I'm reading a physics book and in the section on relativity they are using the Einstein summation convention, with 4vectors and matrices.(adsbygoogle = window.adsbygoogle || []).push({});

They say that the transformations take the form:

[tex]x^{\prime\mu}=x^{\nu}\Lambda^{\mu}_{\nu}+C^{\mu}[/tex]

where it is required that [itex]\Lambda^{\mu}_{\nu}[/itex] satisfy the following relation:

[tex]\eta_{\mu\nu}\Lambda^{\mu}_{\alpha}\Lambda^{\nu}_{\beta}=\eta_{\alpha\beta}[/tex]

(note: I found the same thing on wikipedia, so you can see it in context if you like. http://en.wikipedia.org/wiki/Lorentz_transformation#Spacetime_interval it appears a tiny bit down from the section that the link takes you to.)

My problem is that this seemsimpossibleto satisfy by my current understanding, but I know I must be wrong, I just cannot see how.

So we are summing over [itex]\mu[/itex] and [itex]\nu[/itex] in the above relation right? and we do this for all [itex]\alpha[/itex] and [itex]\beta[/itex] in order to satisfy all the components of the matrices.

My problem is what happens when we get to the following situation?:

[tex]\mu=0, \nu=1, \alpha=0, \beta=0[/tex]

But, [itex]\eta_{01}=0[/itex], and [itex]\eta_{00}=-1[/itex]. So there is no possible values of the [itex]\Lambda[/itex]'s that will satisfy this because we now have 0=-1, which is a contradiction.

Where did I go wrong with my thinking? Thanks.

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# Inhomogeneous (poincare) lorentz transormation

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