﻿ Special Relativity - Formulas Contents

## Collected Formulas

For reference, this page collects all of the formulas mentioned elsewhere on this site. It's worth noting that β, Γ, and D are all dimensionless quantitities: they are pure numbers, with no units attached to them.

The speed is usually expressed as a fraction of the speed limit: When used as a velocity along some axis, then β will also have a sign, either positive or negative.

The square of the space-time interval between any pair of events, with Δd for the distance: The warp factor (or Lorentz factor) for time dilation and other effects: The boost transformation (or Lorentz transformation), relating event coordinates in one grid (unprimed), to a second boosted grid (primed), moving along the x axis at speed β (-1<β<1) with respect to the first: If y and z dimensions are included: Boost for velocity, with each component of the speed expressed (as usual) as a fraction of the speed limit:   The Doppler factor, with θ as the angle between the line-of-sight and the line-of-motion. The Doppler neutral angle, where D=1: The aberration of light: In this diagram explaining the geometry, S is the source emitter, P is the photon:

The apparent velocity of an object, as seen in a detector. The angle θ is between 0° and 180°. It's the angle between the line of sight and the object's direction of motion. There are two components, transverse (t) and radial (r).    