At the level of individual particles, the answer is less obvious. Many equations of classical and quantum mechanics can be reversed in time: reverse every motion in the right way and the calculation also describes the return journey. For the real glass, however, every shard would not only have to fly back exactly. Air currents, sound waves, heat and deformations in the floor would also have to converge with unimaginable precision and feed themselves back into the fracture.
What does entropy count?
Statistical mechanics distinguishes the visible macrostate from the many microscopic arrangements compatible with it. Boltzmann linked entropy to the number of these microstates; in modern notation: S = kB ln W. An intact glass standing on a table is a highly special state. There are incomparably more microscopic possibilities for scattered shards and for energy dispersed into their surroundings.
“More entropy” therefore does not simply mean “more disorder”. It means that a macrostate can be realised in many more ways. With overwhelming probability, a system develops toward the larger region of its possibilities. This is the thermodynamic arrow of time: we distinguish before from after by the direction in which entropy typically increases.
Is the return journey forbidden?
No, not as an absolute prohibition. Brief events with negative entropy production can be observed in very small systems and described by fluctuation theorems. In a glass with an enormous number of participating degrees of freedom, however, a spontaneous collective reversal is so unlikely that it is excluded for every practical purpose. No responsible numerical probability can be assigned to the real glass without knowing its complete microscopic state.
Repair does not contradict the second law either. We can collect and glue shards or melt the glass anew. That requires work and energy; heat and further traces arise in the surroundings. Entropy may decrease locally while not decreasing in the sufficiently large closed system as a whole.
How does the world know this direction?
Probability alone does not yet explain why the lower-entropy side is the past for us. The usual statistical account assumes an exceptionally low entropy in the universe's early history. How that boundary condition should be understood remains a foundational question. The everyday arrow of time is therefore robust, but its deepest origin cannot be settled in a single sentence.
The shattered glass shows that the past is not merely a position on a clock's scale. It leaves distributions behind: shards, heat, sound, memories. We can restore a form, but we do not erase the event from the world. Every repair becomes part of its history. Perhaps we recognise time less by a uniform beat than by traces that cannot all be called back together.
Sources
Ludwig Boltzmann, On the Relationship between the Second Fundamental Theorem of the Mechanical Theory of Heat and Probability Calculations (1877), English translation in Entropy (2015)
MIT OpenCourseWare, Mehran Kardar, Statistical Mechanics I, Lectures 2, 6 and 9
Tiago B. Batalhão et al., Irreversibility and the Arrow of Time in a Quenched Quantum System, Physical Review Letters 115 (2015)
Stanford Encyclopedia of Philosophy, Thermodynamic Asymmetry in Time, revised 2026