Linear polarization interference occurs when two linearly polarized waves, one aligned with the x-axis and the other with the y-axis, interact. In a vacuum, these waves do not interfere because their electric fields are orthogonal, meaning they do not combine to form a resultant wave. The absence of matter that could alter the polarization is crucial, as any medium could potentially change the alignment and allow for interference. The discussion emphasizes the importance of understanding wave properties and polarization in physics. Ultimately, the consensus is that without external factors, linear polarization does not lead to interference.