Black holes = quantum particles?
This article is compiled from Quanta Magazine[1].
When two black holes collided, the super-strong impact rippled through the universe. Physicists used Albert Einstein's theory of gravity to predict the rough outlines of these gravitational waves as they passed through Earth, and the LIGO and Virgo gravitational-wave detectors have confirmed wave after wave. But physicists are starting to get bogged down as they try to use Einstein's controversial equations to extract the ultra-precise shapes of all possible reverberations. These as-yet-unknown details are critical to fully understanding the subtle fluctuations that the next generation of observatories should capture.
However, the breach could come from a seemingly impossible direction. Over the past few years, physicists who specialize in the mysterious behavior of quantum particles have turned their mathematical machines toward black holes -- particles that look like particles at a distance. Several teams have made surprising discoveries recently. They have shown that the behavior of gravitational waves (or electromagnetic waves) can be fully understood through just one of its myriad particles, just as we can understand the precise contours of a tsunami after examining a single water molecule.
Radu Roiban, a theoretical physicist at Penn State University who was not involved in the study, said: "I don't think it's possible, and I'm still a little bit reluctant to accept that."
These results could help future researchers explain the more dramatic space-time jitters that future observatories will record. They also mark the next step in understanding how quantum particle theory captures events happening on the level of our greater reality.
Zvi Bern, a theoretical particle physicist at UCLA's Bhaumik Institute for Theoretical Physics, said: "What precise connection do these quantum ideas have with the real world? That's what their research is about, and it provides a better understanding than we've ever had before ."
Zvi Bern, a theoretical particle physicist at the Bhaumik Institute for Theoretical Physics at the University of California, Los Angeles.
Quantum Cheat Codes
In principle, most physicists agree that quantum equations can also handle large objects. After all, we're mostly a cloud of electrons and quarks. In practice, however, Newton's laws are sufficient. If we're calculating the arc of a cannonball, it doesn't make sense to start with electrons.
"No one in their right mind would say, 'Let's think about quantum theory, solve this problem, and lead to classical physics,'" Bern said. "That would be silly."
But gravitational-wave astronomy is driving physicists to consider desperate measures. When two black holes spiral toward each other and slam together, the shape of the churn in spacetime depends on their mass, spin and other properties. To fully understand the cosmic rumble felt by the gravitational-wave facility, physicists calculated in advance how various black hole pairings would shake spacetime. Einstein's equations of general relativity were too complex to solve precisely, so some of LIGO/Virgo's waveforms came from precise supercomputer simulations. Some may take a month. The LIGO/Virgo collaboration relies on the collection of hundreds of thousands of waveforms cobbled together through simulation and other faster but cruder methods.
In at least some cases, particle physicists believe they can get faster and more accurate results. From a zoomed-in perspective, black holes look a bit like massive particles, and physicists have spent decades thinking about what happens when particles collide in a vacuum.
"We've had really good results over the years with quantum scattering in gravity," Bern said. "We have all these amazing tools that allow us to do these very complex calculations."
Their main tool is amplitude, a mathematical expression that gives the probability of a quantum event. For example, the "four-point" amplitude describes two particles entering and two particles leaving. In recent years, Bern and other theorists have applied four-point quantum amplitudes to the motion of massive classical black holes, reaching or in some cases exceeding the precision of some advanced waveform calculations.
"It's amazing how fast these people are progressing, and they're really pushing this," said Alessandra Buonanno, director of the Max Planck Institute for Gravitational Physics and an award-winning theorist who specializes in predicting the shape of gravitational waves.
Alessandra Buonanno, director of the Max Planck Institute for Gravitational Physics
All in One
Classical physicists eschew amplitude for good reason. They are full of infinite possibilities. Even a collision described by a four-point function—two particles entering, two particles leaving—can temporarily produce an arbitrary number of short-lived particles. The more of these transient particles a calculation takes into account, the more "loops" it "loops" and the more precise it becomes.
It got worse. A four-point function can have an infinite number of possible loops. But the four-point function isn't the only possibility when two black holes meet. The researchers also had to consider the five-point function (one radiated particle collides), the six-point function (two particles from one collision), and so on. Gravitational waves can be thought of as collections of an infinite number of "graviton" particles, and an ideal calculation would cover all of them -- with infinitely many functions, each with infinitely many loops.
It's like looking for a needle in a haystack. In this quantum "haystack" of infinite width and depth, the amplitude researchers needed to identify the classical needles that influence the shape of the wave.
A clue emerged in 2017 [2], when Walter Goldberger of Yale University and Alexander Ridgway of Caltech studied the classical radiation emitted by two colliding objects with a certain charge. They took inspiration from a strange relationship between gravity and other forces, known as a double copy, and used it to turn a charged object into the analog of a black hole. They calculated the shape of the wave rolling outward and found a surprisingly simple and surprising quantum expression.
"You have to close your eyes and look at some terms," said theoretical physicist Donal O'Connell of the University of Edinburgh. "But it seems to me that they are calculating five-point amplitudes."
Donal O'Connell, a theoretical physicist at the University of Edinburgh
Out of curiosity, O'Connell and his collaborators explored further. They first [3] used a general quantum framework to calculate the simple properties of collisions between two large classical objects. Then in July 2021, they extended this method to calculate the properties of certain classical waves [4], confirming that the five-point amplitude is actually the right tool for the job.
Researchers stumbled upon an unexpected pattern in a haystack search. This suggests that they do not need infinite amplitudes to study classical waves. Instead, they can stop at a five-point amplitude -- which involves just one radiating particle.
"The five-point amplitude really matters," O'Connell said. "Every graviton or every photon that makes up the wave, doesn't care if there's another."
Further calculations revealed why the five-point amplitude tells us everything we need to know about the classical world.
The quantum results have two decisive features. They have uncertainty. For example, electrons diffuse into a nebulous cloud. Furthermore, the equations that describe them, like the Schrodinger equation, have a constant of nature known as Planck's constant.
Classical systems, such as gravitational waves passing through Earth, are so clear that they can even be described by Planck's constant. These properties gave O'Connell's team a touchstone for determining which amplitudes are classical: they must be free of uncertainty, and there cannot be Planck's constant in the final description. The team found that the simplest five-point amplitude has two "segments," one with Planck's constant and one without. The first fragment is a quantum fragment that can be safely ignored. The second is classical radiation - the part useful for gravitational wave astronomy.
They then turned their attention to the loopless six-point amplitude -- the emission of two radiating particles. This amplitude gives the wave's uncertainty because having two radiating particles is like measuring the magnetic field twice. At first glance, this amplitude is difficult to explain, and Planck's constant is everywhere.
But when they calculated the results in detail [5], many of the Planck constant terms canceled each other out. Ultimately, O'Connell and his collaborators found that the six-point uncertainty also divides into a classical segment and a quantum segment. It is inevitable that the classical uncertainty proves to be zero. And the quantum part doesn't. In other words, the six-point amplitude has no classical information at all. In retrospect, this outcome seems somewhat inevitable. But before examining the fragments in detail, the researchers naively expected that the six-point amplitude might still have some subtle classical meaning.
"It's purely quantum," O'Connell said. "It's a little shocking to me, at least."
O'Connell studied a force related to the electromagnetic force. So to test whether this result also holds for gravity, Ruth Britto of Trinity College Dublin and others used various technical shortcuts to calculate the loopless six-point amplitude of two massive particles [6]. They found that it also had no classic content.
Riccardo Gonzo, also at Trinity College Dublin, who worked on both results, said: "Unless you do the calculations, it's hard to believe."
Similar logic led the researchers to expect that at higher loops, all amplitudes beyond five points are either quantum and therefore negligible, or can be expressed as a simple function of known amplitudes. Endless, uncertain relationships all but guarantee this.
"One would expect that quantum field theory does describe classical physics, and it turns out that it does so in such a way that uncertainty is zero in certain states," Roiban said.
It turns out that classical waves are easier to describe in the language of quantum mechanics than researchers feared. "Gravitational waves, or any type of wave, are big, soft things," Roiban said. "It should depend on a lot of little things, but once you know the collision plus a photon or a graviton in its final state, then you know everything."
Spiraling Toward Mergers
When LIGO/Virgo picked up gravitational waves, there was 10% noise in the signal. Future detectors, such as space-based LISA, may record fluctuations in space-time with 99 percent or better fidelity. At this level of clarity, researchers expect gravitational waves to reveal a wealth of information, such as the hardness of merging neutron stars. Recent advances in using quantum amplitudes to predict the shape of waves give researchers hope of unlocking this information.
"It would be great if it turns out to be the case," Buonanno said. "I think it will simplify the calculations eventually, but we'll have to wait and see."
For now, however, computing true astrophysical waveforms from amplitudes remains an ambitious project. The four-point and five-point amplitudes capture what happens when black holes "scatter" or eject from each other, and the technique can currently be extrapolated to understand simple mergers where black holes don't spin. But in their current state, these amplitudes are difficult to fully describe the more complex mergers detected by gravitational-wave observatories. Amplitude researchers believe they can adapt their method to calculate the real waveforms of various mergings, but they haven't done so yet.
Beyond gravitational waves, the general nature of the study suggests that the way the uncertainty principle organizes quantum haystacks may prove useful in other areas of quantum theory. The infinite relationship between amplitudes enables independent cross-checks, for example, providing valuable guidance for calculations that take months. It could be a poignant test of distinguishing quantum theories that can describe the macroscopic world from those that cannot.
"It used to be an intuition, now it's a clear standard," Roiban said. "It's a calculation, and it's hard to argue with a calculation."
Link:
[1]https://www.quantamagazine.org/massive-black-holes-shown-to-act-like-quantum-particles-20220329/
[2] https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.125010
[3] https://arxiv.org/abs/1811.10950
[4] https://arxiv.org/abs/2107.10193
[5] https://arxiv.org/abs/2112.07556v1
[6] https://arxiv.org/abs/2112.07036
