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43.4 $E=mc^2$

Module 43 - $E=mc^2$ Problem 2

Earlier we noted that even though spatial and temporal separations, $\Delta x$ and $\Delta t$, change from one reference frame to another, the combination $(-c^2 (\Delta t)^2 + (\Delta x)^2)$ does not change. As discussed, this is an example of an “invariant”.

We have now encountered two new quantities, $E=m_0c^2\gamma$. Because $\gamma$ depends directly on $v$, both $E$ and $p$ change values from one frame to another. However, as with $\Delta x$ and $\Delta t$, there is a combination of $E$ and $p$ that does not change, which is the subject of this problem.

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