REL-30

Twin proper time

Inertial twin ageing.

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GoverningTwin proper time

Governing equation

\tau=t/\gamma

where

t: t (y)
beta: beta (—)
tau: Twin proper time (y)

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-30 — Twin proper time) is the form associated with Twin proper time. Working symbols: $t$ , $beta$ $\rightarrow$ $tau$ . Inertial twin ageing. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

tau

from

t

beta

in Relativity via

\tau=t/\gamma

Inertial twin ageing. Use it when a real relativity question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

t = 10.000\,\mathrm{y}

beta = 0.800\,\mathrm{—}

, the governing relation

\tau=t/\gamma

yields

tau = 6.000\,\mathrm{y}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

t t10 ybeta beta0.8 —

Outputs

Twin proper time tau6.000 y

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Inertial twin ageing. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube