Minkowski Diagram: Clarifying One-Dimensional Question

[Jarwulf]

I need a clarification about this diagram

On a one dimensional line two objects are riding along on the t and t' axis.

One present moment of black's is represented by the red line. Since the green segment defined from the origin to the red line is longer than the black segment defined from the origin to the red line wouldn't that mean from black's pov time for green is moving faster?

Also why do people multiply c to t for these diagrams? If you wanted a 45 degree angle for light wouldn't you just use t/c assuming you used meters for the x axis?

 

[Nabeshin]

Also why do people multiply c to t for these diagrams? If you wanted a 45 degree angle for light wouldn't you just use t/c assuming you used meters for the x axis?

To make the dimensions match. The x-axis has dimensions of length, and so does ct (for example in SI, m/s * s = m).

 

[Entropia]

The Minkowski diagram is a graphical representation of special relativity, which shows how time and space are interconnected in different reference frames. In this diagram, the t-axis represents time and the x-axis represents space.

To answer your first question, the green segment being longer than the black segment does not necessarily mean that time is moving faster for the green object from the black object's perspective. It could also mean that the green object is moving at a faster velocity, causing it to cover more distance in the same amount of time.

As for your second question, the reason why c (the speed of light) is multiplied by t in the Minkowski diagram is to account for the fact that the speed of light is constant in all reference frames. This is a fundamental principle in special relativity and is represented by the diagonal line on the diagram, known as the "light cone." By multiplying c with t, the angle of the light cone is maintained and the diagram accurately represents the relationship between time and space in special relativity.

I hope this clarifies your questions about the Minkowski diagram. It can be a complex concept to grasp, but with some practice and understanding of the principles behind it, it can be a useful tool in understanding special relativity.