Why Are the Angles in a Minkowski Diagram Equal for Different Observers?

Click For Summary
SUMMARY

The discussion focuses on proving that the angles of the moving observer's axes in a Minkowski diagram are equal for different observers, specifically addressing observers A (stationary) and B (moving with velocity v). The key conclusion is that the angles, denoted as /alpha and /beta, are equal due to the constant velocity of observer B and the properties of the Lorentz transformation. The speed of light, represented as a 45° angle in the diagram, plays a crucial role in this relationship.

PREREQUISITES
  • Minkowski diagrams
  • Lorentz transformations
  • Basic principles of special relativity
  • Understanding of simultaneity in different reference frames
NEXT STEPS
  • Study the derivation of the Lorentz transformation equations
  • Learn how to construct and interpret Minkowski diagrams
  • Explore the concept of simultaneity in special relativity
  • Investigate the implications of constant velocity on time dilation and length contraction
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the geometric interpretation of special relativity and the behavior of different observers in spacetime.

Powergade
Messages
2
Reaction score
1
1. Homework Statement

In a diagram where I have two observers (one still (A) and one moving with a "v" velocity (B)), where the two parts disagre in the simultaneity of events, how can I prove that the angles of the B person axis that are put in the A person axis are equal. (/alpha=/beta , in the image U'.)
241px-MinkScale.svg.png

Homework Equations


---

The Attempt at a Solution



I tried to show that the angles /alpha and /beta follow the same rate of change because the velocity of the B person is constant. Is it because the speed of light goes in a 45° angle? Do I need to calculate something?
 
Last edited:
Physics news on Phys.org
Welcome to PF Powergade!

Forget what I said in my earlier post about trying to find the angle of the axes to the line x = ct using the Lorentz transformations. It is much simpler.

Use the Lorentz transformation find the equation for the t' and x' axes in terms of x and t (hint: the x' axis is defined by t' = 0). Then find the slopes of each of those axes (dx/dt) and compare them.

AM
 
Last edited:

Similar threads

Minkowski diagram, where to put an event
  • · Replies 6 ·
Replies
6
Views
2K
Interpretation of Negative Time in Minkowski Diagram
  • · Replies 1 ·
Replies
1
Views
964
Calculate the speed and angle of the center of mass before a collision
  • · Replies 3 ·
Replies
3
Views
1K
A moving boat with a flag on its mast
  • · Replies 15 ·
Replies
15
Views
1K
The speed of the point of intersection of two uniformly moving lines
  • · Replies 24 ·
Replies
24
Views
2K
Convert to Center of Mass Reference Frame
  • · Replies 9 ·
Replies
9
Views
1K
High School Drawing a Minkowski diagram to show multiple Points of View
  • · Replies 7 ·
Replies
7
Views
1K
Rope between inclines with maximum length of hanging middle portion
  • · Replies 46 ·
2
Replies
46
Views
7K
Undergrad Question about the Minkowski diagram
  • · Replies 14 ·
Replies
14
Views
2K
Angle that makes kinetic and potential energy of simple pendulum equal
  • · Replies 2 ·
Replies
2
Views
2K