Is d⁴x really Lorentz Invariant? | Physics Riddle

The integral measure d4x is Lorentz invariant. The easiest way to see this, is to consider a Lorentz transformation Lambda, under which x goes to Lambda times x. Under a coordinate transformation, the integration measure d4x picks up the Jacobian, the determinant of the transformation matrix. Since the determinant of Lambda is plus one, the integral measure stays invariant.But can we also observe this for every component?

00:00 Introduction
00:26 Components
01:09 Wedge Product

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Видео Is d⁴x really Lorentz Invariant? | Physics Riddle канала Pretty Much Physics