160 research outputs found
Spacetime topology from the tomographic histories approach: Part II
As an inverse problem, we recover the topology of the effective spacetime
that a system lies in, in an operational way. This means that from a series of
experiments we get a set of points corresponding to events. This continues the
previous work done by the authors. Here we use the existence of upper bound in
the speed of transfer of matter and information to induce a partial order on
the set of events. While the actual partial order is not known in our
operational set up, the grouping of events to (unordered) subsets corresponding
to possible histories, is given. From this we recover the partial order up to
certain ambiguities that are then classified. Finally two different ways to
recover the topology are sketched and their interpretation is discussed.Comment: 21 pages, slight change in title and certain minor corrections in
this second version. To apear in IJT
Spacetime topology from the tomographic histories approach I: Non-relativistic Case
The tomographic histories approach is presented. As an inverse problem, we
recover in an operational way the effective topology of the extended
configuration space of a system. This means that from a series of experiments
we get a set of points corresponding to events. The difference between
effective and actual topology is drawn. We deduce the topology of the extended
configuration space of a non-relativistic system, using certain concepts from
the consistent histories approach to Quantum Mechanics, such as the notion of a
record. A few remarks about the case of a relativistic system, preparing the
ground for a forthcoming paper sequel to this, are made in the end.Comment: 19 pages, slight chang in title and corrected typos in second
version. To appear to a special proceedings issue (Glafka 2004) of the
International Journal of Theoretical Physic
Causal Sets: Quantum gravity from a fundamentally discrete spacetime
In order to construct a quantum theory of gravity, we may have to abandon
certain assumptions we were making. In particular, the concept of spacetime as
a continuum substratum is questioned. Causal Sets is an attempt to construct a
quantum theory of gravity starting with a fundamentally discrete spacetime. In
this contribution we review the whole approach, focusing on some recent
developments in the kinematics and dynamics of the approach.Comment: 10 pages, review of causal sets based on talk given at the 1st MCCQG
conferenc
Dynamics & Predictions in the Co-Event Interpretation
Sorkin has introduced a new, observer independent, interpretation of quantum
mechanics that can give a successful realist account of the 'quantum
microworld' as well as explaining how classicality emerges at the level of
observable events for a range of systems including single time 'Copenhagen
measurements'. This 'co-event interpretation' presents us with a new ontology,
in which a single 'co-event' is real. A new ontology necessitates a review of
the dynamical & predictive mechanism of a theory, and in this paper we begin
the process by exploring means of expressing the dynamical and predictive
content of histories theories in terms of co-events.Comment: 35 pages. Revised after refereein
Distinguishing Initial State-Vectors from Each Other in Histories Formulations and the PBR Argument
Following the argument of Pusey, Barrett and Rudolph (Nature Phys. 8:476,
2012), new interest has been raised on whether one can interpret state-vectors
(pure states) in a statistical way (-epistemic theories), or if each of
them corresponds to a different ontological entity. Each interpretation of
quantum theory assumes different ontology and one could ask if the PBR argument
carries over. Here we examine this question for histories formulations in
general with particular attention to the co-event formulation. State-vectors
appear as the initial state that enters into the quantum measure. While the PBR
argument goes through up to a point, the failure to meet some of the
assumptions they made does not allow one to reach their conclusion. However,
the author believes that the "statistical interpretation" is still impossible
for co-events even if this is not proven by the PBR argument.Comment: 25 pages, v2 published versio
Spacetime Coarse Grainings in the Decoherent Histories Approach to Quantum Theory
We investigate the possibility of assigning consistent probabilities to sets
of histories characterized by whether they enter a particular subspace of the
Hilbert space of a closed system during a given time interval. In particular we
investigate the case that this subspace is a region of the configuration space.
This corresponds to a particular class of coarse grainings of spacetime
regions. We consider the arrival time problem and the problem of time in
reparametrization invariant theories as for example in canonical quantum
gravity. Decoherence conditions and probabilities for those application are
derived. The resulting decoherence condition does not depend on the explicit
form of the restricted propagator that was problematic for generalizations such
as application in quantum cosmology. Closely related is the problem of
tunnelling time as well as the quantum Zeno effect. Some interpretational
comments conclude, and we discuss the applicability of this formalism to deal
with the arrival time problem.Comment: 23 pages, Few changes and added references in v
Spacelike distance from discrete causal order
Any discrete approach to quantum gravity must provide some prescription as to
how to deduce continuum properties from the discrete substructure. In the
causal set approach it is straightforward to deduce timelike distances, but
surprisingly difficult to extract spacelike distances, because of the unique
combination of discreteness with local Lorentz invariance in that approach. We
propose a number of methods to overcome this difficulty, one of which
reproduces the spatial distance between two points in a finite region of
Minkowski space. We provide numerical evidence that this definition can be used
to define a `spatial nearest neighbor' relation on a causal set, and conjecture
that this can be exploited to define the length of `continuous curves' in
causal sets which are approximated by curved spacetime. This provides evidence
in support of the ``Hauptvermutung'' of causal sets.Comment: 32 pages, 16 figures, revtex4; journal versio
The Generalized Second Law implies a Quantum Singularity Theorem
The generalized second law can be used to prove a singularity theorem, by
generalizing the notion of a trapped surface to quantum situations. Like
Penrose's original singularity theorem, it implies that spacetime is null
geodesically incomplete inside black holes, and to the past of spatially
infinite Friedmann--Robertson--Walker cosmologies. If space is finite instead,
the generalized second law requires that there only be a finite amount of
entropy producing processes in the past, unless there is a reversal of the
arrow of time. In asymptotically flat spacetime, the generalized second law
also rules out traversable wormholes, negative masses, and other forms of
faster-than-light travel between asymptotic regions, as well as closed timelike
curves. Furthermore it is impossible to form baby universes which eventually
become independent of the mother universe, or to restart inflation. Since the
semiclassical approximation is used only in regions with low curvature, it is
argued that the results may hold in full quantum gravity. An introductory
section describes the second law and its time-reverse, in ordinary and
generalized thermodynamics, using either the fine-grained or the coarse-grained
entropy. (The fine-grained version is used in all results except those relating
to the arrow of time.) A proof of the coarse-grained ordinary second law is
given.Comment: 46 pages, 8 figures. v2: discussion of global hyperbolicity revised
(4.1, 5.2), more comments on AdS. v3: major revisions including change of
title. v4: similar to published version, but with corrections to plan of
paper (1) and definition of global hyperbolicity (3.2). v5: fixed proof of
Thm. 1, changed wording of Thm. 3 & proof of Thm. 4, revised Sec. 5.2, new
footnote
Efficient and Secure Delegation of Exponentiation in General Groups to a Single Malicious Server
Group exponentiation is an important and relatively expensive operation used in many public-key cryptosystems and, more generally, cryptographic protocols. To expand the applicability of these solutions to computationally weaker devices, it has been advocated that this operation is delegated from a computationally weaker client to a computationally stronger server. Solving this problem in the case of a single, possibly malicious, server, has remained open since the introduction of a formal model. In previous work we have proposed practical and secure solutions applicable to two classes of specific groups, related to well-known cryptosystems. In this paper, we investigate this problem in a general class of multiplicative groups, possibly going beyond groups currently subject to quantum cryptanalysis attacks. Our main results are efficient delegation protocols for exponentiation in these general groups. The main technique in our results is a reduction of the protocol's security probability (i.e., the probability that a malicious server convinces a client of an incorrect exponentiation output) that is more efficient than by standard parallel repetition. The resulting protocols satisfy natural requirements such as correctness, security, privacy and efficiency, even if the adversary uses the full power of quantum computers. In particular, in our protocols the client performs a number of online group multiplications smaller by 1 to 2 orders of magnitude than in a non-delegated computation
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