Fermions cannot convert into bosons in a vacuum due to conservation laws, which include energy and momentum. However, interactions involving multiple particles can lead to transformations, such as an electron and positron annihilating to form photons. The discussion highlights that while photons can be compressed and share quantum states, fermions are restricted by the Pauli exclusion principle. The term "compressible" is debated, with the focus on the ability of bosons to form Bose-Einstein condensates, a phenomenon not possible for fermions. Overall, the conversion between these particle types is complex and constrained by fundamental quantum principles.