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Relativity mix-up............


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1 joule is, among other things,

  • The work done on some object by a force of one newton as the object moves a distance of one meter, from [math]W=\oint \mathbf F \cdot d\mathbf l[/math]
  • The kinetic energy of a 2 kilogram mass moving at the non-relativistic velocity of 1 meter per second, from [math]KE=\frac 1 2 m v^2[/math]


These expressions have the same fundamental units and the same numerical value:


[math]1\,\text{joule} = 1\,\text{newton}\,*\,1\,\text{meter} = 1\,\text{kg}\,\text{meter}/\text{second}^2\,*\,1\,\text{meter} = \frac 1 2\,*\,2\,\text{kg}\,*\,(1\,\text{meter}/\text{second})^2[/math]


Energy has units of mass*velocity squared. The expression [math]mc^2[/math] has units mass*velocity squared -- energy.

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