Dhairya Shah

I propose a version of quantum mechanics featuring a discrete and finite number of states that is plausibly a model of the real world. The model is based on standard unitary quantum theory of a closed system with a finite-dimensional Hilbert space. Given certain simple conditions on the spectrum of the Hamiltonian, Schrödinger evolution is periodic, and it is straightforward to replace continuous time with a discrete version, with the result that the system only visits a discrete and finite set of state vectors. The biggest challenges to the viability of such a model come from cosmological considerations. The theory may have implications for questions of mathematical realism and finitism.

The nature of time, causality, and temporal displacement remains a foundational problem in modern physics. While relativity treats time as a geometric dimension and quantum interpretations introduce branching histories, the question of whether a physical system can access its own future without violating causal structure remains unresolved. We propose Worldline Consistency Theory (WCT), a principle asserting that any forward-proper-time displacement of a physical system that bypasses causal continuity cannot occur within a single spacetime history. Such a displacement necessitates a transition between distinct universes, where the arrival event is already embedded in the past of the destination universe. This framework preserves local causality, eliminates temporal paradoxes, and reinterprets “time travel” as inter-universal relocation rather than intra-universal motion. The theory is formulated using standard relativistic causal structure and does not posit a mechanism for temporal displacement, focusing solely on consistency conditions. “We present a causal consistency condition on worldlines in Lorentzian spacetime, without introducing new dynamics.” ________________________________________.