Quantum coherence down the wormhole

It is shown that pure quantum states will appear to decay into mixed states in any theory of quantum gravity that allows the topology of spacetime to be non simply connected. The reason is that the final state may contain little closed universes. There is no way one can detect the existence of these closed universes, or measure their quantum state. This means that the part of the final state that is in asymptotically flat spacetime, appears to be in a mixed state. The loss of quantum coherence in particle collisions is estimated. It comes from a wormhole connecting two asymptotically euclidean regions. The effect would be significant for scalar particles. It would make any scalar field that was not coupled to a Yang-Mills field constant throughout spacetime. It could have an important effect on Higgs particles but the effect would be small for particles of higher spin.     

Spacetime path formalism for massive particles of any spin

Earlier work presented spacetime path formalism for relativistic quantum mechanics arising naturally from the fundamental principles of the Born probability rule, superposition, and spacetime translation invariance. The resulting formalism can be seen as a foundation for a number of previous parametrized approaches to relativistic quantum mechanics in the literature. Because time is treated similarly to the three-space coordinates, rather than as an evolution parameter, such approaches have proved particularly useful in the study of quantum gravity and cosmology. The present paper extends the foundational spacetime path formalism to include massive, non-scalar particles of any (integer or half-integer) spin. This is done by generalizing the principle of translational invariance used in the scalar case to the principle of full Poincaré invariance, leading to a formulation for the non-scalar propagator in terms of a path integral over the Poincaré group. Once the difficulty of the non-compactness of the component Lorentz group is dealt with, the subsequent development is remarkably parallel to the scalar case. This allows the formalism to retain a clear probabilistic interpretation throughout, with a natural reduction to non-relativistic quantum mechanics closely related to the well-known generalized Foldy-Wouthuysen transformation.     

Poincaré Covariance of Relativistic Quantum Position

A great number of problems of relativistic position in quantum mechanics are because of the use of coordinates that are not inherent objects of spacetime, cause unnecessary complications, and can lead to misconceptions. We apply a coordinate-free approach to rule out such problems. Thus it will be clear, for example, that the Lorentz covariance of position, required usually on the analogy of Lorentz covariance of spacetime coordinates, is not well posed and we show that in a right setting the Newton–Wigner position is Poincaré covariant.     

Tunneling through bridges: Bohmian non-locality from higher-derivative gravity

A classical origin for the Bohmian quantum potential, as that potential term arises in the quantum mechanical treatment of black holes and Einstein–Rosen (ER) bridges, can be based on 4th-order extensions of Einstein's equations. The required 4th-order extension of general relativity is given by adding quadratic curvature terms with coefficients that maintain a fixed ratio, as their magnitudes approach zero, with classical general relativity as a singular limit. If entangled particles are connected by a Planck-width ER bridge, as conjectured by Maldacena and Susskind, then a connection by a traversable Planck-scale wormhole, allowed in 4th-order gravity, describes such entanglement in the ontological interpretation. It is hypothesized that higher-derivative gravity can account for the nonlocal part of the quantum potential generally.     

Nondifferentiable Dynamic: Two Examples

Some nondifferentiable quantities (for example, the metric signature) can be the independent physical degrees of freedom. It is supposed that in quantum gravity these degrees of freedom can fluctuate. Two examples of such quantum fluctuation are considered: a quantum interchange of the sign of two components of the 5D metric and a quantum fluctuation between Euclidean and Lorentzian metrics. The first case leads to a spin-like structure on the throat of a composite wormhole and to a possible inner structure of the string. The second case leads to a quantum birth of the non-singular Euclidean Universe with frozen 5^th dimension. The probability for such quantum fluctuations is connected with an algorithmical complexity of the Einstein equations.     

Spherically Symmetric Wormhole Gravitational Lens Deflection Angle Signifying Braneworld Cosmology

Previously, the gravitational lens of a wormhole was introduced by various researchers. Their treatment was focused basically on the lens signature that describes wormhole geometrical character such as the differences from a black hole or between any various types of wormhole models. The braneworld scenario provides the idea of spacetime with underlying extra-dimensions. The inclusion of extra-dimensional terms in the lens object spacetime line element will result in some variation in the expression for its gravitational lens deflection angle.Thus in this paper we investigate such variation by deriving this deflection angle expression. As such, this paper not only shows the existence of such variation but also suggests the potential utilization of gravitational lensing to prove the existence of extra dimensions by studying the deflection angle characteristic in accordance with the spacetime expansion rate of the universe.     

Curved traversable wormholes in (3+1)-dimensional spacetime

We present the general method of constructing curved traversable wormholes in (3+1)-d spacetime and proceed to thoroughly discuss the physics of a zero tidal force metric without cross-terms. The (3+1)-d solution is compared with the recently studied lower-dimensional counterpart, where we identify that the much richer physics—involving pressures and shear forces of the mass-energy fluid supporting the former—is attributed to the mixing of all three spatial coordinates. Our (3+1)-d universe is the lowest dimension where such nontrivial terms appear. An explicit example, the static zero tidal force (3+1)-d catenary wormhole is analysed and we show the existence of a geodesic through it supported locally by non-exotic matter, similar to the (2+1)-d version. A key difference is that positive mass-energy is used to support the entire (3+1)-d catenary wormhole, though violation of the null energy condition in certain regions is inevitable. This general approach of first constructing the geometry of the spacetime and then using the field equations to determine the physics to support it has the potential to discover new solutions in general relativity or to generalise existing ones. For instance, the metric of a time-evolving inflationary wormhole with a conformal factor can actually be geometrically constructed using our method.     

Λ and the Heisenberg Principle

A time dependent “cosmological constant” Λ(t) is conjectured, in terms of the Gaussian curvature of the causal horizon. It is nonvanishing even in Minkowski space because of the lack of informations beyond the light cone. Using the Heisenberg Principle, the corresponding energy of the quantum fluctuations localized on the past or future null horizons is proportional to Λ^1/2. We compute Λ(t) for the (Lorenzian version) of the (conformally flat) Hawking wormhole geometry (written in static spherical Rindler coordinates) and for the de Sitter spacetime. A possible explanation of the Hawking temperature is proposed, in terms of a constant Λ.     

Reconciling Spacetime and the Quantum: Relational Blockworld and the Quantum Liar Paradox

The Relational Blockworld (RBW) interpretation of non-relativistic quantum mechanics (NRQM) is introduced. Accordingly, the spacetime of NRQM is a relational, non-separable blockworld whereby spatial distance is only defined between interacting trans-temporal objects. RBW is shown to provide a novel statistical interpretation of the wavefunction that deflates the measurement problem, as well as a geometric account of quantum entanglement and non-separability that satisfies locality per special relativity and is free of interpretative mystery. We present RBW’s acausal and adynamical resolution of the so-called “quantum liar paradox,” an experimental set-up alleged to be problematic for a spacetime conception of reality, and conclude by speculating on RBW’s implications for quantum gravity.     

Foliation of the Kottler–Schwarzschild–de Sitter spacetime by flat spacelike hypersurfaces

There exist Kruskal like coordinates for the Reissner–Nordstrom (RN) black hole spacetime which are regular at coordinate singularities. Non-existence of such coordinates for the extreme RN black hole spacetime has already been shown. Also the Carter coordinates available for the extreme case are not manifestly regular at the coordinate singularity, therefore, a numerical procedure was developed to obtain free fall geodesics and flat foliation for the extreme RN black hole spacetime. The Kottler–Schwarzschild–de Sitter (KSSdS) spacetime geometry is similar to the RN geometry in the sense that, like the RN case, there exist non-singular coordinates when there are two distinct coordinate singularities. There are no manifestly regular coordinates for the extreme KSSdS case. In this paper foliation of all the cases of the KSSdS spacetime by flat spacelike hypersurfaces is obtained by introducing a non-singular time coordinate.     

Faster than Hermitian quantum mechanics

Given an initial quantum state |psi(I)> and a final quantum state |psi(F)>, there exist Hamiltonians H under which |psi(I)> evolves into |psi(F)>. Consider the following quantum brachistochrone problem: subject to the constraint that the difference between the largest and smallest eigenvalues of H is held fixed, which H achieves this transformation in the least time tau? For Hermitian Hamiltonians tau has a nonzero lower bound. However, among non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, tau can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from |psi(I)> to |psi(F)> can be made short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing.     

Wormhole solutions in Gauss–Bonnet–Born–Infeld gravity

A new class of solutions which yields an (n + 1)-dimensional spacetime with a longitudinal nonlinear magnetic field is introduced. These spacetimes have no curvature singularity and no horizon, and the magnetic field is non singular in the whole spacetime. They may be interpreted as traversable wormholes which could be supported by matter not violating the weak energy conditions. We generalize this class of solutions to the case of rotating solutions and show that the rotating wormhole solutions have a net electric charge which is proportional to the magnitude of the rotation parameter, while the static wormhole has no net electric charge. Finally, we use the counterterm method and compute the conserved quantities of these spacetimes.     

Quantum Gravity If Non-Locality Is Fundamental

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.     

Fidelity for States of Spin- \frac{1}{2} Particles Moving in a Traversable Wormhole Spacetime

Fidelity for states of spin- particles moving in a static spherically symmetric traversable wormhole spacetime is discussed. When the centroid of the corresponding wave packet moves along a specified path in the gravitational field, both acceleration and gravity cause to transform the state of the particle. For circular orbits of the centroid coinciding the throat of wormhole, the fidelity between initial and final states of the whole system as well as the fidelity of the spin parts of the states are equal to the unity. This means that, the error in quantum communication diminishes on such a paths. For fixed elapsed proper time and angular momentum of the centroid, there always exists one circular orbit with determined radius on which the fidelity of spin parts is minimum. The fidelity for wave packets moving along a radial geodesic toward the throat of wormhole is also discussed. In this case, the centroid traverses the wormhole and reaches to the other side, with a perfect fidelity for the spin parts, though the fidelity for the states of the whole system is not perfect.     

Glafka 2004: Generalizing Quantum Mechanics for Quantum Gravity

Familiar quantum mechanics assumes a fixed spacetime geometry. Quantummechanics must therefore be generalized for quantum gravity where spacetime geometry is not fixed but rather a quantum variable. This extended abstract sketches a fully fourdimensional generalized quantum mechnics of cosmological spacetime geometries that is one such generalization.This contribution to the proceedings of the Glafka Conference is an extended abstract of the author's talk there. More details can be found in the references cited at the end of the abstract expecially (Hartle, 1995).