To answer this question, we need to understand the context of the special theory of relativity and its development by Albert Einstein.
Option A) While reading David Hume - This option is incorrect. David Hume was a philosopher, not a physicist, and his works primarily focused on areas such as epistemology and metaphysics, rather than physics or the theory of relativity.
Option B) Lunchbreak at the patent office - This option is incorrect. While Einstein did work at the patent office in Bern, Switzerland during the time he developed the special theory of relativity, it is not accurate to say that he had a eureka moment during his lunchbreak.
Option C) In his sleep - This option is correct. The final pieces of the special theory of relativity did indeed come to Einstein in a dream or during his sleep. According to Einstein himself, he had a dream or a thought experiment that led him to the realization of the theory's key concepts, such as time dilation and the constancy of the speed of light.
Option D) While hiking in the Alps - This option is incorrect. While Einstein did spend time in the Swiss Alps and enjoyed hiking, there is no evidence to suggest that he had any breakthroughs regarding the theory of relativity during his hikes.
The correct answer is C) In his sleep. This option is correct because Einstein famously stated that the final jigsaw pieces of the special theory of relativity came to him in a dream or during his sleep.