# Relativity: can two observers see two events in reverse?

1. May 1, 2012

### Aziza

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

S' moves at velocity 0.6c with respect to S, and x=x'=0 at t=t'=0.
Two events are recorded.
In S, event 1 occurs at x=0 and t=0, and event 2 occurs at x=3000m and t=4μs.
At what times does S' say the events happened?
Does S' see the events in reverse order from S?

3. The attempt at a solution

Clearly S' will also see event 1 at t'=0 and x'=0, but he will say event 2 happened at t'= -2.5μs. This much is right according to my solution manual. However, the solution manual says that S' will SEE the events in reverse order from S.
My argument is that S' will SAY the events happened in reverse order, but he will see them in same order as S (ie, the light from event 2 will not reach S' before S' reaches the origin and sees event 1, because:
According to S', event 2 occurs at x':
x' = γ(x-vt) = 2850 m

However, in the time t = 2.5μs, the light will travel:
x = ct = 750 m

So by the time S' reaches the origin (and sees event 1), the light from event 2 will still be very far away from S', so he must see event 1 before event 2...

am i right or missing something important???
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited: May 1, 2012
2. May 2, 2012

### Aziza

if no one knows the answer to my specific textbook problem can someone just tell me if in general, from your experiences of doing problems, is it ever possible for two observers to actually see two events in reverse order? I have exam coming up and so would like to know at least in general if such a result is at all possible, in which case my above reasoning is probably wrong, so then i will try to find my error better

3. May 2, 2012

### phinds

Yes, it is called the "relativity of simultaneity". Two different observers can, in the right circumstances, disagree on which of two events occurred first.

4. May 2, 2012

### Aziza

yes i know that they can SAY two events occurred in reverse order, as in if they calculate backwards, they will disagree on which event actually happened first, but can the light from the two events actually reach each observer in reverse order, so that they will actually SEE the events in reverse order?

I think my textbook is using the words "see" and "say" interchangeably. But i think that even if you "say" two events happened in some order, you will not necessarily actually "see" them in that order?

5. May 2, 2012

### phinds

How would the observers know when they thought the event occurred if the light did not reach them?

6. May 2, 2012

### Aziza

no of course the light reaches them, im not saying it doesnt reach them at all, im just saying that even if they say two events occurred in reverse order, the light wont necessarily reach them in reverse order, and my general question is if it can even actually reach them in reverse order.
like in my above initial problem, i calculated that the two observers will disagree on the "actual" order of the events. Maybe my initial problem was too detailed to follow and so i will try to simplify and generalize: One observer S' will say that some distant event occurred some time before he reached the origin of another observer S. Once S' reaches origin of S, he sees another event. However, when both origins coincide, the light from the distant event still has not reached neither S nor S'. So even though S' (unlike S) says that the distant event "actually" occurred before the event at the origin (which both S and S' see AND say happened at t=t'=0), both S and S' will see the light from the distant event AFTER they saw the light from the event at the origin, so they will still SEE the events in the same order, even though they disagree on the "actual" order of the events. My solutions manual, however, is saying that they will still "see" the events in reverse order. I am agreeing that they will "say" the events are in reverse order, but i am not agreeing that they will "see" they events in reverse order..

7. May 2, 2012

### Aziza

nvm my professor finally emailed me back saying i am right and book made mistake

8. May 2, 2012

### Staff: Mentor

You need to think of S not just as a single observer, but as a whole team of observers deployed along the x axis of the S reference frame, and that each member of this team carries a clock that has been synchronized with all the other clocks in the S inertial reference frame. Similarly for the S' reference frame. Now, once you do this, you can determine what individual observers within each of the reference frames observe who are physically present at specific events.
You can also determine how long it takes for light to travel from a specific event to other observer's locations within each of the two reference frames. And, as you noted, you can then determine whether the light from two specific events arrives at any given observer's location within either of the two reference frames, to determine the order at which the light from the two specific events arrives at his location.
But, the implication from the problem statement strongly implies focusing on the times that the two events occurred in each of the two reference frames as measured by the observers physically present at the two events. And, if an observer in a given reference frame is physically present at a specific event, all the other clocks in his reference frame also display this time when the event occurred.

9. May 3, 2012

### Aziza

Ohhhh true true if you think of it this way it makes sense, thanks!