# Can someone help me interpret this spacetime diagram?

• Vitani1
In summary, the conversation discusses the line EB and its significance in understanding the time interval AE in the frame of the observer O¯. It is mentioned that this line is a line of simultaneity for the O' frame and that an observer at rest in this frame would say that events E and B happened at the same time. The conversation also mentions that this information can be found in the book "A first course in general relativity" by Schutz.
Vitani1
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

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.

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.

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.

Vitani1
Thank you.

## 1. What is a spacetime diagram?

A spacetime diagram is a visual representation of the relationship between space and time. It shows how objects move and interact in a specific reference frame, taking into account the effects of both space and time.

## 2. How do I read a spacetime diagram?

A spacetime diagram typically has a horizontal axis representing space and a vertical axis representing time. Objects are represented by lines or curves on the diagram, with the slope of the line indicating their velocity. The closer the lines are to each other, the closer the objects are in space and time.

## 3. What does the shape of a spacetime diagram tell us?

The shape of a spacetime diagram can tell us about the relative motion of objects in a specific reference frame. For example, a straight line on the diagram indicates constant velocity, while a curved line indicates acceleration. The angle of the line can also indicate the direction of motion.

## 4. How can a spacetime diagram help us interpret events?

A spacetime diagram can help us visualize and understand the relationship between space and time in a specific event. By plotting the positions of objects over time, we can see how they move and interact with each other. This can also help us make predictions about future events.

## 5. What are some common applications of spacetime diagrams?

Spacetime diagrams have many applications in physics, including understanding the motion of objects in special relativity, visualizing the effects of gravity on objects, and studying the behavior of particles in quantum mechanics. They are also used in other fields, such as cosmology and astrophysics, to study the large-scale structure of the universe.

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