<Tr> <Td> Electromagnetic four potential </Td> <Td> Electric potential (divided by c), φ / c </Td> <Td> Magnetic potential, A </Td> </Tr> <P> For a given object (e.g., particle, fluid, field, material), if A or Z correspond to properties specific to the object like its charge density, mass density, spin, etc., its properties can be fixed in the rest frame of that object . Then the Lorentz transformations give the corresponding properties in a frame moving relative to the object with constant velocity . This breaks some notions taken for granted in non-relativistic physics . For example, the energy E of an object is a scalar in non-relativistic mechanics, but not in relativistic mechanics because energy changes under Lorentz transformations; its value is different for various inertial frames . In the rest frame of an object, it has a rest energy and zero momentum . In a boosted frame its energy is different and it appears to have a momentum . Similarly, in non-relativistic quantum mechanics the spin of a particle is a constant vector, but in relativistic quantum mechanics spin s depends on relative motion . In the rest frame of the particle, the spin pseudovector can be fixed to be its ordinary non-relativistic spin with a zero timelike quantity s, however a boosted observer will perceive a nonzero timelike component and an altered spin . </P> <P> Not all quantities are invariant in the form as shown above, for example orbital angular momentum L does not have a timelike quantity, and neither does the electric field E nor the magnetic field B . The definition of angular momentum is L = r × p, and in a boosted frame the altered angular momentum is L ′ = r ′ × p ′ . Applying this definition using the transformations of coordinates and momentum leads to the transformation of angular momentum . It turns out L transforms with another vector quantity N = (E / c) r − tp related to boosts, see relativistic angular momentum for details . For the case of the E and B fields, the transformations cannot be obtained as directly using vector algebra . The Lorentz force is the definition of these fields, and in F it is F = q (E + v × B) while in F ′ it is F ′ = q (E ′ + v ′ × B ′). A method of deriving the EM field transformations in an efficient way which also illustrates the unit of the electromagnetic field uses tensor algebra, given below . </P> <P> Throughout, italic non-bold capital letters are 4 × 4 matrices, while non-italic bold letters are 3 × 3 matrices . </P>

Show that under classical limit lorentz transformation reduces to galilean transformation