Therefore, a black hole in the multiway causal graph may be characterized by the presence of two distinct horizons: a standard event horizon corresponding to regular causal disconnection, and an entanglement event horizon corresponding to multiway disconnection, which always lies strictly on the exterior of the causal event horizon. As such, from the point of view of an external observer in the multiway causal graph watching an infalling object to a black hole, the object will appear to “freeze” (due to quantum Zeno effects that are the multiway analog of time dilation) at the entanglement horizon, and will never get close to the true causal event horizon. Since Hawking radiation (which occurs as a consequence of non-convergent branch pairs in the multiway evolution graph) is emitted from the entanglement horizon and not the causal event horizon, the particles that get radiated from the black hole may be perfectly correlated with the information contained within the infalling object, without any apparent or actual violation of special relativity (since no information ever crossed a spacetime event horizon), thus resolving the black hole information paradox.

This resolution is formally quite similar to the standard resolution to the black hole information paradox implied by the holographic principle and the AdS/CFT duality.

Recall that the multiway causal graph encodes both the structure of the (purely quantum mechanical) multiway evolution graph, as well as the structures of the (purely relativistic) causal graphs corresponding to each branch of multiway evolution. Therefore, one can imagine “walling off” a certain bundle of causal edges in the multiway causal graph corresponding to some particular branch of multiway evolution, such that all of the causal edges inside the boundary of the wall correspond to edges in a purely relativistic causal graph (i.e. they designate causal relations between events in spacetime), whilst all of the causal edges intersecting the boundary of the wall correspond to edges in a purely quantum mechanical multiway graph (i.e. they designate causal relations between events in branchtime). As such, one immediately obtains a duality between the bulk gravitational theory on the interior of the wall, and the boundary quantum mechanical theory on the surface of the wall, just as in AdS/CFT. ]]>

Thinking about such a universe from the point of view of its causal structure, we can see that it therefore starts off with an arbitrarily large value for the speed of light (since the causal graph is arbitrarily densely connected, allowing information propagation at abnormally high speeds), which then converges down to a much lower value at late times. This makes such a universe compatible with a so-called “VSL” or “variable speed of light” cosmology; VSL cosmologies are known to yield similar observational consequences to standard inflationary models, and, in particular, allow for valid solutions to the horizon and flatness problems of ΛCDM cosmology.

]]>More precisely, a formal statement of the ER=EPR conjecture is that the Bekenstein–Hawking entropy of a pair of entangled black holes is equivalent to their entanglement entropy. If Hawking radiation effects occur as a result of branch pairs that fail to reconverge as a consequence of disconnections in the multiway causal graph, the ER=EPR conjecture is really just a rather elementary statement about the geometry of branchtime (in other words, it states that the natural distance metric in branchtime is the entanglement entropy of pairs of microstates, which one can prove directly from the properties of the Fubini–Study metric tensor).

]]>The analog of a gravitational singularity is a spatially localized but temporally extended structure in the causal graph with an unusually high density of causal edges. For certain classes of rules, spatially localized structures with sufficiently high causal edge density necessarily break off into locally disconnected regions of the causal graph; as such, these rules can be thought of as being consistent with Penrose’s weak cosmic censorship hypothesis.

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