REL-03

Time dilation

Δt = γ Δτ for a moving clock.

Reading speed

Special relativityEinstein 1905

Governing equation

\Delta t=\gamma\Delta\tau

where

\Delta\tau: Proper time (µs)
v/c: Speed in c (—)
\Delta t: Lab time (µs)

Lecture brief

Historical brief

Einstein’s 1905 Lorentz kinematics and 1915 field equation, then Schwarzschild (1916) and Hawking temperature, recast time, mass and gravity. The lab computes dilation, E=mc² and horizon scales. This sheet (REL-03 — Time dilation) is the form associated with Einstein 1905. Working symbols: $\Delta\tau$ , $v/c$ $\rightarrow$ $\Delta t$ . A clock at rest in a boosted frame ticks proper time Δτ; the lab interval is stretched by γ, confirmed by muon lifetime and GPS.

Purpose

Purpose: compute

\Delta t

from

\Delta\tau

v/c

in Relativity via

\Delta t=\gamma\Delta\tau

Δt = γ Δτ for a moving clock. Use it when a real relativity question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\Delta\tau = 2.200\,\mathrm{\mu s}

v/c = 0.980\,\mathrm{—}

, the governing relation

\Delta t=\gamma\Delta\tau

yields

\Delta t = 11.055\,\mathrm{\mu s}

. Inertial motion, enter v/c and proper time. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Proper time \Delta\tau2.2 µsSpeed in c v/c0.98 —

Outputs

Lab time \Delta t11.055 µs

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

Inertial motion, enter v/c and proper time.

A clock at rest in a boosted frame ticks proper time Δτ; the lab interval is stretched by γ, confirmed by muon lifetime and GPS.

Reading speed

Watch on YouTube