# Homework Help: Spacelike, timelike, relativity and simultaneity of events

1. May 23, 2008

### TFM

1. The problem statement, all variables and given/known data

Two events, A and B, are seperated in space. In one frame of reference, event A occurs first and is seen to cause event B. Is it possible to find other frames of reference where event B occurs before event A?

If the order of two events does depend upon the frame of reference, is the interval between the spacelike or timelike?

2. Relevant equations

N/A

3. The attempt at a solution

For the first part, I have said that it is possible to have a frame of reference where B occurs first. But I am not quites sure on the second part. I tried searching for the definitions of Timelike and Spacelike, but could seem to find any.

Any help would be most appreciated,

TFm

2. May 23, 2008

### EngageEngage

To determine whether or not an event is space like or time like you must remember to use the spacetime interval:
$$(\Delta s)^{2} = (c\Delta t)^{2}-(\Delta x)^2-(\Delta y)^2-(\Delta z)^2$$
For 2 events to be time like, the difference in ct coordinates must be greater than the the difference in position coordinates. Therefore, if an event is time like, your spacetime interval will be positive.
To see if two events are dependent of one another, it is most helpful to draw minkowski (or spacetime) diagrams and then tilt the ct' and x' axes to see if you can get the interval to align with either the ct' or x' axes, without breaking the physical laws

3. May 23, 2008

### George Jones

Staff Emeritus
Are you sure?

4. May 24, 2008

### TFM

We did an example in a previous lecture about a gun fight at relativitic speeds. In one frame the shots were fired at the same time, in another frame, one person shot the other first, and another, the other person shot first. Would this still stand for the question scenario?

Also, how would you use the spacetime interval, since we have been given no numbers?

Thanks,

TFM

5. May 24, 2008

### George Jones

Staff Emeritus
No.

If then event A is one gun being fired, event B is the other gun being fired, and the guns are fired independently,then event A didn't cause event B, so the first question is not like the example given in the lecture.

Let event A be the firing of a gun and event B be the hitting of a target by the bullet fired by this gun. Here event A causes event B.

6. May 24, 2008

### TFM

That makes sense, you wouldn't have a bullet bouncing off a traget before being fired. Thanks.

TFM

7. May 24, 2008

### TFM

How would we use this formula, though:

$$(\Delta s)^{2} = (c\Delta t)^{2}-(\Delta x)^2-(\Delta y)^2-(\Delta z)^2$$

We aren't given any data?

TFM

8. May 24, 2008

### George Jones

Staff Emeritus
If event A causes event B, what type of spacetime interval separates A and B?

9. May 24, 2008

### TFM

Would it be timelike, since they are seperated by time and not by distance?

TFM

10. May 24, 2008

### CompuChip

You don't need any data, just one very special property of $(\Delta s)$ (and the characterization of causal events in terms of that interval, which George Jones is hinting at).

Do you know about light cones?

11. May 24, 2008

### TFM

Aren't they from thefact that on a Minkowski Diagran, where the world line of light os at 45 degrees, and is twisted round into a egg-timer pair of cones, with the joinging of the cones at the origin?

TFM

12. May 24, 2008

### TFM

Anothe piece of info, which I think is relevant, I have just remembered, if an event occurs inside the cone, it is spacelike, outside the cone it is timelike?

TFM

13. May 24, 2008

### George Jones

Staff Emeritus
Yes.

In what frame (in my example) do the events have non-zero time separation and zero space separation?

14. May 24, 2008

### TFM

I am not quite sure, would it be the contere of mass/momentum frame?

TFM

15. May 24, 2008

### George Jones

Staff Emeritus
The frame of the bullet. In this frame the bullet doesn't move, but a watch strapped to the bullet shows an increase of time.

What can be said about the time-ordering of events that are timelike related?

16. May 24, 2008

### TFM

Would this be to do with causaility, since they are timelike, the order of events cannot change?

TFM

17. May 24, 2008

### George Jones

Staff Emeritus
Right.

If events are timelike related, then their time ordering is the same in all inertial frames of reference.

More should be said about intervals and light cones, but family life has intervened; my wife and little daughter are now up.

Maybe CompuChip is still around.

18. May 24, 2008

### CompuChip

I agree, but the same goes here (as far as the family life is concerned, no wife and daughter yet .

Basically, it comes down to combining two things:
- things inside the light cone are causally related
- the spacetime interval is invariant (i.e.: things inside the lightcone, stay inside the lightcone)