My direct question is at the bottom of this post, but I thought I would set the scene. Skip the first part if you wish.(adsbygoogle = window.adsbygoogle || []).push({});

The magnitude of any 4-vector is scalar and therefore the same in all frames. For the velocity vector

[tex]u = (\gamma c, \gamma v)[/tex]

wherevis a 3-vector velocity term, we can therefore switch frames to a frame where the object in question is at rest. In this frame

[tex]u = (c, 0, 0, 0)[/tex]

because [tex]v = (0, 0, 0)[/tex] and [tex] \gamma = 1[/tex].

So the magnitude ofuisc.

My text justifies this strange derivation by saying that because magnitudes are scalar weneed4-vector magnitudes to be c, because c does not change with our frame of reference. Furthermore he says that "speeds (magnitudes of 3-vectors) are relative but the magnitude of a 4-vector must be invariant."

So my question:what is the meaning of a 4-vector's magnitude? It's always c, but what is 'it'?

(I believe this is related to a recent thread where an author claimed "all things are moving around at the speed of light...")

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# Magnitude of a 4-vector

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