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## Main Question or Discussion Point

I know that if you go an accelerated observer's frame, the 4-acceleration is $$a^\mu=(0,{\bf a})$$ which means the magnitude is just $$-{\bf a}^2$$ which should be invariant. But I'm having a hard time showing this from the general expression for the 4-acceleration. I get to $$a_\mu a^\mu=-\gamma^4|{\bf a}|^2-\gamma^6\frac{|{\bf v\cdot a}|^2}{c^2}.$$ But I don't know where to go from here. Any ideas or am I just wrong somehow?

Thanks!

Thanks!