If black holes lose information in an event horizon, then do we have a paradox with our cosmic horizon?
“The history of astronomy is a history of receding horizons.” –Edwin Hubble
Perhaps the biggest surprise of all about the Universe came at the very end of the 20th century: the discovery of dark energy and the accelerated expansion of the Universe. Rather than being pulled towards us gravitationally, the most distant galaxies in the Universe are speeding away from us at ever faster-and-faster speeds, destined to disappear from our view. But does that create its own information paradox? Rob Hansen wants to know, and inquires:
The universe’s expansion means our visible horizon is retreating; things faraway are vanishing continuously. (Albeit slowly, right now.) This would seem to imply we are losing information about the universe. So why is it the idea of losing information in a black hole’s event horizon is so controversial, if we’re constantly losing information to another horizon?
There’s a lot to unpack here, so let’s start with the accelerated expansion of the Universe.
If you want to imagine the early Universe, you have to picture something very different than the Universe today. Rather than stars and galaxies separated by vast, cosmic distances of virtual emptiness, the young Universe was hot, dense, full of matter and radiation, and expanding extremely rapidly. At an incredible rate, the Universe was getting less dense, with all the particles in it rushing away from one another on average. Yet over time, that expansion rate slowed down, as the gravitational influence of matter and energy worked to attempt to recollapse the Universe.
It was a close race, and if the Universe were imbalanced just a little, it could have expanded into oblivion, preventing stars and galaxies from ever forming, or have recollapsed entirely, imploding in a fantastic Big Crunch. Yet neither one of those two possibilities came to pass. For billions of years, it looked like the Universe was going to be right on the edge — the critical case — where it would neither expand forever into nothingness nor recollapse. Instead, the expansion rate would asymptote down to zero.
But all that changed in the late 1990s. By observing distant supernovae and measuring how the Universe had expanded over billions of years, astronomers discovered something remarkable, puzzling and entirely unexpected. After maybe seven billion years of the expansion rate slowing down, with gravitation fighting the initial outward push of the Big Bang, distant galaxies stopped slowing down as they receded from us. Instead, they began accelerating, and speeding away faster and faster. This accelerated expansion of the Universe not only has continued ever since, but has allowed us to predict the far future of the distant Universe. It isn’t pretty.
Galaxies that are more distant than about 15 billion light years away are already beyond our reach. The light we’re emitting right now, 13.8 billion years after the Big Bang, will never reach them, and the light they’re emitting will never reach us. If you were to survey the entire observable Universe, you’d find that approximately 97% of all the galaxies in it have already reached this point. They are forever unreachable by us, even if we left today, even at the speed of light.
But does that necessarily mean information is disappearing? We might not be able to reach those galaxies, but is that the same as losing information about them?
Not really. As time goes on, the most distant galaxies will disappear in a practical sense, but not in an absolute one. While the physical galaxies may be gone, the information from them continues to exist in our Universe. Photons that left a distant galaxy a long time ago get stretched by the expansion of the Universe, their wavelength lengthens, they drop in energy, and the number density of photons goes way down. But still, even as time goes on, information from these distant galaxies continues to arrive at our eyes, and there will even be stars and galaxies into the far future whose light becomes newly exposed to us for the first time.
Information isn’t being destroyed in any sense; we’re simply not collecting new information beyond a certain point about these galaxies. The cosmic horizon may be receding from us, but even as galaxies slip out to become unreachable, there’s no loss of information that already existed from our point of view. It remains in our Universe, accessible in principle with a large, powerful enough observatory of the right wavelength. In 100 billion years, it might take a telescope the size of a galaxy to see it, but the information is still around.
The black hole analogy is almost a perfect one, by the way, because if it weren’t for quantum physics, it would behave almost the same way as our Universe.
When you throw a book into a black hole, it simply adds mass to the black hole, growing the event horizon larger. But that’s not a problem for information; a larger, more massive black hole has more information encoded in it. In particular, the information about what was in the book gets encoded — albeit not in a practically retrievable sense — onto the black hole’s event horizon. From our perspective, outside the black hole, it takes an infinite, asymptotically long time for the book to fall in, meaning that if we can measure the gravitationally redshifted photons well enough and for a long enough time, we can continue to access that book’s information.
The information problem only comes when the black hole decays. While there were a specific number of protons, neutrons, electrons, etc. in the book — not to mention words, sentences and additional information — what comes out from a decaying black hole is simply randomized blackbody radiation. It’s just a thermal bath of particles. And as the event horizon goes away, so does the information. As Sabine Hossenfelder eloquently explained, nobody knows where a black hole’s information goes, or if it’s conserved at all.
But the Universe doesn’t decay. The distant galaxies disappear, but they aren’t destroyed. And the information from them becomes inaccessible to us, but only in a practical sense, not in an absolute one. Only if some new physics arises to cause our cosmic horizon to decay would this begin to present a paradox. The Universe might be accelerating; dark energy might come to dominate 99.99%+ of the energy of the Universe; the galaxies might all become inaccessible. But as disastrous and counterintuitive as dark energy is, at least it doesn’t break the conservation of information.
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