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Register a new userCan a Nucleus be Larger Than an Atom (QUANTUM Last Supper-Position)
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In this work we consider an extraordinary quantum mechanical effect when, roughly speaking, the nucleus of an atom becomes (linearly) larger than the whole atom. Precisely, we consider Helium ion (in the ground state of the electron) moving translationally with the speed much smaller than speed of the electron rotation. This translation, effectively, changes neither the total momentum, nor the de Broglie wave length of the electron, nor the linear size of the atom corresponding to the diameter of the electron orbit. But, this translation implies a small nucleus momentum and nuclear de Broglie wavelength almost hundred times larger than the electron de Broglie wavelength. In the measurement of the nucleus wavelength using a diffraction apparatus with a characteristic length constant proportional to the proposed nucleus wavelength, according to standard quantum mechanical formalism, the nucleus behaves practically certainly as a wave. Then the unique, irreducible linear characteristic size for such a nucleus is de Broglie wavelength. Such a measurement effectively influences neither the electron dynamics nor linear size of the atom. This implies that, in such measurement, the size of the nucleus is in one dimension larger than the whole atom, i.e. electron orbital. All this corresponds metaphorically to the famous Leonardo fresco Last Supper where Jesus words coming from the nucleus, i.e. center of the composition, cause an expanding superposition or dramatic wave-like movement of the apostles.
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I show that Matsumoto conjectured inequality between relative length and Finsler length is false. The incorrectness of the claim is easily inferred from the geometry of the indicatrix.
General Relativity has had tremendous successes on both theoretical and experimental fronts for over a century by now. However, the theory contents are far from being exhausted. Only very recently, with gravitational wave detection from colliding black holes, have we started probing gravity behavior in the strongly non-linear regime. Even today, black hole studies keep revealing more and more paradoxes and bizarre results. In this paper, inspired by David Hilberts startling observation, we show that, contrary to the conventional wisdom, a freely falling test particle feels gravitational repulsion by a black hole as seen by an asymptotic observer. We dig deeper into this relativistic gravity surprising behavior and offer some explanations.
Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical understanding of the relationships between these two kinds of methodology, and limited understanding of relative strengths and weaknesses. Moreover, existing results have been obtained primarily in the setting of convex functions (for optimization) and log-concave functions (for sampling). In this setting, where local properties determine global properties, optimization algorithms are unsurprisingly more efficient computationally than sampling algorithms. We instead examine a class of nonconvex objective functions that arise in mixture modeling and multi-stable systems. In this nonconvex setting, we find that the computational complexity of sampling algorithms scales linearly with the model dimension while that of optimization algorithms scales exponentially.
This paper has few different, but interrelated, goals. At first, we will propose a version of discretization of quantum field theory (Chapter 3). We will write down Lagrangians for sample bosonic fields (Section 3.1) and also attempt to generalize them to fermionic QFT (Section 3.2). At the same time, we will insist that the elements of our discrete space are embedded into a continuum. This will allow us to embed several different lattices into the same continuum and view them as separate quantum field configurations. Classical parameters will be used in order to specify which lattice each given element belongs to. Furthermore, another set of classical parameters will be proposed in order to define so-called probability amplitude of each field configuration, embodied by a corresponding lattice, taking place (Chapter 2). Apart from that, we will propose a set of classical signals that propagate throughout continuum, and define their dynamics in such a way that they produce the mathematical information consistent with the desired quantum effects within the lattices we are concerned about (Chapter 4). Finally, we will take advantage of the lack of true quantum mechanics, and add gravity in such a way that avoids the issue of its quantization altogether (Chapter 5). In the process of doing so, we will propose a gravity-based collapse model of a wave function. In particular, we will claim that the collapse of a wave function is merely a result of states that violate Einsteins equation being thrown away. The mathematical structure of this model (in particular, the appeal to gamblers ruin) will be similar to GRW collapse models.
Turbulence is defined as an eddy-like state of fluid motion where the inertial-vortex forces of the eddies are larger than any other forces that tend to damp the eddies out. By this definition, turbulence always cascades from small scales where vorticity is created to larger scales where turbulence fossilizes. Fossil turbulence is any perturbation in a hydrophysical field produced by turbulence that persists after the fluid is no longer turbulent at the scale of the perturbation. Fossil turbulence patterns and fossil turbulence waves preserve and propagate energy and information about previous turbulence. Ignorance of fossil turbulence properties can be dangerous. Examples include the Osama bin Laden helicopter crash and the Air France 447 Airbus crash, both unfairly blamed on the pilots. Observations support the proposed definitions, and suggest even direct numerical simulations of turbulence require caution.
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