Once upon a time, there was no such thing as GPS and no such thing as the internet. There existed purely mechanical clocks and watches, which were not particularly accurate, so they needed to be set fairly often. Starting in the 1930s, in many places there was a phone number you could call to obtain the current time.
Back when I was in first or second grade, my father got a fancy new clock-radio for his birthday. He gave me his old mechanical wind-up alarm clock. He went into great detail explaining how to wind it and set it: this knob only goes this way, that knob only goes the other way, and so forth.
That evening I set the alarm-hand for the appointed time and went off to sleep. I woke up the next morning before the appointed time, but just for fun I waited in bed, waiting for the alarm to go off....
At dinner the next evening I mentioned that the clock hadn’t done what I’d expected. My father asked
My father was about to say something, but before he even got started I solved the mystery and blurted out the answer:
At the time, I really liked this line of argument. I thought it was powerful and beautiful. I still like it. The most amazing part is that it is independent of mechanism. The clock could have been made of springs and gears, or made of hydraulics, or whatever – the mechanism didn’t matter. There was no way the clock could, by itself, figure out what time it was.
In grown-up terms, I can explain it in more sophisticated terms, but the idea is the same:
This time-shift invariance is related to conservation of energy, which is one of the most profound and useful principles of physics.
This limitation on the flow of information is related to the second law of thermodynamics, since entropy is basically just the opposite of information. This is another very profound and useful law of physics.
Both of these laws (conservation of energy and paraconservation of entropy) are independent of mechanism.
Sometimes you can use a mechanism-based argument to obtain a thermodynamic result, but the result is usually more general than the argument used to obtain it. For example, you might use an argument about rates to discover something about chemical equilibrium. However, the result is more general than the argument used to obtain it, because catalysis will change the rates by orders of magnitude, without changing the equilibrium point at all. As another example, Einstein’s analysis of the Brownian motion of a pollen grain led him to an equation that relates drift to diffusion. The equation applies to a wide range of situations – including the electrons in transistors – not just pollen grains in water.
This stuff is like magic, only better, because it’s real.