Here, β = (β, 0, 0) is used. These results can be summarized by E ∥ ∥ ′ = E ∥ ∥ B ∥ ∥ ′ = B ∥ ∥ E ⊥ ⊥ ′ = γ γ ( E ⊥ ⊥ + β β × × B ⊥ ⊥ ) = γ γ ( E + β β × × B ) ⊥ ⊥ , B ⊥ ⊥ ′ = γ γ ( B ⊥ ⊥ − − β β × × E ⊥ ⊥ ) = γ γ ( B − − β β × × E ) ⊥ ⊥ , and are independent of the metric signature. For SI units, substitute E → E ⁄ c. Misner, Thorne & Wheeler (1973) refer to this last form as the 3 + 1 view as opposed to the geometric view represented by the tensor expression F μ μ ′ ν ν ′ = Λ Λ μ μ ′ μ μ Λ Λ ν ν ′ ν ν F μ μ ν ν , and make a strong point of the ease with which results that are difficult to achieve using the 3 + 1 view can be obtained and understood. Only objects that have well defined Lorentz transformation properties (in fact under any smooth coordinate transformation) are geometric objects. In the geometric view, the electromagnetic field is a six-dimensional geometric object in spacetime as opposed to two interdependent, but separate, 3-vector fields in space and time. The fields E (alone) and B (alone) do not have well defined Lorentz transformation properties. The mathematical underpinnings are equations (T1) and (T2) that immediately yield (T3). One should note that the primed and unprimed tensors refer to the same event in spacetime. Thus the complete equation with spacetime dependence is F μ μ ′ ν ν ′ ( x ′ ) = Λ Λ μ μ ′ μ μ Λ Λ ν ν ′ ν ν F μ μ ν ν ( Λ Λ − − 1 x ′ ) = Λ Λ μ μ ′ μ μ Λ Λ ν ν ′ ν ν F μ μ ν ν ( x ) .