommodate both folk notions and physicists’ spacetime colocation.

Alexander R Pruss said...


That seems to me to be the best account so far in this discussion. I like that.

And if I went for that, then I would either abandon the concept of simultaneity proper or restrict it to cases of being in the exact same spacetime location.