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

In summary, the conversation discusses finding the equality of angles between two observers in a diagram where one is moving with a velocity and the other is still. The person moving has a constant velocity and the question is whether the speed of light at a 45° angle affects this. The solution is to use the Lorentz transformation to find the equations for the axes and compare their slopes.
  • #1
Powergade
2
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


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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?
 
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  • #2
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
 
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Related to Why Are the Angles in a Minkowski Diagram Equal for Different Observers?

What is a Minkowski diagram?

A Minkowski diagram is a graphical representation of the special theory of relativity, developed by physicist Hermann Minkowski. It is used to visualize the relationship between space and time in special relativity, where time and space are combined into a four-dimensional "spacetime" continuum.

What is the purpose of a Minkowski diagram?

The purpose of a Minkowski diagram is to illustrate the effects of special relativity on the measurement of space and time. It allows us to visualize how an observer's perception of time and space changes as they move at different speeds or in different directions.

What do the angles on a Minkowski diagram represent?

The angles on a Minkowski diagram represent the relationship between two events or frames of reference. In special relativity, time and space are relative, so the angles on the diagram show how time and space are perceived differently by observers in different frames of reference.

How do you calculate angles on a Minkowski diagram?

Angles on a Minkowski diagram can be calculated using trigonometric functions, similar to how angles are calculated on a traditional two-dimensional graph. However, in a Minkowski diagram, the vertical and horizontal axes represent time and space, respectively, rather than just x and y coordinates. This means that the equations for calculating angles are slightly different.

Why is the Minkowski diagram important in physics?

The Minkowski diagram is important in physics because it helps us understand and visualize the fundamental principles of special relativity. It allows us to see how time and space are interconnected and how they are perceived differently by observers in different frames of reference. The Minkowski diagram is also used in a variety of fields, including cosmology, astrophysics, and high-energy physics, to study the effects of special relativity on the behavior of particles and objects in the universe.

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