Posted: Apr 08, 2015 8:57 am
From what little I had the patience to read, I gather it concerns the hypothesis that the real-valued space we live in is linked to a series of p-adic-valued "spiritual" spaces, one for each prime. It then proceeds to rewrite general relativity using the adele algebra (a coproduct of the real numbers with all the p-adic algebras -- and as if that weren't weird enough already, it doesn't even smash together the rational numbers!). This seems to be a common theme on various physics websites, although usually it's quantum theory that's being rewritten.
Although it's accepted that spacetime is not necessarily continuous, the way to put this into math is to replace coordinates with operators that don't commute, representing our obvious ignorance about what kind of extremely small-scale structure spacetime would have instead.
P-adic numbers, however, commute just like ordinary numbers. The difference is that they're ordered as a fractal (like a Cantor set in the shape of a flower with p-1 petals) instead of a line. So instead of humbly assuming there might be some unknown structure behind space as we know it, they're boldly implying an exact structure that has absolutely nothing whatsoever to do with physics.
Although it's accepted that spacetime is not necessarily continuous, the way to put this into math is to replace coordinates with operators that don't commute, representing our obvious ignorance about what kind of extremely small-scale structure spacetime would have instead.
P-adic numbers, however, commute just like ordinary numbers. The difference is that they're ordered as a fractal (like a Cantor set in the shape of a flower with p-1 petals) instead of a line. So instead of humbly assuming there might be some unknown structure behind space as we know it, they're boldly implying an exact structure that has absolutely nothing whatsoever to do with physics.