32,143 research outputs found
Operational quantum theory without predefined time
The standard formulation of quantum theory assumes a predefined notion of
time. This is a major obstacle in the search for a quantum theory of gravity,
where the causal structure of space-time is expected to be dynamical and
fundamentally probabilistic in character. Here, we propose a generalized
formulation of quantum theory without predefined time or causal structure,
building upon a recently introduced operationally time-symmetric approach to
quantum theory. The key idea is a novel isomorphism between transformations and
states which depends on the symmetry transformation of time reversal. This
allows us to express the time-symmetric formulation in a time-neutral form with
a clear physical interpretation, and ultimately drop the assumption of time. In
the resultant generalized formulation, operations are associated with regions
that can be connected in networks with no directionality assumed for the
connections, generalizing the standard circuit framework and the process matrix
framework for operations without global causal order. The possible events in a
given region are described by positive semidefinite operators on a Hilbert
space at the boundary, while the connections between regions are described by
entangled states that encode a nontrivial symmetry and could be tested in
principle. We discuss how the causal structure of space-time could be
understood as emergent from properties of the operators on the boundaries of
compact space-time regions. The framework is compatible with indefinite causal
order, timelike loops, and other acausal structures.Comment: 15 pages, 7 figures, published version (this version covers the
second half of the original submission; the first half has been published
separately and is available at arXiv:1507.07745
Purification of Mixed State with Closed Timelike Curve is not Possible
In ordinary quantum theory any mixed state can be purified in an enlarged
Hilbert space by bringing an ancillary system. The purified state does not
depend on the state of any extraneous system with which the mixed state is
going to interact and on the physical interaction. Here, we prove that it is
not possible to purify a mixed state that traverses a closed time like curve
(CTC) and allowed to interact in a consistent way with a causality-respecting
(CR) quantum system in the same manner. Thus, in general for arbitrary
interactions between CR and CTC systems there is no universal 'Church of the
larger Hilbert space' for mixed states with CTC. This shows that in quantum
theory with CTCs there can exist 'proper' and 'improper' mixtures.Comment: Latex2e, No Figs, 4 + pages, An error corrected, Results unchange
Worlds in the Everett Interpretation
This is a discussion of how we can understand the world-view given to us by
the Everett interpretation of quantum mechanics, and in particular the role
played by the concept of `world'. The view presented is that we are entitled to
use `many-worlds' terminology even if the theory does not specify the worlds in
the formalism; this is defended by means of an extensive analogy with the
concept of an `instant' or moment of time in relativity, with the lack of a
preferred foliation of spacetime being compared with the lack of a preferred
basis in quantum theory. Implications for identity of worlds over time, and for
relativistic quantum mechanics, are discussed.Comment: Latex, 27 pages. To appear in Studies in the History and Philosophy
of Modern Physic
Analytical Models for the Energetics of Cosmic Accretion Shocks, their Cosmological Evolution, and the Effect of Environment
We present an analytical description of the energetics of the population of
cosmic accretion shocks, for a concordance cosmology. We calculate how the
shock-processed accretion power and mass current are distributed among
different shock Mach numbers, and how they evolve with cosmic time. We
calculate the cumulative energy input of cosmic accretion shocks of any Mach
number to the intergalactic medium as a function of redshift, and we compare it
with the energy output of supernova explosions as well as with the energy input
required to reionize the universe. In addition, we investigate and quantify the
effect of environmental factors, such as local clustering properties and
filament preheating on the statistical properties of these shocks. We find that
the energy processed by accretion shocks is higher than the supernova energy
output for z<3 and that it becomes more than an order of magnitude higher in
the local universe. The energy processed by accretion shocks alone becomes
comparable to the energy required to reionize the universe by z~3.5. Finally,
we establish both qualitative and quantitatively that both local clustering as
well as filament compression and preheating are important factors in
determining the statistical properties of the cosmic accretion shock
population.Comment: 13 pages, 5 figures, emulateap
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