Origin of Einstein and Grossmann’s adoption of the term “tensor”

Determine the historical pathway and rationale by which Albert Einstein and Marcel Grossmann chose to generalize the term “tensor” to designate systems transforming linearly under first derivatives of the coordinates in their 1913 Entwurf paper, replacing Ricci and Levi-Civita’s terminology of “covariant and contravariant systems.” Identify the sources, influences, and documentary evidence (e.g., Hamilton’s quaternion usage, Voigt’s crystal mechanics, and contemporary vector analysis) that led to this idiosyncratic substitution.

Background

Appendix A explains that, where Ricci and Levi-Civita spoke of “covariant and contravariant systems,” Einstein and Grossmann introduced the more general use of the term “tensor” for all systems transforming linearly under first derivatives of the coordinates in the Entwurf paper. Contemporary commentators noted this novel usage, and the appendix surveys earlier meanings of “tensor” (e.g., Hamilton’s scalar magnitude in quaternions, Föppl’s electrodynamics) as well as Voigt’s introduction of tensor triples in crystal mechanics.

Despite this historical context, the paper emphasizes that the specific decision-making process by which Einstein and Grossmann adopted and generalized the term “tensor” has not been traced in surviving documents and remains unsettled. Clarifying this would illuminate how analytic and vectorial traditions were subsumed into the mathematical framework of general relativity.