Dad's Theory of Physics

A long time ago I aspired to be a theoretical physicist. Eventually I came up with a discovery that I now believe is quite significant, but it took more than a decade before I started to understand what it meant. Since my postdoc only lasted four years, I ran out of funding and went on to do something else. However, my wife insists that I must explain to our children what I spent so much time on even after I had left academia. This will be done in a series of posts over the next three weeks. 

Explaining a discovery in mathematical physics is not so easy, especially not to lay-people. I could say (and have said) that I generalized the Virasoro extension of the algebra of diffeomorphisms on the circle to higher-dimensional manifolds, and discovered how to build off-shell representations thereof. Alas, that sentence is generally met with a blank stare. Instead I will try to explain the main physical ideas, initially using a minimum of formulas. This will be the topic of the first week, where I introduce the notion of horizontal fuzziness and explain why it is a necessary ingredient in any quantum theory of gravity.

In the first week I plan to cover the following topics:

* Horizontal Fuzziness
* The Equivalence Principle
* The Need for Renormalization
* Quantum Jet Theory
* Partial and Complete Observables

The second week I will describe the mathematical discovery underlying these ideas. This will require quite a bit of mathematical formalism, but I will try to introduce the necessary background material first. What should be emphasized is that the ideas introduced during the first week do not come out of thin air. Instead, they are the physical interpretation of the off-shell representations of the multi-dimensional Virasoro algebra.

The third week I will discuss some consequences of horizontal fuzziness. Just as vertical fuzziness (quantum mechanics) is different from no fuzziness (classical mechanics), we can expect that horizontal fuzziness is significant too.