Four-dimensional commutation relations and Hamiltonian dynamics with constraints are discussed. The invariant volume element |b|d3x/co in common relativity is employed to give a meaning to the invariant probability |ψI(xμ)|2 d4x in quantum theory. In fuzzy quantum mechanics, the co-ordinate and the momentum variables are “fuzzy continuous matrices” which can never be diagonalized. They have fuzzy values and fuzzy basic vectors which satisfy a new closure relation. Fuzzy matrices satisfy a new law of matrix multiplication. The values of a fuzzy dynamical variable cannot be experimentally measured with unlimited accuracy. In particular, a physically realizable wave packet must satisfy Δqmin ≈R≠0, whereR is a radical length, which characterizes the fuzziness of space at short distances. The modification of the superposition principle due to the radical lengthR≲10−18 cm is also discussed. The results do not contradict experiments.