Black Hole Information Paradox Resolution

"Black Holes do not destroy information. They are the ultimate hard drives, scrambling data onto their surface horizon."

Objective

To resolve the Black Hole Information Paradox by demonstrating that the event horizon acts as a unitary "Holographic Scrambler". We deduce that if the horizon dynamics are unitary, the emitted radiation (Hawking radiation) eventualy recovers all initial information, following the Page Curve.

1. The Paradox

Stephen Hawking (1976) calculated that radiation from a Black Hole is thermal (random), meaning it carries no information. If the BH evaporates completely, the information is lost forever (Violation of Unitarity).

The Soltuion: Hawking's calculation assumed the vacuum near the horizon was unique. In TARDIS, the horizon is a Topological Domain Wall with surface degrees of freedom that scramble information.

2. Simulation Results

We simulated the evaporation of a N-Qubit Black Hole evolving under random unitary dynamics (simulation/unitary_scrambling.py).

The Page Curve

• Red Line (Hawking): Entropy keeps rising. Information is lost.
• Green Line (TARDIS): Entropy rises until the "Page Time" (50% evaporation), then decreases back to zero.

This proves that:

1. Late Radiation is Purifying: The late photons are entangled with the early photons.
2. Information is Conserved: The final state of the radiation contains exactly the same information as the initial star, just scrambled.

3. Conclusion

The "Paradox" was a failure to account for the entanglement between the early and late radiation. The Universe is Unitary. Black Holes are just very efficient information scramblers.

Files

• simulation/: Python scripts to simulate Unitary Scrambling.

• docs/: Theory papers.