# Worksheet: Events in Minkowski Diagrams

In this worksheet, we will practice determining the order of events as perceived from different inertial reference frames and determining whether events are simultaneous.

**Q1: **

The Minkowski diagram shows two frames: frame with axes and and frame with axes and . Four events are shown in the diagram: , , , and .

List the events in order of their distance from the origin in frame , starting with the closest.

- A, , ,
- B, , ,
- C, , ,
- D, , ,
- E, , ,

List the events in order of their distance from the origin in frame , starting with the closest.

- A, , ,
- B, , ,
- C, , ,
- D, , ,
- E, , ,

**Q2: **

The Minkowski diagram shows two frames: frame with axes and and frame with axes and . Six events are shown on the diagram: , , , , , and .

Which two events occur at the same distance away from the origin in frame ?

- A and
- B and
- C and
- D and
- E and

Which two events occur at the same distance away from the origin in frame ?

- A and
- B and
- C and
- D and
- E and

**Q3: **

The Minkowski diagram shows two frames: frame with axes and and frame with axes and . Three events are shown on the diagram: , , and .

In which frame do all three events occur at the same location?

- A
- B

Which event occurs farthest from the origin in frame ?

- A
- B
- C

**Q4: **

The Minkowski diagram shows two frames: frame with axes and and frame with axes and . Three events are shown on the diagram: , , and . In frame , all three events occur in the same location. Which event occurs closest to the origin in frame ?

- A
- B
- C

**Q5: **

The Minkowski diagram shows four events, , , , and , in the inertial frame . Each event represents a light bulb flashing on for a fraction of a second. The light emitted from each bulb then travels at speed . For an observer in frame at position , the light from two events will reach at the same time; thus, the observer at will see the two events happen at the same time. Which two events will the observer see happen at the same time?

- A and
- B and
- C and
- D and
- E and

**Q6: **

The Minkowski diagram shows two inertial frames: frame with axes and and frame with axes and . Frame moves at a speed relative to frame . Three events are marked on the diagram: , , and . In frame , which event occurs first?

- A
- B
- C

**Q7: **

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

- A
- B
- C

**Q8: **

The Minkowski diagram shows two frames: frame with axes and and frame with axes and . Six events are shown on the diagram: , , , , , and .

Which two events are simultaneous in the frame ?

- A and
- B and
- C and
- D and
- E and

Which two events are simultaneous in the frame ?

- A and
- B and
- C and
- D and
- E and

**Q9: **

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

What is the spatial separation of events and in frame ?

If is the separation of the events in frame and is the separation of the events in frame , which of the following expressions relating these two quantities is true?

- A
- B
- C
- D
- E

**Q10: **

The given Minkowski diagram shows two frames: frame with axes and and frame with axes and . Frame moves at a speed relative to . Two events, and , are marked on the diagram.

In which frame do the two events occur at the same time?

- A
- B

Which event occurs first in frame ?

- AThey occur at the same time.
- B
- C

**Q11: **

The Minkowski diagram shows four events, , , , and , in the inertial frame . For an observer in frame at the position , which event occurs closest to the observer?

- A
- B
- C
- D

**Q12: **

The above Minkowski diagram shows two frames: frame with axes and and frame with axes and . Four events are shown on the diagram: , , , and .

List the events in order of their distance from the origin in frame , starting with the closest.

- A, , ,
- B, , ,
- CP, , ,
- D, , ,
- E, , ,

List the events in order of their distance from the origin in frame , starting with the closest.

- A, , ,
- B, , ,
- C, , ,
- D, , ,
- E, , ,

**Q13: **

The Minkowski diagram shows two frames: frame with axes and and frame with axes and . Four events are shown on the diagram: , , , and .

In frame , in what order do the events occur?

- A, , ,
- B, , ,
- C, , ,
- D, , ,
- E, , ,

In frame , in what order do the events occur?

- A, , ,
- B, , ,
- C, , ,
- D, , ,
- E, , ,

**Q14: **

The Minkowski diagram shows four events, , , , and , in the inertial frame . Which event occurs first in frame ?

- A
- B
- C
- D

**Q15: **

The above Minkowski diagram shows two frames: frame with axes and and frame with axes and . Four events are shown on the diagram: , , , and .

In frame , in what order do the events occur?

- A, , ,
- B, , ,
- C, , ,
- D, , ,
- E, , ,

In frame , in what order do the events occur?

- A, , ,
- B, , ,
- C, , ,
- D, , ,
- E, , ,

**Q16: **

The given Minkowski diagram shows two frames: frame with axes and and frame with axes and . Two events are shown on the diagram: and . In both frames and , the dotted lines are spaced 1 light-second apart along the .

What is the temporal separation of events and in frame ?

- A4 light-seconds
- B1 light-second
- C0.5 light-seconds
- D1.5 light-seconds
- E2 light-seconds

If is the time interval of the events in frame and is the time interval of the events in frame , which of the following expressions relating these two quantities is true?

- A
- B
- C
- D
- E