A black hole walks into a bar and orders a drink.
The bartender asks if it would like food with that.
The black hole says, “No thanks, I’m a light eater.”
Nature, it seems, is a pretty good confidant after all.
In a paper published in Physical Review Letters, researchers at Los Alamos National Laboratory (LANL) in the US show that once a message has been scrambled by a black hole, not even an advanced quantum computer can put it back together.
In other words, black holes are nature’s fastest data-scramblers, and any secrets thrown into them may be more secure than previously thought.
According to a report by Jacob Marks in Physics World, scramblers (also referred to as a randomizer) are quantum systems that take local information and spread it across the entire system, generating quantum entanglement between distant regions.
Or, to put it simply, it is a device that manipulates a data stream before transmitting.
While black holes are perhaps the most famous example, scramblers also exist in simple systems such as “spin chains” — 1D arrangements of quantum particles with coupling between nearest neighbours — and in “strange” metals.
Electrons in strange metals dissipate energy as fast as they’re allowed to under the laws of quantum mechanics, and the electrical resistivity of a strange metal, unlike that of ordinary metals, is proportional to the temperature.
Although the scrambling process is deterministic — that means, a fixed input yields a fixed output — scrambling systems can give rise to tremendously complex behaviour, distributing information in seemingly random fashion, the report said.
This emergence of apparent randomness is known as “quantum chaos,” in analogy with classical chaos theory, where similarly simple systems produce equally intricate dynamics.
Quantum chaos is the field of physics attempting to bridge the theories of quantum mechanics and classical mechanics.
So what draws physicists to scramblers at the intersection of quantum mechanics and gravity in deep space? Why do we care?
In part, because of the so-called “black hole information paradox” — a puzzle which has captured the imagination of scientists around the world.
This paradox revolves around the ultimate fate of information that falls past the event horizon and into a black hole.
After a message is scrambled across the surface of a black hole, is its information trapped in the black hole forever, or does it somehow manage to escape?
That nasty e-mail, your wrote about your mother-in-law, and tossed into a black hole? It might be coming back to haunt you.
According to Einstein’s general theory of relativity, the gravity of a black hole is so intense that nothing can escape it. Ultimate doom for anybody or anything.
But one school of thought holds that information does escape from black holes in the form of photons emitted via a process known as Hawking radiation (after famed theoretical physicist Stephen Hawking), the report said.
In a series of breakthrough papers, some theoretical physicists now say with confidence, information does escape a black hole.
Remember the classic fable of Humpty Dumpty?
Poor fellow, he had a great fall, and all the kings horses and all the king’s men, couldn’t put Humpty back together again.
Well, if this egg-citing fellow, would have fallen into a black hole, he would not be gone for good. Particle by particle, the information needed to reconstitute Humpty would re-emerge, thus forever ruining the point of the fable.
To be fair, most physicists have long assumed it would; that was the upshot of string theory, the leading candidate for a unified theory of nature.
But the new calculations, though inspired by string theory, stand on their own.
Information gets out through the workings of gravity itself — just ordinary gravity with a single layer of quantum effects.
While this theory received some corroboration in 2019 (see Prof. Don Page, below), the jury is still out.
In 2007, while investigating this paradox, physicists Patrick Hayden and John Preskill came up with a thought experiment, the report said.
Assuming that black holes do encode information in Hawking radiation, they showed that when a message is sent into a black hole, its pieces can be rapidly recovered by capturing a few of the emitted photons — a process akin to recovering the slices of a shredded document from the heat given off by the shredder.
However, while the black hole’s scrambling behaviour makes such a recovery possible, the Hawking radiation alone doesn’t tell you how to unscramble a scrambled message.
Other approaches are needed to, in effect, reassemble the shredded document from its paper strips.
Enter machine learning algorithms.
These powerful pattern-identifying tools “learn” how to best approximate a physical system by comparing outputs of the real system to their own outputs, tweaking their internal model, and then rinsing and repeating until reality and approximation align.
Sounds easy, right?
The central quantity in this learning process is a mathematical quantity known as the “cost function,” which captures the degree of deviation between the model and the real system, the report said.
In classical machine-learning methods, the cost function is like a mountain range, replete with peaks and troughs that represent its higher and lower values.
Minimizing the cost function — and learning a model for the system — is like finding a descending path and following it down to base camp.
When the model is a quantum system modelled on a quantum computer, however, the cost function landscape isn’t as rich, the report said.
In fact, the LANL researchers showed that when the algorithm is asked to model a scrambler, it suffers from the problem of “barren plateaus.”
“The cost function is essentially flat everywhere,” says Zoe Holmes, a postdoctoral scholar at LANL and lead author on the paper.
This absence of features in the cost function renders quantum machine learning ineffective, because finding a random starting point within the landscape is almost impossible without a downward path to follow.
“If you’re learning using a cost function evaluated on a quantum computer, no matter how many training pairs you have, you won’t be able to learn the scrambler,” Holmes says, “at least without prior knowledge.”
This flaw rules out the possibility of reconstructing a message, which would entail inverting the scrambling process.
Furthermore, the LANL researchers concluded that even if the pieces of a scrambled message are known, putting them back together poses a problem that quantum computers cannot help us solve.
It is also worth noting, that research by University of Alberta professor Don Page, has also had a profound effect on understanding what goes on, inside a black hole.
According to a report by George Musser at Quanta Magazine, Page considered an aspect that had been relatively neglected: quantum entanglement.
Einstein would describe it as “spooky action at a distance” because of the instantaneousness of the apparent remote interaction between two entangled particles, no matter how far they are apart.
The emitted radiation maintains a quantum mechanical link to its place of origin. If you measure either the radiation or the black hole on its own, it looks random, but if you consider them jointly, they exhibit a pattern.
It’s like encrypting your data with a password. The data without the password is gibberish. The password, if you have chosen a good one, is meaningless too. But together they unlock the information.
Maybe, thought Page, information can come out of the black hole in a similarly encrypted form.
Page calculated what that would mean for the total amount of entanglement between the black hole and the radiation, a quantity known as “entanglement entropy.”
Initially, as radiation trickles out of the black hole, the entanglement entropy grows. Page reasoned that this trend has to reverse.
The entropy has to stop rising and start dropping if it is to hit zero by the endpoint. Over time, the entanglement entropy should follow a curve shaped like an inverted V.
This is now known, as the “Page Curve.”
With that, the problem got much more acute.
Physicists had always figured that a quantum theory of gravity came into play only in situations so extreme that they sound silly, such as a star collapsing to the radius of a proton.
Now Page was telling them that quantum gravity mattered under conditions that, in some cases, are comparable to those in your kitchen.
This left physicists to calculate the entanglement entropy.
Does the entanglement entropy follow an inverted V or not? If it does, the black hole preserves information, which means particle physicists were right. If it doesn’t, the black hole destroys or bottles up information, and general relativists can help themselves to the first doughnut at faculty meetings.
Over the past two years, physicists have shown that the entanglement entropy of black holes really does follow the Page curve, indicating that information gets out.
It dribbles out in a highly encrypted form — in fact, it is so encrypted that it doesn’t look as if the black hole has given up anything.
Sources: Physics World, Quanta Magazine, Wikipedia, World Science Festival, Phys.org