In this work, the space-time Fourier transform (SFT) introduced by E. Hitzer, satisfies some uncertainty principles of the algebra for space-time Cl(3,1)-valued signals over the space-time vector space R(3,1). An analog of the Beurling theorem for the (SFT) is obtained. As a straightforward consequence of Beurling's theorem, other versions of the uncertainty principle, such as the Hardy, Gelfand-Shilov, Cowling-Price and Morgan theorems are also deduced.