Posted by It’s 10pm on a Sunday night, and I’m driving west on Interstate 10 right through the middle of downtown Houston. Focused on getting to my destination safely, I obey the traffic laws and proceed through the comparatively deserted interstate at the maximum speed allowed by law. To experimentally do otherwise is a bit hazardous, so instead of trying this in reality I follow Einstein’s lead and imagine an experiment:
I jam on my brakes and swerve to the left across several lanes of traffic. I floor the gas and spin the wheel to the right, overshooting my starting point. Driving like a lunatic with few cars around will have predictable results: the cars within sight of me will avoid me, and I’ll probably eventually get sent to jail for reckless operation. But do I affect anyone other than me? So long as I don’t actually wreck, the most that happens is a small alteration in the course of nearby vehicles. Vehicles farther away won’t even notice. The correlation length – measuring how far the effects of my car’s motions are felt – is small, maybe a few hundred feet. The overall state of the traffic flow remains unaltered no matter what I do.
Now change the picture a bit. It’s now 4:30 pm on a Monday afternoon. Traffic is bumper to bumper and inching along when it’s not actually stopped. I’m not physically able to go swerving wildly around, but I can still try to figure out how far away my movements can affect traffic. In this case too the correlation length is still small. If I tailgate or hold back and try to change lanes or whatever, all that happens is a possible small response by the cars around me. Anything I do gets washed out in the random stop-and-go of all the tens of thousands of cars inching down the road.
From the perspective of my individual car not much is happening in the wide-open-spaces version of traffic or the traffic jam. They have their own statistical properties and characteristics, each interesting and important in their own way. A scientist studying the bulk properties of traffic will have plenty to study even in those cases, just like a scientist can make a career studying the properties of solids or gases. But the transitions between those phases are also certainly key, and as usual they’re harder to deal with. Science prises generalized properties from disparate physical situations all the time however, and transition of traffic flow patters is no exception. It follows some of the same rules as the phase transitions of bulk matter.
As the density of traffic changes from light to heavy, the correlation length between the motions of any one car and its neighbors increases. Very slowly at first, but as the density increases the length begins increasing more rapidly. I brake, and the car behind me brakes, and the car behind him brakes… and suddenly what I do ends up affecting traffic quite far away. Eventually the random motions of the traffic will dissipate my effects, but it takes a greater and greater distance. Suddenly, despite the fact that no obvious single event seems to have happened, the greater traffic density reaches a critical point and the correlation length reaches an “infinite” asymptote. The correlation length becomes infinite, tiny random motions propagate all throughout the traffic, and the traffic changes phase from thick and fast to thick and slow. And the correlation length collapses back down to something small as the individual motions of the slow cars don’t propagate outward very far.
This concept of correlation length becoming infinite is characteristic of almost all phase transitions, from cars to stadium crowds to superfluid helium. Nature is pretty weirdly universal like that.
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