Essay Abstract

Modeling reality is a zoom-in/out process best implemented as a resolution of finite type, in the mathematical sense. This means that at each level of details a finite number of independent degrees of freedom are introduced: dimensions, "digits", graphs etc. The local corresponding properties ("particle" aspects) are complemented by global properties/correlations ("wave" aspects), providing the framework for the classical-quantum duality. Explicit examples are discussed: real numbers, Haar wavelets and Feynman graphs. The conclusion is: reality is discrete, hierarchic of finite type, well modeled by a duality of the type homology-cohomology. The development of physics, experimental and theoretical, ample supports this claims.

Author Bio

Lucian Miti Ionescu is associate professor of mathematics at Illinois State University with an established record of publications in mathematical-physics at international level. With a strong background in computer science, complemented by extensive work done in this area, the author proposes a project to design a new physics starting from general principles, from a point of view unifying quantum physics and theory of information, based on the current state-of-the-art in quantum mathematical physics and quantum computing.

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10 days later

Dear Prof. Ionescu,

very profound and dense essay. I think that promoting the "Feynman legacy" to this rank can trigger insights like those you presented. I have some technical difficulties understanding some of the things you mention, mostly because I don't know much about some of the results on which your ideas rely. For example, I only know about Kontsevich that he provided a path to non-commutative geometry, other than the more popular of Connes. Clearly there is a rich world of discrete features that can be exhibited by continuous structures, and this world is much richer if freed from the background manifold.

Best regards,

Cristi

16 days later

Dear Lucian

Fascinating and impressive, at least the parts I understood. I'd value your views on mine, though from a different place! - needing good dynamic visualisation skills.

Best of luck

Peter

Dear Lucian,

A very impressive piece of work! I welcome your desire to formulate physics in a new way. In my essay I seek to do the same, but with a very different approach. Mathematically it does not involve anything beyond multivariable calculus and continuous real functions. I mathematically derive Planck's Law for blackbody radiation and show that this Law is actually a mathematical tautology that describes the interaction of measurement. This is what really explains why the experimental spectrum is so indistinguishable from the theoretical. All the results and definitions I use are mathematical, with the 'prime physis quantity eta' (undefined and undefinable) providing the only connection to physical reality. Thus, in principle, the same theory so developed can be applied in any variety of ways to other contexts. Please read and comment if you are so inclined. Support my efforts, if you can, to place these results before the panel for review. As I am supporting your exceptional significant work.

Just a few days ago, I posted a mathematical proof of the following proposition.

"If the speed of light is constant, then light is a wave"

best wishes,

Constantinos

8 months later

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