D O C U M E N T 1 2 K A L U Z A ’ S T H E O R Y 3 1 ds2 = gμνdxμdxν (1) whose coefficients (gμν = gνμ) g11 g12 g13 g14 g15 g21 g22 g23 g24 g25 — — — — — — — — — — g51 g52 g53 g54 g55 should not, according to what has been said, depend on x5. The components g11 ... g44 should describe the gravitational field g15, g25, g35, g45 would be the electric potentials, g55 a field value that still awaits interpretation and may perhaps be related to the Poincaré pressure that played a kind of awkward stand-in role in the theory of the electron. Kaluza’s essential hypothesis, now, consists of the assumption that the laws of nature should be generally covariant in this five-dimensional world. Thus the ways and means by which the electromagnetic potentials occur in the laws of nature are necessarily connected with the ways and means by which the gravitational poten- tials occur, which signifies a trenchant limitation of the possibilities. Thus the pos- sibility arises for us to construct the physical worldview on a uniform Hamiltonian function that does not contain heterogeneous terms superficially welded together by a plus sign. Mr. Kaluza introduces another tensor for the material current besides the magnitudes gμν, however. But it is clear that the introduction of such a tensor only serves to give a preliminary, merely phenomenological description of matter, whereas the ultimate goal we envision today is a pure field theory in which the field variables represent the field of “empty space” as well as the electric elementary particles that make up “matter.” Nonetheless, the fundamental weak points of Kaluza’s idea must not be left unmentioned. In the general theory of relativity, which operates with the four- dimensional continuum, ds2 = gμνdxμdxν means a directly measurable magnitude for a local inertial system using measuring rods and clocks, whereas the ds2 of the five-dimensional manifold in Kaluza’s ex- tension initially stands for a pure abstraction that seems not to deserve direct met- rical significance. Therefore, from the physical point of view, the requirement of general covariance of all equations in the five-dimensional continuum appears completely unfounded.[7] Moreover, it is a questionable asymmetry that the re- quirement of the cylinder property distinguish one dimension above the others and yet with reference to the structure of the equations all five dimensions should be equivalent. [p. 3]