Spacelike, timelike, relativity and simultaneity of events

[TFM]

Homework Statement

Two events, A and B, are separated 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?

Homework Equations

N/A

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

 

[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

 

[George Jones]

Homework Statement

Two events, A and B, are separated 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?

Homework Equations

N/A

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.

Are you sure?

 

[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

 

[George Jones]

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?

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.

 

[TFM]

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

TFM

 

[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

 

[George Jones]

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

TFM

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

 

[TFM]

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

TFM

 

[CompuChip]

Wow, this thread evolves quickly. When I pressed Reply, there were already a few new posts.

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

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).

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

Do you know about light cones?

 

[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

 

[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

 

[George Jones]

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

TFM

Yes.

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

 

[TFM]

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

TFM

 

[George Jones]

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

TFM

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?

 

[TFM]

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

TFM

 

[George Jones]

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

TFM

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.

 

[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)