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thanx

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thanx

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selfAdjoint

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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 transformationselfAdjoint said:

Pete

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Technically, boosts and spatial rotations are examples of a Lorentz Transformation. It's the boosts that don't form a group. Finally, you have to adjoin the translations to the [Proper] Lorentz Group SO(3,1) to get the "inhomogeneous Lorentz Group", a.k.a. the Poincare group, ISO(3,1).

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If you are looking for a non mathematical answer to your question, it's also possible to say that Lorentz transformations are a direct consequence of two pre-requizites: 1°) Two observers must have the possibility to compare their space-time coordinates via a linear transformation (and not via a bilinear one); 2°) speed of light (in vacuum) must appear to be the same for both observers if each of them is at the origin of what he calls an inertial frame. These two conditions are sufficient one to (for exemple) find the special formulation of the Lorentz transformations.preet0283 said:

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