Jokodo
Veteran Member
Any prediction requires knowledge of the initial conditions. In the case of a coin toss, if you were to know the initial conditions with sufficient precision, a purely deterministic Model of reality is sufficient to predict its behavior with a much higher accuracy than you could ever hope to measure. No need to refer to QM at all.
The range of hypothetically possible outcomes for the sum of a septillion dice is from one to six septillions. In that range, you only ever need to concern yourself with values between 3.4999999999 and 3.500000001 septillions, and probably several orders of magnitude narrower. The same Holds for a tumbling coin consisting of a septillion particles. Even is every particle has an uncorrelated chance of being in any arbiträre state along its range of possibilities, itself, I believe, a misunderstanding, the sum is everything but unpredictable. QM or the observer effect Play no role in explaining our inability to predict the outcome.
It doesn't work as such.
You can not compute probilities of a coin toss based on the particles without a wave function.
It's worse than that: You cannot (meaningfully) compute probabilities of a coin toss based on the particles, period.
There's a million reasons why it is practically impossible to predict which side a coin will fall on, and wave-particle dualism isn't one of them. Incomplete knowledge about the position, direction and momentum of the coin in the instant it's dropped, incomplete knowledge of its actual mass distribution and about the friction coefficient in different areas of its surface dominate any role quantum effects might have. It's a chaotic process, meaning that small differences in the input will lead to enormous differences in the output - but a deterministic one.
That one extra atom of lead that's embedded in the copper lattice of the bottom part of the coin, making it ever so slightly denser than the top part and shifting the coins balance point, or that microscopic scratch you inadvertently made with your thumbnail as you flipped it, slightly increasing the friction on one side, the sub-millimeter-scale air turbulence lingering on from when a fly passed this way a minute ago? Yes, they might affect which side it lands on. But not wave collapse.
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Show the steps in your reasoning. I do not see it'
Whether the uncertainties represented by QM that appear to underly reailit are a property of reality or a function of our limitations is an old question'
Not one that's relevant to deciding what causes the result of a coin toss to appear random.
Even if there were no qualitative difference between the behaviour of particles and that of macroscopic objects, even if the behaviour of a penny (~2.5 grams of 95% copper, thus several septillion particles) were best described as the product (not sum!) of it's septillion particles' wave functions, this still wouldn't get us to where the coin landing on one side or the other is in any meaningful way a quantum effect. Counterintuitive as it may seem, a system of a septillion entities acting at random behaves in effect like a septillion particles acting in a deterministic fashion. Throwing a septillion dice, each having an equal probability of showing any of its six sides, and summing up the results is in no appreciable manner different from throwing a septillion dice with the number "3.5" written on all faces.
Have a look at AnyDice.com and play around a bit with numbers in the 3-digit range by entering e.g. "501d6" for 501 tosses with a six-sided die (you'll get a timeout error if you go much beyond). As expected, the probability of getting at least 1754 eyes total (=more than 1753.5, the 501 * 3.5) is exactly 50%. The probability of getting at least 1700 is already well over 90%, despite the fact that the range of hypothetically possible results starts at 500. People who are better at math than me have derived a formula of sqrt(n * (k²-1)/12) as the standard deviation of results for k-sided dice after n tosses. With a septillion "tosses" (i. e. a septillion particles in a coin), that implies for all intents and purposes deterministic behaviour, and a larger role for that extra lead atom.