Is temperature the speed of time? Thermal time and the Tolman effect

          @misc{ scivideos_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 for Theoretical Physics},
            year = {2010},
            month = {nov},
            note = {PIRSA:10110071 see, \url{https://scivideos.org/pirsa/10110071}}
          }
          

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.