In the paper “Toward a Phenomenologically Acceptable Quantum Cyclic Universe” (arXiv:2605.30405), Carroll, Diachenko, and Dulani demonstrate that exact cosmic repetition does not violate the Heisenberg Uncertainty Principle (Δx · Δp ≥ ℏ/2) because uncertainty governs the spread of non-commuting observables within a single state, whereas repetition refers to the exact deterministic evolution of the global quantum state vector |ψ(t)⟩ through Hilbert space. Assuming the universe is described by a finite-dimensional Hilbert space of dimension D ≈ e^S_dS (where S_dS ∼ 10¹²² is the de Sitter entropy), its unitary evolution under the Schrödinger equation is given by |ψ(t)⟩ = ∑ c_k e^(−i E_k t / ℏ) |k⟩; by constraining the Hamiltonian’s energy eigenvalues E_k to be commensurable—meaning all energy differences are integer multiples of a fundamental energy scale E₀—the phase factors realign identically at fixed period T = 2πℏ / E₀. This forces |ψ(t + T)⟩ = |ψ(t)⟩ along a closed one-dimensional trajectory in Hilbert space, allowing the entire universe to repeat precisely as a high-dimensional harmonic oscillator while fully preserving all quantum mechanical uncertainties and avoiding the Boltzmann Brain problem at every instant.
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This is my biggest fear Apocalypse.
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@Apocalypse Im not so certain I wanna relive this thing. How do I stop and get off?
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