Are coin flips quantum random to my conscious brain-parts?

One quantum mechanics homework problem I was assigned in grad school was to determine how long it would take a perfectly balanced perfectly sharp ice pick to fall over just from quantum uncertainty driving it off balance. There was no specific 'correct' answer, and the answers we came up with were in the range 5-15 seconds.

Neurons are much much smaller, and will lose their coherence on a much shorter timescale.

That said, that doesn't at all mean that coin flips are quantum random. If all of those decoherent branches end up as heads, well, it's going to be heads. That has a lot more to do with the non-quantum aspects of the system - the dependency graph - than the quantum part that underlies it.

Certainly you're not going to get any coherent interference between heads and tails.

See this.

Jaynes analyzes coin flipping on pages 317-320 of PTTLOS. He might have more in a separate paper somewhere. Pretty sure he did, because I remember a state space and control discussion that seems similar to what you're getting at that isn't in the book.

Also, I prefer his terms of ontological and epistemological randomness. From a mechanical perspective, a coin flip will be epistemologically random if the state space is finer than your control space - i.e., the result is completely determined by the physics, but your lack of precision in controlling the flip parameters, and therefore lack of knowledge about them, makes you unable to predict the outcome.

But Jaynes goes on about how to control a flip by the method of flipping - he finds a state space where an ordinary person has sufficient precision to be able to control the outcome of the toss.

Others have done the same analysis, and confirm both the theoretical and empirical results - they can do it too.

http://seas.harvard.edu/softmat/downloads/2011-10.pdf

Why coins specifically? One can ask a similar question about any classical interaction where more than a single outcome is possible apriori. The interesting question is, how deep "down" one has to go for the question "is this process classical?" to start making sense. For example:

• Is scoring a goal a quantum event? (I use it instead of a coin flip because it's ostensibly much less predictable.)

• Is you reacting to the goal being scored a quantum event?

• How about the player moving their limb in the right position to score?

• What about moving their eyes the right way at the right time to notice the ball?

• Thinking (possibly subconsciously) about looking where the ball might be?

• Neurochemicals released/neurons firing to construct this thought?

• Ion channels opening in order to release the chemicals or depolarize the membrane?

• A single ion channel opening?

• A voltage-sensitive gating trigger consisting of a few molecules somewhere deep inside the channel shifting to cause the channel opening.

Well, this last thing is probably "quantum", in the same sense radioactive decay is quantum: one can write the interaction Hamiltonian, solve the Schrodinger equation and calculate probabilities using the Born rule.

Now, going all the way up, does it make sense to write the state of the world as (channel triggered x goal scored)+(channel not triggered x goal not scored)?

(Out of time, will continue later, but feel free to comment)

I don't know if it is the same question, but I would like to know how fast can quantum effects propagate to macroscopic outcomes, especially through the human brain.

Let's say than in a moment T0 I choose one Everett branch that includes me, and I am interested only in its future branches. In the following moments, in some branches some atoms of my brain move randomly. How long is it (seconds? minutes?) until I start doing different things (observable by another human, e.g. speaking different words) in different branches?

I know the question needs some numbers, so please use some reasonable values. For example my task is to say randomly either "one" or "two", in some usual condition. What is the shortest time interval such that if we choose Everett branches starting from one point, at the end of the interval I say "one" in at least 20% of branches, and "two" also in at least 20% of branches?

Analogically for the article: If I choose one Everett branch in a moment when I give my muscles a command to flip the coin, what distribution of outcomes should I expect at the end? Assume average person in average conditions. Is it 50:50? Or 99:1?

The way to tackle this problem is just to imagine writing a Schrodinger equation for the whole system consisting of an electronically controlled coin-flipping device, the coin it flips, and the environment in which the coin flip occurs.

There's basically no prospect of a coherent superposition involving the coin flipper and the coin. If there's an ambient gas, molecular collisions will be decohering both coin and flipper. Any computational processes in the flipper which dissipate energy will cause decoherence. Even in a vacuum, the thermal radiation from both objects should be decohering them. It's very interesting that something as large as a buckyball can apparently maintain coherent superposition even though it's in a thermal state, but the larger an object gets, the cooler it needs to be, to avoid decohering itself through thermal radiation.

In short, the wavefunction of the combined system will be a superposition of divergent classical histories (wavepackets moving through vastly separated regions of configuration space).

Simpler question: Is it possible to learn to cheat at coin flips?

If you can cheat at an actual "fair" coin flip (not just making it wobble or using a rigged coin), then it's at least possible for your brain to build a correlation between desired and actual outcomes. Given that this is a common decision making tool, I'd expect positive and negative reinforcement to have resulted in at least mild entanglement in that case; the two aren't completely independent.

I've learned to bias "fair" dice rolls, so I'd assume it's possible to develop similar muscle reflexes with coins. It was over a decade ago, so I don't remember how well I did with coins, alas :)

tl;dr: If you can cheat, it's probably entangled. If you can't cheat, it can't be entangled!

Like Mark Twain, I am happy to be able to answer this question without any hesitation: I don't know.

But I'm sceptical that we can observe superposition of quantum states on that kind of macroscopic scale.

Also, the universe may be a fixed 4-dimensional shape, part of which includes the past and future states of you and the coin, and the illusion of different possible futures for you or the coin is just that. I have no evidence for or against this, though.

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.

Coinflips aren't quantum random because "random" isn't a property of objects, but a property of observers. "Random" merely describes outcomes that you can't predict and that you don't know of any agent that can predict with better accuracy than random guessing. "Quantum randomness" is a particularly difficult-to-guess special case of randomness.

Not all randomness is quantum randomness, even if everything includes a -component- of quantum randomness.

The issue is that "randomness" is a poorly-defined word. You're letting different, and opposing, definitions of randomness bleed together here (and probably in your thought processes as well). Taboo "random"; you'll rapidly see the issue. You're including chaos - that is, an essentially deterministic outcome that is impossible to predict due to the number of variables - randomness in with your quantum randomness.

ETA: You -can- define a problem such that quantum randomness applies instead of chaos randomness; simply state that the outcome of the coin flip is dependent upon an unobserved quantum event, that, say, may interrupt a single nervous signal which determines whether the coin comes up heads or tails. However, this problem is pretty far removed from the problem of coin flips in general; the coin becomes wholly unnecessary.

I think that as long as you aren't a professional gambler who has practiced flipping coins for months on end, any coin toss you do is random enough.