# Reverse sequence of events

1. Aug 20, 2004

### Gerinski

If I understand it correctly it is possible that due to relativistic effects, 2 events A and B may be perceived by one observer as A happening before B, while for another observer B may happen before A.

Can someone give a layman explanation of under which circumstances this would happen (i.e A and B must not be causally related -does that mean their light cones must not intersect?-, could the 2 observers communicate to eachother etc) and if possible try to describe a practical example?

TX !

2. Aug 20, 2004

### pmb_phy

If two events have what is called a spacelike spacetime seperation then it is possible for one observer to see A happen before B while another observer sees B happen before A. Two events are said to have a spacelike spacetime seperation when a light signal cannot leave one event and get to the other before it occurs. If you're familar with the usual example given in relativity with an observer on a train and one on the ground then you can determine which one measures which event to occur first. But its 4:04am here and I can't think straight.
What you're looking for is A and B must not be causally related.

Pete

3. Aug 20, 2004

### Tom Mattson

Staff Emeritus
That's right.

You've pretty much got it. Two nonsimultaneous events in frame S can be observed in the reverse order in another frame S' only if they cannot be causally related. That means that it must not be possible for the spacetime coordinates of event A to be connected to those of event B with a light signal.

Simple example:

Let Observer S' be moving with respect to Observer S in the +x-direction with speed v=0.6c. Let two flares be set up in the frame of S.

Event A: Red flare ignites.
Observer S assigns spacetime coordinates (x,y,z,t)=(0,0,0,0) to the event. (Note: spatial coordinates are in meters, and temporal coordinates are in seconds).

Event B: Blue flare ignites.
Observer S assigns spacetime coordinates (x,y,z,t)=(3E8,0,0,0.5).

We have, for observer S:

&Delta;x=xB-xA=3E8
&Delta;t=tB-tA=0.5

Note that these events cannot be connected by a light signal, because &Delta;x/&Delta;t=2c.

Using the Lorentz transformation to find &Delta;x' and &Delta;t', we have:

&Delta;x'=&gamma;(&Delta;x-v&Delta;t)
&Delta;x'=(5/4)(3E8-1.2E8)=2.25E8 m

&Delta;t'=&gamma;(&Delta;t-v&Delta;x/c2)
&Delta;t'=(5/4)(0.5-0.6)=-0.12 s

You can see that &Delta;t'<0.

4. Aug 20, 2004

### Gerinski

TX, clear !
So in even more layman language, both observers S ans S' can see both A and B, but A and B could never "see" eachother.

However, could observers S and S' see eachother? (can their spacetime coordinates be connected by a light signal?)

Last edited by a moderator: Aug 20, 2004
5. Aug 20, 2004

### Tom Mattson

Staff Emeritus
A and B aren't observers, they are events. Of course, if you stationed an observer at the locations of events A and B, then neither observer would have any trouble seeing both events. But that's not what we're talking about here; we're talking about causality. In order for one event to cause the other, a necessary condition is that the information of the first event must propagate from the spacetime coordinates of the first event, to the spacetime coordintates of the second. It is this that cannot be done with the example I gave. A light pulse emitted from Event A would never make it to the spatial location of Event B before that event occurs.

No stipulation was made on the coordinates of S and S', just their relative states of motion. You have to specify spacetime coordinates to determine if they can be connected by a light signal.

But even if they can't, it doesn't mean that S and S' can't see each other.

6. Aug 20, 2004

### robphy

When events A and B are not causally related,
event B is not inside the light-cone of A and
event A is not inside the light-cone of B.

Suppose there is an observer Al who experiences event A and an observer Bill who experiences event B.
A signal emitted at event A can reach Bill if there is a portion of Bill's worldline inside the future light-cone of A. A similar statement involves event B and Al's worldline.

With a trigger from your brain, snap your fingers on each hand.
Event A is "the left-hand-finger-snap".
Event B is "the right-hand-finger-snap".
If those events are simultaneous and spatially separated in your reference frame, then those events are not causally related.

7. Aug 20, 2004

### Gerinski

Oeps .... sorry this I didn't understand. If they can't be connected by a light signal, how could they ever see eachother?

8. Aug 20, 2004

### Tom Mattson

Staff Emeritus
It's the spacetime coordinates of the events that cannot be connected by a light signal. Any two sets of space coordinates can be connected by a light signal, but the question is, "At what time does the signal arrive?"

In frame S, Event A had space coordinates (x,y,z)=(0,0,0). Event B had space coordinates (x,y,z)=(3E8,0,0). Of course, light from Event A would eventually reach the location of Event B, but it would take 1 second. Since Event B occurs 0.5 seconds after Event A (in frame S), it is not possible to connect the spacetime coordinates of Events A and B with a light signal.