REL-02

Rest energy E = mc²

E0 = m c², the inertia of energy.

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Mass–energyEinstein 1905

Governing equation

E_0=mc^2

where

m: Mass (u)
E_0: Rest energy (MeV)
E_0: Rest energy (pJ)

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-02 — Rest energy E = mc²) is the form associated with Einstein 1905. Working symbols: $m$ $\rightarrow$ $E_0$ , $E_0$ . Einstein showed that a body's inertial mass and its energy content are the same quantity, E0 = m c² in the rest frame.

Purpose

Purpose: compute

E_0

E_0

from

m

in Relativity via

E_0=mc^2

E0 = m c², the inertia of energy. Use it when a real relativity question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

m = 1.000\,\mathrm{u}

, the governing relation

E_0=mc^2

yields

E_0 = 931.494\,\mathrm{MeV}

E_0 = 149.2418\,\mathrm{pJ}

. Rest frame. Enter mass in u (atomic mass units). Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Mass m1 u

Outputs

Rest energy E_0931.494 MeV
Rest energy E_0149.2418 pJ

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Narration of this film

Rest frame. Enter mass in u (atomic mass units).

Einstein showed that a body's inertial mass and its energy content are the same quantity, E0 = m c² in the rest frame.

Reading speed

Watch on YouTube