2,499 research outputs found
A Topos Foundation for Theories of Physics: III. The Representation of Physical Quantities With Arrows
This paper is the third in a series whose goal is to develop a fundamentally
new way of viewing theories of physics. Our basic contention is that
constructing a theory of physics is equivalent to finding a representation in a
topos of a certain formal language that is attached to the system. In paper II,
we studied the topos representations of the propositional language PL(S) for
the case of quantum theory, and in the present paper we do the same thing for
the, more extensive, local language L(S). One of the main achievements is to
find a topos representation for self-adjoint operators. This involves showing
that, for any physical quantity A, there is an arrow
\breve{\delta}^o(A):\Sig\map\SR, where \SR is the quantity-value object for
this theory. The construction of is an extension of the
daseinisation of projection operators that was discussed in paper II. The
object \SR is a monoid-object only in the topos, , of the theory,
and to enhance the applicability of the formalism, we apply to \SR a topos
analogue of the Grothendieck extension of a monoid to a group. The resulting
object, \kSR, is an abelian group-object in . We also discuss
another candidate, \PR{\mathR}, for the quantity-value object. In this
presheaf, both inner and outer daseinisation are used in a symmetric way.
Finally, there is a brief discussion of the role of unitary operators in the
quantum topos scheme.Comment: 38 pages, no figure
A Topos Foundation for Theories of Physics: IV. Categories of Systems
This paper is the fourth in a series whose goal is to develop a fundamentally
new way of building theories of physics. The motivation comes from a desire to
address certain deep issues that arise in the quantum theory of gravity. Our
basic contention is that constructing a theory of physics is equivalent to
finding a representation in a topos of a certain formal language that is
attached to the system. Classical physics arises when the topos is the category
of sets. Other types of theory employ a different topos. The previous papers in
this series are concerned with implementing this programme for a single system.
In the present paper, we turn to considering a collection of systems: in
particular, we are interested in the relation between the topos representation
for a composite system, and the representations for its constituents. We also
study this problem for the disjoint sum of two systems. Our approach to these
matters is to construct a category of systems and to find a topos
representation of the entire category.Comment: 38 pages, no figure
Correlations of Partial Waves for Multi-Reaction Analyses
In the search for missing baryonic resonances, many analyses include data
from a variety of pion- and photon-induced reactions. For elastic
scattering, however, usually the partial waves of the SAID or other groups are
fitted, instead of data. We provide the partial-wave covariance matrices needed
to perform correlated fits, in which the obtained equals the
actual up non-linear and normalization corrections. For any analysis
relying on partial waves extracted from elastic pion scattering, this is a
prerequisite to assess the significance of resonance signals and to assign any
uncertainty on results. The influence of systematic errors is also considered.Comment: 7 pages, 3 figures; Acknowledgements update
Charge fluctuations and electric mass in a hot meson gas
Net-Charge fluctuations in a hadron gas are studied using an effective
hadronic interaction. The emphasis of this work is to investigate the
corrections of hadronic interactions to the charge fluctuations of a
non-interacting resonance gas. Several methods, such as loop, density and
virial expansions are employed. The calculations are also extended to SU(3) and
some resummation schemes are considered. Although the various corrections are
sizable individually, they cancel to a large extent. As a consequence we find
that charge fluctuations are rather well described by the free resonance gas.Comment: 32 pages, 18 figure
Development of Intra-Individual Value Structures in Middle-Childhood: A Multicultural and Longitudinal Investigation
Introduction
We examined changes in value inter-relations during middle-childhood. In line with the Personal Values Theory (Schwartz, 1992), we expected a value system, with individuals similarly valuing related motivations, and setting priorities between conflicting motivations (Döring et al., 2016; Schwartz, 1992). We hypothesized this system to develop dynamically during middle-childhood, as children deepen their understanding of their own values (Shachnai & Daniel, 2020).
Method
Using unfolding analysis (Borg et al., 2017; Skimina et al., 2021), we estimated intra-individual value structure coherence, i.e., the extent to which the inter-relations among a childâs values are similar to the hypothesized inter-relations. Cross-Cultural Study 1 (N=â4,615 6-12-year-old children) included children from 12 countries. Cross-Sequential Study 2 (N=â629, 6-10-year-old children at Time 1), included three annual measurements.
Results
In Study 1, we found a curvilinear association between age and intra-individual value structure coherence: Childrenâs values were more coherent at ages 9-10 than before or after. Study 2 confirmed this pattern of within-individual development.
Conclusions
We propose that development in coherence with the theoretical value structure offers insight into childrenâs understanding of values as well as changes in value priorities
A Topos Foundation for Theories of Physics: II. Daseinisation and the Liberation of Quantum Theory
This paper is the second in a series whose goal is to develop a fundamentally
new way of constructing theories of physics. The motivation comes from a desire
to address certain deep issues that arise when contemplating quantum theories
of space and time. Our basic contention is that constructing a theory of
physics is equivalent to finding a representation in a topos of a certain
formal language that is attached to the system. Classical physics arises when
the topos is the category of sets. Other types of theory employ a different
topos. In this paper, we study in depth the topos representation of the
propositional language, PL(S), for the case of quantum theory. In doing so, we
make a direct link with, and clarify, the earlier work on applying topos theory
to quantum physics. The key step is a process we term `daseinisation' by which
a projection operator is mapped to a sub-object of the spectral presheaf--the
topos quantum analogue of a classical state space. In the second part of the
paper we change gear with the introduction of the more sophisticated local
language L(S). From this point forward, throughout the rest of the series of
papers, our attention will be devoted almost entirely to this language. In the
present paper, we use L(S) to study `truth objects' in the topos. These are
objects in the topos that play the role of states: a necessary development as
the spectral presheaf has no global elements, and hence there are no
microstates in the sense of classical physics. Truth objects therefore play a
crucial role in our formalism.Comment: 34 pages, no figure
Ramsey interferometry with an atom laser
We present results on a free-space atom interferometer operating on the first
order magnetically insensitive |F=1,mF=0> -> |F=2,mF=0> transition of
Bose-condensed 87Rb atoms. A pulsed atom laser is output-coupled from a
Bose-Einstein condensate and propagates through a sequence of two internal
state beam splitters, realized via coherent Raman transitions between the two
interfering states. We observe Ramsey fringes with a visibility close to 100%
and determine the current and the potentially achievable interferometric phase
sensitivity. This system is well suited to testing recent proposals for
generating and detecting squeezed atomic states.Comment: published version, 8 pages, 3 figure
Pulsed pumping of a Bose-Einstein condensate
In this work, we examine a system for coherent transfer of atoms into a
Bose-Einstein condensate. We utilize two spatially separate Bose-Einstein
condensates in different hyperfine ground states held in the same dc magnetic
trap. By means of a pulsed transfer of atoms, we are able to show a clear
resonance in the timing of the transfer, both in temperature and number, from
which we draw conclusions about the underlying physical process. The results
are discussed in the context of the recently demonstrated pumped atom laser.Comment: 5 pages, 5 figures, published in Physical Review
Equivalent Radar Cross Section: What Is It and Why Is It Important?
The goal of radiometric calibration in synthetic aperture radar (SAR) is to achieve comparability between
measurement results acquired with different systems (e.g. RADARSAT-2 and Sentinel-1), at different times
(e.g. image stacks over many years), or with different system settings (e.g. center frequency or polarization).
At the beginning of the calibration process stands the definition of the measurement quantity. We argue that
the currently accepted measurement quantity for point targets, radar cross section (RCS), is not actually the
quantity that a SAR system measures, and propose to replace the quantity with equivalent radar cross section
(ERCS):
The equivalent radar cross section (ERCS) shall be equal to the radar cross section of a perfectly
conducting sphere which would result in an equivalent pixel intensity if the sphere were to replace
the measured target.
The concept âERCSâ has been introduced before [1]. In this presentation, we attempt to communicate the
problem from different angles to make it more easily comprehensible and to contribute to a discussion in the
CEOS community on a new definition of the radiometric measurement quantity in SAR. These topics are:
âą Mathematical view: By reviewing the basic SAR convolution integral and the definition of RCS it
becomes obvious why RCS cannot be the radiometric measurement quantity in SAR.
âą Historical view: Considering early, comparably low resolution SAR systems with narrow bandwidths
and small angular ranges, it is apparent why RCS has been an acceptable quantity in the past. The
advancement towards higher accuracy and higher resolution systems makes a distinction between
RCS and ERCS paramount though for todayâs and tomorrowâs systems.
âą Comparison with black bodies: The radiation characteristics of certain surfaces are completely
specified if their temperature is known. These black bodies do not exist in nature; they are an
idealization. The blackbody radiation at a given wavelength depends only on the temperature. A
single number (the brightness temperature) is therefore sufficient to summarize the complex Planck
spectrum of a blackbody.
This is similar to a large, perfectly conducting sphere in SAR which is used as an idealized object in the
ERCS definition. A single number (the sphereâs cross sectional area) summarizes its properties.
âą Comparison with stellar photometry: In the 18 th century, different astronomers used different optical
equipment to measure and compare the brightness of stars. Due to varying passbands (transfer
functions) of lenses and photographic film, the results were not comparable. The problem was later
solved by introducing standard photometric systems, where the passbands of the used equipment is
standardized and calibrated.
A comparable interaction exists between a SAR instrument and the measured terrain reflectivity due
to the convolution operation in the processor. This we call the SAR passband problem [2]. We
propose a similar approach to resolve the SAR passband problem by introducing standardized
passbands (weighting/apodization functions at defined bandwidths).
By adopting ERCS as the measurement quantity in the future, calibration and measurement results become
truly compatible across current and future narrow and particularly wideband, high-resolution, and high-
accuracy SAR systems
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