After a year and half
Quantum Fractals are out:
Quantum Fractals
From Heisenberg's Uncertainty to Barnsley's Fractality
By (author): Arkadiusz Jadczyk (Quantum Future Group Inc., USA)
About This Book
Starting with numerical algorithms resulting in new kinds of amazing fractal patterns on the sphere, this book describes the theory underlying these phenomena and indicates possible future applications. The book also explores the following questions:
What are fractals?
How do fractal patterns emerge from quantum observations and relativistic light aberration effects?
What are the open problems with iterated function systems based on Mobius transformations?
Can quantum fractals be experimentally detected?
What are quantum jumps?
Is quantum theory complete and/or universal?
Is the standard interpretation of Heisenberg's uncertainty relations accurate?
What is Event Enhanced Quantum Theory and how does it differ from spontaneous localization theories?
What are the possible applications of quantum fractals?
Contents:
What are Quantum Fractals?
Cantor Set
Iterated Function Systems
Cantor System Through Matrix Eigenvector
Quantum Iterated Function Systems
The ‘Impossible’ Quantum Fractal
Lorentz Group
SL(2,C), and Relativistic Aberration
Hyperbolic Quantum Fractals
Platonic Quantum Fractals for a Qubit
Controlling Chaotic Behavior and Fractal Dimension
Quantum Fractals on N-Spheres
Clifford Algebras
Frobenius–Perron Operator
Computer Simulations
Foundational Questions
Stochastic Nature of Quantum Measurement Processes
Are There Quantum Jumps?
Bohmian Mechanics
Ghirardi–Rimini–Weber Spontaneous Localization
Event Enhanced Quantum Theory
Heisenberg's Uncertainty Principle and Quantum Fractals
Are Quantum Fractals Real?
Limits of Quantum Computation
Readership: Students and professionals in quantum chaos, as well as philosophers of science.
This book provides a handy introduction to quantum fractals a new kind of fractals that arise in quantum-like jump random processes involving noncommuting operations. It describes the basic theoretical concepts, algorithms and also touches upon philosophical questions of the foundations of quantum theory.
An overview: The science of fractals is young and growing fast. Quantum fractals are even younger and are still crawling on all fours. But the time seems to be ripe for them to get up and look around. As we hope it will become clear from this book- various possible applications abound. Roughly: quantum fractals are patterns generated by iterated function systems, with place dependent probabilities, of Mobius transformations on spheres or on more general projective spaces. In quantum physics quantum fractals can be interpreted as traces of quantum jumps during simultaneous monitoring of several non-commuting observables. These quantum jumps accompany events with information exchanges between the quantum system and the classical information processing devices. While mathematically completely clear such a concept brings an almost revolutionary novelty into quantum physics. Until now it has usually been assumed that simultaneous "measurements" of non-commuting observables makes no sense, and that it cannot lead to any useful predictions. In this book we challenge the standard position by proposing that such experiments may lead to organized chaotic behavior that can be experimentally verified. The phenomenon is general enough to be present in applications of the quantum formalism beyond physics and beyond quantum computing, for instance in quantum games, quantum psychology etc. Here possible deviations from linearity are also touched upon.
