The implications of a holographic universe for quantum information science and the nature of physical law
Several lines of evidence suggest that the total information content of the observable universe is bounded by a finite number given by the area of a cosmological surface divided by the Planck area. This is referred to as the holographic principle. The current bound is roughly 10 bits, but in the past it was smaller, varying like t in the early universe. Although the bound is too large today to affect most of everyday physics, it does have profound implications for highly complex systems and for cosmology. For example, the project to build a useful quantum computer, which is projected to exploit states possessing exponential complexity, comes into conflict with the information bound at a level of entanglement of about 400 qubits, suggesting a breakdown of unitary evolution at this threshold, possibly associated with the emergence of classicality. If the information bound is applied to the quantum vacuum, it yields an energy density close to the observed density of cosmological dark energy. However, because the bound is timedependent, the vacuum energy will vary in time too, and consistency with energy conservation then demands that G or c varies with time over cosmological time scales. Further sweeping implications follow if one adopts the philosophy that information is primary (‘the universe is a computer’), and that the laws of physics do not exist in a transcendent Platonic realm of perfect mathematical forms and operations, as is conventionally supposed, but are fundamentally tied to the real physical universe, with its finite age and resources, and subject to the holographic information bound. I suggest a generalization of the information bound based on this point of view, formulated in terms of algorithmic information theory, and briefly mention some of consequences for black holes and the inflationary universe scenario.