The reduced visibility experienced by drivers in a line of cars surrounded by heavy fog can create effects similar to an astrophysical black hole. The same mathematical equations used to determine the boundaries of these dense regions of the Universe from which nothing can escape—not even light—can also be used to identify the most dangerous sections of a road in heavy fog, where the risk of traffic accidents is highest. In this vehicular black hole, drivers do not have enough time to react to the brake lights of the car in front.
“Our work is a proof of principle,” explains theoretical physicist George Matsas of São Paulo State University (UNESP), lead author of an article published in the American Journal of Physics in September in which he proposed the existence of this black hole analog on certain stretches of a road or highway. “Inspired by the general theory of relativity, we showed that the space-time diagrams used to follow the transmission of information in a black hole can also be used to understand the dynamics of vehicular traffic.” Master’s student Luanna Karen de Souza, supervised by Matsas, was another of the paper’s authors. Whether this approach could actually help prevent road traffic accidents is still something that needs to be studied under real conditions.
According to the scientists, a dangerous foggy stretch of road can be considered equivalent to a black hole because both phenomena present a delimited region of space and time that marks the beginning of a zone from which no information can return—known as the event horizon. The concept, originally derived from relativity, represents the boundary between the inner and outer regions of a black hole. Matter, energy, or any other kind of information that crosses the event horizon is pulled into the black hole, a relatively small region with enormous linear density. After crossing the event horizon, nothing can escape the black hole’s gravitational pull—anything that goes beyond this boundary is stuck there, with no connection to the outside.
Matsas and Souza’s calculations indicate that a similar phenomenon occurs in a simplified model emulating the behavior of a line of cars on a road with low visibility due to fog. “The mathematics used in the study is simple,” says the UNESP physicist. The pair simulated cars moving at a constant speed, the same distance apart. The occurrence of heavy fog forces the first vehicle in the line to slow down by braking, which turns on the car’s brake lights, warning the driver behind so that they can do the same. Thus begins a chain of information, with each vehicle’s brake lights alerting the next, leading to successive deceleration.
In the mathematical simulations, as long as the drivers pressed the brakes before a certain point on the road, no accidents occurred. All drivers were able to see the brake lights on the car in front of them, decelerate, and avoid a collision. The information signaling the action to stop was passed down the chain of vehicles without issue. But if a car started braking after the determined point, all the drivers behind a certain vehicle in the chain were unable to brake in time to avoid successive collisions.
The point on the foggy road at which light information can no longer reach the following motorist is the event horizon of the vehicular black hole. Like matter and energy that lose all connection with the rest of the Universe as it enters a cosmic black hole, light information within the event horizon of the line of traffic is not accessible to anyone outside its boundary. “This break in the flow of information causes each driver to brake slightly further into the event horizon, leading to crashes,” explains Matsas.
Mathematical physicist Alberto Saa of the University of Campinas (UNICAMP), who did not participate in the study, agrees with the comparison proposed by Matsas in the article. “The analogy between what happens at the event horizon of a gravitational black hole and a foggy stretch of road makes perfect sense,” he says. “The adoption of a simplified vehicular traffic model is not a problem in this study. It simply highlights that even in a system with few elements, a region similar to an event horizon appears.”
The notion that other forms of black holes exist besides those formed in the cosmos by the gravitational warping of space-time is not new. The existence of event horizons has already been proposed in several other contexts, such as in Bose-Einstein condensates—a group of atoms or molecules that behave as a single entity when cooled to extremely low temperatures. The black hole analogy in vehicular traffic could be the first proposal of a region presenting such characteristics in everyday life.
Mute holes in vehicular traffic (nº 19/18616-4); Grant Mechanism Master’s (Msc) Fellowship; Supervisor George Matsas (UNESP); Beneficiary Luanna Karen de Souza; Investment R$50,540.40.
SOUZA, L. K. & MATSAS, G. E. A. Black-hole analog in vehicular traffic. American Journal of Physics. Vol. 9, no. 9. Sept. 2022.