Problem — Reproducibility of oil density

Problem

A classmate says: “I measured the density of the oil once and found 0.92 g/cm³. That’s a scientific result.” (a) What is missing from his work for it to be truly scientific? (b) List three things to specify so that others can reproduce the measurement. (c) Why does a non-reproducible measurement have no scientific value, even if it happened to be the true one?

Solution

(a) What is missing. A single measurement is not enough for a scientific result. At least three elements are missing:

• repetitions of the measurement: with a single trial one cannot estimate how stable the result is;
• the uncertainty estimate: writing $0{,}92$ g/cm³ without a $\pm$ does not say how reliable the figure is;
• the description of instruments and procedure: without knowing how the measurement was made, the number cannot be checked by others.

A well-posed scientific result has the form $\rho = (0{,}92 \pm \delta\rho)\ \text{g/cm}^3$, obtained from several trials and with a documented procedure.

(b) Three things to specify to reproduce the measurement.

1. The temperature of the oil, because the density of liquids depends significantly on temperature.
2. The instruments used and their sensitivity: balance (range and resolution) and graduated cylinder (smallest readable volume).
3. The measurement protocol: how the mass and volume were determined (container tare, meniscus reading level, number of trials).

(c) Why reproducibility is essential. Science is founded on intersubjectivity: a result has value only if others, following the same procedure, can obtain it again. A non-reproducible measurement is neither verifiable nor falsifiable: there is no way to check it independently, so it cannot enter the shared body of knowledge. Even if, hypothetically, it were “the only true one”, without reproducibility it would remain a private belief, indistinguishable from an error or a lucky fluke, and therefore devoid of scientific value.

$\ev{\text{Scientifico} \Rightarrow \text{ripetuto} + \text{con incertezza} + \text{procedura documentata e riproducibile}}$

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Topics: Metodo sperimentale Concepts: Cifre significative e incertezza