Can someone help me interpret this spacetime diagram?

Click For Summary

Homework Help Overview

The discussion revolves around interpreting a spacetime diagram from a general relativity textbook, specifically focusing on the meaning of a line labeled EB. The original poster seeks clarification on how this line relates to the concept of simultaneity in different reference frames.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand the significance of the line EB in the context of simultaneity and its implications for time intervals between events in different frames. Some participants explore the relationship between the line EB and the events observed in different frames, questioning how simultaneity is perceived by observers O and O' at various points.

Discussion Status

Participants have engaged in a back-and-forth regarding the interpretation of the line EB and its implications for simultaneity. Some clarifications have been made about the nature of the line in the O' frame, and the discussion appears to be productive, with participants building on each other's insights.

Contextual Notes

The original poster expresses a need for additional information regarding the x-coordinate in observer O's frame at a specific event, indicating potential gaps in the provided diagram. The discussion is framed within the constraints of homework guidelines, emphasizing the exploration of concepts rather than providing direct answers.

Vitani1
Messages
51
Reaction score
9
Homework Statement
Borrowed from "A first course in General Relativity" by Schutz. This is question 12 of chapter 1.
Relevant Equations
S^2=S'^2
spacetime diagra.png


My question in specific is understanding what this line EB exactly represents. This was borrowed from the book "A first course in general relativity" by Schutz. There is a question on page 30 (number 12) which asks the following:
"Use the fact that the tangent to the hyperbola DB in Fig. 1.14 is the line of simultaneity for O¯ to show that the time interval AE is shorter than the time recorded on O¯’s clock as it moved from A to B. "

I see that there exists an event in the unbarred observer's frame with coordinates (C,F) corresponding to an event in the frame of O' with coordinates (B,0). In order to do the above proof I assume I need to know some information about the x-coordinate in observer O's frame at this time E but this diagram doesn't (I think) give this information. Certainly do not give me the answer because this is still homework. I'm mostly curious about this line EB.
 
Physics news on Phys.org
Actually I was able to prove that the time to pass from points A to C in O's frame is shorter than the time in required in the frame of O ' prime to pass from A to B. This by extension would imply that the time to go from A to E is less than this path A to B as well. In any case can anyone help me with understanding what this line EB is referring to?
 
It's a line of simultaneity for the O' frame.
 
What you are saying, then, is that in O' frame this line is the line by which when crossed happens to be the point in spacetime when this observer sees O with the same coordinates?
 
Oh - it says that in the book. Thanks.
 
Vitani1 said:
What you are saying, then, is that in O' frame this line is the line by which when crossed happens to be the point in spacetime when this observer sees O with the same coordinates?
No. It's a line where ##t'=\rm constant##, so an observer at rest in O' would say that events E and B happened at the same time.
 
  • Like
Likes   Reactions: Vitani1
Would observer O say the events happened at the same time at event C?
 
Yes, an observer at rest in frame O would say that C and B happened at the same time.
 
  • Like
Likes   Reactions: Vitani1
Thank you.
 

Similar threads

Worldlines and spacetime diagrams
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Uncover Traps in Spacetime Diagrams: Bob & Alice's Cases
  • · Replies 33 ·
2
Replies
33
Views
3K
Undergrad Please help with my spacetime diagrams (relativity problem)
  • · Replies 27 ·
Replies
27
Views
3K
Undergrad Gamma - A Minkowski Spacetime Diagram Generator
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Request for Input: 2D Minkowski Spacetime Diagram Generator
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Trying to understand space-time diagrams
  • · Replies 61 ·
3
Replies
61
Views
7K
Undergrad Understand Spacetime Diagrams: Calculating Proper Time
  • · Replies 20 ·
Replies
20
Views
3K
High School Understanding Spacetime Diagrams from "Reality is not What it Seems
  • · Replies 6 ·
Replies
6
Views
2K
High School Any interest in a spacetime diagram generator?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Clarification on Rindler coordinates definition
  • · Replies 16 ·
Replies
16
Views
4K