The Black Hole Information Paradox

The infamous black hole information paradox stems from the theory put forward by Stephen Hawking in his infamous paper “Particle Creation by Black Holes” in which he discusses whether black holes are immortal or not. According to Hawking’s paper, space is full of quantum fluctuations where virtual particles of matter and antimatter constantly materialize and then instantly annihilate one another, the energy is borrowed from nearby (or even from the empty vacuum of space itself) and then returned when annihilation occurs. When this phenomenon occurs near a black hole, one of the virtual particles can theoretically be sucked into the black hole leaving its partner alone. As a result, the energy is not returned to the black hole since one of the virtual particles does not have a partner hence it is emitted as radiation thus coining the term “Hawking Radiation”, hence this implies that black holes shrink and eventually die out. However, this theory violates a key aspect of quantum mechanics, particularly, the “No-hiding theorem” and “unitarity”, in which quantum information cannot be destroyed but is r conserved in some form or other. Kumar, Pati, Samal from the Indian Institute of Science explain this concept perfectly in one of their papers “Experimental Test of the Quantum No-Hiding Theorem” in which it is stated “The no-cloning and the no-deleting theorems are the consequences of linearity and the unitarity. Together with the stronger no-cloning theorem they provide permanence to quantum information, thus suggesting that in the quantum world, information can be neither created nor destroyed.”The conundrum of the black hole information paradox comes in at this point because, if quantum information cannot be destroyed, then what happens to all the information of matter that was sucked in by the black hole at the end of its life?

There are many possible solutions to the black hole information paradox, some sound outlandish whilst others seem more in the realm of possibility. The most convincing solution was recently brought up by Don N. Page who worked with Hawking and was close friends. In his research paper “Black Hole Information”, Page looked more into quantum entanglement, \a phenomenon that occurs when a group of ‘entangled’ particles exist such that their quantum state is dependent on one another thus meaning that their behavior is shared in one way or another. Page implies that there is a quantum entanglement that exists within the virtual particle that is sucked in and the particle that is emitted as radiation meaning that the black hole itself and the Hawking Radiation are connected through quantum means. Originally, Hawking’s theory dictates that the entanglement entropy, the degree of quantum entanglement and information between two subsystems (in this case the black hole and Hawking radiation), increases till the end of the black hole’s life cycle. However, Page argues that if black holes were to also release information, then for it to mathematically make sense, the entanglement entropy must initially increase and then after the halfway point of a black hole’s life the entanglement entropy must decrease so all the information can escape. Essentially for this approach to work, there must be a special event that occurs at the halfway point of a black hole’s life. Hawking radiation’s semiclassical approach to the life cycle of black holes is theoretically impressive but due to the hypothesized lifespan of black holes there is a lack of empirical evidence that supports Hawking and this also holds true to Page’s potential solution.However, Page’s work points physicists in the right direction in finally solving the black hole information paradox and towards a theory unifying quantum and relativistic mechanics.

Page’s approach as explained by Quanta Magazine

Bibliography:

Hawking, Stephen. Particle Creation by Black Holes. University Of Cambridge.

Rani Samal, Jharana, et al. Experimental Test of the Quantum No-Hiding Theorem. Indian Institute of Science.

N. Page, Don. Black Hole Information. University of Alberta.

Sutter, Paul. “A Spiderweb of Wormholes Could Solve a Fundamental Paradox First Proposed by Stephen Hawking.” livescience.com, 21 Mar. 2022, www.livescience.com/black-hole-paradox-solution.