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Using simple elastic bands to explain quantum mechanics: a conceptual review of two of Aert's machine-models
From the beginning of his research, the Belgian physicist Diederik Aerts has
shown great creativity in inventing a number of concrete machine-models that
have played an important role in the development of general mathematical and
conceptual formalisms for the description of the physical reality. These models
can also be used to demystify much of the strangeness in the behavior of
quantum entities, by allowing to have a peek at what's going on - in structural
terms - behind the "quantum scenes," during a measurement. In this author's
view, the importance of these machine-models, and of the approaches they have
originated, have been so far seriously underappreciated by the physics
community, despite their success in clarifying many challenges of quantum
physics. To fill this gap, and encourage a greater number of researchers to
take cognizance of the important work of so-called Geneva-Brussels school, we
describe and analyze in this paper two of Aerts' historical machine-models,
whose operations are based on simple breakable elastic bands. The first one,
called the spin quantum-machine, is able to replicate the quantum probabilities
associated with the spin measurement of a spin-1/2 entity. The second one,
called the \emph{connected vessels of water model} (of which we shall present
here an alternative version based on elastics) is able to violate Bell's
inequality, as coincidence measurements on entangled states can do.Comment: 15 pages, 5 figure
Interferometers as Probes of Planckian Quantum Geometry
A theory of position of massive bodies is proposed that results in an
observable quantum behavior of geometry at the Planck scale, . Departures
from classical world lines in flat spacetime are described by Planckian
noncommuting operators for position in different directions, as defined by
interactions with null waves. The resulting evolution of position wavefunctions
in two dimensions displays a new kind of directionally-coherent quantum noise
of transverse position. The amplitude of the effect in physical units is
predicted with no parameters, by equating the number of degrees of freedom of
position wavefunctions on a 2D spacelike surface with the entropy density of a
black hole event horizon of the same area. In a region of size , the effect
resembles spatially and directionally coherent random transverse shear
deformations on timescale with typical amplitude . This quantum-geometrical "holographic noise" in position is not
describable as fluctuations of a quantized metric, or as any kind of
fluctuation, dispersion or propagation effect in quantum fields. In a Michelson
interferometer the effect appears as noise that resembles a random Planckian
walk of the beamsplitter for durations up to the light crossing time. Signal
spectra and correlation functions in interferometers are derived, and predicted
to be comparable with the sensitivities of current and planned experiments. It
is proposed that nearly co-located Michelson interferometers of laboratory
scale, cross-correlated at high frequency, can test the Planckian noise
prediction with current technology.Comment: 23 pages, 6 figures, Latex. To appear in Physical Review
Relating Theories via Renormalization
The renormalization method is specifically aimed at connecting theories
describing physical processes at different length scales and thereby connecting
different theories in the physical sciences.
The renormalization method used today is the outgrowth of one hundred and
fifty years of scientific study of thermal physics and phase transitions.
Different phases of matter show qualitatively different behavior separated by
abrupt phase transitions. These qualitative differences seem to be present in
experimentally observed condensed-matter systems. However, the "extended
singularity theorem" in statistical mechanics shows that sharp changes can only
occur in infinitely large systems. Abrupt changes from one phase to another are
signaled by fluctuations that show correlation over infinitely long distances,
and are measured by correlation functions that show algebraic decay as well as
various kinds of singularities and infinities in thermodynamic derivatives and
in measured system parameters.
Renormalization methods were first developed in field theory to get around
difficulties caused by apparent divergences at both small and large scales.
The renormalization (semi-)group theory of phase transitions was put together
by Kenneth G. Wilson in 1971 based upon ideas of scaling and universality
developed earlier in the context of phase transitions and of couplings
dependent upon spatial scale coming from field theory. Correlations among
regions with fluctuations in their order underlie renormalization ideas.
Wilson's theory is the first approach to phase transitions to agree with the
extended singularity theorem.
Some of the history of the study of these correlations and singularities is
recounted, along with the history of renormalization and related concepts of
scaling and universality. Applications are summarized.Comment: This note is partially a summary of a talk given at the workshop
"Part and Whole" in Leiden during the period March 22-26, 201
Gravity as an emergent phenomenon: a GFT perspective
While the idea of gravity as an emergent phenomenon is an intriguing one,
little is known about concrete implementations that could lead to viable
phenomenology, most of the obstructions being related to the intrinsic
difficulties of formulating genuinely pregeometric theories. In this paper we
present a preliminary discussion of the impact of critical behavior of certain
microscopic models for gravity, based on group field theories, on the dynamics
of the macroscopic regime. The continuum limit is examined in light of some
scaling assumption, and the relevant consequences for low energy effective
theories are discussed, the role of universality, the corrections to scaling,
the emergence of gravitational theories and the nature of their thermodynamical
behavior.Comment: 1+26 page
Four-dimensional understanding of quantum mechanics and Bell violation
While our natural intuition suggests us that we live in 3D space evolving in
time, modern physics presents fundamentally different picture: 4D spacetime,
Einstein's block universe, in which we travel in thermodynamically emphasized
direction: arrow of time. Suggestions for such nonintuitive and nonlocal living
in kind of "4D jello" come among others from: Lagrangian mechanics we use from
QFT to GR saying that history between fixed past and future situation is the
one optimizing action, special relativity saying that different velocity
observers have different present 3D hypersurface and time direction, general
relativity deforming shape of the entire spacetime up to switching time and
space below the black hole event horizon, or the CPT theorem concluding
fundamental symmetry between past and future.
Accepting this nonintuitive living in 4D spacetime: with present moment being
in equilibrium between past and future - minimizing tension as action of
Lagrangian, leads to crucial surprising differences from intuitive "evolving
3D" picture, in which we for example conclude satisfaction of Bell inequalities
- violated by the real physics. Specifically, particle in spacetime becomes own
trajectory: 1D submanifold of 4D, making that statistical physics should
consider ensembles like Boltzmann distribution among entire paths, what leads
to quantum behavior as we know from Feynman's Euclidean path integrals or
similar Maximal Entropy Random Walk (MERW). It results for example in Anderson
localization, or the Born rule with squares - allowing for violation of Bell
inequalities. Specifically, quantum amplitude turns out to describe probability
at the end of half-spacetime from a given moment toward past or future, to
randomly get some value of measurement we need to "draw it" from both time
directions, getting the squares of Born rules.Comment: 13 pages, 18 figure
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