# How are space-like intervals important?

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1. May 4, 2015

### Clueless

Time-like and light like separations between events make sense, because a particle or a light flash can travel between them. However, how can you have a space-like interval when even light cannot travel such an interval (because its velocity is not greater than c). Obviously the first event cannot cause the second event for a space-like interval.

I suppose it boils down to what I understand about WHAT is actually travelling between two events. "Information" is said to travel between these events. So what is this "information" that can travel above the speed of light? Or have I got it all wrong?

2. May 4, 2015

### Staff: Mentor

Spacelike intervals are important because if two events are separated by a spacelike interval then different observers will differ about which one happened first. Thus, there is no observer-independent way of saying which happened first, and thus no possibility that one of them caused the other (because the the cause must precede the effect for all observers).

In contrast, with timelike-separated events all observers will agree about which happened first and therefore it is possible that the first event was the cause of the second.

3. May 4, 2015

### PAllen

To add to what Nugatory said, events with spacellike separation are the relativistic generalization of Newtonian simultaneous events. Instead the Newtonian case, where you can definitely say simultaneous events occurred at the same time, in relativity you can say that any pair of events with spacelike separation may plausibly be considered to be simultaneous.

4. May 4, 2015

### Staff: Mentor

Just a clarifying note, the same is true of null-separated events.

5. May 5, 2015

### Clueless

Thanks for the replies. I suppose I now have anroader understanding of the purpose and necessity of such an interval. However (I may very well be mistaken), this does not answer my question about how "information" can travel above the speed of light.

BTW what are null separated events?. Is it when some time interval is zero or...?

6. May 5, 2015

### Staff: Mentor

Information cannot travel faster than the speed of light.
If it were (hypothetically) possible, the events "message transmitted" and "message received" would be separated by a spacelike interval, which means that the two could not be causally related - but we can't have reception without transmission, so they must be causally related so must be timelike-separated.

Events are null-separated when the spacetime interval between them is zero. You'll often hear this called "lightlike" because the emission of a flash of light at one place and its arrival at another are always null-separated eventS.

7. May 5, 2015

### Ibix

If you are familiar with the concept of a light cone, then events that are space-like separated are outside each other's light cones, events that are time-like separated are inside each other's light cone (one in the other's future, the other in the one's past), and events that are null- or light-like separated are in the surface of each other's cones.

That's kind of the diagrammatic version of what Nugatory said.

8. May 5, 2015

### Mentz114

When constructing local axes in the Fermi-Walker way, the spatial axes are the 3-spacelike lines orthogonal to each other and the time direction.

All axes may be space-like, I think.

9. May 5, 2015

### Staff: Mentor

All three of the spatial axes are, yes. If you are constructing an orthonormal basis (which is how Fermi normal coordinates are constructed), it must have three spacelike axes and one timelike axis. It is possible to construct coordinate charts with all four basis vectors spacelike (for example, Painleve coordinates inside the horizon of a black hole), but the coordinate basis for such a chart cannot be orthonormal.