Black Holes and the Information Paradox: a Solution?

Gravity has a good sense of humour. On the one hand, it’s the weakest force we know. The upward push of your chair is more than enough to counteract the pull of the entire planet! Yet gravity has an ace up its sleeve – unlike all other forces, it’s always attractive. For larger objects, the other forces start bickering and cancelling out. But gravity just keeps on getting stronger, until it’s impossible to escape – a black hole!

As a theoretical physicist, I tend to carry a black hole whenever I’m travelling.

As you can see, the top of this bucket is the surface of a black hole, otherwise known as the event horizon. When I release water from a glass above the black hole, it is attracted to the black hole, and falls inexorably towards it, never to be seen again.

Okay, I suppose my bucket isn’t a real black hole. After all, it’s the gravity of the Earth that pulls the water in. And light can definitely escape because I can see inside it! But it does accurately represent the bending of space and time. Albert Einstein taught us that everything in the universe rolls around on the cosmic quilt of spacetime, like balls on an elastic sheet. A heavy ball distorts the sheet, creating my black hole bucket.

You might not feel too threatened by black holes – after all, the nearest one is probably 8 billion billion miles away. But in actual fact you could be falling into a black hole right now without noticing! Turns out that for a large enough black hole, the event horizon is so far away that gravity there is very weak. So there’s no reason why you should experience anything special.

This disturbing fact has an unexpected consequence from the microscopic world of quantum mechanics. Every quantum theory must have a single vacuum, essentially the most boring and lazy state of affairs. If I stand still the vacuum is just empty space. But as soon as I start accelerating something weird happens. Particles suddenly appear from nowhere!

What does that mean for our black hole? Well if you’re not falling in, you must be accelerating away to oppose the huge pull of gravity! This means that you should see the black hole glowing with particles called Hawking radiation. Remember my black hole full of water? Well, you haven’t fallen in. And that means I have to cover you with Hawking radiation!

Luckily for your computer, the Hawking confetti that came out isn’t the same as the water that went in. From your perspective the water has simply disappeared! Exactly the same thing seems to happen for real black holes.

This black hole magic trick has become infamous among scientists, resisting all efforts at explanation. But a solution might be at hand, courtesy of Hawking himself! What if you could slightly change the vacuum every time something dropped into the black hole? Then, if you’re very careful, you might just be able to reconstruct the original water from the confetti of Hawking radiation.

Put another way, the event horizon takes a lock of soft hair from every passing particle as a memento of its existence. This information is eventually carried off by Hawking’s magic particles, reminding us of what we’d lost. It remains for soft experts, like myself, to work out the exact details.

This post is based on a talk given for the Famelab competition. You can read the full paper by Stephen Hawking, Malcolm Perry and Andy Strominger here.

Tidbits from the High Table of Physics

This evening, I was lucky enough to dine with Brenda Penante, Stephane Launois, Lionel Mason, Nima Arkani-Hamed, Tom Lenagan and David Hernandez. Here for your delectation are some tidbits from the conversation.

• The power of the renormalisation group comes from the fact that the $1$-loop leading logarithm suffices to fix the leading logarithm at all loops. Here’s a reference.
• The BPHZ renormalisation scheme (widely seen in the physics community as superseded by the Wilsonian renormalisation group) has a fascinating Hopf algebra structure.
• The central irony of QFT is thus. IR divergences were discovered before UV divergences and “solved” almost instantly. Theorists then wrangled for a couple of decades over the UV divergences, before finally Wilson laid their qualms to rest. At this point the experimentalists came back and told them that it was the IR divergences that were the real problem again. (This remains true today, hence the motivation behind my work on soft theorems).
• IR divergences are a consequence of the Lorentzian signature. In Euclidean spacetime you have a clean separation of scales, but not so in our world. (Struggling to find a reference for this, anybody know of one?)
• The next big circular collider will probably have a circumference of 100km, reach energies 7 times that of the LHC and cost at least £20 billion.
• The Fourier transform of any polynomial in $cos(x)$ with roots at $\pm (2i+1) / (2n+1)$ for $1 \leq i \leq n-1$ has all positive coefficients. This is equivalent to the no-ghost theorem in string theory, proved by Peter Goddard, and seems to require some highly non-trivial machinery. (Again, does anyone have a reference?)

and finally

• Never, ever try to copy algebra into Mathematica late at night!