REL-09

Mass–energy

E = m c². Rest energy of a mass m.

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RelativityEinstein

Governing equation

E=mc^2

$m \in \left[0.001, 240\right]$

where

m: Mass (u)
E: Rest energy (MeV)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

E=mc^2

$m \in \left[0.001, 240\right]$

$m = 0.001$ $E = 0.931$

Along the curve

②

Domain of the variable — blue

m_{\min} = 0.001,\quad m_{\max} = 240

$m \in \left[0.001, 240\right]$

$m = 0.001$ $m = 0.001$

Along the curve

③

Response curve — green

E=mc^2

$m \in \left[0.001, 240\right]$

$m = 0.001$ $E = 0.931$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}E}{\mathrm{d}m}

$m \in \left[0.001, 240\right]$

$m = 1.51$ $E^{\prime} = 931.5$

Along the curve

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-09 — Mass–energy) is the form associated with Einstein. Working symbols: $m$ $\rightarrow$ $E$ . The full relation is E² = (pc)² + (mc²)². At rest p = 0.

Purpose

Purpose: compute

E

from

m

in Relativity via

E=mc^2

E = m c². Rest energy of a mass m. 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=mc^2

yields

E = 931.494\,\mathrm{MeV}

. A mass, a light-speed square, an energy. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Mass m1 u

Outputs

Rest energy E931.494 MeV

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Narration of this film

A mass, a light-speed square, an energy.

The full relation is E² = (pc)² + (mc²)². At rest p = 0.

Reading speed

Watch on YouTube