Quantum Fractals are out...

ark

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After a year and half Quantum Fractals are out:
QF_cover800.jpg


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.
 
I certainly do not understand everything. But I might have answers, such as whether the thoughts, ideas and knowledge are fractals?
 
Aragorn said:
Congrats, Ark!

I'm looking forward to read it. :)

Lotsa luck! I edited the grammar and punctuation and quickly fell into "skip" mode when hitting the equations.
 
Laura said:
Aragorn said:
Congrats, Ark!

I'm looking forward to read it. :)

Lotsa luck! I edited the grammar and punctuation and quickly fell into "skip" mode when hitting the equations.

:lol: I actually swore & shook my head when I read the contents. Hopefully there will be some colloquial discussions on the book sometime in the future. You know, so I don't feel dumb! Anyway, congratulations. :grad:
 
Congratulations, Ark! I hope too that there will be some discussion here that would provide those who don't quite understand it , including me, with some easier-to-understand explanations of the concepts in the book.
 
Congratulations!! :thup: It sounds so exciting! :)

H-kqge said:
:lol: I actually swore & shook my head when I read the contents. Hopefully there will be some colloquial discussions on the book sometime in the future. You know, so I don't feel dumb! Anyway, congratulations. :grad:

Like "Quantum Fractals for dummies - Questions and answers with Ark"? Some of us don't have brains for math, but still a rich imagination. :P
 
Congratulations, Ark! I don't have a clue where quantum fractals are concerned so I'd like to say that the cover is beautiful. I'm sure the rest of the book is excellent, too. :)
 
Laura said:
Aragorn said:
Congrats, Ark!

I'm looking forward to read it. :)

Lotsa luck! I edited the grammar and punctuation and quickly fell into "skip" mode when hitting the equations.

For someone who has read the book, could a person who isn't well versed with the mathematical aspects of the topic discussed still understand the contents?
 
Many congratulations on publishing your book, Ark! I would dearly love to read it, but physics to me was always written in some kind of Elvish which I could never understand. I wish you every success with the book.

:clap: :thup: :rockon:
 
Quantum Fractal Question

I just saw Ark's book thread, and from the overview I looked up iterated function systems as that is a new term for me.

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.

The overview of iterated function systems basically says they are a system of constructing fractals that are self similar. They are usually contractive but can be expansive. The expansive one are related to projective transformations and Möbius transformations.

Forgive me in advance if my question is not posed exactly correctly, as I still have a lot of gaps in my knowledge and I am going to use visuals as examples because I have no formulaic mathematical knowledge to ask this.

I was looking at this crop circle and its' design:

https://cassiopaea.org/forum/index.php?topic=31601.0 ( Attachment 1)

By a long series of associations I came to find two expressions of this structure. In my opinion one contractive and one projective/transformative.

Arkaim in Russia is the one I think is contractive of the Sri Yantra crop circle. ( Attachment 2)

Here is an article on it from SOTT - http://www.sott.net/article/136853-Anomalous-zones-of-Russia-Arkaim-town


AmarKantak in India is the one I think is expansive/projective of the Sri Yantra crop circle ( Attachment 3)

Both are expressions of the Sri Yantra fractal pattern as far as I can tell. Am I in the right ball park with this example in understanding this or somewhere off in left field again?
 

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Eboard10 said:
For someone who has read the book, could a person who isn't well versed with the mathematical aspects of the topic discussed still understand the contents?

You would probably understand about 25% or so of the entire book since about 75% of it is math or images or computer code. Having said that, the parts I DID understand were interesting!
 
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