Is math physically complete?

topsquark

Math Team
Beyond horizons, all "information" exchange is noncausal, but otherwise probabilistic and approaching completeness in this regard.
I second that.

Beyond horizons, what? Non-causal, yes. Probabilistic, yes, depending on what you mean. Completeness? I have no idea what you mean by this.

-Dan

romsek

Math Team
another key question is information exchange between who?

If the at least two involved in the who are on opposite sides of the horizon we're positing that there is no information exchange.

If both are on the far side of the horizon then we here on the near side of the horizon have virtually zero information on anything happening on the far side much less any information exchanges going on.

There's actually some good videos out there about this, what do folks on opposite sides of an event horizon observe regarding one another.

I'm pretty sure that all of this is worked out mathematically. Penrose diagrams illustrate pretty well the whole situation.

As I understand things, which is not well, there are two candidates for saving unitarity.

One is that Hawking radiation can somehow be descrambled, at least theoretically, and so any quantum information that passed the horizon is actually discernable, perhaps in the distant future.

The other is that all information resides intact on the event horizon itself. But I think this leads to the firewall that violates the equivalence principle. Hawking's last paper before his death addressed this though most physicists treat that paper with some skepticism. I've seen a few authors claim to have solved this issue. To be honest it's all way above my level of mathematics and understanding of QFT and GR.

Loren

Consider a unitary decay, with two photons oppositely expanding and entangled with each other, defining a horizon.

Centered within this horizon, an observer can communicate information causally with any other entity inside.

From the horizon, only thermal (Hawking-probabilistic) information communicates to the center (or vice versa), thus the Bell inequality.

Relatively centered expansion beyond light speed defines limiting spacetime, outside of which only one-way signaling is permitted.