  We present a short account of our work to provide quantum electrodynamics
with a 'product picture'. It aims to complement the longer exposition in a
recent paper in 'Foundations of Physics' and to help to make that work more
accessible. The product picture is a formulation of QED, equivalent to standard
Coulomb gauge QED, but in which the Hilbert space arises as (a certain physical
subspace of) a product of a Hilbert space for the electromagnetic field and a
Hilbert space for charged matter (i.e. the Dirac field) and in which the
Hamiltonian arises as the sum of an electromagnetic Hamiltonian and a charged
matter Hamiltonian and an interaction term. (The Coulomb gauge formulation of
QED is not a product picture because, in it, the longitudinal part of the
electromagnetic field is made out of charged matter operators.) We also recall
a 'Contradictory Commutator Theorem' for QED which exposes flaws in previous
attempts at temporal gauge quantization of QED and we explain how our product
picture appears to offer a way to overcome those flaws. Additionally, we
discuss the extent to which that theorem generalizes to Yang-Mills fields. We
also develop a product picture for nonrelativistic charged particles in
interaction with the electromagnetic field and point out how this leads to a
novel way of thinking about the theory of many nonrelativistic electrically
charged particles with Coulomb interactions. We explain how the provision of a
product picture for QED gives hope that one will be able likewise to have a
product picture for (Yang Mills and) quantum gravity -- the latter being needed
to make sense of the author's 'matter-gravity entanglement hypothesis'. In an
afterword, we briefly discuss similarities and differences between that
hypothesis and its predictions and ideas of Roger Penrose related to a possible
role of gravity in quantum state reduction and to cosmological entropy.
