REL-23

Relativistic energy

Total energy of a free particle.

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GoverningRelativistic energy

Governing equation

E=\gamma m c^2

$beta \in \left[0.01, 0.99\right]$

where

m: m (u)
beta: beta (—)
E: Relativistic 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=\gamma m c^2

$beta \in \left[0.01, 0.99\right]$

$beta = 0.01$ $E = 931.5$

Along the curve

②

Domain of the variable — blue

beta_{\min} = 0.01,\quad beta_{\max} = 0.99

$beta \in \left[0.01, 0.99\right]$

$beta = 0.01$ $beta = 0.01$

Along the curve

③

Response curve — green

E=\gamma m c^2

$beta \in \left[0.01, 0.99\right]$

$beta = 0.01$ $E = 931.5$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}E}{\mathrm{d}beta}

$beta \in \left[0.01, 0.99\right]$

$beta = 0.016$ $E^{\prime} = 15.06$

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-23 — Relativistic energy) is the form associated with Relativistic energy. Working symbols: $m$ , $beta$ $\rightarrow$ $E$ . Total energy of a free particle. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

E

from

m

beta

in Relativity via

E=\gamma m c^2

Total energy of a free particle. 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}

beta = 0.600\,\mathrm{—}

, the governing relation

E=\gamma m c^2

yields

E = 1164.368\,\mathrm{MeV}

. 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

m m1 ubeta beta0.6 —

Outputs

Relativistic energy E1164.368 MeV

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Narration of this film

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

Total energy of a free particle. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube