A familiar driving frustration has now been explained with surprising mathematical clarity. Researchers have developed a model showing why a slower car that has been overtaken often seems to catch up again at the next traffic light. The phenomenon, informally dubbed “Voorhees law,” highlights the subtle interplay between speed, timing, and randomness in everyday traffic behavior, tells Phys.org.
The study focuses on a simple but overlooked scenario: two cars traveling at different constant speeds along the same route. Intuition suggests that once a faster driver overtakes, the distance between the vehicles should continue to grow. However, this assumption ignores the effect of traffic signals, which act as unpredictable interruptions in motion.
To analyze this, the researcher modeled traffic lights as random events within their red-green cycle. When a faster car gains a lead, the timing of the next signal determines whether that advantage is preserved or erased. If the faster driver encounters a red light while the slower car arrives during green, the gap can shrink or disappear entirely. Across many such interactions, gains and losses tend to balance out, meaning the faster car often ends up no further ahead than before.
The effect becomes even more pronounced in urban environments with multiple traffic lights. Each additional signal increases the probability that the slower car will eventually catch up at least once, making the experience feel almost inevitable.
Importantly, the research also points to a psychological component. Drivers are more likely to remember moments when a slower car reappears after being overtaken, reinforcing the illusion that such events happen more frequently than they actually do.
Beyond curiosity, the findings carry practical implications. They suggest that overtaking in signal-heavy traffic may offer little real advantage, raising questions about the safety and efficiency of aggressive driving. By isolating the interaction between just two vehicles, the study provides a fresh lens on traffic dynamics, emphasizing that even simple systems can produce counterintuitive outcomes.