Probability

Hello. A roll of dice is supposed to be the perfect example of randomness, but it's easy to see how you might go about explaining why someone got a 1 instead of 6. The die was this way up when it hit the table at this angle, it had this amount of force, there were certain weight imbalances that caused it to spin this way rather than that, etc. So is there really such a thing as chance, or is that just the word we use for when something is too complex for us to disentangle all the cause and effect that goes into it?

Comments

Good question.

Good question. In fact, most people who work on these matters wouldn't agree that a roll of a die is a perfect example of randomness. And you are quite right: we believe that if we knew enough about the prevailing conditions when the die was rolled (and if we could do the calculations!) we could figure out how the die would land. That convinces many people that dice rolls aren't really chance events at all, though not everyone agrees. The issues about "deterministic chance" tend to get technical, but they have partly to do with the amount of complexity involved in disentangling the causes and effects.

But your question still stands whatever our view on whether determinism and chance can somehow fit together. That question is: are all apparent examples of chance cases where a complete account of the details would determine the outcome of the supposedly "chance" process? The answer is a solid "Maybe not." The reason is quantum mechanics. Quantum mechanics, as you may know, is a theory in which probability is the order of the day. For example: suppose we prepare a beam of photons (light quanta) so that each of them is certain to get past a filter for polarization in the vertical direction. But suppose that instead, we set up a filter at 45 degrees to the vertical. Quantum mechanics says that for each photon, there is a probability of 50% that it will get past the filter. But it says no more, and given the mathematics of quantum theory, there's no way to make it say more without adding extra assumptions.

It's possible to do that. There are theories that posit an underlying deterministic story. One important example is Bohmian mechanics. It's deterministic but it calls for faster-than-light action-at-a-distance. Some people think that the experimental and theoretical arguments more or less force us to accept that; others disagree.

Another way to recover determinism is to adopt the Everettian or "many worlds" account of quantum mechanics. That story doesn't call for faster-than-light signals, but it tells us that when we perform a polarization experiment like the one we described, the world branches. Both outcomes occur; in one set of branches, the photon gets past the filter; in another set, it doesn't. Some researchers think that this is the best, most natural way to understand quantum theory. It would amount to determinism with branching. For others, this is the least attractive alternative.

To make matters worse, in virtually any realistic scenario both Bohmian mechanics and Many-Worlds quantum mechanics make the same experimental predictions as more orthodox views . Simply making more measurements is extremely unlikely to settle the debate.

Where does this leave your question? Unsettled. Some people believe that quantum processes are deeply random, with no underlying deterministic process. Others disagree and believe that there is an underlying deterministic story, though they disagree about what the story should be like. If I had to pick, I'd side with the non-determinists, but there's a whole lot of room to argue.

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