The fact that spin–momentum of massive particles become entangled (disentangled) as seen by moving observers, is used to investigate the properties of von Neumann entropy, as a measure of spin–momentum entanglement. To do so, we partition the total Hilbert space into momentum and spin subspaces so that the entanglement occurs between total spin states and total momenta of two spin-$\dfrac{1}{2}$ particles. Assuming that the occurrence of spin–momentum states is determined by Gaussian probability distributions, we show that the degree of entanglement ascends for small rapidities, reaches a maximum and diminishes at high rapidity. We further report how the characteristics of this behaviour vary as the widths of distributions change. In particular, a separable state, resulting from equal distribution widths, indeed becomes entangled in moving frames.

In the present article, we use negativity to investigate the entanglement between two massive particles in the spin degrees of freedom, as seen by moving observers. Assuming that the occurrence of spin-momentum states is determined by Gaussian probability distributions, we show that the degree of entanglement monotonically descends to a diminishingly small value at high rapidities. We further report, how the characteristics of this behaviour vary as the widths of distributions change. In particular, the degree of maximally entangled spin–spin states, resulting from equal distribution widths, is shown to exhibit extrema, depending on the width, at certain rapidities. The material presented in this paper then supports the idea that, for relativistic particles, a consistent reduced spin density (from which the negativity is derived) is impossible to construct.