Can you tell what a black hole has been eating?

Black holes have a justifiably terrifying reputation. If you drop your keys in there, forget them, because they are gone. But are matters really so bad? Can a black hole "remember" what it's eaten? In this week's "Ask a Physicist" we'll find out.

'Shop by Reddit user malmazuke

The final winning question from our free book giveaway comes from Tony, who asks (referring to the material that falls into a black hole):

Is information physical?

Just to understand the question itself is going to require a little unpacking, and a fair amount of context. But let's start with a few handy reminders about black holes.

Black Holes and Entropy

Black holes – or at least the non-rotating ones – are incredibly simple objects. They have a point of no return, the so-called event horizon, an unknowable singularity at the center, and structurally, that's about it. If you decide to foolishly have your robot companion ("Your plastic pal who's fun to be with!") explore a black hole and he drops below the event horizon, even for an instant, he's gone forever. That's what "nothing can escape" is all about.

But to abuse an analogy, you are what you eat. Your doctor could tell what you've been shoving down your gullet by examining your blood, your vitals and, um, your leavings.

Can the same be said of a black hole? Can we tell what's fallen in just by examining the gravitational field?

According to General Relativity, there are just 3 numbers that suffice to describe everything about a black hole: Its mass, its electric charge, and its angular momentum, and for the most part, only that first number even really matters.

You're going to need a lot more than 3 numbers to reconstruct a whole robot. On the face of it, black holes are the ultimate in universal simplification. You put an object into one, and poof! No matter how complicated or how simple, it's gone. This seems to fly in the face of one of the most fundamental ideas in physics: the 2nd law of thermodynamics.

The essence of the 2nd Law is that entropy – essentially a measure of the disorder of the universe – will perpetually increase over time. But it seems as though dumping all of your entropy into a black hole allows you to violate the 2nd law entirely. Looking at the thermodynamics of it all, they're as cold as you can get – absolute zero – which means that they have no entropy at all (and, incidentally, will last forever).

Fortunately (at least for our hypothetical ongoing relationship with our robot that we dumped into the black hole at the beginning of this question), black holes have a little more going on. The randomness of the universe is going to make the event horizons astoundingly interesting places. But to understand why, we need to delve into the world of information.

Entropy and Information

In 1948, Claude Shannon, a research scientist at Bell Labs, founded a branch of research known as information theory. Just as quantum mechanics made all of modern computing physically possible, information theory revolutionized cryptography and communication and helped make innovations like the Internet possible.

One of the major results of information theory is that information and entropy are intimately related. Just as the entropy of a gas describes the number of different ways that the atoms can be interchanged with one another, the information of a signal describes the number of different messages that can be transmitted.

Suppose I send a message that is exactly two characters long. I could in principle send you 26 × 26 = 676 different messages, but most of those letter combinations would be completely meaningless. Only a few (the Scrabble dictionary lists 101) are actual words.

To the computer scientists among you, this means that while in principle it would require about 10 bits (the 1s and 0s that are used to store data) to differentiate between every possible two-letter combination, if you know that you’re transmitting a word, you only need about 7 bits. What a savings!

Communications can be significantly compressed by noticing that certain letters are used less frequently than others. Es, for example, show up way more often than Zs in the English language. If you’re playing hangman, simply knowing that a Z appears in a word dramatically decreases the number of possibilities. This is why the former is worth only one point in Scrabble and the latter is worth ten, and why the letter E in Morse code is

.

whereas the letter Z is

– – . .

Z takes far longer to tap out, but that’s okay, because you’re going to do it far less frequently. The more complicated (or unlikely) a message is, the more information it carries, and the more bytes of data you’d need to store it on a computer.

There are clearly some configurations of memory that are more special than others. Much like with the Scrabble letters, we could simply recognize that most combinations of 1s and 0s are garbage, but even so, picking tiles out of a bag will occasionally give us a real word. The problem is that a randomly generated (but otherwise meaningful) sequence on the board looks just as real as a word that somebody played intentionally.

If you found a disk drive with lots of seemingly random 1s and 0s, you’d quite reasonably assume that all of those bits represented real data stored on the drive. In other words, we generally assume that whatever complicated patterns are in our brain or on a Scrabble board or in the physics of the universe are somehow an accurate reflection of what really happened in the past.

Information and entropy are not the same, even though mathematically they look a lot alike. In many ways, they're opposite. A system in very high entropy contains very little information, because we know almost nothing about it. But on the other hand, a system which appears to be very high entropy can also be thought of a device with the potential for storing a great deal of information, if only you're willing to look at it closely enough.

Black Holes Leak

This brings us to black holes, and back to the original question. If black holes contain next to no information, how can they possible remember what fell into them?

In 1974, Stephen Hawking realized that black holes must ultimately radiate away into nothingness. Why? Because the vacuum of space is constantly awash with the creation of particles and antiparticles, and some get swallowed by the black hole, and some escape to make the black hole dimly (very dimly) glow.

There are some big differences between "classical" black holes (as understood by Einstein), and "quantum" black holes (extended by Hawking).

For one thing, Classical black holes last forever, so the information of what's inside isn't really an issue (as what goes inside, stays inside). Likewise, classical black holes (as we've seen) only have 3 numbers worth of information.

But once you introduce quantum mechanics things become far more interesting. For one thing, quantum black holes radiate (and ultimately evaporate), which is a fancy was of saying that they have some heat to them. Heat is the bread and butter of thermodynamics, and with it, there comes the possibility to encode information.

Black holes have a huge amount of entropy. To put things in perspective, there is about as much entropy on the surface of a single supermassive black hole (like at the center of our Galaxy) as there was in the entire observable universe at the beginning of time. All those possible "microstates" carry with them the potential for storing huge amounts of information. I should note, however, that at the moment, it's not entirely clear how information might be encoded on to the surface of a black hole.

What's more, since black holes will eventually (over quadrillions of years) evaporate, shouldn't the radiation that it sends out into the universe contain enough information to reconstruct your robot pal?

Maybe, and I don't say this to be coy. I say this because really understanding how quantum mechanics and black holes interact in a fundamental way needs to wait for a theory of Quantum Gravity that we, unfortunately, still don't have.

But that doesn't prevent us from speculating. Stephen Hawking himself has said:

If you jump into a black hole, your mass energy will be returned to our universe but in a mangled form which contains the information about what you were like but in a state where it can not be easily recognized. It is like burning an encyclopedia. Information is not lost, if one keeps the smoke and the ashes. But it is difficult to read. In practice, it would be too difficult to re-build a macroscopic object like an encyclopedia that fell inside a black hole from information in the radiation, but the information preserving result is important for microscopic processes involving virtual black holes.

What this means is that when black holes evaporate, the radiation that they give off wouldn't be a perfectly random. Instead, there would be little bumps and wiggles to the spectrum that would (if you knew enough to decode them) allow you to reconstruct what fell in. I, for one, lack that sort of patience.

Also, I'm afraid that long-term "what fell in" will include us, or at least our constituent atoms.

Does it give you any comfort that your essence will subtly encoded in a thin, freezing cold bath of radiation?

Me neither.

Dave Goldberg is a Physics Professor at Drexel University. His newest book, The Universe in the Rearview Mirror is here! You should definitely become a fan on facebook, or better yet, send a (non-contest) question about the universe.