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Quantum physics revealed that particles changed their behaviour when observed. Ng theorised that the experience of "shoulder creeping" was related to quantum phenomena. (AUDIO: ScrapeJane)
Quantum theory was one of the subjects studied by Susan before she and the First Doctor settled at Totter's Lane. (PROSE: Losing the Audience)
While waiting for Clara Oswald to finish her day of work at Coal Hill School, (PROSE: The Day of the Doctor) the Eleventh Doctor read a book on Advanced Quantum Mechanics, (TV: The Day of the Doctor) which bored him after he failed to find Wally anywhere and had to resort to reading the text. (PROSE: The Day of the Doctor)
Behind the scenes
The 2019 Companion Chronicles audio story Daybreak establishes that fixed points in time are only created "once a waveform has collapsed". This is a clear allusion to wave function collapse, a concept in quantum mechanics. This is when a wave function in a superposition (ie. with multiple possible quantum states) is "observed" (measured), and thus collapses into only one possibility.