Paul M. Sutter is an astrophysicist at SUNY Stony Brook and the Flatiron Institute, host of “Ask a Spaceman” and “Space Radio,” and author of “How to Die in Space.” Sutter contributed this article to Space.com’s Expert Voices: Op-Ed & Insights.
Our knowledge of black holes comes from the specific mathematics of Albert Einstein‘s theory of general relativity, but one of the beauties of mathematics (and physics) is its universality; once you find an analogous setup, you can use the same language to describe it.
And if you’ve ever been stuck in a nightmare traffic jam, you know that “black hole from which you can never escape” captures the feeling well.
Related: Where do black holes lead to?
But that analogy is more than just colorful words to describe your morning commute. In a new paper, two physicists have developed a mathematical model of traffic jams and found that they could use the language of relativity — and black holes — to describe what’s going on. What’s more, this mathematical insight could potentially give urban planners better tools to cut down on traffic problems and warn drivers before they reach vehicular “event horizons.”
The road most traveled
The setup is pretty simple, according to the paper, published online in the preprint database arXiv. Imagine a line of cars, all of which are traveling in the same direction and at the same speed down a single lane of highway with a fixed distance between them. If the car in front taps its brakes, the next car in line will see the brake signal and know that something’s up. In response, that car will also begin to brake. But that process takes time, depending on the reaction time of the driver and the road conditions. For example, if it’s extremely foggy, it may take longer for the driver to realize that the car in front is braking.
This process continues down the line of cars, with each one getting the brake signal from the car in front of them, delaying them by some amount of time and applying their own brakes.
If the speeds are slow enough, and the distances between cars is large enough, then this process is no big deal. There’s plenty of time for every car to get the information and apply their brakes before hitting the car in front of them. The entire line of cars slows down but continues moving.
But what if the cars are moving too fast? Or the distance between them is too small? Or the reaction time for each driver is too long?
Then you get a vehicular black hole.
Black holes are information lockboxes. Outside their event horizons, information (light rays, particles, spaceships) can propagate wherever it pleases. Close to the event horizon, this becomes more of a struggle. The extreme gravity of a black hole makes it harder for that information to escape. It still can if it wants to; it just has to expend a lot of energy.
It’s just like Earth‘s surface: In principle, you can escape — you just need to get on a rocket first.
For light, the enormous gravity of the black hole sucks more and more energy out of it as it tries to leave, causing its frequencies to shift down into redder parts of the spectrum. The closer the light is to the event horizon of the black hole, the redder it becomes when it finally escapes.
The event horizon itself is the place where nothing can escape. A bit of light that launches from the event horizon will never, ever escape. It would take an infinite amount of energy, and it would have to redshift to an infinite degree, because it could. Lastly, anything that tries to leave the black hole cannot; it is trapped, its information content forever locked away from the rest of the universe.
The physicists found the same scenario play out in their simple model of traffic. If conditions are too fraught, then an event horizon appears in the flow of traffic. There simply isn’t enough time for the brake signals to propagate down the line. In effect, the information gets “trapped” behind the event horizon. Cars within the horizon will learn about the brake signals in front of them, but the cars outside the horizon never will.
The end result of this process is a pileup of car crashes. As soon as one driver fails to get a brake signal in time — because the driver in front of them didn’t have enough time to react and apply their own brakes — they will crash into the car in front of them. Then, the next car will collide with the first two, then the next and the next.
This is exactly what happens to matter that falls into a black hole. Because it can never escape, it’s forced to continue toward the center of the black hole, drawn by the immense gravity there. That center is the singularity, a point of infinite density where all the matter that formed the black hole has been crushed into oblivion.
So goes for black holes, so goes for traffic: As soon as a vehicular event horizon appears, it signals that that singularity — a pileup of car crashes — is imminent.
And it isn’t just a fun analogy; the physicists found that this situation is baked into the mathematics that describe traffic, the same way it’s baked into the mathematics of black holes. Knowing that this situation can arise can help urban planners — not to mention, autonomous-vehicle designers — prevent it.