The problem of time resulted from the Wheeler-DeWitt equation an attempt to combine ideas of quantum mechanics and general relativty.
Doubts to the existence of time have been well known even before. As Ernst Mach in 1983 said1:
It is utterly beyond our power to measure the changes by time. Quite the contrary, time is an abstraction, at which we arrive by means of the changes of things.
J. M. E. McTaggart published his best known philosophical work exploring contradictions that occur when defining and discussing time as it’s commonly understood2.
Recently discussed, is the idea that time itself does not exist. As the Julian Barber work The End of Time3 published in 2000 explains. A more concise, summary paper “The Nature of Time”4 won first prize on March 7th 2009 from the Foundational Questions Institute.
MACH, E. (1893). THE SCIENCE OF MECHANICS. United States: Open Court. Page 224. ↩︎
McTaggart, J. M. E. (1908). The Unreality of Time. United Kingdom: Aberdeen University Press. ↩︎
Barbour, J. (2001). The End of Time: The Next Revolution in Physics. United Kingdom: Oxford University Press, USA. ↩︎
Barbour, J. (2009). The nature of time. arXiv preprint arXiv:0903.3489 ↩︎