The discussion revolves around the nature of time-like events in the context of relativity, particularly focusing on the implications of absolute time order and its relationship to spatial order across different reference frames. Participants explore the concepts of causality, spatial ordering, and the distinctions between time-like and space-like intervals, engaging in both conceptual clarifications and technical reasoning.
The discussion features multiple competing views regarding the nature of spatial order and its relationship to time-like events. Participants express differing opinions on whether space can be considered ordered and the implications of this for understanding causality in physics. No consensus is reached on these points.
Participants note that the discussion involves complex concepts that may depend on specific definitions and assumptions, particularly regarding the nature of ordering in space and time. The relationship between Minkowski spacetime and other physical laws is also highlighted as a point of contention.
If you are driving along a straight road from south to north and pass through a town at 2pm, then "the town at 1pm" occurs to the north of you and "the town at 3pm" occurs to the south of you.BLevine1985 said:Well in spacelike intervals the time order doesn't matter, since the events can't be causally linked. So I was wondering about the converse. In the time-like interval where the time order is absolute, what does that imply about the space order? Is there such a thing?
Space isn't ordered anyway.BLevine1985 said:what does that imply about the space order? Is there such a thing?
3D space isn't, but a 1D spacelike line is. Note that @DrGreg carefully gave a 1D example in post #4.Dale said:Space isn't ordered anyway.
You seem to have used the terms correctly later, so perhaps this is just a typo, but be aware that "time-like events" doesn't make sense. Events can be time-like separated, but are not themselves time-like, space-like or otherwise.BLevine1985 said:time-like events
In general I agree, although you can impose an ordering by picking one direction and only comparing displacement in that direction, as @DrGreg did. It's probably worth noting that the fact you have to restrict yourself to one dimension is why you see talk of time ordering (naturally one dimensional) but not much of spatial ordering.Dale said:Space isn't ordered anyway.
Even for a 1D line I would disagree. Or at least the ordering is not natural. There is no natural sense in which a point on the left is smaller than a point on the right. You can artificially impose an ordering but there is no natural "arrow of space" like there is a natural arrow of time.PeterDonis said:3D space isn't, but a 1D spacelike line is. Note that @DrGreg carefully gave a 1D example in post #4.
The timelike ordering is not "smaller than" and "larger than"; it is "before" and "after". These are symmetric in the same way that "north of" and "south of" are in @DrGreg's example. You don't have to have a concept of "size" of items to have an ordering. You just have to have a relation that satisfies the properties of an ordering relation.Dale said:the ordering is not natural. There is no natural sense in which a point on the left is smaller than a point on the right
The second law of thermo disagrees about the symmetry of "before" and "after".PeterDonis said:The timelike ordering is not "smaller than" and "larger than"; it is "before" and "after". These are symmetric in the same way that "north of" and "south of" are
But the second law of thermo is not something you can derive from Minkowski spacetime and its geometry. As far as the latter is concerned, "before" and "after" are symmetric.Dale said:The second law of thermo disagrees about the symmetry of "before" and "after".
Nevertheless there is a clear and unambiguous physical meaning for ##t_a < t_b## whereas there is not a clear and unambiguous physical meaning for ##x_a<x_b##, even considering each restricted to a single 1D worldline (timelike and spacelike respectively). I don't think that we are required to turn off all of our other knowledge of physics when discussing relativity. In the physical world Minkowski geometry is not a standalone entity divorced from the other laws of physics.PeterDonis said:But the second law of thermo is not something you can derive from Minkowski spacetime and its geometry. As far as the latter is concerned, "before" and "after" are symmetric.
I disagree; @DrGreg described a clear and unambiguous physical meaning for ##x_a < x_b## along a single 1D spacelike line. The difference with space is that a single 1D spacelike line is only a restricted subset of space, whereas a 1D worldline is the full history of a timelike observer (at least an idealized pointlike one).Dale said:there is a clear and unambiguous physical meaning for ##t_a < t_b## whereas there is not a clear and unambiguous physical meaning for ##x_a < x_b##, even considering each restricted to a single 1D worldline (timelike and spacelike respectively).
Sure, the "real line" can be ordered in the one or the other way, and if this "real line" models a spatial direction, there's not so much different in choosing the one or the other ordering. If the "real line" models a temporal direction, that's a different business in physics, because we assume that there is a "causal ordering", i.e., that if one event is the cause of another event these events must be ordered such that the cause is "before" its "effect". In my opinion that's a basic assumption behind all of physics since without causality it wouldn't make sense to look for "natural laws" to begin with.PeterDonis said:The timelike ordering is not "smaller than" and "larger than"; it is "before" and "after". These are symmetric in the same way that "north of" and "south of" are in @DrGreg's example. You don't have to have a concept of "size" of items to have an ordering. You just have to have a relation that satisfies the properties of an ordering relation.
Although, never eat shredded wheat!Dale said:Sure, whatever. I stand by my statement that space isn't ordered.