Lorentz transformations on spacetime

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Homework Help Overview

The discussion revolves around the application of Lorentz transformations to spacetime 4-vectors, specifically focusing on expressing these transformations in matrix form and proving properties related to the Minkowski spacetime metric.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the formulation of the Lorentz transformations and the identification of the matrix L. There are inquiries about which specific expressions should be considered in the context of the standard Lorentz transformation equations.

Discussion Status

The conversation is ongoing, with participants providing guidance on identifying relevant equations and clarifying terminology related to superscripts and indices. There is an emphasis on exploring the standard forms of the Lorentz transformations.

Contextual Notes

There is a mention of the need to prove that the matrix L satisfies the condition Lτ gL = g, where g represents the Minkowski spacetime metric. Participants are navigating the specifics of the problem setup and the definitions involved.

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Homework Statement


A3. Show that the Lorentz transformations on a spacetime 4-vector can be written as
x'μ = (Lμν)*(χν)
. Find the matrix L. Prove that (in matrix notation) Lτ gL = g where g is
the Minkowski spacetime metric.

Homework Equations


Any help suggesting at least equations will be appreciated. μ , τ and ν are exponents.

The Attempt at a Solution

 
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hi helpcometk! welcome to pf! :smile:

(try using the X2 and X2 icons just above the Reply box :wink:)
helpcometk said:
Show that the Lorentz transformations on a spacetime 4-vector can be written as
x'μ = (Lμν)*(χν)

you should be able to write out L just by looking at the standard Lorentz transformation equations

(and btw, they're not exponents, they're superscripts, or just indices :wink:)
 


Thanks for the reply Tim.
Specifically which expressions i have to take into account?
 
The standard Lorentz equations :rolleyes:

the ones with x' y' z' t' on the left and x y z t on the right!
 

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