The short answer
Read the historical record, work through the invented example, then identify which conclusions depend on the example’s assumptions.
Read the distinctions
Separate the epistemic steps
Compare the kind of statement being made before treating two claims as equivalent.
| Question | Input or statement | What it permits |
|---|---|---|
| Historical measurement | Mass-dependent transition temperature. | A constraint on possible mechanisms. |
| Stipulated relation | Tc×√M=constant. | The fictional numerical prediction. |
| One residual | 3.90−40/11≈0.264 K | A question requiring uncertainty and scope, not an automatic universal verdict. |
Chronology
A timeline of the turning points
Experimental clue
Mercury isotope measurements informed the search.
Microscopic account
Bardeen, Cooper and Schrieffer published their theory.
Retrospective
Bardeen discussed the theory–experiment relationship.
A theory faced more than zero resistance
The 1957 Bardeen–Cooper–Schrieffer abstract addresses several superconducting properties, including an energy gap, thermal behaviour, magnetic response and isotope dependence. This is a set of constraints on an explanation, not a claim that one numerical match establishes the entire theory.
Only the indexed abstract and first-page excerpt of that paper were inspected. The later lecture supplies the historical account used below; it is a retrospective source, not the 1950 experimental reports themselves.
The earlier measurement and the later account
Bardeen’s 1972 lecture describes 1950 mercury-isotope measurements by the Rutgers group and Maxwell at the National Bureau of Standards. Their result could be interpreted as Tc×√M approximately constant, where M is isotope mass. The ionic-mass dependence directed attention to lattice vibrations.
That empirical relation is not the whole BCS theory. A dependence on mass can help choose between explanations without determining every detail of a microscopic mechanism. The exercise turns one explicitly assumed relation into a prediction, keeping that inference separate from the historical evidence.
Sources for this section: [2]
Invented masses and transition temperatures
Stipulate a teaching model with Tc×√M exactly constant. Use the same arbitrary mass unit throughout. Material A has M=100 and Tc=4 K. Change only the isotope mass to 121. Predict Tc for B. Then suppose an invented measurement instead gives 3.90 K. Calculate the difference between that value and the prediction, and identify what extra information would be needed to assess the disagreement.
These are invented values, not mercury data. Treating the relation as exact is an exercise assumption; it does not assert an exact universal isotope rule for all superconductors. Do not infer a real material’s properties from this fixture.
Sources for this section: [2]
Reference answer
The model’s constant is 4×√100=40 in the chosen combined units. Hence Tc(B)=40/√121=40/11 K, approximately 3.636 K. The invented measurement exceeds that prediction by 3.90−40/11 K, approximately 0.264 K. The temperature ratio is 10/11, not 100/121, because the relation uses a square root.
To assess disagreement one would need measurement uncertainty, sample comparability and the relation’s domain of validity. A large residual could challenge this simplified fixture without, by itself, deciding every form of superconductivity theory. Agreement would likewise support only the tested prediction. Other observations remain independent constraints.
Sources for this section: [2]
Continue the chronology
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Biography context
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People behind the records
Quick answers
Common questions
- Are the numerical values historical data?
- No. They were chosen for a transparent square-root calculation; the source-derived relation and invented inputs are explicitly separated.
Primary and institutional sources
How this history was checked
The cited records have different dates and purposes. All worked examples are newly invented and are not historical measurements. This article was reviewed on 31 October 2026.