was one reason why Nordström turned to scalar theories of gravitation (while Einstein explored tensor theories). Nordström's first attempt to propose a suitable relativistic scalar field equation of gravitation was the simplest and most natural choice imaginable: simply replace the Laplacian in the Newtonian field equation with the D'Alembertian or wave operator, which gives . This has the result of changing the vacuum field equation from the Laplace equation to the wave equation, which means that any "news" concerning redistribution of matter in one location is transmitted at the speed of light to other locations. Correspondingly, the simplest guess for a suitable equation of motion for test particles might seem to be where the dot signifies differentiation with respect to proper time, subscripts following the comma denote partial differentiation with respect to the indexed coordinate, and where is the velocity four-vector of the test particle. This force law had earlier been proposed by Abraham, but it does not preserve the norm of the four-velocity as is required by the definition of proper time, so Nordström instead proposed . However, this theory is unacceptable for a variety of reasons. Two objections are theoretical. First, this theory is not derivable from a Lagrangian, unlike the Newtonian field theory (or most metric theories of gravitation). Second, the proposed field equation is linear. But by analogy with electromagnetism, we should expect the gravitational field to carry energy, and on the basis of Einstein's work on relativity theory, we should expect this energy to be equivalent to mass and therefore, to gravitate. This implies that the field equation should be nonlinear. Another objection is more practical: this theory disagrees drastically with observation. Einstein and von Laue proposed that the problem might lie with the field equation, which, they suggested, should have the linear form , where F is some yet unknown function of , and where Tmatter is the trace of the stress–energy tensor describing the density, momentum, and stress of any matter present. In response to these criticisms, Nordström proposed his second theory in 1913. From the proportionality of inertial and gravitational mass, he deduced that the field equation should be , which is nonlinear. Nordström now took the equation of motion to be or . Einstein took the first opportunity to proclaim his approval of the new theory. In a keynote address to the annual meeting of the Society of German Scientists and