Relativistic Addition of Velocities

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration considers the composition of velocities in accordance with the special theory of relativity. Consider a system moving with velocity represented by the red arrow, with magnitude and direction , with respect to a stationary frame of reference. The red disk recapitulates this magnitude, which has an upper limit extending to the red circle, corresponding to the speed of light . The blue arrow represents a second velocity, which has a magnitude and direction , with respect to the moving frame of reference. The velocity with respect to the original stationary frame is then represented by . A compact formulation gives the components of parallel and perpendicular to : The gray arrow represents the vector .

Contributed by: S. M. Blinder (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

Snapshot 1: for , the Galilean result is a good approximation

Snapshot 2: if or , then

Snapshot 3: the collinear case reduces to Einstein's well-known formula

Snapshots 4, 5: velocity addition is not commutative;

Reference: J. D. Jackson, Classical Electrodynamics, 3rd ed., New York: John Wiley & Sons, 1998 p. 531.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send