Research Statement

A more detailed presentation of my research will be written to document my research in mathematics and physics, with its impacts on the current paradigm of Calculus, Physics and Science in general. It will document the content and role of my The Digital World Theory, Quantum Information Dynamics and its brief presentation in Infotronics: Theory and Experiment, especially regarding the impact on what calculus should be.

In this document only the main ideas are sketched.

 

1)      Mathematics Research (Recall). The 30 years tentative to fundament a rigorous implementation of the Feynman Path Integral quantization method in quantum physics was ended with the Cohomology of Faynman Diagrams paper/theory I obtained by developing the work of Kontsevich (Field medalist) on Formality Theorem, unifying it with the algebraic approach of A. Connes and D. Kremer to renormalization in quantum field theory (how to get read of infinities yielded by Feynman integrals).

The importance of my result was acknowledged by Kontsevich (indirect source: John Briden), as proves the subsequent TWO visits at IHES as his guest.

 

2)      Mathematical Research (New). The subsequent “pure” mathematical research revolves on deformation theory, and while very important, as a continuation of Lie’s Theory of Lie Groups and Algebras, is not as “hot” as the mathematical-physics research and its implications to Physics and Science. At this stage it was clear for me what the mathematical language for physics is, and the huge implications: the change in the paradigm in mathematics and physics from Continuum to Discrete.

 

3)      Mathematical-Physics Research (2005 – 2010). In this way The Digital World Theory was born. The main change, comparable with the change in paradigm of the Copernican Revolution: NEITHER Time NOR Space exit at a fundamental level; only classical information (0 and 1, True and False), with associated local properties (“particles”) in duality with quantum information, which appears as global information, built out of elementary pieces called qubits: 0 AND 1, True AND False (corresponds to what physicists call spinors).

 

4)      Physics Research (2005-2010). Once the mathematical-physics framework became reasonably clear, I started to reformulate the physics interface, using the understanding gained in the prior stages of my research.

To understand the implications to physics I will recall the prior and current status of  theoretical physics.

 

-          “Physics is in Trouble”, says Lee Smolin – there is a need for a background space-time independent theory (my initial motivation for DWT). It also documents the inadequacy of governmental funding policies which encourages too much MAIN Stream Research, in the detriment of new ideas and research avenues.

-          It is well known and loudly stated by some leaders of String Theory, that String Theory is in a dead end as a fundamental theory; it is not even “physics” being experimentally out of reach.

-          The Standard Model is a collection of results conforming to data; totally unsatisfactory. A decade ago it was considered almost complete: “we only need to find the Higgs boson” … Now: there are DARK Energy and DARK matter we have no idea what it is made of (not the elementary particles of the Standard Model), yet it is 75% (or so) of the matter in the universe! In other words, we’re back to the beginning … new physics is needed.

-          R. Feynman (1970’s): I can safely say that nobody really understands quantum mechanics”. With QID, the “mysteries” of quantum mechanics become obvious; the key point: there is no ambient space-time in which matter moves or propagates!

-          Prof. C. Meade, “Collective Electrodynamics”, MIT, preface: “It is my firm belief that history will consider the past SEVEN decades as the dark ages of physics”!

 

My QID explains why String Theory fails, explains the mysteries and paradoxes of Quantum Mechanics, it is compatible with the new developments in Quantum Computing, and plays the role of a Theory of Everything (or Grand Unified Theory), with the qubit as the Hopf monopole fibration having the role of the unifying gauge group (of GUT). My article was thoroughly reviewed by a Math-Physics reviewer, and the main type of objection was the lack of details and justification; it is not easy to convince the reviewers and the specialists of this generation, as Max Planck so well put it: “A scientific theory does not triumph by convincing its opponents. But rather the opponents die and a new generation grows up that is familiarized with the idea from the beginning”.

It our duty as teachers to mention these new ideas if possible, to give a “heads-up” warning to our students regarding the direction of progress in science. Even better, making these ideas public, self-publishing on the Web is a must, being of a far greater importance than the peer-reviewed publishing process.

 

 

Lucian Ionescu                                                                        12/7/2010