Hello rationality friends! I have a question that I bet some of you have thought about...
I hear lots of people saying that classical coin flips are not "quantum random events", because the outcome is very nearly determined by thumb movement when I flip the coin. More precisely, one can stay that the state of my thumb and the state of the landed coin are strongly entangled, such that, say, 99% of the quantum measure of the coin flips outcomes my post-flip thumb observes all land heads.
First of all, I've never actually seen an order of magnitude estimate to support this claim, and would love it if someone here can provide or link to one!
Second, I'm not sure how strongly entangled my thumb movement is with my subjective experience, i.e., with the parts of my brain that consciously process the decision to flip and the outcome. So even if the coin outcome is almost perfectly determined by my thumb, it might not be almost perfectly determined by my decision to flip the coin.
For example, while the thumb movement happens, a lot of calibration goes on between my thumb, my motor cortex, and my cerebellum (which certainly affects but does not seem to directly process conscious experience), precisely because my motor cortex is unable to send, on its own, a precise and accurate enough signal to my thumb that achieves the flicking motion that we eventually learn to do in order to flip coins. Some of this inability is due to small differences in environmental factors during each flip that the motor cortex does not itself process directly, but is processed by the cerebellum instead. Perhaps some of this inability also comes directly from quantum variation in neuron action potentials being reached, or perhaps some of the aforementioned environmental factors arise from quantum variation.
Anyway, I'm altogether not *that* convinced that the outcome of a coin flip is sufficiently dependent on my decision to flip as to be considered "not a quantum random event" by my conscious brain. Can anyone provide me with some order of magnitude estimates to convince me either way about this? I'd really appreciate it!
ETA: I am not asking if coin flips are "random enough" in some strange, undefined sense. I am actually asking about quantum entanglement here. In particular, when your PFC decides for planning reasons to flip a coin, does the evolution of the wave function produce a world that is in a superposition of states (coin landed heads)⊗(you observed heads) + (coin landed tails)⊗(you observed tails)? Or does a monomial state result, either (coin landed heads)⊗(you observed heads) or (coin landed tails)⊗(you observed tails) depending on the instance?
At present, despite having been told many times that coin flips are not "in superpositions" relative to "us", I'm not convinced that there is enough mutual information connecting my frontal lobe and the coin for the state of the coin to be entangled with me (i.e. not "in a superposed state") before I observe it. I realize this is somewhat testable, e.g., if the state amplitudes of the coin can be forced to have complex arguments differing in a predictable way so as to produce expected and measurable interference patterns. This is what we have failed to produce at a macroscopic level in attempts to produce visible superpositions. But I don't know if we fail to produce messier, less-visibly-self-interfering superpositions, which is why I am still wondering about this...
Any help / links / fermi estimates on this will be greatly appreciated!