Comment by zozbot234
4 days ago
More generally, imposing "self-consistency" on a closed cycle of interactions is just a matter of picking a fixed point. Such a fixed point will always exist if the underlying system is continuous - and continuity may always be assumed if the system be non-deterministic. (For example, a billiard ball enters a wormhole sending it to the past with probability 50%, or else it is knocked away by a billiard ball sent from the future (and does not enter the wormhole) with probability 50%. This system is self-consistent, but this is achieved by a "mixture" of two outcomes.)
Can the ball roll into wormhole, emerge in the past, hit its past self and stop, while its past self it knocked to roll into the wormhole, emerge in the past, hit its past self ...
Sure, this is another self-consistent solution which is discussed at length in the papers referenced above. But the neat thing about non-determinism is that it adds continuity - thus, a guaranteed existence of some self-consistent solution - even when the underlying system is discrete (as in, the ball is only allowed to either enter the wormhole on its own or be knocked off altogether - which is what creates the purported paradox).
Could you elaborate on what you mean by fixed point? Fixed point of what? And what continuity and non-determinism are you referring to exactly?
A fixed point involving the dynamics of "complex interpersonal interactions" (to quote the above-linked Wikipedia article) that are typically involved in these purported time-travel paradoxes. Continuity of the underlying physics is enough to ensure that such a fixed point will definitely exist, and allowing for non-determinism is just a convenient way of recovering a sort of continuity even if the underlying physics is assumed to not be continuous.
(These concerns are somewhat comparable to those that involve issues of so-called "metastability" in electronic circuits and indeed other physical systems which are designed to only have a limited number of "discrete" states.)