Laws of the Instant

Quantum entanglement suggests the existence of delicate non-local relationships that nevertheless cannot be used to transmit information.

In the hope that it will cast some light on this mystery and perhaps help in the creation of a quantum theory of the universe, I will draw attention to something not totally dissimilar in classical general relativity, namely initial-value constraints that, through elliptical equations, relate spatially separated points. Such 'laws of the instant' are already found in Maxwellian electrodynamics in the form of Gauss constraints but appear in a much more remarkable form in general relativity. Maxwell and Einstein showed that acceleration-inducing forces cannot be transmitted instantaneously but in the process created theories in which at any instant all momenta are tightly constrained. Moreover, there are also indications that even the position variables are constrained at the big bang and in black holes. I will present an interpretation of general relativity in which instantaneous shapes of the universe are primary and rods, clocks, duration and distance emerge from shape evolution. The big bang appears in the shape evolution as a unique 'Janus point' that divides the complete evolution into two qualitatively similar halves containing oppositely pointing arrows of time. In this interpretation a scale-invariant entropy-like quantity for the universe as a whole decreases, while there is an increase of the conventional entropy of the self-confined subsystems whose formation corresponds to the decrease of the universe's entropy-like quantity. I will argue that this offers the prospect of reconciling time-reversal symmetry of dynamical laws with the time-asymmetric growth of entropy. If successful, this will eliminate the difficulty Boltzmann encountered in trying to give a completely satisfactory resolution to the problem of the entropic arrow of time.