Stern, Gamow, and the Shabbat Elevator Effect

Abstract

Abstract In addition to being known for their other work, physicists George Gamow and Marvin Stern also published an analysis of an intriguing problem regarding their perception that although both worked on different floors, it seemed that the first elevator to arrive on their respective floors was traveling in the opposite direction of their destination. In this manuscript, a fictitious conversation occurs between the two in regards to the probability of the elevator stopping on every floor (which they term the Shabbat Effect). One claims that it is the number of elevator occupants that predominates whereas the other claims it is the number of floors in the building that predominates in giving rise to this effect. Equations for estimating the probability of the Shabbat Effect are developed and analyzed. The resulting equations show that the relationship between the number of elevator occupants and floors is surprisingly complicated. Consequently, no general rule can be given for whether the probability of the Shabbat Effect increases or decreases for an arbitrary change in the number of occupants and floors. However, it discovered that for similar changes in the number of occupants and floors, it is the number of floors that predominates in determining the probability of the elevator stopping on every floor.