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A new dynamical paradigm merging quantum dynamics with cosmology is discussed. We distinguish between a universe and its background space-time. The universe here is the subset of space-time defined by ${\mathsf{\Psi }}_{\mathsf{\tau }}\left(x\right)\ne 0$, where ${\mathsf{\Psi }}_{\mathsf{\tau }}\left(x\right)$ is a solution of a Schrödinger equation, x is a point in n-dimensional Minkowski space, and $\mathsf{\tau }\ge 0$ is a dimensionless ‘cosmic-time’ evolution parameter. We derive the form of the Schrödinger equation and show that an empty universe is described by a ${\mathsf{\Psi }}_{\mathsf{\tau }}\left(x\right)$ that propagates towards the future inside some future-cone $V_{+}$. The resulting dynamical semigroup is unitary, i.e., ${\int }_{V_{+}}{d}^{4}x{\left|{\mathsf{\Psi }}_{\mathsf{\tau }}\left(x\right)\right|}^2=1$ for $\mathsf{\tau }\ge 0$. The initial condition ${\mathsf{\Psi }}_0\left(x\right)$ is not localized at $x=0$. Rather, it satisfies the boundary condition ${\mathsf{\Psi }}_0\left(x\right)=0$ for $x\notin V_{+}$. For $n=1+3$ the support of ${\mathsf{\Psi }}_{\mathsf{\tau }}\left(x\right)$ is bounded from the past by the ‘gap hyperboloid’ ${\ell }^2\sqrt{\mathsf{\tau }}=c^2{t}^2-x^2$, where ℓ is a fundamental length. Consequently, the points located between the hyperboloid and the light cone $c^2{t}^2-x^2=0$ satisfy ${\mathsf{\Psi }}_{\mathsf{\tau }}\left(x\right)=0$, and thus do not belong to the universe. As $\mathsf{\tau }$ grows, the gap between the support of ${\mathsf{\Psi }}_{\mathsf{\tau }}\left(x\right)$ and the light cone increases. The past thus literally disappears. Unitarity of the dynamical semigroup implies that the universe becomes localized in a finite-thickness future-neighbourhood of ${\ell }^2\sqrt{\mathsf{\tau }}=c^2{t}^2-x^2$, simultaneously spreading along the hyperboloid. Effectively, for large $\mathsf{\tau }$ the subset occupied by the universe resembles a part of the gap hyperboloid itself, but its thickness ${\mathsf{\Delta }}_{\mathsf{\tau }}$ is non-zero for finite $\mathsf{\tau }$. Finite ${\mathsf{\Delta }}_{\mathsf{\tau }}$ implies that the three-dimensional volume of the universe is finite as well. An approximate radius of the universe, $r_{\mathsf{\tau }}$, grows with $\mathsf{\tau }$ due to ${\mathsf{\Delta }}_{\mathsf{\tau }}{r}_{\mathsf{\tau }}^3={\mathsf{\Delta }}_0{r}_0^3$ and ${\mathsf{\Delta }}_{\mathsf{\tau }}\to 0$. The propagation of ${\mathsf{\Psi }}_{\mathsf{\tau }}\left(x\right)$ through space-time matches an intuitive picture of the passage of time. What we regard as the Minkowski-space classical time can be identified with $c{t}_{\mathsf{\tau }}=\int d^{4}x{x}^0{\left|{\mathsf{\Psi }}_{\mathsf{\tau }}\left(x\right)\right|}^2$, so $t_{\mathsf{\tau }}$ grows with $\mathsf{\tau }$ as a consequence of the Ehrenfest theorem, and its present uncertainty can be identified with the Planck time. Assuming that at present values of $\mathsf{\tau }$ (corresponding to 13–14 billion years) ${\mathsf{\Delta }}_{\mathsf{\tau }}$ and $r_{\mathsf{\tau }}$ are of the order of the Planck length and the Hubble radius, we estimate that the analogous thickness ${\mathsf{\Delta }}_0$ of the support of ${\mathsf{\Psi }}_0\left(x\right)$ is of the order of 1 AU, and $r_0^3\sim {\left(c{t}_H\right)}^3\times {10}^{-44}$. The estimates imply that the initial volume of the universe was finite and its uncertainty in time was several minutes. Next, we generalize the formalism in a way that incorporates interactions with matter. We are guided by the correspondence principle with quantum mechanics, which should be asymptotically reconstructed for the present values of $\mathsf{\tau }$. We argue that Hamiltonians corresponding to the present values of $\mathsf{\tau }$ approximately describe quantum mechanics in a conformally Minkowskian space-time. The conformal factor is directly related to $|{\mathsf{\Psi }}_{\mathsf{\tau }}{\left(x\right)|}^2$. As a by-product of the construction, we arrive at a new formulation of conformal invariance of $m\ne 0$ fields. Full article

I take non-locality to be the Michelson–Morley experiment of the early 21st century, assume its universal validity, and try to derive its consequences. Spacetime, with its locality, cannot be fundamental, but must somehow be emergent from entangled coherent quantum variables and their behaviors. There are, then, two immediate consequences: (i). if we start with non-locality, we need not explain non-locality. We must instead explain an emergence of locality and spacetime. (ii). There can be no emergence of spacetime without matter. These propositions flatly contradict General Relativity, which is foundationally local, can be formulated without matter, and in which there is no “emergence” of spacetime. If these be true, then quantum gravity cannot be a minor alteration of General Relativity but must demand its deep reformulation. This will almost inevitably lead to: matter not only curves spacetime, but “creates” spacetime. We will see independent grounds for the assertion that matter both curves and creates spacetime that may invite a new union of quantum gravity and General Relativity. This quantum creation of spacetime consists of: (i) fully non-local entangled coherent quantum variables. (ii) The onset of locality via decoherence. (iii) A metric in Hilbert space among entangled quantum variables by the sub-additive von Neumann entropy between pairs of variables. (iv) Mapping from metric distances in Hilbert space to metric distances in classical spacetime by episodic actualization events. (v) Discrete spacetime is the relations among these discrete actualization events. (vi) “Now” is the shared moment of actualization of one among the entangled variables when the amplitudes of the remaining entangled variables change instantaneously. (vii) The discrete, successive, episodic, irreversible actualization events constitute a quantum arrow of time. (viii) The arrow of time history of these events is recorded in the very structure of the spacetime constructed. (ix) Actual Time is a succession of two or more actual events. The theory inevitably yields a UV cutoff of a new type. The cutoff is a phase transition between continuous spacetime before the transition and discontinuous spacetime beyond the phase transition. This quantum creation of spacetime modifies General Relativity and may account for Dark Energy, Dark Matter, and the possible elimination of the singularities of General Relativity. Relations to Causal Set Theory, faithful Lorentzian manifolds, and past and future light cones joined at “Actual Now” are discussed. Possible observational and experimental tests based on: (i). the existence of Sub- Planckian photons, (ii). knee and ankle discontinuities in the high-energy gamma ray spectrum, and (iii). possible experiments to detect a creation of spacetime in the Casimir system are discussed. A quantum actualization enhancement of repulsive Casimir effect would be anti-gravitational and of possible practical use. The ideas and concepts discussed here are not yet a theory, but at most the start of a framework that may be useful. Full article