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In our recently proposed quantum theory of gravity, the universe is made of ‘atoms‘” of space-time-matter (STM). Planck scale foam is composed of STM atoms with Planck length as their associated Compton wave-length. The quantum dispersion and accompanying spontaneous localization of these STM atoms amounts to a cancellation of the enormous curvature on the Planck length scale. However, an effective dark energy term arises in Einstein equations, of the order required by current observations on cosmological scales. This happens if we propose an extremely light particle having a mass of about $10^{-33}{\mathrm{\text{eV/c}}}^2$, forty-two orders of magnitude lighter than the proton. The holographic principle suggests there are about $10^{122}$ such particles in the observed universe. Their net effect on space-time geometry is equivalent to dark energy, this being a low energy quantum gravitational phenomenon. In this sense, the observed dark energy constitutes evidence for quantum gravity. We then invoke Dirac’s large number hypothesis to also propose a dark matter candidate having a mass halfway (on the logarithmic scale) between the proton and the dark energy particle, i.e. about $10^{-12}{\mathrm{\text{eV/c}}}^2$.

We have recently proposed a Lagrangian in trace dynamics to describe a possible unification of gravity, Yang–Mills fields, and fermions, at the Planck scale. This Lagrangian for the unified entity — called the aikyon — is invariant under global unitary transformations, and as a result possesses a novel conserved charge, known as the Adler–Millard charge. In this paper, we derive an eigenvalue equation, analogous to the time-independent Schrödinger equation, for the Hamiltonian of the theory. We show that in the emergent quantum theory, the energy eigenvalues of the aikyon are characterized in terms of a fundamental frequency times Planck’s constant. The eigenvalues of this equation can, in principle, determine the values of the parameters of the standard model. We also report a ground state, in this theory of spontaneous quantum gravity, which could characterize a non-singular initial epoch in quantum cosmology.

In this paper, I review the basic ideas of “trace dynamics”, as formulated in my 2004 Cambridge University Press book “Quantum Theory as an Emergent Phenomenon”, and then discuss how they have influenced much of my work of the last two decades.

There are various reasons to believe that quantum theory could be an emergent phenomenon. Trace dynamics is an underlying classical dynamics of noncommuting matrices, from which quantum theory and classical mechanics have been shown to emerge, in the thermodynamic approximation. However, the time that is used to describe evolution in quantum theory is an external classical time, and is in turn expected to be an emergent feature — a relic of an underlying theory of quantum gravity. In this essay we borrow ideas from trace dynamics to show that classical time is a thermodynamic approximation to an operator time in quantum gravitational physics. This prediction will be put to test by ongoing laboratory experiments attempting to construct superposed states of macroscopic objects.

We propose an alternate version of the "shadow world" hypothesis for the origin of dark matter. Instead of postulating that the shadow world is a "mirror" world under parity or charge-parity reflection, we suggest that the existence of a shadow world arises from the fact that i or –i can be the imaginary unit in complex quantum mechanics. This mechanism is a natural consequence of "trace dynamics" pre-quantum theory, from which quantum mechanics over the complex number field emerges as a statistical mechanical approximation. Because the pre-quantum dynamics does not pick out a preferred imaginary unit, the emergent quantum dynamics contains two sectors, one based on i and the other on –i, with both sectors coupled to gravity.

Quantum nonlocal correlations and the acausal, spooky action at a distance suggest a discord between quantum theory and special relativity. We propose a resolution for this discord by first observing that there is a problem of time in quantum theory. There should exist a reformulation of quantum theory which does not refer to classical time. Such a reformulation is obtained by suggesting that spacetime is fundamentally noncommutative. Quantum theory without classical time is the equilibrium statistical thermodynamics of the underlying noncommutative relativity. Stochastic fluctuations about equilibrium give rise to the classical limit and ordinary spacetime geometry. However, measurement on an entangled state can be correctly described only in the underlying noncommutative spacetime, where there is no causality violation, nor a spooky action at a distance.

There ought to exist a reformulation of quantum theory which does not depend on classical time. To achieve such a reformulation, we introduce the concept of an atom of space-time-matter (STM). An STM atom is a classical noncommutative geometry (NCG), based on an asymmetric metric, and sourced by a closed string. Different such atoms interact via entanglement. The statistical thermodynamics of a large number of such atoms gives rise, at equilibrium, to a theory of quantum gravity. Far from equilibrium, where statistical fluctuations are large, the emergent theory reduces to classical general relativity. In this theory, classical black holes are far from equilibrium low entropy states, and their Hawking evaporation represents an attempt to return to the [maximum entropy] equilibrium quantum gravitational state.

We start from classical general relativity coupled to matter fields. Each configuration variable and its conjugate momentum, as also spacetime points are raised to the status of matrices [equivalently operators]. These matrices obey a deterministic Lagrangian dynamics at the Planck scale. By coarse-graining this matrix dynamics over time intervals much larger than Planck time, one derives quantum theory as a low energy emergent approximation. If a sufficiently large number of degrees of freedom get entangled, spontaneous localisation takes place, leading to the emergence of classical spacetime geometry and a classical universe. In our theory, dark energy is shown to be a large-scale quantum gravitational phenomenon. Quantum indeterminism is not fundamental, but results from our not probing physics at the Planck scale.

There must exist a reformulation of quantum field theory which does not refer to classical time. We propose a pre-quantum, pre-spacetime theory, which is a matrix-valued Lagrangian dynamics for gravity, Yang–Mills fields, and fermions. The definition of spin in this theory leads us to an eight-dimensional octonionic spacetime. The algebra of the octonions reveals the standard model; model parameters are determined by roots of the cubic characteristic equation of the exceptional Jordan algebra. We derive the asymptotic low-energy value 1/137 of the fine structure constant, and predict the existence of universally interacting spin one Lorentz bosons, which replace the hypothesised graviton. Gravity is not to be quantized, but is an emergent four-dimensional classical phenomenon, precipitated by the spontaneous localisation of highly entangled fermions.