At this special moment,  a memory is writtten as a record before the official publication of the book "Conjugate Construction of Quantum Optics: From Foundations to Applications" by NOVA Science Publishers.

New Book Link: https://novapublishers.com/shop/conjugate-construction-of-quantum-optics-from-foundations-to-applications/

Over 30 years of continuous exploration, we were fighting in the weird quantum fog and experienced countless failures and setbacks. At this special moment, the new book was announced online in the prepress before the official global publication.

In the preface of the new book, there is a brief introduction to the logical connection of the basic contents. At this stage, it is essential for the general audience to know some background information of the new book about its core results, to review the key milestones in writing processes, to trace the origins of important conclusions and to notice witnesses and turning points in specific time periods so that readers who are interested in in-depth exploration can gradually understand the series of innovative structures and contents in conjugate quantum optics.

New Book Introduction

The book consists of three parts, I-III, to establish the quantum measurement foundation on multiple variables of  conjugate complex vector functions. Part I establishes the foundation of the conjugate construction. Part II reviews the important historical development of complex conjugate functions and quantum entanglement, establishes the quantum optical measurement mode and predicts the applications of conjugate construction in the future. Part III brings together more than 240 systematic assertions described in the first two parts through the categories of lemmas, theorems, corollaries, hypotheses, and predictions.

Basic Contribution

Challenging quantum-based major events of the century (Einstein-Bohr debates, Schrödinger's cats, frontier quantum entanglement theories and experiments), there are a series of contradictions/paradox facts in the fundamentals of quantum mechanics, the uncertainty principle, EPR and Bell's inequality.

The fundamental contribution of this book provides definite conclusions for the century debates on the foundations of quantum mechanics between Einstein and Bohr. From the multilevel symmetric/antisymmetric algebraic operators and computational complexity of the hierarchical evidence of logic, algebra, geometry, and complex dynamic system measurement characteristics, the conjugate construction supports 1935 Einstein's famous statement: "Quantum Mechanics is Incomplete!".

Logical Connections in Chapters

Part I consists of four chapters (Chapters 1- 4) to establish the foundation of conjugate construction. Chapter 1 starts from the conjugate vector operators and aims at the overall phase space of the complex dynamic system, and the conjugate complex vector function of the transformation system is established on the complex number plane. Chapter 2 gets going from {0,1} vector logic to form conjugate logic and conjugate algebra and develops conjugate complex functions and their measure spaces to establish the conjugate logic support of quantum measurement. Chapter 3 forms the basis of precise time measurement expressed by mapping the number sequence into the complex number plane. Chapter 4 describes the core structures of stronger quantum interactions based on the conjugate topology and algebraic geometry structure.

Part II consists of three chapters (Chapters 5-7) discussing important historical processes, measurement models of quantum entanglements and future developments. Chapter 5 starts from the origin of complex numbers to discuss the evolution of complex conjugate systems, important events in the historical development of quantum mechanics and quantum entanglements, and a series of essential equivalence principles, such as, Optical Reflection Mirrors ≡ Conjugate Complex Operators.

Superior to the Hilbert space in the complex conjugate coefficient space of the unit circle that supports real eigenvalue solutions, this book proposes a conjugate space based on {0,1} conjugate logic and conjugate algebra on the complex coefficients of the unit circle for eigenvalue solutions of complex vectors. The three units of information measurements,  Bit, Qubit and Cobit (conjugate/complete qubit) form three levels of logical information framework foundations.

The metric unit of the new bit family extends from the two-metametric qubit representing {1,-1} real eigenvalue solutions to the four-metametric cobit representing {1, i, -1, -i} complex numbers. Complex eigenvalue solutions satisfy necessary and sufficient conditions for a complete representation of complex dynamic systems. n qubits provide quantum entanglement with the same number of phase space representations as {0,1} logical eigenvalues of n bits, including {0, 1}ⁿ = {1, -1}ⁿ = 2ⁿ eigenvalues , however, n cobits can fully describe the states of quantum entanglements, and provide {1, i, -1, -i}ⁿ = 4ⁿ = 2ⁿ x 2ⁿ = 2²ⁿ grand vector features in the phase space of vector eigenvalue solutions.

The eigenvalue solutions surpass the phase space dimension of n qubits, and n cobits comprehensively improve the accuracy and description range of the conjugate quantum measurements on the eigenvalue solution space of quantum optics. Conjugate transformation forms the foundation of quantum optics to include conjugate brackets/Lie-Dirac brackets and conjugate algebra/Lie-Dirac algebra where Lie-Dirac algebra is a subgroup of conjugate algebra, and classical quantum theory is a substructure of conjugate transformation.

In the conjugate transformation structure, the measurement framework of quantum optics is integrated into three quantum measurement modes, which meet the general eigenvalue measurement in application requirements of quantum optics and provide a sufficient number of phase space modes. Based on the characteristics of discrete conjugate geometry and topology on conjugate orthogonal eigenvalues of measurement invariants, the stranger quantum entanglement effect that is difficult to describe can be systematically explained.

For conjugate quantum optics, using the series of conjugate measurement operators in the first five chapters as the foundation, the sixth chapter forms six hypotheses and proposes three quantum entanglement measurement modes, gives six detection predictions for quantum entanglement measurement, and establishes the conjugate construction of quantum optics.

Based on the system's elimination of Möbius-type logic paradoxes, Chapter 7 explores the future development of complex dynamic systems of hierarchically structured high-dimensional complex manifolds in complex exploration directions such as conjugate complex vector systems and natural intelligent computing architectures.

Sources of Results and Context

In chronological order, the research results described in Chapter  2 - conjugate transformation structure - is an important part of my PhD thesis Monash in 1994. In 2018, I was preparation for editing the English/Chinese monographs on variant construction published by Springer 2019 and Science Press 2021, I found a research draft between 1994 and 2003 interesting, to explore how to overcome huge difficulties between conjugate {0,1} vector feature clusters and complex number expressions. After systematic improvement and multiple optimizations, the formalized representation of the relationship between the vector logic metric and complex measurement representations was published in Chapter 4 of volume 1 of the Chinese monograph on variant construction by Science Press in 2021. The 2020 article was published as a preprint on the ResearchSquare, and the relevant results were concerned, commented and recognized by Dr. Barry Robson, the founder of the Dirac Foundation.

In 2003, Mr. Bob Beaumont, as an international authority in the fields of EMBA, high-tech enterprise strategy, and complex dynamic system analysis, pointed out the lack of comparison results between the conjugate transformation and the classical dynamic systems, and suggested the author’s basis on a necessary condition to judge the superiority of the conjugate system in quantified features to be compared with classical dynamic systems in multi-level characteristics.

Published the variant logic papers in 2010, the combination of microscopic cluster states and the global visualization of feature clusters have become the core battlefield of probability and statistics and the main direction of the variant construction research team. Measurement and visualization based on segmented genetic sequences has become the core content of the research team since 2014. The systematic research accumulation provides the basic preparation for the entire research team to focus attention on fighting COVID-19 of the precise analysis of batch genetic sequences in 2020.

Facing richer complex and diverse genetic sequences, in addition to various forms of high-dimensional probability distributions, the information entropy (combinatorial entropy, mean entropy, integrated entropy, topological entropy) associated with the overall probability distribution has been developed by the clustering description method of the genetic index and has gradually become an effective tool for visually describing large quantities of new coronavirus sequences from digital measurement data. The series of results laid out the foundation for the research team to publish 24 research papers in the special issue of  COVID-19 analysis in the international journal of EC Neurology in 2021.

In 2020, Professor Harold Szu, an internationally renowned senior scientist in the fields of neural network, machine learning, statistical physics, and natural intelligence, identified a new type of gene index/sequence index in conjugate schemes that contains content beyond information entropy. From the perspective of statistical physics, this type of index is equivalent to the Boltzmann entropy expression to provide potential opportunities for topics such as non-equilibrium statistics of conjugate systems linking theoretical physics.

In-depth exchanges with Dr. Dennis Heim, an expert in quantum physics, from 2014 to 2016,  emphasized to pay attention to the probability distribution of the action states in the position operators, it is also necessary to balance the probability distribution of the action states of the momentum operators. In 2022, he provided answers on the series of paradox questions for the detailed description of quantum entanglement to help the author to clarify that in the classical quantum mechanics theory based on differential equations, various complex constant coefficients do not have the function of distinguishing and analyzing in classical quantum foundation.

In the in-depth communication in 2016, Mr. Xiazhou Yang, an expert in theoretical physics, identified the system eigenvalue solutions of the Dirac quantum mechanical equation in the state phase space of the conjugate transformation. Professor Shu Zhang, an expert in quantum physics, has periodically discussed the special modes of quantum operators and their applications since 2004. In 2022, he observed that the use of pseudo-random sequences to form analog probability distributions through conjugate system algorithms lacks basic symmetry properties. He was creatively suggested that the variant research team complement the configurations of symmetric primitives in the relevant action space. The proposed scheme is fully realized in the conjugate simulation scheme of the equilibrated phase space, showing a series of symmetry diagrams and properties under the condition of conservation of energy or conservation of specific interaction operators.

The timebased models and methods are closely related to the cooperation of Professor Youping Li, a senior academician of the Chinese Academy of Engineering and Professor of Southeast University. Based on the information entropy measurement and description scheme, in 2021, the asynchronous consensus paradox - the FLP impossible triangle paradox that has puzzled Academician Li for more than 20 years - was successfully resolved.  The precision measurement of 3D positions through synchronous measurement of 1D time signal provide a consensus mode of 4D coordinate invariant measurements with unique characteristics for the precise expression and transmission of global synchronous spacetime events.

Based on structural evidences, it is demonstrated that the UCL project developed by the Southeast University is a synchronous time parallel system for the fastest speed of light, with a synchronous consensus mechanism, and is not affected by the asynchronous FLP paradox at all.

Using the global satellite positioning system supported by the precise atomic clock timing 10¹² reference, global time synchronization system, synchronous/asynchronous time series and accompanying probability measurement distribution, a selfconsistent time measurement model is established on the 2D complex number plane.

Based on the precise time series signals, two typical probability measurement distribution models are established for the elapsed time signal sources of each phase without conflict/paradox: the general time measurement distribution and the narrow time measurement distribution. Under the information entropy measurement, the two types of feature index distributions can provide maximum entropy on measurement characteristics with symmetrical distribution properties such as translation invariance in energy conservation.

In 1994, the conjugate transformation structure defined four groups of conjugation operators  {~,*,#,'}, but the basic framework for the representation of conjugate complex vector functions was not successfully completed until June 2022. The early research foundation of conjugate transformation lacked visual image support for geometric representations. The geometric transformation operators of the complex number matrix are applied to effectively distinguish the whole/local integration on the eigenvalue vector solution of the transformation mechanism of the conjugate operator and the imaginary number operator on complex number planes. The measure self-consistently supports the conjugate space, surpasses the infinite-dimensional Hilbert space in an all-round way, and systematically expands the two-meta complex conjugate vectors corresponding to the Poincaré paired angle measures, forming a four-meta conjugate synchronization operators  {~,#,',*}  as the basis. The eight-primitive conjugate complex vector structure - pairwise conjugate quadruplets and four attribute regions in the complex plane. On the unit circle of the complex plane, the multivariate complex coefficient polynomial eigenvalues provide a complete description of the entangled state representation with the exact solution structure on the phase space of the conjugate complex vectors.

It is gratifying that in July 2022,  Professor Xuemou Wu, the original creator of pan system theory, was connected on the WeChat. Professor Wu introduced his early collaborator, Processor Xijin Xiong, the pioneer of pan complex variable functions, and then reading their monographs I deeply understood the characteristics and significance of their work.

In addition to Wiki, Google Scholar search and query tools refer to the history of multitype complex variable functions Gauss, Klein, Hamilton, Hadarmad, Luokeng Hua, Shiingshen Chern and other complex variable function famous works and mathematics history monographs.

Modern information technology provides excellent works of de Morgan, Hamilton, and Clifford, published 200 years ago, recording their foundational explorations in developing balanced logic and complementary geometric visualization modes for conjugate operators through the 2D representation of trigonometric functions.

While looking for the development history and classic works of complex conjugate functions, through various channels, there extensively collect and refine the basic materials of quantum entanglement experiments and theories. As one of the sources of information and materials from bloggers and friends of ScienceNet & WeChat, the author interacted smoothly with many bloggers of ScienceNet to obtain the necessary material support as needed.  In 2021, Dr. Yuan Tian from the team of Professor Jian Li of Beijing University of Posts and Telecommunications suggested that the entanglement mode of quantum cluster states should be introduced in Chapter 5, the review of multiple quantum entanglement states.

The latest quantum entanglement theory and experimental results are collected from Quantum 2022, an international quantum conference coorganized online by the IOPP WYSS CPS committee in October 2022. Relevant exciting content is reflected in the latest series of references and literature in the reviews and comparisons of quantum entanglement in Chapters 5 and 6.

At the time of the contract signed for this book in September 2021, the writing target was "Conjugate Logical Foundations of Quantum Mechanics" with a submission date of March 2022.

At that time, I was busy with heavy planning and preparation work on funding application materials for various cooperative research projects, so it was rare to arrange time for quiet writing. After negotiating with NOVA Publishers, the submission period of the monograph was postponed by 8 to 10 months, and it was scheduled by November 30, 2022, after confirmation by the publisher.

Accompanied by the gradual accumulation of manuscripts, constructing precise mathematical descriptions, optimizing and perfecting the proof structure. After September 2022, I devote myself full time to writing and creation. After the completion of the book, I propose the final title of the book "Quantum Optics Conjugate Systems:From Basics to Applications - Quantum Measurement Foundation on Multiple Variables of Complex Vector Function”

The document was successfully submitted at the end of November 2022, and after a month of careful inspection by the editorial department, as a New Year gift in 2023, it was notified by NOVA Publishers that the manuscript will officially enter the editing status of the publishing house in January 2023. After repeated checks, edits, and corrections through network interaction during the period of 3-5 months, the editing and proofreading of manuscript documents was completed, and the editing and correction of a series of online public release information was completed through interactive checks in early June. The followup is waiting until the end of June 2023, when the monograph will be officially published and distributed globally.