Tuesday, September 19, 2017

Super-number fields: does physics emerge from the notion of number?

A proposal that all physics emerges from the notion of number field is made. The first guess for the number field in question would be complexified octonions for which inverse exists except at complexified light-cone boundary: this has interpretation in terms of propagation of signals with light-velocity 8-D sense. The emergence of fermions however requires super-octonions as super variant of number field. Rather surprisingly, it turns out that super-number theory makes perfect sense. One can define the inverse of super-number and also the notion of primeness makes sense and construct explicitly the super-primes associated with ordinary primes. The prediction of new number piece of theory can be argued to be a strong support for the integrity of TGD.

See the article Super-number fields: does physics emerge from the notion of number?.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.


Stephen A. Crowley said...

Have you seen this guys model system before? http://www.science20.com/johannes_van_leunen/physical_simplicity-226180

Matti Pitkänen said...

No. The article of Baez on octonions is however familiar. Baez has also tried to understand the role of octonions in super string models where the dimension target space is 10 rather than 8. The space of physical polarizations is 8-D.

The marvellous thing would be replacement of partial differential equations with algebraic equations at M^8 level, They are childishly simple computationally. Essentially discretization of data to finite number of bits takes place. The counter part at level of H is preferred extremal.