Question

It is implied, per QM, that the behavior of subatomic particles cannot be precisely predicted. However, these indeterministic effects do have defined probabilities. By the law of large numbers, they can "average" out and result in approximately deterministic laws. For this reason, I presume, we can predict with pinpoint accuracy whether or not atleast some kinds of events will happen in the macro scale even if we can’t know their minute details on a subatomic level. The question then is how fine or loose grained of an event is predictable given all knowledge about antecedent conditions. And how antecedent must these conditions be? Suppose I woke up today at 9 AM and ate toast for breakfast. If I were to know everything that could be possibly known about the configuration of the universe right after the Big Bang, is this event predictable? Can one say, given that knowledge, with assuredness whether or not this will happen?

Answer 1

Given the knowledge of the configuration of the universe post-Big Bang, it's theoretically impossible to predict events at a fine-grained level, such as waking up at 9 AM and eating toast. While certain macro-scale phenomena might seem deterministic due to the law of large numbers, the immense complexity and chaotic nature of interactions at the quantum level make precise predictions unfeasible.

Step-by-step explanation:

At the quantum level, indeterminacy reigns due to Heisenberg's Uncertainty Principle. Though individual particle behaviors might have defined probabilities, these effects, when aggregated, tend to "average out" per the law of large numbers. However, the complexity of even seemingly minor events at the macro scale involves an inconceivable number of particles and interactions. Consider the number of atoms in a slice of toast or the brain processes involved in deciding to wake up at a particular time – these constitute a gargantuan number of variables.

The unpredictability amplifies exponentially as we move further from the initial conditions post-Big Bang. The deterministic predictability diminishes rapidly with cascading implications. Even minute discrepancies in the knowledge of the universe's configuration at the earliest stages magnify significantly over time. Hence, while some broad predictions might be possible at macro levels, events as specific as an individual's actions in a complex environment become utterly unpredictable.

In mathematical terms, the sensitivity to initial conditions (suggested by chaos theory) grows exponentially. Even a tiny uncertainty in the initial state would escalate to significant differences in predictions over time. This concept is captured by the butterfly effect, where small changes in initial conditions lead to vast differences in outcomes. Therefore, despite the apparent determinism in larger scales, predicting specific events like waking up time or breakfast choice would be practically impossible with knowledge post-Big Bang.