Spacetime Foam, Holographic Principle, and Black Hole Quantum Computers

Spacetime foam, also known as quantum foam, has its origin in quantum fluctuations of spacetime. Arguably it is the source of the holographic principle, which severely limits how densely information can be packed in space. Its physics is also intimately linked to that of black holes and computation. In particular, the same underlying physics is shown to govern the computational power of black hole quantum computers.Comment: 8 pages, LaTeX; Talk given by Jack Ng, in celebration of Paul Frampton's 60th birthday, at the Coral Gables Conference (in Fort Lauderdale, Florida on December 17, 2003). To appear in the Proceedings of the 2003 Coral Gables Conferenc

Quantum Entanglement and Communication Complexity

We consider a variation of the multi-party communication complexity scenario where the parties are supplied with an extra resource: particles in an entangled quantum state. We show that, although a prior quantum entanglement cannot be used to simulate a communication channel, it can reduce the communication complexity of functions in some cases. Specifically, we show that, for a particular function among three parties (each of which possesses part of the function's input), a prior quantum entanglement enables them to learn the value of the function with only three bits of communication occurring among the parties, whereas, without quantum entanglement, four bits of communication are necessary. We also show that, for a particular two-party probabilistic communication complexity problem, quantum entanglement results in less communication than is required with only classical random correlations (instead of quantum entanglement). These results are a noteworthy contrast to the well-known fact that quantum entanglement cannot be used to actually simulate communication among remote parties.Comment: 10 pages, latex, no figure

Dark matter as integration constant in Horava-Lifshitz gravity

In the non-relativistic theory of gravitation recently proposed by Horava, the Hamiltonian constraint is not a local equation satisfied at each spatial point but an equation integrated over a whole space. The global Hamiltonian constraint is less restrictive than its local version, and allows a richer set of solutions than in general relativity. We show that a component which behaves like pressureless dust emerges as an "integration constant" of dynamical equations and momentum constraint equations. Consequently, classical solutions to the infrared limit of Horava-Lifshitz gravity can mimic general relativity plus cold dark matter.Comment: 16 pages; (non-)conservation equation for "dark matter" added (v2); note added to comment on some recent preprints (v3); version accepted for publication in PRD (v4

Spontaneous Lorentz Breaking and Massive Gravity

We study a theory where the presence of an extra spin-two field coupled to gravity gives rise to a phase with spontaneously broken Lorentz symmetry. In this phase gravity is massive, and the Weak Equivalence Principle is respected. The newtonian potentials are in general modified, but we identify an non-perturbative symmetry that protects them. The gravitational waves sector has a rich phenomenology: sources emit a combination of massless and massive gravitons that propagate with distinct velocities and also oscillate. Since their velocities differ from the speed of light, the time of flight difference between gravitons and photons from a common source could be measured.Comment: 4 page

An integrated optimisation platform for sustainable resource and infrastructure planning

It is crucial for sustainable planning to consider broad environmental and social dimensions and systemic implications of new infrastructure to build more resilient societies, reduce poverty, improve human well-being, mitigate climate change and address other global change processes. This article presents resilience.io, 2 a platform to evaluate new infrastructure projects by assessing their design and effectiveness in meeting growing resource demands, simulated using Agent-Based Modelling due to socio-economic population changes. We then use Mixed-Integer Linear Programming to optimise a multi-objective function to find cost-optimal solutions, inclusive of environmental metrics such as greenhouse gas emissions. The solutions in space and time provide planning guidance for conventional and novel technology selection, changes in network topology, system costs, and can incorporate any material, waste, energy, labour or emissions flow. As an application, a use case is provided for the Water, Sanitation and Hygiene (WASH) sector for a four million people city-region in Ghana

Spatial search by quantum walk

Grover's quantum search algorithm provides a way to speed up combinatorial search, but is not directly applicable to searching a physical database. Nevertheless, Aaronson and Ambainis showed that a database of N items laid out in d spatial dimensions can be searched in time of order sqrt(N) for d>2, and in time of order sqrt(N) poly(log N) for d=2. We consider an alternative search algorithm based on a continuous time quantum walk on a graph. The case of the complete graph gives the continuous time search algorithm of Farhi and Gutmann, and other previously known results can be used to show that sqrt(N) speedup can also be achieved on the hypercube. We show that full sqrt(N) speedup can be achieved on a d-dimensional periodic lattice for d>4. In d=4, the quantum walk search algorithm takes time of order sqrt(N) poly(log N), and in d<4, the algorithm does not provide substantial speedup.Comment: v2: 12 pages, 4 figures; published version, with improved arguments for the cases where the algorithm fail

Bigravity and Lorentz-violating Massive Gravity

Bigravity is a natural arena where a non-linear theory of massive gravity can be formulated. If the interaction between the metrics $f$ and $g$ is non-derivative, spherically symmetric exact solutions can be found. At large distances from the origin, these are generically Lorentz-breaking bi-flat solutions (provided that the corresponding vacuum energies are adjusted appropriately). The spectrum of linearized perturbations around such backgrounds contains a massless as well as a massive graviton, with {\em two} physical polarizations each. There are no propagating vectors or scalars, and the theory is ghost free (as happens with certain massive gravities with explicit breaking of Lorentz invariance). At the linearized level, corrections to GR are proportional to the square of the graviton mass, and so there is no vDVZ discontinuity. Surprisingly, the solution of linear theory for a static spherically symmetric source does {\em not} agree with the linearization of any of the known exact solutions. The latter coincide with the standard Schwarzschild-(A)dS solutions of General Relativity, with no corrections at all. Another interesting class of solutions is obtained where $f$ and $g$ are proportional to each other. The case of bi-de Sitter solutions is analyzed in some detail.Comment: 25 pages. v3 Typos corrected, references added. v4 Introduction extende