The Theory Experiment Connection: Rn Space and Inflationary Cosmology

Based on a discussion of the theory experiment connection, it is proposed to tighten the connection by replacing the real and complex number basis of physical theories by sets R n , C n of length 2n finite binary string numbers. The form of the numbers in R n is based on the infinite hierarchy of 2n figure outputs from measurements of any physical quantity with an infinite range (distance, energy, etc.). A space and time based on these numbers is described. It corresponds to an infinite sequence of spherical scale sections R n,e (e an integer). Each section has the same number of points but the size increases exponentially with increasing e. The sections converge towards an origin which is a space singularity. Iteration of a basic order preserving transformation, F < or its inverse shows exponential expansion or contraction of the space with the origin as a source or sink of space points. The suitability of R n space as a framework for inflationary cosmology is based on a constant iteration rate for F < and making e and n = n(t) time dependent. At t = 0 all space is restricted to a region of scale sections R n0,e with n 0 (small) and e ≤ e 0 (negative). Inflation, which occurs naturally, is stopped at a time when all points in the outermost ∆ scale sections are expanding away from the origin at velocities > c. Then n increases to n I > n 0 where n I is such that the outermost ∆ scale sections of R n0 space are contained in the scale section R nI ,0 of R nI space. This is needed if R nI ,0 space is to be similar to the usual R space. Hubble expansion and the redshift are accounted for by a continuing slow increase in n. Comparison with experimental data suggests that the rate of increase must be at least one n unit every 30 − 60 million years.