In this blog, I challenge the vaulted role that tensor calculus enjoys today. I will define a concrete example of what I consider to be a technical flaw in the tools of tensor calculus in all modern physics theories. The complaint is about completeness, that partial stories are not good enough. Please feel free to defend the status quo in the comments.
The relativistic quantum field equation for a spin 0 particle is the Klein-Gordon equation (written in natural units):
One takes the first derivative of the wave function. Also take three spatial derivatives. Then take the second time derivative of the wave function, and similarly for the three spatial derivatives.