After half a century of flummoxing physicists, a mystery which reveals an incompatibility between our theories of the colossal (general relativity) and the miniscule (quantum mechanics) called the “Black Hole Information Paradox” may have been resolved.
Professors Xavier Calmet from the University of Sussex's School of Mathematical & Physical Sciences, and Stephen Hsu from Michigan State University, published a paper in the journal Physical Review Letters earlier this month claiming “quantum hair” is the key to the resolution of the paradox, expanding on the refutation of John Wheeler’s “No Hair theorem” hinted at earlier by cosmologist and physicist Stephen Hawking.
The heart of the paradox is this: Wheeler, who coined the term “black hole” in 1967, proved that all black holes can be perfectly described using only their mass, electric charge, and speed of rotation. This means that once a black hole forms, all the information about the dead star from which it had formed and what might have fallen into it in its lifetime is irrelevant to its description.
Wheeler called it the “no hair” theorem, claiming that black holes were “bald”. When Hawking proved that black holes die by emitting “Hawking Radiation”, it meant that all the information about its entire history is permanently lost with its evaporation.
This result is in direct conflict with quantum mechanics’ axiom of the conservation of information which, simply put, states that information cannot be created or destroyed. Nevertheless, that’s exactly what black holes seem to be doing, bringing the two most successful scientific theories ever into fundamental conflict.
In Hawking’s own words: “This apparent loss of information, known as the information paradox, has troubled scientists for the last forty years, and still remains one of the biggest unsolved problems in theoretical physics.”
Speaking to The Guardian, Dr. Calmet said “It was generally assumed within the scientific community that resolving this paradox would require a huge paradigm shift in physics, forcing the potential reformulation of either quantum mechanics or general relativity,”. Several such approaches which tinker with general relativity and quantum mechanics, such as the “fuzzball” theory, “firewall” theory, string theory, and even wormholes have been formulated, but scientific consensus is far from established on them.
“What we found – and I think is particularly exciting – is that this isn’t necessary.” Calmet added. Dubbed as the “Yes Hair Theorem”, the new proposed solution doesn’t rely on modifying the two pillars of contemporary physics, but produces a novel mathematical model indicating that not all the information about what went into the black hole is erased after its death.
Instead, information about what went into the hole is encoded in the gravitational field of the black hole. Therefore, two black holes with identical mass, charge, and speed of rotation will, according to this theory, have slightly different gravitational fields according to the history of what fell into them within their lifetimes. This is what the paper refers to as “quantum hair” -- the source of finding the missing information and allegedly resolving the paradox.
However, empirical methods to test the new theory are beyond the reach of present day science. The difference in gravitational fields would be so small as to be practically immeasurable, leaving all the double-checking to an analysis of the assumptions used in the new theory and the mathematics involved in interpreting it.
This new paper is hardly the first declaration from physicists that the paradox has been conclusively resolved. For example, Quanta magazine reported researchers claiming to have resolved the paradox with their own “semi-classical” model in October, 2021.
“I’m very resistant to people who come in and say, ‘I’ve got a solution in just quantum mechanics and gravity because it’s taken us around in circles before.” said Nick Warner of the University of Southern California, speaking to Quanta about the research it had published.
In large part, this exemplifies the reservations Calmet and Hsu’s new theory will also have to overcome. “It’s a good thought-experiment, but without a theory of quantum-gravity, we should remain skeptical about the paradox having been conclusively resolved until we hear more from the physicist community” said Arun Mangalam, theoretical physicist at the Indian Institute of Astrophysics (IIA), while speaking to Mint.
Even if the model turns out to be correct, it only proves that some information about the black hole’s history is encoded into the gravitational field. However, it doesn’t quantify if all or precisely how much of the black hole’s information is encoded into the field, whereas a proof that all the information is conserved in the gravitational field is key to a comprehensive resolution of the paradox.
“That they haven’t shown and that’s the crux of the paradox,” said Prof Toby Wiseman, a theoretical physicist at Imperial College London, while speaking to The Guardian.
For his part, Calmet understands his colleagues’ skepticism. “It is going to take a while for people to accept that you don't need a radical solution to crack the issue," he said to the BBC.
Binit Priyaranjan is a freelance journalist, author and poet.