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REL-02

Rest energy E = mc²

E0 = m c², the inertia of energy.

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Mass–energyEinstein 1905

Governing equation

E0=mc2E_0=mc^2

m∈[5×10−4,240]m \in \left[5\times 10^{-4}, 240\right]

where

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

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REL-02 · relativity
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①

Governing law — red

E0=mc2E_0=mc^2

m∈[5×10−4,240]m \in \left[5\times 10^{-4}, 240\right]

m=5×10−4m = 5\times 10^{-4}E0=0.466E_0 = 0.466

②

Domain of the variable — blue

mmin⁡=5×10−4,mmax⁡=240m_{\min} = 5\times 10^{-4},\quad m_{\max} = 240

m∈[5×10−4,240]m \in \left[5\times 10^{-4}, 240\right]

m=5×10−4m = 5\times 10^{-4}m=5×10−4m = 5\times 10^{-4}

③

Response curve — green

E0=mc2E_0=mc^2

m∈[5×10−4,240]m \in \left[5\times 10^{-4}, 240\right]

m=5×10−4m = 5\times 10^{-4}E0=0.466E_0 = 0.466

④

Rate of change — amber

dE0dm\frac{\mathrm{d}E_0}{\mathrm{d}m}

m∈[5×10−4,240]m \in \left[5\times 10^{-4}, 240\right]

m=1.51m = 1.51E0′=931.5E_0^{\prime} = 931.5

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: mm →\rightarrow E0E_0, E0E_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 E0E_0, E0E_0 from mm in Relativity via E0=mc2E_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 um = 1.000\,\mathrm{u}, the governing relation E0=mc2E_0=mc^2 yields E0=931.494 MeVE_0 = 931.494\,\mathrm{MeV}, E0=149.2418 pJE_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

Outputs

  • Rest energy E_0931.494 MeV
  • Rest energy E_0149.2418 pJ
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REL-02 · relativity
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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