Theory Without Spacelike Separations: Can It Exist?

[Gerenuk]

TL;DR Summary

Spacelike separated events never affect each other. Could you have a theory without them?

From what I understand only the past and future timelike separated events ever matter for me as an observer.

Does that mean there could be a theory where a thing like spacelike separated events does not exist? I mean they never matter for any prediction anyway?

 

[martinbn]

Summary: Spacelike separated events never affect each other. Could you have a theory without them?

From what I understand only the past and future timelike separated events ever matter for me as an observer.

Does that mean there could be a theory where a thing like spacelike separated events does not exist? I mean they never matter for any prediction anyway?

Of course they matter, even for you. If something explodes somewhere away from you, that event is space-like separated from an even on your world line. But this doesn't mean that the blast will not affect you later on.

 

[Gerenuk]

Of course they matter, even for you. If something explodes somewhere away from you, that event is space-like separated from an even on your world line. But this doesn't mean that the blast will not affect you later on.

Oh right. But for the equations of motion I only need timelike steps as only those affect each other?

 

[Ibix]

Oh right. But for the equations of motion I only need timelike steps as only those affect each other?

Not sure what you mean. Are you talking about worldlines in some specified spacetime, or solving Einstein's equations in an initial value formulation?

 

[Gerenuk]

Not sure what you mean. Are you talking about worldlines in some specified spacetime, or solving Einstein's equations in an initial value formulation?

It's not related to a particular calculation. I'm thinking if there are alternative theories which have no concept of spacelike separation, because for equations of motion you don't seem to need them. It's a bit vague, I know.

 

[martinbn]

It's not related to a particular calculation. I'm thinking if there are alternative theories which have no concept of spacelike separation, because for equations of motion you don't seem to need them. It's a bit vague, I know.

It is also not true. In what sense do you not need them for the equations of motion?

 

[Ibix]

It's not related to a particular calculation. I'm thinking if there are alternative theories which have no concept of spacelike separation, because for equations of motion you don't seem to need them. It's a bit vague, I know.

I don't think it makes sense. We usually specify problems in terms of initial conditions and evolve them forwards or backwards in terms of timelike steps, sure. But that doesn't mean you can avoid thinking about spacelike separations. For example, in Minkowski space the vectors $(2,\pm 1)$ are timelike, but their difference is $(0,2)$ which is spacelike. So if you try to remove spacelike separations your vectors are no longer vectors (because there are cases where a sum of vectors is not a vector).

 

[Dale]

It's not related to a particular calculation. I'm thinking if there are alternative theories which have no concept of spacelike separation, because for equations of motion you don't seem to need them. It's a bit vague, I know.

No, it is not possible. A given event on your worldline can only be affected by events in your past light cone. But many of those events are spacelike separated from each other.

 

[Gerenuk]

It is also not true. In what sense do you not need them for the equations of motion?

Equations of motion use infinitesimal steps and these equation are all that really matters. And since for the evolution only timelike steps (influences) matter, only timelike infinitesimal steps are needed. And if equations of motion are handled with pure timelike steps, maybe there is a way to write an theory equivalent to special relativity where you never get that some kind of infinitesimal distance is of the "other sign". Not sure how to phrase this mathematically.

 

[Gerenuk]

I don't think it makes sense. We usually specify problems in terms of initial conditions and evolve them forwards or backwards in terms of timelike steps, sure. But that doesn't mean you can avoid thinking about spacelike separations. For example, in Minkowski space the vectors $(2,\pm 1)$ are timelike, but their difference is $(0,2)$ which is spacelike. So if you try to remove spacelike separations your vectors are no longer vectors (because there are cases where a sum of vectors is not a vector).

I'm thinking if only timelike steps are needed, maybe there is a way to write the math differently, but never get infinitesimal distances of "different signs". This also mean that other theory could drop the concept of Minkowski space and its vectors.

 

[Dale]

I am not aware of such a theory and doubt that it is possible. If you find a professional scientific reference exploring such a theory then please open a new thread on the topic, citing that reference as a discussion point. Until then, this topic is closed.