Notes

Unitary evolution may be the key to understanding time
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Benjamin Franklin once quipped in a letter to a friend that “in this world nothing can be said to be certain, except death and taxes.” Perhaps taxes are timeless but death is not so. Rather, it is intimately linked to the direction time flows — the arrow of time. If time flowed backward, I would say that nothing is certain except birth and taxes. (Or maybe “sexat dna htrib”.)
Most people talk about the arrow of time in the context of the 2nd law of thermodynamics, the law that entropy always increases with time. But this “law” is statistical, and it is a classical law based on classical assumptions about physics that we know, in the context of quantum physics, to be false.
People also talk about how all dynamics in the universe are time reversible. That means that if you watch a video run forwards or backwards the path of each and every particle in that video obeys the same laws of physics. It is only the aggregate paths of those particles that gives you an idea of which direction is forward.
But all dynamics in the universe may not be time reversible if this one quantum law is not correct. This is called the law of unitary evolution.
Unitary evolution is at the heart of all questions about time reversibility including the black hole information paradox (the death of which has been greatly exaggerated.) If unitary evolution is true, then time really is reversible and the arrow of time is a mystery. If it is false, then time reversibility is likewise false and the arrow is built into the true laws of physics — we just got ours wrong.
To understand what unitary evolution is, you have to know a little quantum physics. Rather than get into the mathematics of Schrödinger’s equation (where it pops out), I am going to explain it from the perspective of the quantum measurement paradox.
The quantum measurement paradox is best explained by the double slit experiment. In this experiment, a laser is trained on a barrier containing two closely spaced, narrow slits. On the opposite side of the barrier is a screen where the light from the laser is recorded. The laser is tunable so that it can emit only individual light particles. We can see these particles show up as individual dots on the screen.

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