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 mathematicalphysics
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) MathematicalPhysics 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 (20052010). Once the mathematicalphysics 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 spacetime 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 spacetime 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 MathPhysics
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 “headsup” warning to our students
regarding the direction of progress in science. Even better, making these ideas
public, selfpublishing on the Web is a must, being of a far greater importance
than the peerreviewed publishing process.
Lucian Ionescu 12/7/2010