Take the tour ×  Newton's 2nd law which is central to Newtonian
dynamics, is a vector equation   Same with Maxwell's equations
in the covariant form.  On the other hand, general relativity is
governed by the tensor equation  $\displaystyle
R_{\mu\nu}-\frac{1}{2}R~g_{\mu\nu} =\frac{8\pi G}{c^4}
T_{\mu\nu}$  My questions are:    1. Is there a deep reason why
some dynamical equations are tensor (of the 2nd rank) equations
and others are vector equations?   2. Is Schrodinger equation a
scalar equation?   3. Are there dynamical equations in physics
which are tensor equations of rank higher than 2?   4. Is there
an upper bound on the highest rank a physics tensor equation can
have? from some physical argument may be? share|improve this
question A tensor is mathematically a vector, since the set of
all such-and-such tensors forms a vector space. A vector is also
a tensor, since it is a linear map from the dual space onto the
field over which the vector space is defined. So there doesn't
seem to be that much of a dif