  The predicted Standard Model (SM) electric dipole moments (EDMs) of electrons
and quarks are tiny, providing an important window to observe new physics.
Theories beyond the SM typically allow relatively large EDMs. The EDMs depend
on the relative phases of terms in the effective Lagrangian of the extended
theory, which are generally unknown. Underlying theories, such as
string/M-theories compactified to four dimensions, could predict the phases and
thus EDMs in the resulting supersymmetric (SUSY) theory. Earlier one of us,
with collaborators, made such a prediction and found, unexpectedly, that the
phases were predicted to be zero at tree level in the theory at the unification
or string scale $\sim\mathcal{O}(10^{16}$ GeV). Electroweak (EW) scale EDMs
still arise via running from the high scale, and depend only on the SM Yukawa
couplings that also give the CKM phase. Here we extend the earlier work by
studying the dependence of the low scale EDMs on the constrained but not fully
known fundamental Yukawa couplings. The dominant contribution is from two loop
diagrams and is not sensitive to the choice of Yukawa texture. The electron EDM
should not be found to be larger than about $ 5\times 10^{-30} e$ cm, and the
neutron EDM should not be larger than about $5\times 10^{-29}e$ cm. These
values are quite a bit smaller than the reported predictions from Split SUSY
and typical effective theories, but much larger than the Standard Model
prediction. Also, since models with random phases typically give much larger
EDMs, it is a significant testable prediction of compactified M-theory that the
EDMs should not be above these upper limits. The actual EDMs can be below the
limits, so once they are measured they could provide new insight into the
fundamental Yukawa couplings of leptons and quarks. We comment also on the role
of strong CP violation. EDMs probe fundamental physics near the Planck scale.
