Robert Jack was born at Quarter, near Hamilton, Lanarkshire, Scotland, on 4 November 1877, the son of Janet Park and her husband, Hugh Jack, a schoolmaster. He was educated at the Hamilton Academy and at the University of Glasgow, where he gained an MA with first-class honours in mathematics and natural philosophy. His postgraduate career took him to the Université de Paris and to Göttingen university in Germany. There he continued research into the effect of magnetic fields on the spectra of atoms (the Zeeman effect). His work in this and related fields led to a DSc from Glasgow University.
After four years as a lecturer in physics at Queen's University, Belfast, Jack came to New Zealand in 1914 as professor of physics at the University of Otago in Dunedin. During the next 33 years he was at various times chairman of the professorial board, a member of the university council and dean of the Faculty of Arts and Science.
Beyond the university Jack introduced the people of Dunedin to many aspects of physics through popular open lectures. However, his greatest impact on the public was as the pioneer of radio broadcasting in New Zealand. Radio signals had been transmitted within the country before Jack arrived, but there had been no transmissions of voice and music. Jack developed the technology to make this possible and promoted public interest in broadcasting. He began his research into 'wireless' radio on his arrival and continued experimenting after the First World War. In 1920–21 he visited the United Kingdom, where he examined the latest naval radio communications and discussed equipment with his brother Hugh, a prominent electrical engineer. He returned to New Zealand with various items, including high-voltage direct current generators and two Edison valves that would form the basis of his radio transmitter.
Jack was assisted by a team from the university's physics department, notably his technician, Jack Sutherland. Within a year of the world's first radio stations going on air in the United States and Holland, the team had assembled a small transmitter at Otago University. On 21 May 1921 they were able to transmit voice and music across the laboratory. In July Jack's interest in radio as a provider of information and not just a purveyor of music was heightened when he picked up broadcasts of a world championship boxing match from the United States. He claimed that 'the whole life of the community will be broadened and educated by being brought into more effective touch with the life of the whole world'.
On Saturday 17 November 1921 Jack and the team broadcast New Zealand's first radio programme (although during that year ships' wireless operators had broadcast 'gramophone records'). Jack continued the transmissions two nights a week and the programmes – a mixture of announcements, live music, and gramophone records – were heard in all parts of the country and even on a ship near the Australian coast. In April 1922 Jack made a special broadcast, directed to the Philosophical Institute of Canterbury, in Christchurch, but it was affected by atmospheric conditions and was not entirely successful. However, in August a concert from Allen Hall at Otago University was successfully relayed. Jack's wife, Isabella Finlay Manson, provided music for his broadcasts. The couple had married on 27 May 1922, in Dunedin. Isabella, a fellow Scot, was the matron of Knox College.
Robert Jack's experimental work was built on by a group of enthusiasts who established the Otago Radio Association on 11 November 1921 and elected him patron. The association began regular broadcasts on 15 November 1922. Despite changes of call sign and ownership, the original station is still on air as Radio Dunedin, 4XD, one of the oldest radio stations in the world. Jack's association with radio continued mainly through the research work of his students. By 1924, along with other Dunedin enthusiasts, he was experimenting with television transmission, and by 1928 he was able to 'transmit' a picture from one side of the room to the other using a system similar to the 'flying spot' apparatus developed by John Logie Baird.
During the Second World War Jack undertook research for the government on infra-red radiation and served as chairman of a committee on deferred military service. Although best known to the public for his broadcasting innovations and his clear vision of how radio would develop, the greater part of Jack's life was spent as a scientist and as a university teacher and administrator. His recreational pursuits included golf and bowls. Bobbie Jack, as he was known to his students, retired in 1947. He died in Dunedin on 1 May 1957. His wife, Isabella, had died in 1941. There were no children of the marriage.