Without being fairly certain on this detail, the entire, expensive project—‘No other nation had the mental and physical resources.. $2 bn.. entire towns built’ [Clark] —would not have been started. The answer seems to be the line from the Curies to Fermi. It’s true that e=mc2 seems to be used as a buttressing argument, but the defining evidence was empirical. Moreover, there is some doubt as to the correctness of nuclear reactions and their thermodynamics; thus etc. are given with seeming confidence.
Yet of course there are long processes
Of inference, possibly wrong, going into these calculations. The complete failure of fusion power adds weight to this suggestion. I would suggest that e=mc2 was b2c datasets adopted simply because it gave a big number, rather than through any cogency in argument. It's possible that nuclear reactions involve large amounts of energy because the nucleus is harder to alter than the outer parts of atoms: so that, if all the products of an atom bomb were collected together, perhaps they would add up to exactly the original contents—though this would be a difficult experiment to try.
It seems that the atomic bomb was certainly
Helped by some aspects of 20th century physics—the fairly simple sort listed above. The supposedly theoretical stuff, from relativity and quantum theory to Schrödinger’s waves and uncertainty principle as popularly misunderstood, probably had not the slightest effect. The situation in atomic physics—except that lucky discoveries seem to have petered out—is the same combination of accident and observation. Advances are largely delusory. Look for example at nuclear power.