The use of the word see in relativity

[homology]

The use of the word "see" in relativity

Homework Statement

From Spacetime and Geometry by Carroll:

problem 1.3) Three events A, B, and C are seen by observer O to occur in the order ABC. Another observer O' sees events to occur in the order CBA. Is it possible that a third observer sees the events in the order ACB? Support your conclusion by drawing a spacetime diagram.

Homework Equations

I've done this, constructed the diagrams and the answer is yes. Disturbingly my instructor has decided to interpret the problem differently than I. He thinks the problem is ambiguous and that 'seeing' could mean the physiological act as opposed to thinking of entire frames as observers. The consequence of this is as follows:

So he's accepted the following, which I believe is rubbish:

Take 1 inertial frame, put three spatially separated observers in it. so you have three vertical world lines. Now put three events on the x-axis, spatially separated. Draw the light cones of these events. The boundaries of these light cones (the light rays themselves) intersect the vertical worldlines in different orders. So these observers "see" the events occur in different orders.

But this is not a lack of simultaneity, all of these observers can do physics and determine and agree on the actual spacetime coordinates of each of the events. I wanted others to weigh in on this.

Thanks (apologies if this is the wrong place for it, but it was a homework problem)

Kevin

 

[256bits]

Problem doesn't say anything about moving frames.
You instructor has interpreted the problem correctly - one frame with 3 observers in it, and recording the events A, B, and C as they perceive the events to occur. It seems to be a geometric problem rather than simultaneity.

 

[homology]

@256bits

Naturally I disagree. That interpretation requires absolutely no relativity. The loss of a universal simultaneity is a hallmark of special relativity. The instructor's interpretation make the exercise irrelevant to any of the physics of the text. The word "see" clearly (to me) refers to frames. Carroll even uses the very common O and O-bar notation which refer to different frames of reference. There is implied language here because the author expects the reader to be fluent in SR already.

 

[jedishrfu]

It looks like the instructor took the simple route of having the observers in the same fram so he could draw verticals on the spacetime chart. It wouldn't matter though because even if they were moving ie their line would no longer be vertical. they would still observe the events in the same order.

so an observer to the far left of pt A sees A -> B -> C occur

and an observer to the far right of pt C sees C -> B -> A occur

if an observer is between pt A and pt B might see A -> B -> C or B->A->C

and similarly if an observer between pt B and pt C might see C -> B -> A or B -> C -> A

The only way I could think of is if B is a planet the event occurs on the other side and traverses the universe before coming home so that in that case you don't see B occur but you do see A -> C -> eons later B after the B ignal circled the universe (if its closed)

 

[homology]

this is sort of my point. If they are all in the same reference frame they can determine (and agree) on the distances (spatial) from themselves to the objects and figure out the 'actual' time each event occurred and they will agree because all of their clocks run the same.

however, if you take three frames moving relative to one another, their clocks do not run the same. They will not agree, even when distance is accounted for, on the 'actual' time the events occurred. Chronology is relative for observers moving relative to each other, but just "apparently" relative for those in the same frame "perceiving" events happening in a different order.

 

[jedishrfu]

this is sort of my point. If they are all in the same reference frame they can determine (and agree) on the distances (spatial) from themselves to the objects and figure out the 'actual' time each event occurred and they will agree because all of their clocks run the same.

however, if you take three frames moving relative to one another, their clocks do not run the same. They will not agree, even when distance is accounted for, on the 'actual' time the events occurred. Chronology is relative for observers moving relative to each other, but just "apparently" relative for those in the same frame "perceiving" events happening in a different order.

But on the spacetime diagram its the order in which the A B and C lines cross the observers line that determines the sequence he/she sees them. So basically I couldn't find an example of an observer seeing A then C then B.

 

[homology]

But that's just the thing. In SR when we talk about observer's we are actually talking about frames. Inertial frames are equivalence classes of observers. Just because you 'see' a supernova in the sky tomorrow night doesn't mean you'd actually say it happened in January 2012. As a physicist you'd figure out the actual date (in your frame) of the event.

Inertial frames ARE observers. :)

 

[vela]

For what it's worth, I agree with your interpretation of the problem. Your instructor's interpretation makes the problem trivial.

 

[homology]

For what it's worth, I agree with your interpretation of the problem. Your instructor's interpretation makes the problem trivial.

That's sort of the point of the post. He's out of practice and I'm trying to respectfully debate the point with him. I feel like its quite obvious but wanted to get other folks perspective. Maybe I should have put this in SR/GR forum?

Thanks

 

[vela]

I think your question is appropriate for the homework forum. I moved it to the intro physics forum, however, since it strikes me as more of a lower-division level problem.

 

[ahsanxr]

Relevant if you are in Fowler's relativity class at UVA: I went to his office hours today and asked him about the same problem. He seemed to have realized a mistake of his and said to himself "oh that means I completely misguided that other fellow". I'm not sure about what mistake he made but when I asked him, he thought the problem was asking whether BAC was possible instead of ACB.