Abstract
Since Boltzmann’s works, there is the question of explaining the arrow of time in statistical physics: While many microscopic physical theories do not know a preferred direction of time, one experiences an arrow of time in the macroscopic world. Glass shatters when it falls on the ground whereas we never see the reverse process. The usual explanations for that are based on a very special initial condition, a state of very high order which under the dynamics evolves in a natural way into a state of higher disorder. Here one can see (order \(\rightarrow \) disorder) the asymmetry in the propagation in time. This explanation, however, shifts the problem to the question of where the initial state of high order came from. In the following we will discuss different possible explanations for the emergence of a macroscopic arrow of time, in particular we will discuss an idea going back to V. A. Antonov who found that the growth in disorder can be explained without assuming a special initial condition.
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Notes
- 1.
In fact there is an infinite number of such times s. This, however, is irrelevant for the argument.
- 2.
Note that temperature is a form of kinetic energy, but not kinetic energy per se. A stone falling in a gravitational field in the absence of friction will increase the total kinetic energy of the system while the temperature of the stone remains unchanged. While temperature is proportional to the variance in the momentum-direction and thus directly related to disorder of the system and thus entropy, kinetic energy is not. That is why temperature should be used as a macro-variable, not kinetic energy.
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Acknowledgements
The authors are most grateful to Detlef Dürr for everything he did for us, and in particular for starting the collaboration on the topic and for all the inspiring meetings we had over the years.
We also wish to thank Julian Barbour, Tim Koslowski, Dustin Lazarovici, Tim Maudlin and Paula Reichert for helpful discussions on the topic.
The authors acknowledge support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) project-number 417613818 (“A microscopic model for explaining the arrow of time”).
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Pickl, P., Schaal, A. (2024). The Arrow of Time. In: Bassi, A., Goldstein, S., Tumulka, R., Zanghì, N. (eds) Physics and the Nature of Reality. Fundamental Theories of Physics, vol 215. Springer, Cham. https://doi.org/10.1007/978-3-031-45434-9_19
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