I maintain that the mathematical concept of a point in a continuum has no direct physical significance. It has no meaning to say the value of a coordinate x... has a value x = sqrt(2) in. or x = π cm. [...]Max Born, quoted in Brillouin (1962, p303). Though I'm wondering whether this is any more true of irrational than rational numbers. A coordinate of 2 cm is just as much a point in a continuum as π cm, is it not?
Modern physics has achieved its greatest successes by applying the methodological principle that concepts which refer to distinctions beyond possible experience have no physical meaning and ought to be eliminated … The most glaringly successful cases are Einstein's foundation of relativity based on the rejection of the concept of aether ... and Heisenberg's foundation of quantum mechanics .. I think that this principle should be applied also to the idea of physical continuity
- Brillouin, L.
- Science and Information Theory
- Academic Press, 2nd ed. 1962