# Is a dice roll deterministic?

This should be understood as distinct from the question of is it possible to predict the outcome of a roll, which seems to be an issue related to intractability and observation?

What I'm really asking is, if quantum indeterminacy is a factor of more than just observational limitations and intractability, where outcomes may be independent of of the prior state of the system, does it affect outcomes in the world of classical mechanics?

My interest is related to certain combinatorial problems, whether random number generation needs to be integrated, and if so, how it might be treated differently from uncertainty arising out of imperfect or incomplete information or intractability.

• arxiv.org/abs/1212.0953 Jun 17, 2017 at 23:38
• @CountIblis Outstanding! This is related to a question I asked earlier on Philosophy about the quantum vs. combinatorial and game theoretic conceptions of uncertainty. Jun 18, 2017 at 0:35
• You might also find Floris's calculation here related and intriguing. Jun 18, 2017 at 5:41
• The question to ask here is: is rolling dice chaotic in the mathematical sense? Because if it is then there is sensitive dependence on initial conditions, and if there is that then however small any uncertainty in initial configuration the outcome will, on general, be unpredictable. And that means that quantum effects do indeed matter, as SDIC can blow them up. In the case of throwing dice this probably would influence only some throws of course (ie they would be deterministic for many initial conditions, but not all).
– user107153
Jun 18, 2017 at 9:37
• @DukeZhou Yes, there is. It is impossible to predict the outcome of some measurements in QM even in principle: however well you know the initial conditions the result can not be predicted. This can, in some cases, be blown up to alter macroscopic systems.
– user107153
Jun 28, 2017 at 19:06

Quantum effects will be too small to effect a macroscopic objects like dice. From classical mechanics if the initial conditions are the same then the final condition will be the same. Of course one cant get the initial condition exactly the same, but it can be made close enough for a coin toss so probably could for dice as well.

• Would the same hold true for lightning? (I ask because it manifests in the macroscopic, but is a function of charge...) Jun 18, 2017 at 19:17
• That video is superb. Aug 24, 2017 at 4:00
• I meant this video: youtu.be/AYnJv68T3MM Aug 26, 2017 at 0:45

What I'm really asking is, if quantum indeterminacy is a factor of more than just observational limitations and intractability,

Indeterminancy is inherent in the probabilistic postulates of quantum mechanics, where only the probability of getting a single measurement can be calculated exactly, and not the number.

where outcomes may be independent of of the prior state of the system, does it affect outcomes in the world of classical mechanics?

Let us take a perfect dice: the probability distribution will be flat at 1/6 for any throw.

Suppose you get from a specific dice this plot: Your question amounts to asking :can this bias be due to quantum mechanical effects?

The general answer is that quantum mechanics describes dimensions commensurate with h_bar and the number of molecules in a dice are of order 10^23 and the statistics will decohere a usual ensemble of atoms . BUT cystals are a macroscopic , dimensions of a dice, manifestation of quantum mechanics, as is crystal growth. Thus I could think of a way of biasing a dice using quantum mechanical knowledge: for example build one face of the crystal with a heavier isotope.

So the answer is very improbable unless extra measures are taken.

PS. Maybe this answer of mine for a different question might interest you.

• very nicely put! I'd be very interested in your thoughts on a related question I asked about quantum indeterminacy on Philosophy if you feel so inclined. :) Jun 18, 2017 at 19:14
• sorry, the question too philosophically inclined for an experimentalist. Jun 19, 2017 at 4:16
• no worries. i appreciate the the link to the postulates of QT, and the trick for loading dice. Jun 19, 2017 at 4:38
• This isn't really correct, even with a 'perfect dice', i.e., one that is invariant with changes of labels on the faces, $p=1/6$ is a choice that reflects the dice-thrower system and our knowledge of it. Aug 24, 2017 at 3:51

You are asking about the origin of probability in dice rolls. As argued convincingly by e.g. Jaynes in LoS, probability in dice rolls and coin tosses originates from our ignorance of the initial conditions. Were we cognisant of the initial state (the position and velocity of the coin or dice) with sufficient precision, we could evolve them in time and determine the final state. The fact that we might suppose every outcome of dice to have equal probability is a reflection of our ignorance about the dice (it may have imperfections) and the mechanism by which it is thrown (which may favour particular outcomes). Even if it were the case that the behaviour of the dice was quantum mechanical or chaotic, our choice that $p=1/6$ would still represent our limited knowledge of the dice-thrower system.

• Thanks for answering! I'd say this falls under "factors beyond calculation"/chaos/lack-of-information . My direct interest is in how indeterminacy is introduced into games, with a heavy, but not exclusive, Combinatorial Game Theory, definition of games. At a fundamental level, there seem to be only 3 methods of creating indeterminacy: Hidden Information (Incomplete of Imperfect) and Intractability (as a function of complexity) seem to constitute deterministic methods of introducing indeterminacy, which is distinct from true random number generation for which dice are an analog. Aug 24, 2017 at 18:46