Saakshi Dulani

We put forward a quantum model of cosmology that is exactly periodic but avoids the Boltzmann Brain problem. If the universe is described by a quantum state evolving unitarily in a finite-dimensional Hilbert space, its evolution will be recurrent: given enough time, the state will return arbitrarily close to its initial state. There is a worry that such a scenario cannot be phenomenologically acceptable, because the state will spend most of its time in a high-entropy equilibrium macrostate, with rare fluctuations downward in entropy, and the vast majority of observers will be minimal fluctuations away from equilibrium, or “Boltzmann Brains.” Here we show that this is not necessarily true. If the differences in energy eigenvalues are commensurable, the evolution is not simple recurrent, but exactly periodic. Moreover, if the state starts at minimum thermodynamic entropy, its evolution can feature a distinguished entropy excursion that is much more pronounced than one would expect from the conventional expression P(∆S)∝exp(−∆S). This excursion could represent our Big Bang, with relatively few Boltzmann fluctuations occurring in the subsequent equilibrium phase before a Big Crunch occurs and the cycle begins again. We speculate on the spacetime interpretation of this kind of quantum universe.

Recently, several philosophers and physicists have increasingly noticed the hegemony of unitarity in the black hole information loss discourse and are challenging its legitimacy in the face of the measurement problem. They proclaim that embracing non-unitarity solves two paradoxes for the price of one. Though I share their distaste over the philosophical bias, I disagree with their strategy of still privileging certain interpretations of quantum theory. I argue that information-restoring solutions can be interpretation-neutral because the manifestation of non-unitarity in Hawking's original derivation is unrelated to what's found in collapse theories or generalized stochastic approaches, thereby decoupling the two puzzles.

This paper examines the case for preferring density matrix realism over wave function realism, as an approach to the fundamental ontology of our world. To date, there are two arguments that have been used to motivate density matrix realism. One is that we get a simpler and more appealing metaphysics if we move from wave function realism to density matrix realism. The second is that density matrices are more general than wave functions. In both cases, a key purported advantage is that density matrix realists can allow that the universe could be in a mixed state. To be convincing, however, these arguments can’t simply assume that our universe could be in a mixed state, since standard definitions of mixedness seem to preclude such a possibility. Thus, to make density matrix realism plausible, one would need to appeal to some scientifically backed argument that standard definitions of mixedness need revision, that what seemed to be perplexing before represents a genuine way that our world could fundamentally be. Here, Hawking’s model of black hole evaporation seems poised to come to the rescue, and so, we develop a novel argument to this effect. Although we find this way of arguing for density matrix realism to be intriguing and worthy of investigation, we show that there is substantial reason to be cautious. Most physicists, including Hawking, believe that this model will be superseded by a more fundamental theory of quantum gravity. Despite a lack of agreement on the details of such a theory, the guiding principles that do enjoy some consensus point away from an interpretation of black hole evaporation in which the universe as a whole evolves into an (objectively) mixed state. We conclude that there do not seem to be compelling motivations coming from fundamental physics to favour a metaphysics in which the universe is fundamentally a density matrix rather than a wave function.

Recently, several philosophers and physicists have increasingly noticed the hegemony of unitarity in the discourse on black hole information loss and are challenging its legitimacy in the face of the measurement problem. They proclaim that embracing non-unitarity solves two paradoxes for the price of one. Although I share their distaste regarding the philosophical bias, I disagree with their strategy of still privileging certain interpretations of quantum theory. I argue that information-restoring solutions can be interpretation-neutral because the manifestation of non-unitarity in Hawking’s original derivation is unrelated to what’s found in collapse theories or generalized stochastic approaches, thereby decoupling the two puzzles.

The black hole information loss paradox is a catch-all term for a family of puzzles related to black hole evaporation. For almost 50 years, the quest to elucidate the implications of black hole evaporation has not only sustained momentum, but has also become increasingly populated with proposals that seem to generate more questions than they purport to answer. Scholars often neglect to acknowledge ongoing discussions within black hole thermodynamics and statistical mechanics when analyzing the paradox, including the interpretation of Bekenstein-Hawking entropy, which is far from settled. To remedy the dialectical gridlock, I have formulated an overarching, unified framework, which I call ``Black Hole Paradoxes'', that integrates the debates and taxonomizes the relevant `camps' or philosophical positions. I demonstrate that black hole evaporation within Hawking's semi-classical framework insinuates how late-time Hawking radiation is an entangled global system, a contradiction in terms. The relevant forms of information loss are associated with a decrease in maximal Boltzmann entropy and an increase in global von Neumann entropy respectively, which engender what I've branded the ``paradox of phantom entanglement''. Prospective solutions are then tasked with demonstrating how late-time Hawking radiation is either exclusively an entangled subsystem, in which a black hole remnant lingers as an information safehouse, or exclusively an unentangled global system, in which information is evacuated to the exterior. The disagreement between safehouse and evacuation solutions boils down to the statistical interpretation of thermodynamic black hole entropy, i.e., Bekenstein-Hawking entropy. Safehouse solutions attribute Bekenstein-Hawking entropy to a minority of black hole degrees of freedom, those that are associated with the horizon. Evacuation solutions, in contrast, attribute Bekenstein-Hawking entropy to all black hole degrees of freedom. I argue that the interpretation of Bekenstein-Hawking entropy is the litmus test to vet the overpopulated proposal space. So long as any proposal rejecting Hawking's original calculation independently derives black hole evaporation, globally conserves degrees of freedom and entanglement, preserves a version of semi-classical gravity at sub-Planckian scales, and describes black hole thermodynamics in statistical terms, then it counts as a genuine solution to the paradox.