Spacetime diagram problem (spacelike intervals)

• Moataz
In summary, the conversation discusses two events on a spacetime diagram, one at x=-4, t=5 and the other at x=0, t=6. The question asks for the relative speed of a frame in which these two events occur simultaneously. The answer provided is Beta=Delta(t)/Delta(x)=0.25, but Chet argues that the correct relative speed should be 4.
Moataz

Homework Statement

Suppose on a spacetime diagram, an event happens at x=-4, t=5 and another event happens at x=0 and t=6. If there is a frame such that the two events happen simultaneously, what would the relative speed of that frame be?

The Attempt at a Solution

I know this interval is spacelike ( between the two events) but the answer says Relative speed=Beta=Delta(t)/Delta(x)=0.25 But I do not understand why is the speed=time over distance here?

In a spacetime diagram, a point is an event. If a line connects two points, or two events, the line is called the line of simultaneity. The slope of the line of simultaneity is the inverse of the slope of the world line of a moving frame. Therefore, you can find the slope of the line of simultaneity from the two point you are given and then find the slope of the world line.

Moataz said:

Homework Statement

Suppose on a spacetime diagram, an event happens at x=-4, t=5 and another event happens at x=0 and t=6. If there is a frame such that the two events happen simultaneously, what would the relative speed of that frame be?

The Attempt at a Solution

I know this interval is spacelike ( between the two events) but the answer says Relative speed=Beta=Delta(t)/Delta(x)=0.25 But I do not understand why is the speed=time over distance here?
I agree with you. The relative speed should be 4.

Chet

1. What is a spacetime diagram?

A spacetime diagram is a graphical representation of the relationship between space and time, usually used in the context of special relativity. It shows how events in space and time are connected and how objects move through spacetime.

2. What is a spacelike interval?

A spacelike interval is a measurement of the distance between two events in spacetime that are separated by a spatial distance. In other words, it is the distance between two events that could not have influenced each other due to the speed of light limit.

3. How is a spacetime diagram used to solve a spacelike interval problem?

A spacetime diagram can be used to visualize and calculate the spacelike interval between two events. By drawing a straight line connecting the two events and measuring the length of the line, the spacelike interval can be determined using the Pythagorean theorem.

4. What is the significance of spacelike intervals in special relativity?

Spacelike intervals play a crucial role in special relativity as they represent events that are not causally connected. This means that these events could not have influenced each other, even if they occurred at the same time. Spacelike intervals also help to illustrate the concept of time dilation and the relativity of simultaneity.

5. Can spacelike intervals be negative?

No, spacelike intervals cannot be negative. They are always positive values that represent the distance between two events in spacetime. Negative values would imply that the events were causally connected, which goes against the principles of special relativity.

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