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Deadstar
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Homework Statement
4-velocity [tex]\overline{U} = (U^0, U^1, U^2, U^3)[/tex] is related to 3-velocity [tex]\underline{v}[/tex] by [tex]\overline{U} = \gamma(v) (1,\underline{v})[/tex]
Express [tex]U^{\alpha}[/tex] in terms of [tex]\underline{v}[/tex], where [tex]\alpha[/tex] represents the spatial components and takes values 1,2,3.
Homework Equations
[tex]\gamma(v) = \frac{1}{\sqrt{1-v^2}}[/tex].I can't see how this is possible.
[tex]U^{\alpha} = \frac{dx^{\alpha}}{d \tau}[/tex]
[tex]v^{\alpha} = \frac{1}{\gamma (v)} \frac{dx^{\alpha}}{d \tau}[/tex]
How can you do it for just v..?!?
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