In this paper the physical implications of quaternion quantum mechanics are further explored. In a quanternionic Hilbert space H_Q , the lattice of subspaces has a symmetry group which is isomorphic to the group of all co-unitary transformations in H_Q . In contrast to the complex space H_C (ordinary Hilbert space), this group is connected, while for H_C it consists of two disconnected pieces. The subgroup of transformations in H_Q which associates with every quaternion q of magnitude 1, the correspondence ψ → qψq⁻¹ for all ψ∈ H_Q (called Q conjugations), is isomorphic to the three-dimensional rotation group. We postulate the principle of Q covariance: The physical laws are invariant under Q conjugations. The full significance of this postulate is brought to light in localizable systems where it can be generalized to the principle of general Q covariance: Physical laws are invariant under general Q conjugations. Under the latter we understand conjugation transformations which vary continuously from point to point. The implementation of this principle forces us to construct a theory of parallel transport of quaternions. The notions of Q-covariant derivative and Q curvature are natural consequences thereof. There is a further new structure built into the quaternionic frame through the equations of motion. These equations single out a purely imaginary quaternion η(x) which may be a continuous function of the space-time coordinates. It corresponds to the i in the Schrödinger equation of ordinary quantum mechanics. We consider η(x) as a fundamental field, much like the tensor g_μν in the general theory of relativity. We give here a classical theory of this field by assuming the simplest invariant Lagrangian which can be constructed out of η and the covariant Q connection. It is shown that this theory describes three vector fields, two of them with mass and charge, and one massless and neutral. The latter is identifiable with the classical electromagnetic field.