Shred a document, and you can piece it back together. Burn a book, and you could theoretically do the same. But send information into a black hole, and it’s lost forever. That’s what some physicists have argued for years: That black holes are the ultimate vaults, entities that suck in information and then evaporate without leaving behind any clues as to what they once contained.

**But new research shows that this perspective may not be correct.**

“According to our work, information isn’t lost once it enters a black hole,” says Dejan Stojkovic, PhD, associate professor of physics at the University at Buffalo. “It doesn’t just disappear.”

Stojkovic’s new study, “Radiation from a Collapsing Object is Manifestly Unitary,” appeared on March 17 in Physical Review Letters, with UB PhD student Anshul Saini as co-author.

The paper outlines how interactions between particles emitted by a black hole can reveal information about what lies within, such as characteristics of the object that formed the black hole to begin with, and characteristics of the matter and energy drawn inside.

This is an important discovery, Stojkovic says, because even physicists who believed information was not lost in black holes have struggled to show, mathematically, how this happens. His new paper presents explicit calculations demonstrating how information is preserved, he says.

The research marks a significant step toward solving the “information loss paradox,” a problem that has plagued physics for almost 40 years, since Stephen Hawking first proposed that black holes could radiate energy and evaporate over time. This posed a huge problem for the field of physics because it meant that information inside a black hole could be permanently lost when the black hole disappeared—a violation of quantum mechanics, which states that information must be conserved.

### Information Hidden in Particle Interactions:

In the 1970s, Hawking proposed that black holes were capable of radiating particles, and that the energy lost through this process would cause the black holes to shrink and eventually disappear. Hawking further concluded that the particles emitted by a black hole would provide no clues about what lay inside, meaning that any information held within a black hole would be completely lost once the entity evaporated.

Though Hawking later said he was wrong and that information could escape from black holes, the subject of whether and how it’s possible to recover information from a black hole has remained a topic of debate. Stojkovic and Saini’s new paper helps to clarify the story.

Instead of looking only at the particles a black hole emits, the study also takes into account the subtle interactions between the particles. By doing so, the research finds that it is possible for an observer standing outside of a black hole to recover information about what lies within.

Interactions between particles can range from gravitational attraction to the exchange of mediators like photons between particles. Such “correlations” have long been known to exist, but many scientists discounted them as unimportant in the past.

“These correlations were often ignored in related calculations since they were thought to be small and not capable of making a significant difference,” Stojkovic says. “Our explicit calculations show that though the correlations start off very small, they grow in time and become large enough to change the outcome.”

### Further information on the Black hole information paradox

The **black hole information paradox** results from the combination of quantum mechanics and general relativity. It suggests that physical information could permanently disappear in a black hole, allowing many physical states to devolve into the same state. This is controversial because it violates a commonly assumed tenet of science—that in principle complete information about a physical system at one point in time should determine its state at any other time. A fundamental postulate of quantum mechanics is that complete information about a system is encoded in its wave function up to when the wave function collapses. The evolution of the wave function is determined by a unitary operator, and unitarity implies that information is conserved in the quantum sense. This is the strictest form of determinism

##### Principles in action

There are two main principles in play:

**>** Quantum determinism means that given a present wave function, its future changes are uniquely determined by the evolution operator.

**>** Reversibility refers to the fact that the evolution operator has an inverse, meaning that the past wave functions are similarly unique.

The combination of the two means that information must always be preserved.

Starting in the mid-1970s, Stephen Hawking and Jacob Bekenstein put forward theoretical arguments based on general relativity and quantum field theory that not only appeared to be inconsistent with information conservation but was not accounting for the information loss and state no reason for it. Specifically, Hawking’s calculations indicated that black hole evaporation via Hawking radiation does not preserve information. Today, many physicists believe that the holographic principle (specifically the AdS/CFT duality) demonstrates that Hawking’s conclusion was incorrect, and that information is in fact preserved. In 2004 Hawking himself conceded a bet he had made, agreeing that black hole evaporation does in fact preserve information.

##### Hawking radiation

In 1975, Stephen Hawking and Jacob Bekenstein showed that black holes should slowly radiate away energy, which poses a problem. From the no-hair theorem, one would expect the Hawking radiation to be completely independent of the material entering the black hole. Nevertheless, if the material entering the black hole were a pure quantum state, the transformation of that state into the mixed state of Hawking radiation would destroy information about the original quantum state. This violates Liouville’s theorem and presents a physical paradox.

More precisely, if there is an entangled pure state, and one part of the entangled system is thrown into the black hole while keeping the other part outside, the result is a mixed state after the partial trace is taken into the interior of the black hole. But since everything within the interior of the black hole will hit the singularity within a finite time, the part which is traced over partially might disappear completely from the physical system.

Hawking remained convinced that the equations of black-hole thermodynamics together with the no-hair theorem led to the conclusion that quantum information may be destroyed. This annoyed many physicists, notably John Preskill, who bet Hawking and Kip Thorne in 1997 that information was not lost in black holes. The implications that Hawking had opened led to a “battle” where Leonard Susskind and Gerard ‘t Hooft publicly ‘declared war’ on Hawking’s solution, with Susskind publishing a popular book, The Black Hole War, about the debate in 2008. (The book carefully notes that the “war” was purely a scientific one, and that at a personal level, the participants remained friends.) The solution to the problem that concluded the battle is the holographic principle, which was first proposed by ‘t Hooft but was given a precise string theory interpretation by Susskind. With this, “Susskind quashes Hawking in the quarrel over quantum quandary”.

There are various ideas about how the paradox is solved. Since the 1997 proposal of the AdS/CFT correspondence, the predominant belief among physicists is that information is preserved and that Hawking radiation is not precisely thermal but receives quantum corrections. Other possibilities include the information being contained in a Planckian remnant left over at the end of Hawking radiation or a modification of the laws of quantum mechanics to allow for non-unitary time evolution.

In July 2004, Stephen Hawking published a paper presenting a theory that quantum perturbations of the event horizon could allow information to escape from a black hole, which would resolve the information paradox. His argument assumes the unitarity of the AdS/CFT correspondence which implies that an AdS black hole that is dual to a thermal conformal field theory. When announcing his result, Hawking also conceded the 1997 bet, paying Preskill with a baseball encyclopedia “from which information can be retrieved at will.” However, Thorne remains unconvinced of Hawking’s proof and declined to contribute to the award.

According to Roger Penrose, loss of unitarity in quantum systems is not a problem: quantum measurements are by themselves already non-unitary. Penrose claims that quantum systems will in fact no longer evolve unitarily as soon as gravitation comes into play, precisely as in black holes. The Conformal Cyclic Cosmology advocated by Penrose critically depends on the condition that information is in fact lost in black holes. This new cosmological model might in future be tested experimentally by detailed analysis of the cosmic microwave background radiation (CMB): if true the CMB should exhibit circular patterns with slightly lower or slightly higher temperatures. In November 2010, Penrose and V. G. Gurzadyan announced they had found evidence of such circular patterns, in data from the Wilkinson Microwave Anisotropy Probe (WMAP) corroborated by data from the BOOMERanG experiment. The significance of the findings was subsequently debated by others.

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