相关论文: SpaceTime from Hilbert Space: Decompositions of Hi…

We explain why and how the Hilbert space comes about in quantum theory. The axiomatic structures of vector space, of scalar product, of orthogonality, and of the linear functional are derivable from the statistical description of quantum…

As a contribution to the field of quantum mereology, we study how a change of tensor product structure in a finite-dimensional Hilbert space affects its entanglement properties. In particular, we ask whether, given a time-evolving state,…

In a previous effort [arXiv:1708.05492] we have created a framework that explains why topological structures naturally arise within a scientific theory; namely, they capture the requirements of experimental verification. This is…

Space-time measurements and gravitational experiments are made by using objects, matter fields or particles and their mutual relationships. As a consequence, any operationally meaningful assertion about space-time is in fact an assertion…

A deformation of special relativistic kinematics (possible signal of a theory of quantum gravity at low energies) leads to a modification of the notion of spacetime. At the classical level, this modification is required when one considers a…

Any Hilbert space with composite dimension can be factorized into a tensor product of smaller Hilbert spaces. This allows to decompose a quantum system into subsystems. We propose a simple tractable model for a constructive study of…

We propose entanglement entropy as a probe of the architecture of spacetime in quantum gravity. We argue that the leading contribution to this entropy satisfies an area law for any sufficiently large region in a smooth spacetime, which, in…

Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…

Entanglement is defined for each vector subspace of the tensor product of two finite-dimensional Hilbert spaces, by applying the notion of operator entanglement to the projection operator onto that subspace. The operator Schmidt…

We study covariant models for vacuum spherical gravity within a canonical setting. Starting from a general ansatz, we derive the most general family of Hamiltonian constraints that are quadratic in first-order and linear in second-order…

We prove that any complete metric space has a unique decomposition as a direct product of a possibly finite or zero-dimensional Hilbert space and a space that does not split off lines.

Despite the fact that the fundamental physical laws are symmetric in time, most observed processes do not show this symmetry. Especially the phenomenon of decay seems to involve a kind of irreversibility that makes the definition of a…

The space-time disclination is studied by making use of the decomposition theory of gauge potential in terms of antisymmetric tensor field and $\phi$-mapping method. It is shown that the self-dual and anti-self-dual parts of the curvature…

We summarize the arguments that space and time are likely to be emergent notions; i.e. they are not present in the fundamental formulation of the theory, but appear as approximate macroscopic concepts. Along the way we briefly review…

We establish new and different kinds of proofs of properties that arise due to the orthogonal decomposition of the Hilbert space, including projections, over the unit interval of one dimension. We also see angles between functions,…

We study the quantization of geometry in the presence of a cosmological constant, using a discretiza- tion with constant-curvature simplices. Phase space turns out to be compact and the Hilbert space finite dimensional for each link. Not…

The concept of space-evolution (or space-time duality) has emerged as a promising approach for studying quantum dynamics. The basic idea involves exchanging the roles of space and time, evolving the system using a space transfer matrix…

Time is, figuratively and literally, becoming the new dimension for crystalline matter. As such, rapid recent progress on time-varying media gave rise to the notion of temporal and spatiotemporal crystals. Fundamentally rethinking the role…

We consider the relativistic phase space coordinates (x_{\mu},p_{\mu}) as composite, described by functions of the primary pair of twistor coordinates. It appears that if twistor coordinates are canonicaly quantized the composite space-time…

The hilbert-space structure of quantum mechanics is related to the causal structure of space-time. The usual measurement hypotheses apparently preclude nonlinear or stochastic quantum evolution. By admitting a difference in the calculus of…