How to Visualize a 4 vector (e.g. a velocity)?

[Ashshahril]

Homework Statement

How to Visualize a 4 vector(e.g. velocity)?

Relevant Equations

Velocity = distance/time

Velocity is a 4-vector which has 3 space dimensions and 1 time dimension. It's space parts will be directed at the 3 space directions and time parts will be directed at the time dimension (But it is inverse. So, will it point at the inverse direction?). How can someone Visualize it? How they arrange themselves in a 4d grid line?

Can you show all the 4-vectors at once?

 

[Ibix]

Velocity is a 4-vector which has 3 space dimensions and 1 time dimension. It's space parts will be directed at the 3 space directions and time parts will be directed at the time dimension

A vector is just a magnitude and a direction. Don't think of it in terms of components - just think of it as an arrow at a point, pointing in some direction.

But it is inverse.

I don't know what you mean by "inverse".

How can someone Visualize it?

In (1+1)d, draw a Minkowski diagram. This is a Euclidean representation of a Minkowski plane, but that's as good as it gets. The four velocity is the Minkowski normalised tangent to the particle's worldline.

In (2+1)d you can also draw Minkowski diagrams but they're harder to understand.

I don't know any way to draw (3+1)d diagrams.