Information paradox and black holes in plasmas

Chris Lee
Simulating the event horizon the old fashioned way, with computers.
Black holes are a problem for physics, and the physics community has never fully warmed to the idea of them. That's because, at the center of a black hole, the mathematics go haywire. More specifically, the equations of general relativity predict that the curvature of space should be infinite, and no one hates an infinity more than a physicist.
That was bad enough, but then it was discovered that black holes are not entirely black. At the very point of no return—where the pull of gravity is so strong that not even light can escape—light is emitted in the form of Hawking radiation. Exactly how Hawking radiation is generated doesn't really concern us here. For physicists, this is also a conundrum. The emission of Hawking radiation from a black hole violates the conservation of information. In an effort to resolve this idea through experiments, physicists are turning to the laboratory, where experiments can mimic black holes.

Where does the information go?

In quantum mechanics, a particle is described by a wave function—a mathematical device with no direct measurable physical meaning—that encapsulates all physical knowledge of that particle. I can chuck that particle into a black hole, but the black hole's wave function does not appear to be altered by this event in a way that preserves the information. The Hawking radiation that is emitted later doesn't obviously contain information about the particle, either.
Even though I've grossly over-simplified this to the point of palpable wrong-ness, the conclusion is that all information related to the particles swallowed by the black hole appears to be gone. Quantum mechanics, on the other hand, tells us that the information should either be encoded in the black hole's wave function or contained in the wave function of the emitted light.
Physicists have argued about this for many years, and they eventually concluded that the information is indeed preserved in some manner, but exactly how and where is still being argued. Of the competing ideas, one involves a kind of delayed correlation. During the black hole's lifetime, Hawking radiation is emitted until right near the end. As the black hole dies, it emits a burst of radiation that is correlated to all the radiation emitted earlier in the black hole's life.
It's a nice idea, but no one has a pet black hole they can test this on. Enter physics by analogy. Physics by analogy is something I've a hard time accepting, but it does have its uses. The basic idea is this: in physics, many different physical systems are described by similar or even identical mathematics. You can then use physical measurements on an accessible experiment to understand what is going on in an inaccessible physical system like a black hole.

Big-ass lasers and hot plasmas, oh my

In this case, researchers are proposing to use accelerating plasma mirrors to mimic the event horizon of an evaporating black hole. That short sentence has a lot going on in it, so prepare for a circuitous and tortuous journey into the realm of plasma physics, big-ass lasers, and (maybe) black hole physics.
A plasma is nothing more than a gas of electrons and positively charged ions floating around together as a single fluid. One way to create a plasma is to shine an intense laser pulse on a gas. The laser pulse rips the electrons out of the atoms, creating a cloud of fast-moving electrons so quickly that the positively charged nuclei don't even get a chance to move. Now you have a gas of electrons that acts like a mirror for light. But it's not a stationary mirror. The separation between the electrons and the positively charged nuclei creates a huge electric field that accelerates the electrons to nearly the speed of light. So this is not just a mirror; it's a mirror that's moving at a respectable fraction of the speed of light.
Thanks to that motion, a second laser pulse will not just be reflected; it will also be doppler shifted (exactly like the sound emitted from sirens on emergency vehicles). So you can shine green light on the mirror, and if it's moving toward you, you get X-ray radiation back. That's pretty cool all by itself.
But it doesn't end there. The X-ray radiation can be directed onto a solid material. Not just any solid material, but one where the density is carefully increased the deeper into the material you go (you can do this by drilling holes in the material, for instance, and hoping that everything averages out). The X-Ray pulse will ionize the entire material. But the change in density means there are more positive charges deeper in the material, and the charges accelerate the newly freed electrons into the material. Those stop abruptly as they run into the increasingly solid material.
This second batch of electrons also serves as a plasma mirror, one that behaves like a black hole but with an accelerated lifetime. During the initial part of the acceleration, the equations for the plasma mirror mimic a black hole in its prime, emitting Hawking radiation in a steady stream. The violent end of the mirror looks like a dying black hole and will also emit radiation.
Given the similarity, one can examine how the Hawking radiation is emitted: do you really get a burst of Hawking radiation at the end, and are these last photons highly correlated with either each other or with the Hawking radiation that was emitted earlier? If so, maybe that last burst of radiation does resolve the information paradox.
The nice thing about this is that the experiment can really be done. There are laser facilities in France and the US that are big and bad enough to create exactly the right conditions. The measurements on the analog Hawking radiation are tough, but there is no real reason they can't be done.

An analogy is still a story

But all of this doesn't really help a lot. Let's imagine that the result is that we observe a high degree of correlation between early Hawking radiation and late Hawking radiation. What does that tell us? It tells us that an accelerating plasma mirror emits correlated radiation. It tells us that if black hole physics is fully analogous, then the same mechanisms are at play. It does not tell us that black hole physics is fully analogous. And if the result is negative, in that there is no correlation? Is that because the physics analogy is imperfect, or can we really apply the result to black holes?
The reason we're having this entire argument about information loss in black holes is because the physics is poorly understood. The mathematics could still be wrong, or some other mechanism for maintaining information may be at play. No matter what the experiment tells us, it doesn't actually tell us anything reliable about black holes until we have a properly worked out unified theory of gravity and quantum mechanics. The one true win is that there are many different physical systems that all imitate black holes in slightly different ways and with slightly different assumptions. If they all agree, then maybe a deeper conclusion is possible.
I also know that there are limits to how wrong our models can be, because we have measurements on star systems, neutron stars, galaxies, and the Universe itself to place limits on models. And with every advance in our models, more trust can be placed in physics-by-analogy experiments. That means that we can get useful information from physics-by-analogy experiments. But the event horizon of a black hole is, currently right on the edge of where we know it all goes wrong, so interpret with caution.
Physical Review Letters, 2017, DOI: 10.1103/PhysRevLett.118.045001
Information paradox and black holes in plasmas Reviewed by Bizpodia on 00:27 Rating: 5

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