Natura non facit saltus (Latin for "nature does not make jumps") has been an important principle of natural philosophy. ...Quanta mag reports:
The principle expresses the idea that natural things and properties change gradually, rather than suddenly. In a mathematical context, this allows one to assume that the solutions of the governing equations are continuous, and also does not preclude their being differentiable (differentiability implies continuity). Modern day quantum mechanics is sometimes seen as violating the principle, with its idea of a quantum leap. Erwin Schrödinger in his objections to quantum jumps supported the principle, and initially developed his wave mechanics in order to remove these jumps.
When quantum mechanics was first developed a century ago as a theory for understanding the atomic-scale world, one of its key concepts was so radical, bold and counter-intuitive that it passed into popular language: the “quantum leap.” Purists might object that the common habit of applying this term to a big change misses the point that jumps between two quantum states are typically tiny, which is precisely why they weren’t noticed sooner. But the real point is that they’re sudden. So sudden, in fact, that many of the pioneers of quantum mechanics assumed they were instantaneous.The article goes on to discuss randomness, which is really another issue.
A new experiment shows that they aren’t. By making a kind of high-speed movie of a quantum leap, the work reveals that the process is as gradual as the melting of a snowman in the sun. “If we can measure a quantum jump fast and efficiently enough,” said Michel Devoret of Yale University, “it is actually a continuous process.”
In a 1952 paper called “Are there quantum jumps?,” Schrödinger answered with a firm “no,” his irritation all too evident in the way he called them “quantum jerks.” ...
The techniques developed by the Yale team reveal the changing mindset of a system during a quantum jump.
The slogan applies to everything from electrons to grand ideas. Things change continuously.