Journal of Consciousness Studies issue on the Singularity
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Hi, Gwern. You asked, "... MWI and quantum mechanics implied by Newton? Really?" Yes, the Hamilton-Jacobi Equation, which is the most powerful formulation of Newtonian mechanics, is, like the Schrödinger Equation, a multiverse equation. Quantum Mechanics is the unique specialization of the Hamilton-Jacobi Equation with the specification imposed that determinism is maintained: since the Hamilton-Jacobi Equation is indeterministic, because when particle trajectories cross paths a singularity is produced (i.e., the values in the equations become infinite) and so it is not possible to predict (even in principle) what happens after that. On the inherent multiverse nature of Quantum Mechanics, see physicist and mathematician Prof. Frank J. Tipler's following paper:
Regarding the universe necessarily being temporally closed according to the known laws of physics: all the proposed solutions to the black hole information issue except for Prof. Tipler's Omega Point cosmology share the common feature of using proposed new laws of physics that have never been experimentally confirmed--and indeed which violate the known laws of physics--such as with Prof. Stephen Hawking's paper on the black hole information issue which is dependent on the conjectured String Theory-based anti-de Sitter space/conformal field theory correspondence (AdS/CFT correspondence). (See S. W. Hawking, "Information loss in black holes", Physical Review D, Vol. 72, No. 8 [Oct. 15, 2005], Art. No. 084013, 4 pp.) Hence, the end of the universe in finite proper time via collapse before a black hole completely evaporates is required if unitarity is to remain unviolated, i.e., if General Relativity and Quantum Mechanics--which are what the proofs of Hawking radiation derive from--are true statements of how the world works.
Pertaining to your comments doubting "a universal meta-ethical principal that future AIs will obey!": Prof. Tipler is quite correct regarding his aforecited discussion on ethics. In order to understand his point here, one must keep in mind that the Omega Point cosmology is a mathematical theorem per the known physical laws (viz., the Second Law of Thermodynamics, General Relativity, and Quantum Mechanics) that requires sapient life (in the form of, e.g., immortal superintelligent human-mind computer-uploads and artificial intelligences) take control over all matter in the universe, for said life to eventually force the collapse of the universe, and for the computational resources of the universe (in terms of both processor speed and memory space) to diverge to infinity as the universe collapses into a final singularity, termed the Omega Point. Said Omega Point cosmology is also an intrinsic component of the Feynman-DeWitt-Weinberg quantum gravity/Standard Model Theory of Everything (TOE) correctly describing and unifying all the forces in physics, of which TOE is itself mathematically forced by the aforesaid known physical laws. Thus, existence itself selects which ethics is correct in order for existence to exist. Individual actors, and individuals acting in groups, can of course go rogue, but there is a limit to how bad things can get: e.g., life collectively cannot choose to extirpate itself.
You go on to state, "there are X mind-states we can be in while still maintaining identity or continuity; there are Y (Y < X) that we would like or would value; with infinite computing power, we will exhaust all Y. At that point, by definition, we could choose to not be preserved. Hence, I have proven we will inevitably choose to die even if uploaded to Tipler's Singularity." Yet if Y is infinite, then this presents no problem to literal immortality. Traditional Christian theology has maintained that Y is indeed infinite.
Interestingly, the Omega Point final singularity has all the unique properties (quiddities) claimed for God in the traditional religions. For much more on Prof. Tipler's Omega Point cosmology and the details on how it uniquely conforms to, and precisely matches, the cosmology described in the New Testament, see my following article, which also addresses the societal implications of the Omega Point cosmology:
Additionally, in the below resource are different sections which contain some helpful notes and commentary by me pertaining to multimedia wherein Prof. Tipler explains the Omega Point cosmology and the Feynman-DeWitt-Weinberg quantum gravity/Standard Model TOE.