The existence of time

Of those gauge theories of gravity known to be equivalent to general relativity, only the biconformal gauging introduces new structures - the quotient of the conformal group of any pseudo-Euclidean space by its Weyl subgroup always has natural symplectic and metric structures. Using this metric and symplectic form, we show that there exist canonically conjugate, orthogonal, metric submanifolds if and only if the original gauged space is Euclidean or signature 0. In the Euclidean cases, the resultant configuration space must be Lorentzian. Therefore, in this context, time may be viewed as a derived property of general relativity.Comment: 21 pages (Reduced to clarify and focus on central argument; some calculations condensed; typos corrected

Hidden Dirac Monopoles

Dirac showed that the existence of one magnetic pole in the universe could offer an explanation of the discrete nature of the electric charge. Magnetic poles appear naturally in most grand unified theories. Their discovery would be of greatest importance for particle physics and cosmology. The intense experimental search carried thus far has not met with success. I proposed a universe with magnetic poles which are not observed free because they hide in deeply bound monopole--anti-monopole states named monopolium. I discuss the realization of this proposal and its consistency with known cosmological features. I furthermore analyze its implications and the experimental signatures that confirm the scenario.Comment: Comments: 15 pages, 3 figure

Bubbles created from vacuum fluctuation

We show that the bubbles $S^2\times S^2$can be created from vacuum fluctuation in certain De Sitter universe, so the space-time foam-like structure might really be constructed from bubbles of $S^2\times S^2$ in the very early inflating phase of our universe. But whether such foam-like structure persisted during the later evolution of the universe is a problem unsolved now.Comment: 6 page

Quantum Black Holes as the Link Between Microphysics and Macrophysics

There appears to be a duality between elementary particles, which span the mass range below the Planck scale, and black holes, which span the mass range range above it. In particular, the Black Hole Uncertainty Principle Correspondence posits a smooth transition between the Compton and Schwarzschild scales as a function of mass. This suggests that all black holes are in some sense quantum, that elementary particles can be interpreted as sub-Planckian black holes, and that there is a subtle connection between quantum and classical physics.Comment: 9 pages, 7 figures, 2015 Karl Schwarzschild Meeting on Gravitational Physics, eds. P. Nicolini, J. Mureika, M. Kaminski and M. Bleiche

Time Machine at the LHC

Recently, black hole and brane production at CERN's Large Hadron Collider (LHC) has been widely discussed. We suggest that there is a possibility to test causality at the LHC. We argue that if the scale of quantum gravity is of the order of few TeVs, proton-proton collisions at the LHC could lead to the formation of time machines (spacetime regions with closed timelike curves) which violate causality. One model for the time machine is a traversable wormhole. We argue that the traversable wormhole production cross section at the LHC is of the same order as the cross section for the black hole production. Traversable wormholes assume violation of the null energy condition (NEC) and an exotic matter similar to the dark energy is required. Decay of the wormholes/time machines and signatures of time machine events at the LHC are discussed.Comment: 12 pages, LATEX, comments and references adde

LASSO: Listing All Subset Sums Obediently for Evaluating Unbounded Subset Sums

In this study we present a novel algorithm, LASSO, for solving the unbounded and bounded subset sum problem. The LASSO algorithm was designed to solve the unbounded SSP quickly and to return all subsets summing to a target sum. As speed was the highest priority, we benchmarked the run time performance of LASSO against implementations of some common approaches to the bounded SSP, as well as the only comparable implementation for solving the unbounded SSP that we could find. In solving the bounded SSP, our algorithm had a significantly faster run time than the competing algorithms when the target sum returned at least one subset. When the target returned no subsets, LASSO had a poorer run time growth rate than the competing algorithms solving bounded subset sum. For solving the USSP LASSO was significantly faster than the only comparable algorithm for this problem, both in run time and run time growth rate

Measuring Which-Path Information with Coupled Electronic Mach-Zehnder Interferometers

We theoretically investigate a generalized "which-path" measurement on an electronic Mach-Zehnder Interferometer (MZI) implemented via Coulomb coupling to a second electronic MZI acting as a detector. The use of contextual values, or generalized eigenvalues, enables the precise construction of which-path operator averages that are valid for any measurement strength from the available drain currents. The form of the contextual values provides direct physical insight about the measurement being performed, providing information about the correlation strength between system and detector, the measurement inefficiency, and the proper background removal. We find that the detector interferometer must display maximal wave-like behavior to optimally measure the particle-like which-path information in the system interferometer, demonstrating wave-particle complementarity between the system and detector. We also find that the degree of quantum erasure that can be achieved by conditioning on a specific detector drain is directly related to the ambiguity of the measurement. Finally, conditioning the which-path averages on a particular system drain using the zero frequency cross-correlations produces conditioned averages that can become anomalously large due to quantum interference; the weak coupling limit of these conditioned averages can produce both weak values and detector-dependent semi-weak values.Comment: 17 pages, 12 figures, published version including appendi

Phase Space Formulation of Quantum Mechanics. Insight into the Measurement Problem

A phase space mathematical formulation of quantum mechanical processes accompanied by and ontological interpretation is presented in an axiomatic form. The problem of quantum measurement, including that of quantum state filtering, is treated in detail. Unlike standard quantum theory both quantum and classical measuring device can be accommodated by the present approach to solve the quantum measurement problemComment: 29 pages, 4 figure

NMR implementation of Quantum Delayed-Choice Experiment

We report the first experimental demonstration of quantum delayed-choice experiment via nuclear magnetic resonance techniques. An ensemble of molecules each with two spin-1/2 nuclei are used as target and the ancilla qubits to perform the quantum circuit corresponding the delayed-choice setup. As expected in theory, our experiments clearly demonstrate the continuous morphing of the target qubit between particle-like and wave-like behaviors. The experimental visibility of the interference patterns shows good agreement with the theory.Comment: Revised text, more figures adde

Wigner-Yanase skew information as tests for quantum entanglement

A Bell-type inequality is proposed in terms of Wigner-Yanase skew information, which is quadratic and involves only one local spin observable at each site. This inequality presents a hierarchic classification of all states of multipartite quantum systems from separable to fully entangled states, which is more powerful than the one presented by quadratic Bell inequalities from two-entangled to fully entangled states. In particular, it is proved that the inequality provides an exact test to distinguish entangled from nonentangled pure states of two qubits. Our inequality sheds considerable light on relationships between quantum entanglement and information theory.Comment: 5 page