Gedanken experiments

The gedanken" experiment in Section 3 4.4.2 results in equation 3.4.4-2 suggesting the operations of summation and multiplication in the algebraic sense - not as probabilities. Since this is a simulation why are not the results correct until given the probability interpretation Hint refer to the Venn Diagram discussion (Section 2.2)... 

The presence of this backspillover formed effective double layer is important not only for interpreting the effect of electrochemical promotion, but also for understanding the similarity of solid state electrochemistry depicted in Fig. 7.3 with the case of emersed electrodes in aqueous electrochemistry (Fig. 7.2) and with the gedanken experiment of Trasatti (Fig. 7.1) where one may consider that H2O spillovers on the metal surface. This conceptual similarity also becomes apparent from the experimental results. 

This uncertainty is an inescapable fact of the world we live in, which is illustrated beautifully by the following gedanken experiment suggested by Bohr. Suppose we wish to measure the position of a stationary electron using a microscope as shown in Fig. 2.6. Then from optics the resolution of the microscope will be given by... 

Fig. 2.6 Schematic illustration of Bohr s gedanken experiment. The scattering triangle relates the uncertainty in the momentum of the scattered photon, px, to the angle subtended by the aperture, 0, and momentum, p, of the photon.

In order to calculate the Gibbs free energy of a Gouy-Chapman layer we split its formation into three steps [66,67], In reality it is not possible to do these steps separately but we can do the Gedanken experiment without violating any physical principle. 

We have derived a formula for the molecular partition function by considering a system containing many molecules at equilibrium with a heat bath. We can generalize our statistical mechanics by a gedanken experiment of considering a large number of identical systems, each with volume V and number of particles N at equilibrium with the heat bath at temperature T. Such a supersystem is called a canonical ensemble. Our derivation is the same the fraction of systems that are in a state with energy Et is... 

V. Jacques, E. Wu, F. Grosshans, F. Treussart, Ph. Grangier, A. Aspect, et al., Experimental realization of Wheeler s delayed-choice gedanken experiment, Science 315 (2007) 966-968. 

The EPR effect was demonstrated in terms of a Gedanken experiment to show that quantum systems which became correlated at any time, would stay correlated until the combined system is disturbed by measurement. Two principles of fundamental importance are assumed in this analysis ... 

Cosmoarcheology considers the results of observational cosmology as the sample of the experimental data on the possible existence and features of hypothetical phenomena predicted by particle theory. To undertake the Gedanken Experiment with these phenomena some theoretical framework to treat their origin and evolution in the Universe should be assumed. As it was pointed out in [6] the choice of such framework is a nontrivial problem in the modern cosmology. 

However small the structures under study are, the STM tip always consists of atoms, which have a finite dimension. Hence, the structure of the tip has an influence of what is observed with STM. If one assumes in a Gedanken-experiment that an infinitesimally sharp object is standing on the surface (mathematically a delta-function), then the tip will be convoluted at the object (Fig. 10.16, far right) and visible in the STM image will be the front most tip-end (up-side down) and not the sharp object itself. Hence, sharp tips are crucial for high-resolution in STM and, more general, in all Scanning Probe Methods (SPM). 

To proceed it is helpful to consider a gedanken experiment. Consider two concentric cylinders the annular region of which is filled with a fluid. Now start rotating the inner cylinder uniformly. At first the outer cylinder is stationary nevertheless, after some time the outer cylinder begins to rotate. The inner cylinder imparts tangential momen-... 

The two expansion coefficients ijs and rjv are called the shear and bulk viscosities, respectively. The shear viscosity is all that is required to describe our gedanken experiment. The bulk viscosity describes the viscous or dissipative part of the response to a compression. This linear constitutive relation is called the Newtonian stress tensor. A fluid correctly described by this form is called a Newtonian fluid.16... 

The ramifications for a Gedanken experiment at T = 0 K are sketched in Fig. 4a, revealing the d.c. electrical conductivity for a macroscopic system such as Si P in which d, the average distance between one-electron centers, can be continuously tuned by changes in the composition of the system. For values of d below a critical distance, dc, i.e. d < <4) the system is metallic and the electronic wave-function is completely delocalized over the entire sample. For very large d d > dfj, we have an insulator with a valence electron wavefunction that is completely localized at the individual atomic sites. At a critical distance, d we then have, according to Mott, a first-order (discontinuous) metal-insulator transition. Thus, at r = 0 K one either has a non-metal or an insulator, for which the limiting (low temperature) d.c. electrical conductivity is zero, or a metal, with a finite conductivity at this base temperature. Whether the metal-insulator transition in Si P (Fig. 4a) is continuous or discontinuous is still a source of controversy. 

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