Let’s clear things up a little: you cannot use the category of “quantum random” to actual coin flip, because an object to be truly so it must be in a superposition of at least two different pure states, a situation that with a coin at room temperature has yet to be achieved (and will continue to be so for a very long time). So let’s talk about classic randomness from a Bayesian point of view: when you have no prior information that can correlate with the outcome of an event. That’s the case with the coin flip (and also with the quantum case, according to many-worlds interpretation). Since the face landing depends not only on thumb movement but also on the exact starting position and the movement of air molecules, it’s surely not possible for you to know all this informations in the beginning to a degree precise enough to deduce the side landing up. In this situation, your “throw the coin” motor impulse and the coin landing are uncorrelated, and so the coin flip is random (from your perspective). But the degree to which the coin depends on factors you don’t control is very low: if you practice enough, you can control the movement of your thumb so that it lands, say, 9 times out of 10 the side you want. In this case you have formed a better model of the coin traveling through the air and you have learned to control your thumb more precisely. In this case the correlation with your motor cortex is much higher and the coin flip is of course no more random.
you cannot use the category of “quantum random” to actual coin flip, because an object to be truly so it must be in a superposition of at least two different pure states, a situation that with a coin at room temperature has yet to be achieved (and will continue to be so for a very long time).
Given the level of subtlety in the question, which gets at the relative nature of superposition, this claim doesn’t quite make sense. If I am entangled with a a state that you are not entangled with, it may “be superposed” from your perspective but not from either of my various perspectives.
For example: a projection of the universe can be in state
(you observe NULL)⊗(I observe UP)⊗(photon is spin UP) + (you observe NULL)⊗(I observe DOWN)⊗(photon is spin DOWN)
= (you observe NULL)⊗((I observe UP)⊗(photon is spin UP) + (I observe DOWN)⊗(photon is spin DOWN))
The fact that your state factors out means you are disentangled from the joint state of me and the particle, and so together the particle and I are “in a superimposed state” from “your perspective”. However, my state does not factor out here; there are (at least) two of me, each observing a different outcome and not a superimposed photon.
Anyway, having cleared that up, 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 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 an expected and measurable interference paterns. This is what we have failed to produce at a macroscopic level, and it is this failure that you are talking about when you say
a situation that with a coin at room temperature has yet to be achieved (and will continue to be so for a very long time).
I do not believe I have been shown a convincing empirical test ruling out the possibility that the state is not, from my brain’s perspective, in a superposition of vastly many states with amplitudes whose complex arguments are difficult to predict or control well enough to produce clear interference patterns, and half of which are “heads” state and half of which are “tails” states. But I am very ready to be corrected on this, so if anyone can help me out, please do!
Let’s clear things up a little: you cannot use the category of “quantum random” to actual coin flip, because an object to be truly so it must be in a superposition of at least two different pure states, a situation that with a coin at room temperature has yet to be achieved (and will continue to be so for a very long time). So let’s talk about classic randomness from a Bayesian point of view: when you have no prior information that can correlate with the outcome of an event. That’s the case with the coin flip (and also with the quantum case, according to many-worlds interpretation).
Since the face landing depends not only on thumb movement but also on the exact starting position and the movement of air molecules, it’s surely not possible for you to know all this informations in the beginning to a degree precise enough to deduce the side landing up. In this situation, your “throw the coin” motor impulse and the coin landing are uncorrelated, and so the coin flip is random (from your perspective).
But the degree to which the coin depends on factors you don’t control is very low: if you practice enough, you can control the movement of your thumb so that it lands, say, 9 times out of 10 the side you want. In this case you have formed a better model of the coin traveling through the air and you have learned to control your thumb more precisely. In this case the correlation with your motor cortex is much higher and the coin flip is of course no more random.
Given the level of subtlety in the question, which gets at the relative nature of superposition, this claim doesn’t quite make sense. If I am entangled with a a state that you are not entangled with, it may “be superposed” from your perspective but not from either of my various perspectives.
For example: a projection of the universe can be in state
(you observe NULL)⊗(I observe UP)⊗(photon is spin UP) + (you observe NULL)⊗(I observe DOWN)⊗(photon is spin DOWN) = (you observe NULL)⊗((I observe UP)⊗(photon is spin UP) + (I observe DOWN)⊗(photon is spin DOWN))
The fact that your state factors out means you are disentangled from the joint state of me and the particle, and so together the particle and I are “in a superimposed state” from “your perspective”. However, my state does not factor out here; there are (at least) two of me, each observing a different outcome and not a superimposed photon.
Anyway, having cleared that up, 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 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 an expected and measurable interference paterns. This is what we have failed to produce at a macroscopic level, and it is this failure that you are talking about when you say
I do not believe I have been shown a convincing empirical test ruling out the possibility that the state is not, from my brain’s perspective, in a superposition of vastly many states with amplitudes whose complex arguments are difficult to predict or control well enough to produce clear interference patterns, and half of which are “heads” state and half of which are “tails” states. But I am very ready to be corrected on this, so if anyone can help me out, please do!