Quantum Worlds, Classical Worlds

Our universe, as it is today, is dominated by classical bodies, which produce, and live in, a classical spacetime. This is the substrate shown in the figure below.

There is a sprinkling of systems for which we get to see the actual quantum behaviour. These are shown at the top left of the figure.

Then we realise that classical systems are a limiting case of quantum systems. This is shown by the curved arrowhead on the left of the figure.

Our current formulation of quantum systems embeds them in a classical spacetime, as depicted by the coloured arrow marked `Approximate'. Howsoever successful by the standard of current experiments, this formulation can only be approximate. Because the truth is, we do not really need the classical substrate, nor the classical spacetime, to describe quantum systems. Nor should we have to depend on the classical substrate - it is after all a limiting case of quantum systems and quantum spacetime, and a theory should not have to depend on its own limit, for its formulation.

Quantum systems, produce and live in a quantum spacetime, as shown in the top right. This is where the standard model truly lives, irrespective of what energy scale we study. However we currently describe the standard model only approximately, which is why our understanding of the standard model is only partial.

Note that this diagram makes no reference to the energy scale. It is true at all energies. UV as well as IR.