Classical versus Quantum Coin Toss

The outcome of a classical coin toss is a classically random outcome of heads or tails. However, it is classically possible to measure the actions of a classical coin toss to an arbitrary precision and therefore it is possible to predict a classical coin toss, despite chaos.

A quantum coin, though, has one more attribute besides heads and tails and that is quantum phase. With quantum phase, the coin can still exist as heads or tails, but the quantum coin can also exist as a superposition of both heads and tails. There is no role for quantum phase or superposition in a classical coin toss. A classical coin toss begins with either heads or tails up and then executes a number of flips according to the person or mechanism doing the flipping and then lands either heads or tails up. Classically it is then possible to precisely measure all of those classical actions and therefore to predict a classical outcome to arbitrary precision.

However, any large number of classical actions necessarily entangle some quantum actions as well. This is because the microscopic universe is quantum and uncertain, not classical. A dephased quantum coin in flight will persist in a microscopic superposition until the macroscopic coin lands as heads or tails. Unlike the precise classical measurements that can predict a classical coin toss, there are no measurements that will predict the outcome of a quantum coin toss from a superposition state better than 50%.

In fact, there is really no such thing as a classical coin toss in our quantum world. Instead, a large number of classical macroscopic actions like a flipping coin will ultimately access many microscopic quantum outcomes of quantum phase noise. The classical random noise of chaos is just a convenient macroscopic archetype for the underlying microscopic quantum phase noise of physical reality.

Note that not only the quantum coin exists as a superposition, the quantum actions of starting, flipping, and landing also exist as superpositions with quantum phase. A large number of actions like flipping or neural impulses will also entangle quantum phase noise and therefore be subject to the limits of uncertainty of quantum knowledge. The fact that we cannot therefore ever precisely know a precursor feeling or precisely predict an outcome feeling gives us the archetypes of free will and free choice...