# Lorentz transformations

can ne 1 explain 2 me the basics of lorentz transformations...mathematically i know how things transform bt i want a more revealing explanation ....relate it 2 boosts and rotations also .....
thanx

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Lorentz transformations are linear transofrmations of the Minkowski coordinates that mix space and time. They are orthogonal transformations such that $$\Lambda \Lambda^T = \mathbf I$$. And their determinants are +1, so they preserve the Minkowsi unit $$-c^2t^2 + x^2 + y^2 + z^2$$. They do not form a group because the product of two of them can involve a spatial rotation; so you have to adjoin the space rotation group SO(3) to get the Poincare group SO(1,3). These are then all the special orthogonal transformations on Minkowski spacetime.

Lorentz transformations are linear transofrmations of the Minkowski coordinates that mix space and time. They are orthogonal transformations such that $$\Lambda \Lambda^T = \mathbf I$$. And their determinants are +1, so they preserve the Minkowsi unit $$-c^2t^2 + x^2 + y^2 + z^2$$. They do not form a group because the product of two of them can involve a spatial rotation; so you have to adjoin the space rotation group SO(3) to get the Poincare group SO(1,3). These are then all the special orthogonal transformations on Minkowski spacetime.

Correct me if I'm wrote but Lorentz transformations are not orthogonal transformations since they do not satisfy the orthogonality condition that you stated above. An orthogonal transformation is defined as any transformation A which staisfies the relation AAT = I. Lorentz transformations satisfy don't satisfy that relation. They do, however, satisfy the relation LNLT = N where N = diag(-1, 1, 1, 1)

Pete

Last edited:
robphy