What Would Weyl Do? by Blake Stephen Pollard

Hi Blake Pollard,

The late Hermann Weyl uttered serious doubts about very foundational matters. Figs. 1, 3, 4, and in particular 2 of my current essay should be food for thought not just addressing physicists but also mathematicians. You seem young enough as to occasionally learn in decades to come that my criticism might be justified.

While I would not appreciate you applying what you learned and reject them without due refutation, you are invited to articulate any counterargument.

I consider each out of the five Figs. relevant to the topic of the current contest. Fig. 5 may undermine all accepted interpretations of the MMX which of course implies that Einstein's SR was unfounded. You would be the first one who proved me wrong.

Dear Blake,

Although you say you were pressed for time while writing this, you nonetheless present some very worthwhile ideas, and express them quite well. You also seem to have the mathematical maturity to make these ideas precise. A couple of thoughts.

1. Since Weyl was one of the fathers of representation theory, I thought you might be interested in a different take on this crucial subject. Many approaches to quantum gravity involve nonmanifold structure at small scales, and this makes the use of covariance in the form of the representation theory of the Poincare symmetry group difficult for determining particle states etc. However, one can alternatively view covariance in order-theoretic terms, and this viewpoint is much more general (see my essay here On the Foundational Assumptions of Modern Physics for more details). This opens up the following interesting question: if you use something more general than groups, what do you do about the representation theory? It is also interesting to think about gauge theory in analogous terms.

2. A couple of other essays here that might interest you are the ones by Torsten Asselmeyer-Maluga and Jerzy Kroll. In particular, they involve exotic smoothness structures, which can accomplish some of the same things as magnetic monopoles, among many other interesting properties.

Take care,

Ben Dribus

Dear Pollard,

From your statement in context with Weyl Curvature Tensor, 'Gravity tells space how to curve, and curved space tells gravity how to move', we perceive that, Weyl Curvature Tensor is much applicable to describe the emergence of gravity from the eigen-rotational strings in Coherently-cyclic cluster-matter paradigm of universe.

With best wishes

Jayakar

If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is [math]R_1 [/math] and [math]N_1 [/math] was the quantity of people which gave you ratings. Then you have [math]S_1=R_1 N_1 [/math] of points. After it anyone give you [math]dS [/math] of points so you have [math]S_2=S_1+ dS [/math] of points and [math]N_2=N_1+1 [/math] is the common quantity of the people which gave you ratings. At the same time you will have [math]S_2=R_2 N_2 [/math] of points. From here, if you want to be R2 > R1 there must be: [math]S_2/ N_2>S_1/ N_1 [/math] or [math] (S_1+ dS) / (N_1+1) >S_1/ N_1 [/math] or [math] dS >S_1/ N_1 =R_1[/math] In other words if you want to increase rating of anyone you must give him more points [math]dS [/math] then the participant`s rating [math]R_1 [/math] was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process.

Sergey Fedosin

Hi Blake,

I really liked your essay, and I do believe thzt the "gauge redundancy" that you talk about is important at a fundamental level. I regret not having voted on your essay while the contest was still open.

- Shawn