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I think based on the comments here that people missed a big point of this lecture. The Schrodinger equation describes the evolution of a wave function according to a Hamiltonian which is the generator of time translations. The Hamiltonian in classical gravity is zero, or NH = 0, for N the lapse function. This is a standard result of ADM general relativity. The reason for this, as Andre argued,...

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I think based on the comments here that people missed a big point of this lecture. The Schrodinger equation describes the evolution of a wave function according to a Hamiltonian which is the generator of time translations. The Hamiltonian in classical gravity is zero, or NH = 0, for N the lapse function. This is a standard result of ADM general relativity. The reason for this, as Andre argued, is Guass’ law, where there is no boundary sphere around the universe by which one can integrate out the mass-energy contained within. This argument can be posed according to the nature of coordinate time in general relativity, where this is a frame dependent quantity and physics should not depend upon it. So the Schrodinger equation

i∂ψ/∂t = Hψ = 0

is seen to be zero on both the left and right hand side in a consistent manner. This is the Wheeler-DeWitt equation Hψ = 0, which is the quantum form of the Hamiltonian constrant NH = 0.

This issue of course leads then to the arrow of time, and as Andre pointed out the problem of fine tuning. The arrow of time is something which appears to a local observer as there is a growth in the complexity of the system. We might then say the number of degrees of freedom is large. The work I have done involves a cosmology, or AdS spacetime on a D-brane. A nascent cosmology or spacetime is boosted from another so that the transverse degrees of freedom slow down. If there are high frequency modes these are time dilated an appear in the IR. The higher the boost, the more modes appear, which increases the number of degrees of freedom. This has the effect of making the quantum brane appear classical, which is also involved with the generation of particle states,

We often perform experiments from asymptotic infinity, just as S-matrix theory is based on sending something in from infinity and measuring things at infinity. In the case of the AdS spacetime we observers exist on its boundary. However, there is an imprecision in a measurement, which means an observer on the boundary is unable to make a precise measurement of the quantum gravity configuration of the interior. The e^{-N} error is in terms of the area of the boundary of the AdS_{n} spacetime of n dimensions A = ∂AdS_{n} defines N = A/G_{n} , for G_{n} the Newton gravity constant in n dimensions. The number of degrees of freedom N or information bits is proportional to entropy S = kN . This equals the entropy of the universe as determined on the boundary. This implies a de Sitter horizon, as a de Sitter spacetime is a conformally flat spacetime which can exist on the AdS_{n} boundary. This loss of information by holography is countered by an e^{S} which accounts for the information which is not available to this observer. Thus the observer on the boundary with partial information is a holographic “plate which contains all the information in the interior, which is this e^{+S}, with S > 0 state for emphasis. This means that we are limited in the amount of information we can learn about the universe at large, which is due to quantum gravity. This means that fine tuning is not absolute, such as with a Dedekind cut in mathematics, but there is a graininess to the tuning of fundamental constants

This breakdown in the ability to measure everything about the universe means spacetime is not something which can be assigned to a perfect observable. Spacetime is due to the assignments we make to certain coarse grained observations of the world, but which are approximate and dependent upon something deeper with the symmetries of spacetime This is maybe a subgroup, but where the geometric assignments we impose on these symmetries of spacetime are emergent. We must now identify what exist in our tool box of physics that might be emergent. These are likely then to be time, unitarity, locality and causality.

The last two paragraphs I lifted from the essay I submitted to the contest, and modified some. This should appear in the next few days.

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