Problem
Imagine you could measure every quantity with absolute precision, zero instrumental uncertainty. What would still remain unpredictable in classical physics? And in quantum physics?
Solution
Even zeroing the uncertainty of the instruments, the predictability of the physical world would remain limited, for two profound and quite different reasons.
In classical physics: chaos. Many systems (the motion of three gravitating bodies, the atmosphere, a double pendulum) are chaotic: extremely small differences in the initial conditions grow exponentially in time. Even if the instruments were perfect, the real initial conditions are never known with infinitely many decimal digits: any residual, however tiny, would be amplified until long-term prediction becomes impossible. Classical physics is deterministic in principle, but not predictive in practice for chaotic systems. It is not a matter of instruments, but of sensitivity to initial conditions.
In quantum physics: Heisenberg’s uncertainty. At the microscopic level an even more radical limit intervenes. The uncertainty principle states that This is not a technical limit of the instrument: it is a structural property of nature. Position and momentum do not simultaneously possess well-defined values; determining both jointly with arbitrary precision is impossible in principle. Even with ideal instruments, the single outcome of a quantum measurement remains intrinsically probabilistic.
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Topics: Metodo sperimentale Concepts: Cifre significative e incertezza