46 research outputs found
The Stern-Gerlach Experiment Revisited
The Stern-Gerlach-Experiment (SGE) of 1922 is a seminal benchmark experiment
of quantum physics providing evidence for several fundamental properties of
quantum systems. Based on today's knowledge we illustrate the different
benchmark results of the SGE for the development of modern quantum physics and
chemistry.
The SGE provided the first direct experimental evidence for angular momentum
quantization in the quantum world and thus also for the existence of
directional quantization of all angular momenta in the process of measurement.
It measured for the first time a ground state property of an atom, it produced
for the first time a `spin-polarized' atomic beam, it almost revealed the
electron spin. The SGE was the first fully successful molecular beam experiment
with high momentum-resolution by beam measurements in vacuum. This technique
provided a new kinematic microscope with which inner atomic or nuclear
properties could be investigated.
The original SGE is described together with early attempts by Einstein,
Ehrenfest, Heisenberg, and others to understand directional quantization in the
SGE. Heisenberg's and Einstein's proposals of an improved multi-stage SGE are
presented. The first realization of these proposals by Stern, Phipps, Frisch
and Segr\`e is described. The set-up suggested by Einstein can be considered an
anticipation of a Rabi-apparatus. Recent theoretical work is mentioned in which
the directional quantization process and possible interference effects of the
two different spin states are investigated.
In full agreement with the results of the new quantum theory directional
quantization appears as a general and universal feature of quantum
measurements. One experimental example for such directional quantization in
scattering processes is shown. Last not least, the early history of the
`almost' discovery of the electron spin in the SGE is revisited.Comment: 50pp, 17 fig
Einstein's quantum theory of the monatomic ideal gas: non-statistical arguments for a new statistics
In this article, we analyze the third of three papers, in which Einstein
presented his quantum theory of the ideal gas of 1924-1925. Although it failed
to attract the attention of Einstein's contemporaries and although also today
very few commentators refer to it, we argue for its significance in the context
of Einstein's quantum researches. It contains an attempt to extend and exhaust
the characterization of the monatomic ideal gas without appealing to
combinatorics. Its ambiguities illustrate Einstein's confusion with his initial
success in extending Bose's results and in realizing the consequences of what
later became to be called Bose-Einstein statistics. We discuss Einstein's
motivation for writing a non-combinatorial paper, partly in response to
criticism by his friend Ehrenfest, and we paraphrase its content. Its arguments
are based on Einstein's belief in the complete analogy between the
thermodynamics of light quanta and of material particles and invoke
considerations of adiabatic transformations as well as of dimensional analysis.
These techniques were well-known to Einstein from earlier work on Wien's
displacement law, Planck's radiation theory, and the specific heat of solids.
We also investigate the possible role of Ehrenfest in the gestation of the
theory.Comment: 57 pp
Knotty-Centrality: Finding the Connective Core of a Complex Network
A network measure called knotty-centrality is defined that quantifies the extent to which a given subset of a graph’s nodes constitutes a densely intra-connected topologically central connective core. Using this measure, the knotty centre of a network is defined as a sub-graph with maximal knotty-centrality. A heuristic algorithm for finding subsets of a network with high knotty-centrality is presented, and this is applied to previously published brain structural connectivity data for the cat and the human, as well as to a number of other networks. The cognitive implications of possessing a connective core with high knotty-centrality are briefly discussed
How Awareness Changes the Relative Weights of Evidence During Human Decision-Making
A combined behavioral and brain imaging study shows how sensory awareness and stimulus visibility can influence the dynamics of decision-making in humans