Final answer:
The Wigner function's lack of Lorentz covariance means it cannot account for relativistic effects crucial to space-time and special relativity. This highlights the need for a framework that can combine quantum mechanics with relativity, adhering to Lorentz invariance.
Step-by-step explanation:
The fact that the Wigner function is not Lorentz-covariant implies that this tool for describing quantum states in phase space does not remain unchanged under Lorentz transformations, which are changes of reference frames that are moving relative to each other at constant speeds, as required by special relativity. Special relativity has fundamental implications on all physical theories and phenomena, stating that the laws of physics are the same for all observers in inertial frames of reference.
In quantum mechanics, the wave function is an essential tool for calculating probabilities of various physical quantities, but it is not always Lorentz-covariant. The absence of Lorentz covariance means that the Wigner function cannot fully account for relativistic effects, such as time dilation and length contraction, which arise from the nature of space and time itself, rather than just electromagnetic properties. While the implications of the Wigner function being non-Lorentz invariant might initially seem limited, it actually points towards a deeper need for a framework that can seamlessly integrate quantum mechanics and special relativity, like quantum field theory which ensures all its predictions are Lorentz invariant.