469,958 research outputs found
Quantum cellular automata and free quantum field theory
In a series of recent papers it has been shown how free quantum field theory
can be derived without using mechanical primitives (including space-time,
special relativity, quantization rules, etc.), but only considering the easiest
quantum algorithm encompassing a countable set of quantum systems whose network
of interactions satisfies the simple principles of unitarity, homogeneity,
locality, and isotropy. This has opened the route to extending the axiomatic
information-theoretic derivation of the quantum theory of abstract systems to
include quantum field theory. The inherent discrete nature of the informational
axiomatization leads to an extension of quantum field theory to a quantum
cellular automata theory, where the usual field theory is recovered in a regime
where the discrete structure of the automata cannot be probed. A simple
heuristic argument sets the scale of discreteness to the Planck scale, and the
customary physical regime where discreteness is not visible is the relativistic
one of small wavevectors. In this paper we provide a thorough derivation from
principles that in the most general case the graph of the quantum cellular
automaton is the Cayley graph of a finitely presented group, and showing how
for the case corresponding to Euclidean emergent space (where the group resorts
to an Abelian one) the automata leads to Weyl, Dirac and Maxwell field dynamics
in the relativistic limit. We conclude with some perspectives towards the more
general scenario of non-linear automata for interacting quantum field theory.Comment: 10 pages, 2 figures, revtex style. arXiv admin note: substantial text
overlap with arXiv:1601.0483
Physics Without Physics: The Power of Information-theoretical Principles
David Finkelstein was very fond of the new information-theoretic paradigm of
physics advocated by John Archibald Wheeler and Richard Feynman. Only recently,
however, the paradigm has concretely shown its full power, with the derivation
of quantum theory (Chiribella et al., Phys. Rev. A 84:012311, 2011; D'Ariano et
al., 2017) and of free quantum field theory (D'Ariano and Perinotti, Phys. Rev.
A 90:062106, 2014; Bisio et al., Phys. Rev. A 88:032301, 2013; Bisio et al.,
Ann. Phys. 354:244, 2015; Bisio et al., Ann. Phys. 368:177, 2016) from
informational principles. The paradigm has opened for the first time the
possibility of avoiding physical primitives in the axioms of the physical
theory, allowing a refoundation of the whole physics over logically solid
grounds. In addition to such methodological value, the new
information-theoretic derivation of quantum field theory is particularly
interesting for establishing a theoretical framework for quantum gravity, with
the idea of obtaining gravity itself as emergent from the quantum information
processing, as also suggested by the role played by information in the
holographic principle (Susskind, J. Math. Phys. 36:6377, 1995; Bousso, Rev.
Mod. Phys. 74:825, 2002). In this paper I review how free quantum field theory
is derived without using mechanical primitives, including space-time, special
relativity, Hamiltonians, and quantization rules. The theory is simply provided
by the simplest quantum algorithm encompassing a countable set of quantum
systems whose network of interactions satisfies the three following simple
principles: homogeneity, locality, and isotropy. The inherent discrete nature
of the informational derivation leads to an extension of quantum field theory
in terms of a quantum cellular automata and quantum walks. A simple heuristic
argument sets the scale to the Planck one, and the observed regime is that of
small wavevectors ...Comment: 34 pages, 8 figures. Paper for in memoriam of David Finkelstei
Newtonian Quantum Gravity
Puts forward a complete scenario for interpreting nonlinear field theories
highlighting the role played by gravitational self--energy in enabling a
consistent revival of the Schroedinger approach to unifying micro and macro
physics.Comment: 38 pages, RevTex. Uses epsf. Five "tar.gz" compressed PostScipt
figures included separatel
The principle of relative locality
We propose a deepening of the relativity principle according to which the
invariant arena for non-quantum physics is a phase space rather than spacetime.
Descriptions of particles propagating and interacting in spacetimes are
constructed by observers, but different observers, separated from each other by
translations, construct different spacetime projections from the invariant
phase space. Nonetheless, all observers agree that interactions are local in
the spacetime coordinates constructed by observers local to them.
This framework, in which absolute locality is replaced by relative locality,
results from deforming momentum space, just as the passage from absolute to
relative simultaneity results from deforming the linear addition of velocities.
Different aspects of momentum space geometry, such as its curvature, torsion
and non-metricity, are reflected in different kinds of deformations of the
energy-momentum conservation laws. These are in principle all measurable by
appropriate experiments. We also discuss a natural set of physical hypotheses
which singles out the cases of momentum space with a metric compatible
connection and constant curvature.Comment: 12 pages, 3 figures; in version 2 one reference added and some minor
modifications in sects. II and III mad
Lorentz invariance with an invariant energy scale
We propose a modification of special relativity in which a physical energy,
which may be the Planck energy, joins the speed of light as an invariant, in
spite of a complete relativity of inertial frames and agreement with Einstein's
theory at low energies. This is accomplished by a non-linear modification of
the action of the Lorentz group on momentum space, generated by adding a
dilatation to each boost in such a way that the Planck energy remains
invariant. The associated algebra has unmodified structure constants, and we
highlight the similarities between the group action found and a transformation
previously proposed by Fock. We also discuss the resulting modifications of
field theory and suggest a modification of the equivalence principle which
determines how the new theory is embedded in general relativity
What is General Relativity?
General relativity is a set of physical and geometric principles, which lead
to a set of (Einstein) field equations that determine the gravitational field,
and to the geodesic equations that describe light propagation and the motion of
particles on the background. But open questions remain, including: What is the
scale on which matter and geometry are dynamically coupled in the Einstein
equations? Are the field equations valid on small and large scales? What is the
largest scale on which matter can be coarse grained while following a geodesic
of a solution to Einstein's equations? We address these questions. If the field
equations are causal evolution equations, whose average on cosmological scales
is not an exact solution of the Einstein equations, then some simplifying
physical principle is required to explain the statistical homogeneity of the
late epoch Universe. Such a principle may have its origin in the dynamical
coupling between matter and geometry at the quantum level in the early
Universe. This possibility is hinted at by diverse approaches to quantum
gravity which find a dynamical reduction to two effective dimensions at high
energies on one hand, and by cosmological observations which are beginning to
strongly restrict the class of viable inflationary phenomenologies on the
other. We suggest that the foundational principles of general relativity will
play a central role in reformulating the theory of spacetime structure to meet
the challenges of cosmology in the 21st century.Comment: 18 pages. Invited article for Physica Scripta Focus issue on 21st
Century Frontiers. v2: Appendix amended, references added. v3: Small
corrections, references added, matches published versio
Defect Formation and Critical Dynamics in the Early Universe
We study the nonequilibrium dynamics leading to the formation of topological
defects in a symmetry-breaking phase transition of a quantum scalar field with
\lambda\Phi^4 self-interaction in a spatially flat, radiation-dominated
Friedmann-Robertson-Walker Universe. The quantum field is initially in a
finite-temperature symmetry-restored state and the phase transition develops as
the Universe expands and cools. We present a first-principles, microscopic
approach in which the nonperturbative, nonequilibrium dynamics of the quantum
field is derived from the two-loop, two-particle-irreducible closed-time-path
effective action. We numerically solve the dynamical equations for the
two-point function and we identify signatures of topological defects in the
infrared portion of the momentum-space power spectrum. We find that the density
of topological defects formed after the phase transition scales as a power law
with the expansion rate of the Universe. We calculate the equilibrium critical
exponents of the correlation length and relaxation time for this model and show
that the power law exponent of the defect density, for both overdamped and
underdamped evolution, is in good agreement with the "freeze-out" scenario of
Zurek. We introduce an analytic dynamical model, valid near the critical point,
that exhibits the same power law scaling of the defect density with the quench
rate. By incorporating the realistic quench of the expanding Universe, our
approach illuminates the dynamical mechanisms important for topological defect
formation. The observed power law scaling of the defect density with the quench
rate, observered here in a quantum field theory context, provides evidence for
the "freeze-out" scenario in three spatial dimensions.Comment: 31 pages, RevTex, 8 figures in EPS forma
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