Because probabilities reflect lack of knowledge, new information can cause probabilities to change:
The Monty Hall problem. A prize exists behind one door. Having picked a door (let’s say, door #1), and then shown a booby prize behind one of the two unchosen doors, do you take the offered chance to switch your choice (to door #2)? (interactive demo here)
Such changes in probability due to new information can continue up until the point that the outcome is fully known (as specified by Bayes’ theorem). Less formally, we have the Boy or Girl paradox: if the Smiths have two children, the probability that the oldest is a boy is about 51%. But if I also tell you that at least one is a girl, then the probability drops to about 34%. If I tell you that the oldest child is named Sue, then the probability of that child being a boy drops almost, but not quite, to zero.
In the subatomic physical world, things can get trickier. Heisenberg’s uncertainty principle puts limits on certainty at that level:
Einstein famously found those limitations disturbing. Some Christian theologians aren’t too keen on them either. But the fact that modern technology works constitutes a persuasive verification of the theory.
2 comments:
Can you elaborate on your final sentence: "But the fact that modern technology works constitutes a persuasive verification of the theory."
A lot of modern electronics is grounded in quantum theory, and lends support to the theory's general truth.
The extremely narrow frequency band of lasers is a result of the Heisenberg uncertainty principle: because atoms remain in an excited state for a long time (compared to gas discharge lamps), there is a large time uncertainty and hence a very small energy/frequency uncertainty.
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