How the discovery of the physical meaning of Planck’s constant made it possible to clarify the connections between classical and quantum mechanics and corpuscular-wave mechanics
In its physical meaning, Planck’s constant turned out to be one of the corpuscular-wave quantities (CWQ) of microparticles. In turn, the newly discovered CWQ turned out to be quantities of corpuscular-wave mechanics (CWM), just as corpuscular quantities are quantities of the Newton’s corpuscular classical mechanics (CCM). At the same time, Schrödinger’s wave quantum mechanics (WQM) turned out to be in fact incomplete part of the CWM of non-relativistic electron (NE), and Newton's CCM itself turned out to be derived from the CWM macroscopic body (MB). Thus, to our great surprise, the CWM of a NE turned out to be more general form of Schrödinger’s WQM, and the CWM of a MB turned out to be more general form of Newton’s CCM. In this regard, just Abel discovered the multiplicity of algebras, and Lobachevsky discovered the multiplicity of geometries, similar to them, we encountered the multiplicity of the mechanics of physics.
In its physical meaning, Planck’s constant turned out to be one of the corpuscular-wave quantities (CWQ) of microparticles. In turn, the newly discovered CWQ turned out to be quantities of corpuscular-wave mechanics (CWM), just as corpuscular quantities are quantities of the Newton’s corpuscular classical mechanics (CCM). At the same time, Schrödinger’s wave quantum mechanics (WQM) turned out to be in fact incomplete part of the CWM of non-relativistic electron (NE), and Newton's CCM itself turned out to be derived from the CWM macroscopic body (MB). Thus, to our great surprise, the CWM of a NE turned out to be more general form of Schrödinger’s WQM, and the CWM of a MB turned out to be more general form of Newton’s CCM. In this regard, just Abel discovered the multiplicity of algebras, and Lobachevsky discovered the multiplicity of geometries, similar to them, we encountered the multiplicity of the mechanics of physics.
The hundred and fifty years ago, I.Newton, in his corpuscular classic mechanics (CCM), introduced mass as an initial quantity, and, an its basis, defined other corpuscular quantities of CCM. And a hundred years ago, the corpuscular-wave properties of microparticles testified to the inherent corpuscular-wave quantities (CWQ), which as the initial value had the product of mass and wavelength. Accordingly, just as Newton’s CCM was based on corpuscular quantities, corpuscular-wave mechanics (CWM) should have been based on CWQ in the same way. But a hundred years ago, Plank’s and Einstein, to describe the corpuscular-wave properties of the photon, used hybrid of corpuscular quantities Newton’s CCM and wave quantities of wave optics, which a priori, by their definition, were insufficient to describe the CWQ of the photon. Subsequently, de Broglie and Schrödinger applied the method of Planck and Einstein to the case of a non-relativistic electron (NE), and obtained wave quantum mechanics (WQM). But the WQM he obtained turned out to be a real puzzle, and now, a hundred years later, l was able to discover that in reality WQM is an incomplete version of the CWM NE. The campaign managed to find out that Newton’s CCM arises in the form of a special case of the CWM macroscopic body. In this regard, now, l seem to be a Tajikistan physicist who discovered CWQ and CWM physics.
After unsuccessful arguments with N.Bohr about the incompleteness of the non-relativistic electron (NE) created by Schrödinger in wave quantum mechanics (WQM), Einstein said: " I am more and more inclined do think that extra-spatial structures are necessary for the further development of physics ". And the extra-spatial structures predicted by Einstein had to be constants, since only constants were independent of the space-time continuum. Therefore, it was necessary to find an answer to the question: " How can constants be used as extra-spatial structures for the further development of physics?" The answer this question arose naturally when we managed to find out that Planck’s constant and other constants associated with it are the proper corpuscular-wave (CW) quantities of microparticles. At the same time, the newly discovered extra-spatial CW quantities of microparticles, being constants, turned out to be extra-spatial structures in relation to the Euclidean, Minkowski and Klein-Gordon spaces. In addition it turned out that our newly discovered extra-spatial CW quantities of microparticles inside the space of Euclidean, Minkowski and Klein-Gordon appear in the form of corpuscular, mixed and wave quantities of microparticles that are generally known to this day. Moreover, the emergence within spatial corpuscular quantities from extra-spatial CW quantities made it possible to understand that the corpuscular quantities of Newton’s corpuscular classical mechanics (CCM), which were considered the principles of physics, are not in fact the principles of physics. It turned out that the WQM of a NE created by Schrödinger is an incomplete version of the corpuscular-wave mechanics (CWM) of a NE. No matter discover the extra-spatial predicted by Einstein necessary for the further development of physics in the form of extra-spatial proper CW quantities and the CWM of real objects of Nature.
Science has developed through a variety of investigations more or less over the time scale of human existence. On this scale, quantum mechanics is an extremely young field, existing essentially for only just over a century. Even our understanding of classical mechanics has existed for a comparatively long period—roughly having been formalized with Newton's equations published in his Principia Mathematica , in April 1686 (1687). Up until the very end of the nineteenth century, mechanics in the form of Newton's laws were comfortable, being understood and accepted by all who dealt with the motion of reasonable bodies. With the turn of the new century, however, mechanics would be shaken to its roots. The change began already on December 14, 1900, when Planck (1900) presented his new theory of black-body radiation to the German Physical Society, and this change would affect mechanics in physically small structures (and lead to quantum mechanics). Mechanics of large bodies would similarly be changed in 1905 with the arrival of Albert Einstein's (1905a) relativity theory. In this book, we will deal with only the first of these two great breakthroughs.
Modern attempts to understand light go back to Newton who considered light to be particles, the so called corpuscular theory, and the other school of Huygens, Young and others. Huygens and Young viewpoint emphasised the wave property. This difference of opinions persisted for close to two centuries till Maxwell theory solidly established light as a wave phenomenon associated with Electromagnetism. A serious schism so to speak was introduced into the theory of light with the understanding of "Light gas", the so called Black Body radiation. Einstein's photon hypothesis and Bose's successful derivation of the Planck spectrum put the corpuscular theory back in place, while classical description continues to be used as well. One may then wonder if this being a classical limit may have to be corrected when dealing with quantum phenomena. To most people's surprise, the classical description was in fact a subset of the full quantum description, and the classical states of light could be shown to be subsumed within the fully quantum description without having to take the limit of Planck's constant h going to zero. This was the resolution provided by E. C. G. Sudarshan's Diagonal representation as the most general formalism for dealing with light.
Newton’s force law [Formula: see text] is derived from the Schrödinger equation for isolated macroscopic bodies, composite states of e.g. [Formula: see text] atoms and molecules, at finite body temperatures. We first review three aspects of quantum mechanics (QM) in this context: (i) Heisenberg’s uncertainty relations for their center of mass (CM), (ii) the diffusion of the CM wave packet, and (iii) a finite body temperature which implies a metastable (mixed-) state of the body: photon emissions and self-decoherence. They explain the origin of the classical trajectory for a macroscopic body. The ratio between the range [Formula: see text] over which the quantum fluctuations of its CM are effective, and the body’s (linear) size [Formula: see text], [Formula: see text] or [Formula: see text], tells whether the body’s CM behaves classically or quantum mechanically, respectively. In the first case, Newton’s force law for its CM follows from the Ehrenfest theorem. We illustrate this for weak gravitational forces, a harmonic-oscillator potential, and for constant external electromagnetic fields slowly varying in space. The derivation of the canonical Hamilton equations for many-body systems is also discussed. Effects due to the body’s finite size such as the gravitational tidal forces appear in perturbation theory. Our work is consistent with the well-known idea that the emergence of classical physics in QM is due to the environment-induced decoherence, but complements and completes it, by clarifying the conditions under which Newton’s equations follow from QM, and by deriving them explicitly.