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!

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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.

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.

Yes, and taking this train of thought further, you realize that a clear distinction cannot be made; it's a continuum.

Everything in the Universe is 'quantum random', to some extent. Even a perfectly predictable pseudo-random number generator on a computer that always outputs the same sequence of numbers with the same seed. This is because there is a non-zero probability of quantum fluctuations spontaneously causing some of the bits in the generator to flip, creating an unexpected sequence. Of course, computers have multiple mechanisms for preventing this sort of thing (error correction, etc.) but there is a non-zero probability that the bits will flip in precisely the right pattern to evade those mechanisms. The fact that this usually doesn't happen is just one possibility among a sea of possibilities, albeit by far the most likely one. By using a pseudorandom number generator, you are accepting a small (very small) amount of non-deterministic randomness.

Yep. Origin of probabilities and their application to the multiverse is a short argument that says that there is quantum uncertainty in the firing times of neurons on the order of 1 ms, and that accounts for most of the uncertainty of a coin toss.

Someone brought up Dynamical Bias in the Coin Toss, which has a more serious analysis of coin tossing and would provide a better answer to the question of "How sensitive is the outcome of a coin toss to the motion of the thumb?" I haven't read it.

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.


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)

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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?

This doesn't answer your question, but I expect that if you're asked to randomly say "one" or "two", there are different mental algorithms you can use which all feel random, some of which give an outcome that depend deterministically on the computational state of your brain at the start of the algorithm, and some of which do not.

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!

I don't think the entanglement you mean is the quantum one except in a sense that "everything is quantum".

I can't imagine that something I have conscious control over could be quantum random, since it's not even regular random. If I'm mistaken on that, please let me know :)

See previous comment on Jaynes. He details how to control the outcome of the toss by how you throw it. Whether that amounts to cheating depends on the use you put this mighty power.

There are other papers online as well. Most will refer back to Jaynes, so "jaynes coin flipping" yields some hits.

So, if we've established that you can control the outcome, then it seems obvious that the event isn't going to be properly random :)

I guess I didn't italicize properly. I was just pointing people to Jaynes description of how to bias the coin toss, since I thought it might be of interest.

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.

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!

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've addressed this here.