We study the interplay of Einstein’s Gravitation (GR) and Maxwell’s Electromagnetism, where the distribution of energy‐momentum is not presently known (The Feynman Lectures, Vol 2, Chapter 27, section 4). As Feynman himself stated, one might in principle use Einstein’s equations of GR to find such a distribution. GR (born in 1915) presently uses the Levi‐Civita connection, LCC (the LCC was born two years after GR as a new concept, and not just as the pre‐existing Christoffel symbols that represent it). Around 1927, Einstein proposed for physics an alternative to the LCC that constitutes a far more sensible and powerful affine enrichment of metric Riemannian geometry. It is called teleparallelism (TP). Its Finslerian version (i.e. in the space‐time‐velocity arena) permits an unequivocal identification of the EM field as a geometric quantity. This in turn permits one to identify a completely geometric set of Einstein equations from curvature equations. From their right hand side, one may obtain the actual distribution of EM energy‐momentum. It is consistent with Maxwell’s equations, since these also are implied by the equations of structure of TP. We find that the so‐far‐unknown terms in this distribution amount to a total differential and do not, therefore, alter the value of thetotalEM energy‐momentum. And yet these extra terms are at macroscopic distances enormously larger than the standard quadratic terms. This allows for the generation of measurable gravitational fields by EM fields. We thus answer affirmatively the question of the title. © 2004 American Institute of Physics