Yes, if you consider one branch of the wavefunction, you have less than full information than the full state you branched from. But, the analogous situation would apply to a merger of different branches - you would have less than full information in one of the initial branches regarding the full resulting merged state.

I too would like to see a citation for this proposition
 

> In quantum mechanics, time-reversal is performed by complex conjugation $\psi \to {\psi }^{\ast }$

I worked my way through the QM textbook and this does not compute AFAIK.

Whenever time appears in the wave equations it's multiplied by i, so taking the complex conjugat is equivalent to replacing t with -t.

You're not classical, you just decohere very quickly.

For the rest, I'd have to think about your question more before answering.

Yes, it does generalize.

Don't think of it in terms of interaction. Think of it as relationships within a static network. The laws of physics constrain the network into a quasicrystalline structure.

Some nodes in this network are self-aware. The self-aware nodes tend to form channels which we call "people". When the channels fork we call it "decoherence".

Suppose you run a temporally causal experiment at macrostate $M_0$. For example, you drop a ball and want to see if it falls down to the ground. The results of your experiment cannot be located in the multiverse at $M_0$ because $M_0$ is where you released the ball. The ball has not moved nor has the clock ticked inside your head. Neither can the results of your experiment be located far away from $M_0$ because the initial experimental macrostate $M_0$ is self-locating information^[1]. If such a state existed anywhere in the multiverse then it would be located at $M_0$ by definition.

In a neighborhood of $M_0$, there are many slightly different versions of you and many slightly different versions of the ball. The results (possible futures) of your experiment is $O{m}_{\delta }$ where $m_{\delta }$ is the set of all elements in $m$ such that $0<min|m_{\delta }-O^{-1}{M}_0|<ϵ$ i.e. $m_{\delta }$ is the set of all microstates in a neighborhood of the inverse image $O^{-1}{M}_0$, excluding $O^{-1}{M}_0$ itself.

The entropy of the macrostates where the clock in your head and the ball have both ticked forward in time vastly outnumber the entropy of all alternative macrostates within $O{m}_{\delta }$. To a self-aware macrostate inside the multiverse, time is experimentally equivalent to a random walk along microstates—and is easily mistaken for causality—but time is fundamentally just the inside macrostatic view of a timeless quasicrystalline structure.

My post on Noether's theorem is a follow-up to this post [? · GW] which explains why the Lagrangian should be considered "temporal velocity". The idea of Lagrangian density as "temporal velocity density" comes from dividing both sides of the Lagrangian = "temporal velocity" equation by space.

My theory predicts that time points in the direction maximizing an entropy function. Locally, this theory predicts that the smallest things (localized quantum fields) evolve in the direction of time within their own reference frame i.e. they maximize proper time.