Which Proof We Have against Continuous Trajectories for Particles?

Abstract

It is in general accepted that the concept of continuous trajectories for particles is at odds with the relativistic quantum mechanics. Namely, when examining the evolution of entangled quantum objects according to frames of coordinates in relative move-ment, one gets contradictory trajectories. Such a situation is typically derived from the famous “Hardy’s paradox”. However, it is argued here that if the rationale ignores the principle of quantum contextuality, as happens typically when using Hardy’s thought-experiment, the conclusion—rejection of the assumption of trajectories—is questionable. The issue is exemplified by an additional example: the 101 property of spin 1 bosons implies conflicting trajectories when the singlet state of two such bosons is examined according to frames in relative movement. It is concluded here that in the absence of a rationale which doesn’t violate the quantum contextuality, there are no sufficient arguments for refuting the possibility of a substructure of the quantum mechanics, consisting in particles following continuous trajectories.