Distance Between Physical Theories Based on Information Theory

Abstract

We introduce a concept of distance between physical theories described by an action. The definition of the distance is based on the relative entropy. We briefly discuss potential physical applications.

Dark Energy and the Time Dependence of Fundamental Particle Constants

“…The Planck energy E 0 and its time-dependent generalization E(t) play a central role in the considerations presented here, see (5), (6) and (12). Actually, E 0 has been used in this paper with 2 meanings:…”

“…Not testable in particle processes, it turns out, however, that E(t) from eq. (12) can be directly observed in dark energy measurements. Dark energy observations do not usually concern the very early universe, so that the parabolic approximation (12) should be good enough 2 .…”

“…As for any parabola, hidden in the parabolic dark energy (12) and (15) are 3 parameters, which need to be determined from observations. They may be chosen as Since there are more parameters than in the ansatz of a cosmological constant, the observations will only give relations between i, ii and iii.…”

“…They are in effect testing eq. ( 7), and E(t) in (12) not only governs the ω-term but according to (13) and (??) also enters the G-term on the RHS of (7).…”

Relative entropy and proximity of quantum field theories

“…where each entry is multiplied by an "order one number", as follows from dimensional analysis considerations. As 6 The diagonal c = 4/5 model has primaries with weights hr,s = ((6r − 5s) 2 − 1)/120 for r = 1, ..., 4 and s = 1, ..., r. expected, if we evaluate the proximity of two theories in the IR, there is a power law divergent contribution. In the M S scheme, the leading log contribution is: 7…”