PIRSA:10110071 Scientific Series Quantum Gravity

DOI10.48660/10110071

Series: Quantum Gravity

Smerlak, M. (2010). Is temperature the speed of time? Thermal time and the Tolman effect. Perimeter Institute. https://pirsa.org/10110071

Smerlak, Matteo. Is temperature the speed of time? Thermal time and the Tolman effect. Perimeter Institute, Nov. 16, 2010, https://pirsa.org/10110071 

@misc{ pirsa_PIRSA:10110071,
  doi = {10.48660/10110071},
  url = {https://pirsa.org/10110071},
  author = {Smerlak, Matteo},
  keywords = {Quantum Gravity},
  language = {en},
  title = {Is temperature the speed of time? Thermal time and the Tolman effect},
  publisher = {Perimeter Institute},
  year = {2010},
  month = {nov},
  note = {PIRSA:10110071 see, \url{https://pirsa.org}}
}

Abstract

Why is a vertical column of gas at thermal equilibrium slighly hotter at the bottom than a the top? My answer in this talk will be that time runs slower in a deeper gravitational potential, and temperature is nothing but the (inverse) speed of time. Specifically, I will (i) introduce Rovelli's notion of thermal time, (ii) use it to provide a "principle" characterization of thermal equilibrium in stationary spacetimes, and (iii) effortlessly derive the Tolman-Ehrenfest relation. This approach contrasts with the "constructive" accounts of thermal equilibrium in curved spacetimes given in the literature, and vindicates the time-temperature relationship cropping up in the Hawking-Unruh and Kubo-Martin-Schwinger relations.

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