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Science Tutorial Part 2, Quantum Mechanics and Cold Fusion
• This second science tutorial is titled "Quantum Mechanics and Cold Fusion". It discusses quantum mechanics as needed for understanding LENR cold fusion. The tutorial uses some mathematics and assumes some experience in its use in physics. Hopefully, the concepts expressed by the mathematics can still be understood by those not conversant with the mathematics. The paper discusses "electron orbitals" which are the "electron clouds" that govern chemistry. It extends the orbital picture to include "deuteron orbitals", which are the nuclearly active medium in cold fusion.
• Equations, greek letters, symbols, and subscripts are not properly transcibed. If version with equations wanted, please request by email from tchubb@aol.com
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Quantum Mechanics and Cold Fusion
In order to examine the mechanisms of cold fusion at greater depth it is necessary to make use of the rules of Quantum Mechanics. These rules extend the meaning of quantities that successfully describe the "engineering world", so as to describe the behavior of atomic, molecular and many-body systems embedded in the engineering world. The rules of quantum mechanics were developed to explain laboratory observations of the properties atoms and light. They forced scientists to think in unfamiliar ways. This major change in thinking occurred mostly during the first half of the 20th century. The point to be emphasized is that the rules of quantum mechanics were not developed from first principles, and they were not all developed at one time. There was an evolutionary process that was dictated by continuing experimental discoveries. The discovery of radiationless deuterium fusion is another in this sequence of discoveries, and it forces a clarification of one of the rules of quantum mechanics. The clarification applies only to delocalized subsystems bound within a single volume containing a large number of potential wells.
The kind of many-body system that seems to be the nuclear active state is aptly described by a Russian experimental group. Chernov et al. state: "The experimental results testify: - H atoms occupy regular positions in the crystal lattice, form their own H subsystem - In this subsystem H atoms are connected with each other a much stronger (much more strongly) than with atoms of the matrix." Here, H atoms refer to either protons or deuterons. For radiationless cold fusion the subsystem is a deuterium subsystem.
The physics discipline that applies to a Chernov subsystem is the physics of metals, including the physics of hydrogen in metals. The physics of metals is many-body physics, and it mostly concerns the many-body conduction electron system called the Fermi sea. The normal physics of hydrogen in metals can be viewed as part of quantum chemistry, since it describes hydrogen nuclei located in interstitial sites provided by the metal, with each nuclei neutralized within the boundary of the site by an electron charge. These neutralized deuterons resemble deuterium atoms. But in Pd metal these localized deuterons are not part of the Chernov subsystem and they are not the deuterons that participate in the nuclear reaction. The deuterons of the Chernov subsystem are a second deuteron population, which is delocalized over many lattice locations and resembles the wavelike electrons of the Fermi sea.
There are at least 2 equivalent ways of presenting quantum mechanics. In this paper we use the wave equation approach developed by Schrodinger, in which system energy E is a well defined observable parameter. The wave equation approach in its simplest form describes a stationary state Y, which is stable with respect to time. In the selected Schrodinger representation, a specifiable system energy is selected at the expense of a precisely defined particle position. The result is that even a localized particle is slightly spread-out in physical space. This lack of precision is intrinsic in the microscopic world. When the laws of mechanics were applied to the microscopic world, it was discovered that particle position and momentum could not be precisely defined at the same time. For example, in the Schrodinger equation approach, the position of an electron in an atom can only be defined to the extent of specifying a charge distribution in physical space.
The Schrodinger approach models nature by the combination of a wave equation and the wave function solutions of the wave equation. Equation and solution are equal partners in this description of reality. From the Schrodinger wave function solution one can calculate the charge distribution r(r) as
r(r) = exp( |Y(r)|2)
This equation connects the mathematical for
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Many-Body Physics and How Fusion Energy Heats a Metal
• A good place to start towards understanding many-body physics is the 2-electron helium atom problem. The helium atom orbital is calculated using the principle of system energy minimization. Minimizing system energy provides a means of obtaining a solution of a quantum mechanical time-independent wave equation. A proof is given in a text book by F. Seitz on pages 200 202. Modeling of the helium atom is discussed on pages 231 - 234. The 2-electron orbital of the helium atom is of a form that meets Julian Schwinger's requirement for cold fusion. Schwinger states, "In the very low energy cold fusion, one deals essentially with a single state, described by a single-wave function, all parts of which are coherent. A separation into two independent, incoherent factors is not possible, and all considerations based on such a factorization are not relevant." Inspection of the solution given on page 234 shows that the wave function solution is of this form. The orbital is the square of the wave function, and also is of the required form.
F. Seitz, Modern Theory of Solids (McGraw-Hill, New York, 1940).
• The physical system that can explain LENR cold fusion has a parallel in the physical system referred to as a Bose-Einstein condensate in an optical lattices. Both systems involve atom-mass particles occupying a collection of energy traps called potential wells. A paper by Jaksch et al. models cold atoms in a sequence of potential wells, and shows that if the barrier between adjacent potential wells is not too high, resident atoms become delocalized and configure themselves in the form of standing matter waves. LENR cold fusion depends on deuterons configuring themselves in similar fashion within a series of potential wells provided by a metal.
D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, And P. Zoller, "Cold Bosonic-Atoms in Optical Lattices", Phys. Rev. Lett.., 81, 3108 (1998).
• Many-body physics is modeled using a theory called "second quantization". Second quantization extends the concepts of Schrodinger quantum mechanics. It describes a quantized matter field, where the "field" is a density distribution of matter resulting from a merging of indistinguishable particles. The merging process replaces the particles that joined to form the many-body system with an equal number of "quasiparticles" of the same mass and charge. These quasiparticles are the calculated excitations of the many-body matter field, and are in essence the quanta (the discrete entities) of the field. A mathematical description of second quantization is given in a text book by P. Roman.
P. Roman, Advanced Quantum Mechanics (Addison-Wesley Pub. Co., Readiing, MA, 1965), pp. 63 - 90.
• Suitably selected pairs of quasiparticles can be considered merged into di-particles analogous to the 2 electrons of the helium atom. These merged quasiparticles show different behavior than that attributed pairs of unmerged distinct particles. This difference in behavior is crucial to an understanding of white dwarf stars, which are a well described star type encountered in astronomy. The most famous white dwarf state is Sirius B, in orbit around the star Sirius A. White dwarfs typically have the mass of the sun and the size of the earth. White dwarf star models were developed by Nobel Laureate S. Chandrasekhar. Two quasiparticles occupying the same volume but with quantum indices corresponding to oppositely directed velocities, can be considered to be a di-particle with zero velocity. Having zero horizontal velocity they are not subject to centrifugal force. They behave differently from the stones making up the rings of Saturn. Chandrasekhar does not use centrifugal force in his white dwarf model, Because of not including centrifugal force, he obtains results agreeing with observation.
S. Chandrasekhar, An Introduction to the St
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