Time-Travel Paradox in a Bohmian Extension of Deutsch's Approach: Mandatory Tunneling as the "Banana Peel Mechanism"

We consider a self-prevention paradox in which a particle travels through a wormhole into its own past, encounters its younger version, and blocks its movement. In a specially constructed one-dimensional model, this collision rules out a classically self-consistent history. Deutsch's quantum approach can resolve such contradictions by imposing a self-consistency condition on the density matrix. The physical interpretation of this approach, however, remains debated and may imply the existence of interacting parallel worlds. Here we extend Deutsch's approach within de Broglie--Bohm theory by supplementing the self-consistency condition on the quantum state with a self-consistency requirement for the particle's ontic configuration. This allows us to consider the self consistent evolution of an individual particle. In a two-channel, narrow-band Gaussian approximation, we find a self-consistent solution in which quantum tunneling is mandatory, despite its arbitrarily small probability in an ordinary scattering process. This realizes the ``banana peel mechanism'': to avoid a contradiction during a journey into the past, an event that would ordinarily be extremely unlikely occurs nonetheless.