Understanding quantum theory as an emergent phenomenon

When we say that there is an underlying theory from which quantum theory is emergent, we are interested in some expansion parameter, which can be used to relate the approximate theory to the more exact theory. The way speed of light relates special relativity to Newtonian mechanics, and \hbar relates quantum mechanics to classical mechanics.

However, the present case is not like these examples. We are not relating two mechanical theories. Quantum theory is an emergent phenomenon. It emerges as a statistical thermodynamics [equilibrium] approximation to the underlying dynamics which is trace dynamics. Just as the equilibrium thermodynamics of a fluid is emergent from the statistical thermodynamics of the underlying atomistic theory of molecular motion.

The coarse-graining parameter relating trace dynamics to the emergent quantum theory is a time scale. The underlying microscopic theory holds at Planck time scale resolution. When averaged over time scales much larger than Planck time, using the methods of statistical thermodynamics, the emergent theory is quantum theory.

The trace dynamics has a conserved charge of dimension of action

C = sum [q,p]_B - sum {q,p}_F

i.e. the sum over all bosonic degrees of freedom of the commutators [q_i, p_i] minus the sum over all fermionic degrees of freedom of the anti-commutators {q_i, p_i} At thermodynamic equilibrium this charge is equipartitioned, and each commutator /anti-commutator is set equal to \hbar. This is how QM emerges.

One way to glean information (about the microscopic dynamics) from the emergent theory is to study fluctuations about equilibrium.

Another way is to think of the QFT description of the standard model as a thermodynamic description. Which is what it actually is anyway, in this theory. The free parameters of the standard model are then getting determined and fixed by the underlying microscopic theory of the atoms of space-time-matter [octonionic theory / trace dynamics]. The fact that the underlying theory is able to do so is evidence that quantum theory is an emergent thermodynamic phenomenon.

But is there a control parameter analogous to speed of light, which lets us think of quantum theory as a leading order approximation to trace dynamics. It does not seem so. To my understanding, that is not how statistical thermodynamics works. But I could be wrong about this.

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Attached is Einstein's prophetic view on quantum theory as an emergent phenomenon, as quoted in `Subtle is the Lord' [Pais]

Prof. Stephen Adler's book `Quantum theory as an emergent phenomenon' is a perfect reading of Einstein's mind. He befittingly held the chair Albert Einstein Professor of Physics at the Institute of Advanced Study, Princeton.