Motivic equivalence of quadratic forms

Let X_φ and X_ψ be projective quadrics corresponding to quadratic forms φ and ψ over a field F . If X_φ is isomorphic to X_ψ in the category of Chow motives, we say that φ and ψ are motivic isomorphic and write φ{m}~ψ . We show that in the case of odd-dimensional forms the condition φ{m}~ψ is equivalent to the similarity of φ and ψ . After this, we discuss the case of even-dimensional forms. In particular, we construct examples of generalized Albert forms q_1 and q_2 such that q_1{m}~ q_2 and q_1~ q_2 .