The word “proof” carries enormous weight in mathematics and a much lighter one in physics. In mathematics a theorem is proved once and for all, deductively, starting from axioms; in physics no theory is ever proved, nor can it ever be.
Popper’s falsifiability
Karl Popper understood this with great clarity in the 1930s: a scientific theory is one, first of all, because it is falsifiable, that is, because it forbids certain observational facts.
Criterion of demarcation
If a theory forbids everything and nothing, it is metaphysics. If it forbids something that then turns out to be true, it is false. It is scientific only if it puts something at stake: if there exists a possible observation which, were it to occur, would refute it.
A theory that has survived many attempts at refutation is a corroborated theory, never “proved true”. Newton withstood two centuries of increasingly sophisticated falsification attempts; then Mercury began to precess in a way Newton could not explain, and general relativity arrived to account for it. Newtonian mechanics is not “false” in an absolute sense: it is an extraordinarily accurate theory within a well-defined domain (speeds small compared with , weak gravitational fields), and it is still what we use to build bridges and send probes to Mars. It is false, however, as a universal claim.
The practical consequence in the lab
There is a lesson that directly concerns anyone studying. When an experiment “confirms” a law, it does not mean the law is true: it means that, at least in that experimental context, it has not been falsified.
When, instead, the data are in tension with the law, before discarding it one must ask whether there might be something wrong in our set-up: a badly calibrated instrument, an uncontrolled disturbing variable, a hidden assumption in the calculations. The history of physics is full of both situations — experiments that seemed to falsify correct theories (and later turned out to be flawed) and experiments that revealed the real limits of theories thought to be flawless. The final judgement always requires, besides technique, a good dose of epistemic caution.
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Topics: Metodo sperimentale
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