  There must exist a reformulation of quantum field theory, even at low
energies, which does not depend on classical time. The octonionic theory
proposes such a reformulation, leading to a pre-quantum pre-spacetime theory.
The ingredients for constructing such a theory, which is also a unification of
the standard model with gravitation, are : (i) the pre-quantum theory of trace
dynamics: a matrix-valued Lagrangian dynamics, (ii) the spectral action
principle of non-commutative geometry, (iii) the number system known as the
octonions, for constructing a non-commutative manifold and for defining
elementary particles via Clifford algebras, (iv) a Lagrangian with $E_8 \times
E_8$ symmetry. The split bioctonions define a sixteen dimensional space (with
left-right symmetry) whose geometry (evolving in Connes time) relates to the
four known fundamental forces, while predicting two new forces, $SU(3)_{grav}$
and $U(1)_{grav}$. This latter interaction is possibly the theoretical origin
of MOND. Coupling constants of the standard model result from left-right
symmetry breaking, and their values are theoretically determined by the
characteristic equation of the exceptional Jordan algebra of the octonions. The
quantum-to-classical transition, precipitated by the entanglement of a critical
number of fermions, is responsible for the emergence of classical spacetime,
and also for the familiar formulation of quantum theory on a spacetime
background.
