In order to relate the probabilistic predictions of quantum theory uniquely to measurement results, one has to conceive of an ensemble of identically prepared copies of the quantum system under study. Since the universe is the total domain of physical experience, it cannot be copied, not even in a thought experiment. Therefore, a quantum state of the whole universe can never be made accessible to empirical test. Hence the existence of such a state is only a metaphysical idea. Despite prominent claims to the contrary, recent developments in the quantum-interpretation debate do not invalidate this conclusion.
We consider the problem of characterizing states of a multipartite quantum system from restricted, quasi-local information, with emphasis on uniquely determined pure states. By leveraging tools from dissipative quantum control theory, we show how the search for states consistent with an assigned list of reduced density matrices may be restricted to a proper subspace, which is determined solely by their supports. The existence of a quasi-local observable which attains its unique minimum over such a subspace further provides a sufficient criterion for a pure state to be uniquely determined by it…
Mixed States Uniquely Determined by Marginals and Additivity
LMIB (Beihang University), Ministry of Education, and School of Mathematical Sciences, Beihang University（教育部实验室（北京航空航天大学）及北京航空航天大学数学科学学院）；Department of Mathematics, National University of Singapore（新加坡国立大学数学系）
In this paper, we study the changes of quantum effects of a growing universe by using Wheeler-DeWitt equation (WDWE) together with de Broglie-Bohm quantum trajectory approach. From WDWE, we obtain the quantum modified Friedmann equations which have additional terms called quantum potential compared to standard Friedmann equations. The quantum potential governs the behavior of the early universe, providing energy for inflation, while it decreases rapidly as the universe grows. The quantum potential of the grown-up universe is much smaller than that required for accelerating expansion. This indi…
Indeterministic Quantum Gravity and Cosmology X. Probability-Theoretic Aspect: A Hidden Selector for Quantum Jumps, or How the Universe Plays the Game of Chance
If one analyses the quantum creation of the universe, it turns out that the most natural way in which the universes can be created is in pairs of universes whose time flow is reversely related. It means that the matter that propagates in one of the universes can be seen, from the point of view of the other universe, as antimatter, and viceversa. They thus form a universe-antiuniverse pair. From a global point of view, i.e. from the point of view of the whole multiverse ensemble, the creation of universes in universe-antiuniverse pairs restores the matter-antimatter asymmetry observed in each i…
In a quantum universe with a strong arrow of time, we postulate a low-entropy boundary condition (the Past Hypothesis) to account for the temporal asymmetry. In this paper, I show that the Past Hypothesis also contains enough information to simplify the quantum ontology and define a natural initial condition. First, I introduce Density Matrix Realism, the thesis that the quantum state of the universe is objective and impure. This stands in sharp contrast to Wave Function Realism, the thesis that the quantum state of the universe is objective and pure. Second, I suggest that the Past Hypothesis…
