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Andrew Wiles managed to prove that theorem however on more than one hundred journal pages still recently and utilizing many of the last achievements of mathematics. As they are an infinite set, they imply a corresponding infinite set of different finite measures. Any three real numbers, not being Pythagorean numbers but satisfying the equation in the Pythagorean theorem, share one single common measure for it is necessarily infinitesimal, and any continua are of an equal power.

I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain. The admissible one single measure is necessarily the infinitesimal one.

The utilized concept of measure should be much closer to the Pythagorean one implicitly suggested in the shocked the Pythagoreans incommensurability of the hypotenuse and cathetus of almost all right triangles rather than to the contemporary too generalized notion of measure: It should suggest an equal number of steps of a procedure for any two commeasurable lengths or any quantities.

If the number of steps is different for the shortest possible procedures, the corresponding measure should be accepted as different. However if the number of necessary steps is infinite, the corresponding measure should be accepted as one and the same. However that problem turns out to be rather philosophical than mathematical: Whether a space of events is one and the same where it is standalone as a set and where it is a subset of another.

It seems that neither Gleason touches that question nor it in turn refers to his proof in any way8. However one needs an additional axiom that is the case. Consequently, a second reflection is necessary to elucidate the meaning for the Hilbert space of quantum mechanics to be just the complex one. Whether B is a space or a subspace is not discussed and does not touch the proof. This means that the physical quantity of mass corresponds to the flux of information passing through the present i.

Any symmetry of them corresponds to some law of conservation. That of the physical quantity of action and probability entropy and information seems to be the most important one. If one multiplies as tensors that qubit by the conjugate qubit, i. The physical meaning should be that the physical quantity of action and the probability of an element or a state respectively, entropy or information of the entire system are conserved only transforming into each other. In particular, this implies the conservation of action rather than of energy. In fact, the generalization of conservation from energy to action has been coined already in general relativity and statistic thermodynamics.

This means that the elementary units of time can be different in one and the same point of space-time in relation to a part and to the system as a whole. Thus both the smooth motion of classical physics and the discrete motion introduced in addition by quantum mechanics can be described uniformly correspondingly as an infinite series converges to 10 11 12 Breshears, Gerry Does God play dice with the universe?

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The Quantum Adventure - Does God Play Dice?

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Robert D. Quantum theory is one of the great achievements of twentieth century physics. Born at the very beginning of the century, it attained a definitive form by , yet continued to evolve throughout the century. Its applications remain fully a part of modern life. It should thus come as no surprise that literature on the history of quantum theory is vast, but author Robert D.

Purrington approaches the story from a new angle, by examining the original physics papers and scientific studies from before the creation of quantum mechanics to how scientists think about and discuss the subject today. The Heroic Age presents for the first time a detailed but compact and manageable history of the creation of quantum theory, and shows precisely where each important idea originated. Purrington provides the history of the crucial developmental years of quantum theory with an emphasis on the literature rather than an overview of this period focusing on personalities or personal stories of the scientists involved.

ISBN 13: 9787538291605

This book instead focuses on how the theoretical discoveries came about, when and where they were published, and how they became accepted as part of the scientific canon. The Development of Elementary Quantum Theory. Herbert Capellmann.

Further, it discusses the essential differences between the fundamental equations of Quantum Theory derived by Born and Jordan, logically comprising Quantum Mechanics and Quantum Optics, and the traditional view of the development of Quantum Mechanics.