Arrow of Time: You don’t need a special initial condition. The reason entropy is lower in the past is an effect of quantum mechanics. Take the Schrödinger Equation evolving over time into a superposition of Cat Dead, Cat Alive. An electron interacts with the system, becomes entangled with the system, creating a single measurement outcome, one with a single recorded past (I’m an optimist, so let’s say Cat Alive). Decoherence guarantees the branching, one with a single recorded effect, the other branching away into the unobserved unrecorded. The future (from our position in the global wave function) isn’t recorded, therefore thermodynamic processes will always increase (entropy will always go up, increase). Unitarity guarantees that entropy will always be lower in the past because the past matters (there are less connecting branches, or better still, less complicated entanglements, correlations, configurations). To see this, let’s become pessimistic (The cat died). Let’s run our quantum experiment again, placing a dead cat into the experiment. The state will evolve to a mixed state (Dead cat 1 and Dead cat 2). We open the box, perform our measurement and…well, I’m not sure which version of the dead cat we have. But one thing my prediction can safely rule out. No miracles. The cat won’t come back to life in violation of unitarity. This also takes the mystery out of the measurement process. Measurement is quantum recording of a given quantum state. It is a basic function of quantum unitary evolution. You don’t need minds, or God. QM takes care of the whole operation. The apparent wave function collapse is explained because the past is what is measured, recorded, supervened.

Complementarity: It is built into the Schrödinger Equation, it’s what drives the branching effect. Decoherence is the process that gives the geometry that allows the architecture in which we can speak of a plurality of worlds. “The strong form of complementarity, which takes it beyond relativity, is this: There are many equally valid views of your subject—perspectives, in the general sense of that word—but they are mutually exclusive. In the quantum world, we can realize only one perspective at a time. Quantum cubism is a no-go.”

Boltzmann Brains: Black Hole entropy is fundamental. Quantum Information does not fill in the volume of space; therefore our universe is not globally ergodic. BB is ruled out. Nature is giving us an important clue, a flashing light actually at the event horizon. Warning: A (globally) maximum entropic state is not possible. Proceed with caution.

Black Hole / White Hole: Two sides of the complementarity coin. Outside, it appears as a black hole, inside it appears as a white hole, a Plank star. The energy dissipates from one universe into the creation of another universe. Biology now supersedes physics as each universe gives birth to a new one, diluting matter and radiation from one universe compressing it into low entropy, high-quality energy to start the birth cycle anew. The gate closes, and evaporates away. Another Universe takes hold. And you can’t get there unless you are there. Just like I can’t get to the 2nd BCE of Ancient China. Was information lost? From this (local) universe, yes. But globally (from the multiverse) information is retained in the glow of a New Big Bang.