There are a few things to consider. Older cars use a relay to operate turn signals which work by passing electrical current through a piece of metal until it heats up enough to expand and disconnect the circuit, which then reconnects when the metal cools down and shrinks. Imperfections in the material and manufacturing process and variances in electrical current from car to car makes these relays almost impossible to synchronize.
Also, even with newer digitally controlled circuits, timers aren’t always 100% perfect. Crystal oscillators will have a small percentage of tolerance in the actual frequency in which they oscillate. They will also be affected by stability of source power, temperature, and other small factors. You can have a hundred oscillators that are specified to operate at 32,768 hertz but, in reality, may vary by hundreds of Hertz between them. Though the effect is minimal in most uses, over time it will cause desynchronization. Software controlled lights, which use processor clock speed for timing instead of a crystal oscillator, can cause desynchronization when the processor cannot complete instructions within specified time which cause them to delay in response to other requests. This phenomenon is known as clock drift. This is why GPS timing, as GPS satellites use atomic clocks to provide timing, is important in synchronization sensitive applications, like long distance point to multipoint microwave radio communication or to provide “authoritative time” for logging.
There’s also the fact that people don’t turn on their turn signals at the same exact time.
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