Quantum paradoxes

F. Selleri, in A. van der Merwe (Ed.), Quantum Paradoxes and Physical Reality, Kluwer, Dordrecht, 1990. 

Each volume tells the story of quantum chemieal stmctures from different viewpoints offering new insight to some eurrent quantum paradoxes. 

Coordination Based on Knoivn Free Ligands, Moderate Dissociation Rate, Weaker Electron Affinity of Central Atom Than Ionization Energy of Ligand, and Quantum Paradoxes... 

Y. Aharonov, D. Rohrlich, [93]. Quantum Paradoxes — Quantum Theory for the... 

The molecular electronic polarizability is one of the most important descriptors used in QSPR models. Paradoxically, although it is an electronic property, it is often easier to calculate the polarizability by an additive method (see Section 7.1) than quantum mechanically. Ah-initio and DFT methods need very large basis sets before they give accurate polarizabilities. Accurate molecular polarizabilities are available from semi-empirical MO calculations very easily using a modified version of a simple variational technique proposed by Rivail and co-workers [41]. The molecular electronic polarizability correlates quite strongly with the molecular volume, although there are many cases where both descriptors are useful in QSPR models. 

It is now known that the view of electrons in individual well-defined quantum states represents an approximation. The new quantum mechanics formulated in 1926 shows unambiguously that this model is strictly incorrect. The field of chemistry continues to adhere to the model, however. Pauli s scheme and the view that each electron is in a stationary state are the basis of the current approach to chemistry teaching and the electronic account of the periodic table. The fact that Pauli unwittingly contributed to the retention of the orbital model, albeit in modified form, is somewhat paradoxical in view of his frequent criticism of the older Bohr orbits model. For example Pauli writes,... 

A. Quantum Mixing of a Tunneling Center and the Black-Halperin Paradox... 

Schrodinger, E. (1 983) The present situation in quantum mechanics A translation of Schrodinger s "Cat Paradox" paper,in Wheeler, J. A. and Zurek, W. H.(eds.), Quantum theory and measurement, Princeton University Press, Princeton,New Jersey,pp.152-167. 

Irrespective of whether the photon is considered as a plane wave or a wavepacket of narrow radial extension, it must thus be divided into two parts that pass each aperture. In both cases interference occurs at a particular point on the screen. When leading to total cancellation by interference at such a point, for both models one would be faced with the apparently paradoxical result that the photon then destroys itself and its energy hv. A way out of this contradiction is to interpret the dark parts of the interference pattern as regions of forbidden transitions, as determined by the conservation of energy and related to zero probability of the quantum-mechanical wavefunction. 

In search for an explanation, Aharonov and Bohm worked out quantum mechanics equations based on the measurable physical effect of the vector potential, which is nonnull in a region outside the solenoid. Like many other paradoxes in physics, including the twin paradox, the interpretation of this experiment proposed in 1959 was the subject of an intense controversy among researchers. This controversy is well summarized in a review article [55] and in other references of interest [56-67]. 

In this section we have presented a mathematical foundation for entanglement of quantum systems. This foundation lies behind most modern discussions of quantum computing, as well as the Einstein-Podolsky-Rosen paradox. 

Suppose they approach each other, interact, then move away. This scattering process is described by a joint Schrodinger equation for lP(ql, q2, t) with initial condition (1.17). The point is that after the interaction has taken place the wave function (4i,42,0 no longer factorizes as in (1.17). The separated molecules cannot be described by separate wave functions, but only by the joint wave function, or else by their density matrices pj and p2. This is considered a paradox by those who have not learned to live with quantum mechanics. ... 

A. Einstein, B. Podolski, and N. Rosen, Phys. Rev. 47, 111 (1935) F. Selleri ed., Quantum Mechanics Versus Local Realism - The Einstein-Rosen-Podolski Paradox (Plenum, New York 1988). 

The remarkable conclusion is that the microscopic quantum state, specified by the wave function ip, can be described on a macroscopic level by the probability distribution Pj. A single pure state corresponds to a macroscopic ensemble. The interference terms that are typical for quantum mechanics no longer appear. Incidentally, this resolves the paradox of Schrodinger s cat and, in general, the quantum mechanical measurement problem. )... 

Pope John Paul II "Einstein, Einstein Session of the Pontifical Academy, Vatican City (November 10, 1979). Reprinted in Science, 207, 1165-1167 (1980). Powell, C.S. Can t Get There from Here Quantum Physics Puts a New Twist on Zeno s Paradox, Sci. Amer., 24 (May 1990). 

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