Lesson: Events in Minkowski Diagrams

In this lesson, we will learn how to determine the order of events as perceived from different inertial reference frames and determine whether events are simultaneous.

Worksheet: 10 Questions

Q1:

The Minkowski diagram shows two inertial frames: frame 𝑆 with axes 𝑥 and 𝑐 𝑡 and frame 𝑆 ′ with axes 𝑥 ′ and 𝑐 𝑡 ′ . Frame 𝑆 ′ moves at a speed 𝑢 relative to frame 𝑆 . Each of the events 𝑄 , 𝑅 , and 𝑇 represents a light bulb flashing on for a fraction of a second. The light is emitted from each bulb and then travels at speed 𝑐 . If there is an observer at rest in frame 𝑆 ′ , which light bulb will that observer see flash first?

Q2:

The Minkowski diagram shows two frames: frame 𝑆 with axes 𝑥 and 𝑐 𝑡 and frame 𝑆 ′ with axes 𝑥 ′ and 𝑐 𝑡 ′ . Six events are shown on the diagram: 𝑃 , 𝑄 , 𝑅 , 𝑇 , 𝑊 , and 𝑍 .

Which two events are simultaneous in the frame 𝑆 ?

Which two events are simultaneous in the frame 𝑆 ′ ?

Q3:

The given Minkowski diagram shows two frames: frame 𝑆 with axes 𝑥 and 𝑐 𝑡 and frame 𝑆 ′ with axes 𝑥 ′ and 𝑐 𝑡 ′ . Two events are shown in the diagram: 𝑃 and 𝑄 . In both frames 𝑆 and 𝑆 ′ , the dotted lines are spaced 1 m apart along the 𝑥 -axis.

What is the spatial separation of events 𝑃 and 𝑄 in frame 𝑆 ?

If Δ 𝑥 is the separation of the events in frame 𝑆 and Δ 𝑥 ′ is the separation of the events in frame 𝑆 ′ , which of the following expressions relating these two quantities is true?
Preview Download

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.