This is the fourth in a series of papers on a new theory of relativity [Phys. Essays 4, 68 (1991); ibid., 194; ibid., 532]. We demonstrate that the differential Lorentz transformation is a transformation of motion and not of space-time coordinates as usually interpreted in Einstein's special relativity [A. Einstein, Meaning of Relativity, 5th ed. (Princeton University Press, 1956); HA. Lorentz, A. Einstein, H. minkowski, and H. Weyl, Principle of Relativity, edited by HA. Lorentz (Dover, NE, 1923)]. differential Lorentz transformation is shown to be compatible with Heisenberg's unceriainty pn'nciple [IE. Heisenberg, The Development of the Interpretation of the Quantum Theory, in Niels Bohr and the Development of Physics,' edited by W. Pauli (Pergamon, London, 1955); L.D. landau and E.M. Lifshitz, Quantum Mechanics (Pergamon, London, 1974), Chap. 1], whereas the global Lorentz transformation in Einstein's special relativity is shown to be incompatible with that fundamental principle. Based on the uncertainty pn'nc{Ole, the correct relativistic transformation must be an instantaneous transformation in velocity space (or equivalently in energy-momentum space), but not a transformation in both space-time coordinates space and energy-momentum space.