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If we use Galilean transformation, why is that basic laws in physics are covariant?

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Given that the laws of physics are not invariant under Galilean symmetry, you'll be hard put to do this.

It's Newtonian mechanics that is. And this is shown by showing his three laws of motion are invariant under Galilean symmetry.

Often this is called classical mechanics, but just as often this also includes Electromagnetism and special and general relativity where the symmetry group is the Lorentz group.

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