W Pauli pointed out that the existence of a self-adjoint time operator is incompatible with the semi-bounded character of the Hamiltonian spectrum. As a result, there has been much argument about the time–energy uncertainty relation and other related issues. In this paper, we show a way to overcome Pauli's argument. In order to define a time operator, by treating time and space on an equal footing and extending the usual Hamiltonian Ĥ to the generalized Hamiltonian Ĥμ (with Ĥ0 = Ĥ), we reconstruct the analytical mechanics and the corresponding quantum (field) theories, which are equivalent to the traditional ones. The generalized Schrodinger equation i∂μψ = Ĥμψ and Heisenberg equation d/dxμ = ∂μ + i[Ĥμ, ] are obtained, from which we have: (1) t is to Ĥ0 as xj is to Ĥj (j = 1, 2, 3); likewise, t is to i∂0 as xj is to i∂j; (2) the proposed time operator is canonically conjugate to i∂0 rather than to Ĥ0, therefore Pauli's theorem no longer applies; (3) two types of uncertainty relations, the usual ΔxμΔpμ ≥ 1/2 and the Mandelstam–Tamm treatment ΔxμΔHμ ≥ 1/2, have been formulated.