Probing noncommutative space-time in the laboratory frame

The phenomenological investigation of noncommutative space-time in the laboratory frame is presented. We formulate the apparent time variation of noncommutativity parameter θ_μν in the laboratory frame due to the earth's rotation. Furthermore, in the noncommutative QED, we discuss how to probe the electric-like component θ _E =(θ₀₁,θ₀₂,θ₀₃) by the process e^-e ⁺ → γγ at future e^-e ⁺ linear collider. We may determine the magnitude and the direction of θ _E by detailed study of the apparent time variation of the total cross-section. If no signal is observed, the upper limit on the magnitude of θ _E can be determined independent of its direction.