[FOM] An alternative to the real numbers as a basis for physics

joeshipman@aol.com joeshipman at aol.com
Fri Mar 3 11:07:22 EST 2006

There is a growing literature on the use of alternative completions of 
Q (that is, the p-adic numbers) as a basis for physics. Since 
experimental measurements are always expressed as rational numbers, 
this is less wacky than it may seem. To those who object that the 
choice of p is arbitrary, there is also work with "adeles" and 
"ideles", generalizations of number fields which simultaneously take 
values in R and Qp for all p.

The following paper is a good introduction:


Many more references can be found here:


Here is a quote from Yu. I. Manin:

"On the fundamental level our world is neither real nor p-adic; it is 
adelic. For some reasons, reflecting the physical nature of our kind of 
living matter (e.g. the fact that we are built of massive particles), 
we tend to project the adelic picture onto its real side. We can 
equally well spiritually project it upon its non-Archimediean side and 
calculate most important things arithmetically.
The relations between 'real' and 'arithmetical' pictures of the world 
is that of complementarity, like the relation between conjugate 
observables in quantum mechanics."

I've never seen any discussion of this on the FOM. Is there anyone who 
knows both enough math and enough physics to comment?

-- JS

More information about the FOM mailing list