Don't cry over spilled milk
Notes on heat and the arrow of time
What happens when you drop a ball in an entirely frictionless environment? The ball would bounce perfectly, losing no energy through interactions with the air or the floor. If you videoed its motion you would have a film that looked the same forwards and backward. There would be no sense of the arrow of time.
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If instead you drop the ball in the real world, it loses energy on each bounce and through friction with the air. Now your video has a very obvious forward and backward direction. The loss of energy from the ball has created an observable arrow of time.
However, in the real world case the energy has not disappeared. If you could see the microscopic world as well as you can see the ball, then you would find the energy passing from molecule to molecule and spreading away from the ball.
The reason the ball loses energy (rather than gaining it back from the air and the floor), is that there are so many more equally likely ways for the system to exist when the ball has dispersed the energy than when it has retained it. It is our human focus on the ball as more interesting, more important, more visible, than the other elements of the system that produces the perception of time. If we could take a god-like view of the system that saw each molecule of the air, the floor, the ball, with equal clarity, and could wait long enough for all states of the system to be explored many times, we might once again loose our perception of time.
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By Dr Beth Bromley
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