Today, in my physics class my teacher was talking about how we can never predict the outcome of a coin flip. So I thought: Will the outcome of a coin flip be the same if we do not change the initial conditions (such as launch angle, force position where force is applied,etc.)? Intuitively, I feel that the answer would be yes. But is there something related to quantum mechanics that may produce a different answer?


Today, in my physics class my teacher was talking about how we can never predict the outcome of a coin flip

Your teacher was most likely not talking about this from a QM perspective of how experiments have probabilistic outcomes due to the inherent nature of QM (as we currently understand it).

Your teacher was most likely making a comment about how it is nearly impossible to know all of the relevant initial conditions, system parameters, etc. to accurately predict the result of a coin toss. However, on the spatial and temporal scales a coin toss resides on, it is safe to say we are in the classical mechanics regime. Quantum effects likely play no significant role in any of this. Therefore, you are correct in saying that if we could exactly reproduce the initial conditions of the entire system, then we would most certainly expect the same outcome each time.

In other words, your teacher was talking about inability to predict the outcome based on lack of sufficient information of the system, not because of any underlying quantum mechanical probabilities.

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    $\begingroup$ On a related note people, can and do, create robotic flippers that will flip a coin the exact same way every time. One such example: npr.org/templates/story/… $\endgroup$ – Brad S Jun 25 '19 at 15:24
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    $\begingroup$ @BradS Yeah, I was thinking about going into how one could probably very accurately control the outcome of the toss by making a precise, automated flipping mechanism, but then I decided to be a purist and just implicitly consider a coin toss to be one that is done purely by hand. Although now I am imagining competitive coin flipping events where people have trained for years to have consistent coin flipping outcomes. Anyway... thanks for the link :) $\endgroup$ – Aaron Stevens Jun 25 '19 at 15:51
  • $\begingroup$ I'm pretty sure I've read of people who are able to choose the outcome of a coin toss. It seems like it would be humanly possible, especially if you are tossing it onto another hand. $\endgroup$ – JMac Jun 25 '19 at 18:12
  • $\begingroup$ @JMac That sounds reasonable $\endgroup$ – Aaron Stevens Jun 25 '19 at 18:17

I guess the subject here is chaos, which arises even in classical mechanics, with a very nicely define classical Hamiltonian. "Deterministic chaos" is one of the wonderful oxymorons modern science can produce. In system having exponential dependence to initial conditions, evolution from two "infinitely" close initial states will diverge, and you have a prediction horizon.

If you can reliably predict, say, weather to 3 days and after that all your predictions fail, and you now measure initial conditions 10 times more accurately, you may be able to predict up to 4 days; again 10 times more accurate (100 times from original situation), and you're only able to predict to 5 days. It is likely that you will never be able to predict more than 14 days, whatever precise measures you make.

Flipping a coin raises the same problem.

Edit after discussion in comment section: I'm talking of a coin thrown and landing on a table, which will stabilize after hitting the surface with its edge, bouncing and spinning, which is a chaotic process.

  • $\begingroup$ I am not sure I buy that flipping a coin is a chaotic system (at least in all situations). What are you assuming about your coin tosses that makes you think it is a chaotic system? $\endgroup$ – Aaron Stevens Jun 25 '19 at 16:27
  • $\begingroup$ @AaronStevens When a coin hits a table with its edge, it bounces and turns relatively to the 3 Euler angles of the object in a way very sensitive to the exact incidence angles, and there are multiple bounces. $\endgroup$ – Matt Jun 25 '19 at 17:46
  • $\begingroup$ That is fine. You should specify that you are specifically talking about a coin hitting a table, and that your chaos is in that process. $\endgroup$ – Aaron Stevens Jun 25 '19 at 17:50
  • $\begingroup$ @AaronStevens OK $\endgroup$ – Matt Jun 26 '19 at 11:29

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