What is the physical significance of tensors? Occasionally, motivating statements are made roughly along the lines of "if an equation can be expressed purely in terms of tensors, then it is true for all observers". But that doesn't seem quite complete because different tensor-users would have contradictory views on which coordinate frames do and do not represent physical observers. As I understand it, the exact same set of simple transformation rules is used for translating the components of all tensors between all pairs of coordinate frames. What then distinguishes the tensor equations in relativity theory from tensor equations in Newtonian mechanics (or Engineering)?