On the morning of June 23, 1980, Sanjay Gandhi, a newly elected MP, father of a three-month-old baby, and the prime minister’s favoured son and heir, attempted to do an aerobatic loop in his two-seater plane and crashed, nose first, into the ground. What if he hadn’t lost control, what if he had managed to pull up out of his steep dive? What would have happened then—to Sanjay, to his mother Indira Gandhi, and to India?

It is hard to imagine Sanjay Gandhi as a 57-year-old. At the time of his death, he personified youth and energy, or ‘go’, as his mother put it. In his late 50s, would he be bald and overweight? Would he have aches and pains and high blood pressure? Or had he inherited his mother’s robust adult health, so that he would have been as vital and handsome in middle age as he was in his youth? Would his marriage have survived; would he have fathered more children? And what of his business activities? Would they have made him a multi-millionaire?

Or—the question on everyone’s mind in 1980—would Sanjay Gandhi by 2004 have become India’s prime...