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EPILOGUE: SCIENCE, SCIENCE!Rion is supported by many science-loving staff members.In this series, they will write about their enthusiasm for physics, geology, and chemistry.Part 1 will discuss reversibility and irreversibility.Because We’re Science LoversColumn by Rion staff on their obsession with scienceCan we get “spilled milk” back into the glass?There’s this theorem I nd my mind returning to ever since I rst learned in a lecture at my university more than twenty years ago. In our universe, the theorem says, some processes are reversible, while others are irreversible. There’s the old saying, “There’s no use crying over spilled milk.” The theorem may very well shed some light on whether the proverb is true or false.* *From a mechanical perspective, the physical pheno mena in this world should be reversible. If one motion is possible, its time-reversed motion should also be possible. The direction of time is absent from the fundamental laws of mechanics. For example, consider the countless number of stars seemingly wandering around in space. All their movements have been revealed mathemat-ically. Imagine the planets in our Solar System, which have been in continuous motion for ten or tens of millions of years. What happens if we reverse time? As long as we have the formula for their orbital calculations, we only need to calculate to go back a certain period. If we don’t know where they were 10 years ago, we can apply the formula to nd out. In what’s known as time-reversal symmetry, we can reverse the direction of time and return things to their former state. In other words, we can reverse the process unfolding in front of our eyes simply by ipping the arrow direction of time. This is the same thing as saying that Newton’s equation of motion is invariant for time and space reversal.* *We’re all aware that certain processes follow the laws of mechanics, while others don’t. Imagine a bullet train speeding along the railway track. When the driver applies the brakes, the train stops. Applying the brakes generates friction between mechanical parts and between the bullet train and the rails and converts force into heat. But no matter how we heat or cool the rails and mechanical parts of the brakes of a stationary bullet train, we can’t make the train move. Once force is converted into heat, the process can’t be reversed. We can convert 100% of motion into heat, but we can never con-vert 100% of heat back into motion.* *What fascinated me during a lecture at my univer-sity was a story known as the Ehrenfest urn, which deals with reversibility and irreversibility. Assume we have two urns, with balls numbered 1, 2, 3, …, M, placed randomly into the two urns. Then we take a deck of cards with the same set of numbers 1, 2, 3, …, M printed on them. Now we can start. Draw cards randomly one by one from the deck. When we draw a card with the number 3, we look into the urns for the ball with the corresponding number. If it’s in the right urn, we take it out and drop it into the left urn. If it’s in the left urn, we drop it into the right urn. If the next card we draw has the number 1, we transfer the ball with number 1 from the right urn to the left or from the left to right. We continue randomly moving the balls between the two urns in this way. Since the cards we draw are returned to the deck, a card with a certain number may be drawn multiple times. This process can be considered analogous to the time-invariant rule. In other words, the direction of time is nowhere present in the rule.Assume we start off by placing all of the balls in the left urn and perform the procedure of moving the balls by the above rule. Initially, the number of balls in the right urn is, of course, zero. As we repeat the procedure, a ball may be transferred to the right urn or moved back to the left urn, chang-ing the number of balls inside each urn. Let’s say we repeat the task n number of times. What can we expect when n = 5? It may by chance return to the initial state after the rounds, with the left urn having ve balls and the right having none. What about when n = 1,000, 10,000, 100,000,000, or 1,000,000,000,000? Curiously, as the number of balls increases, the possibility of returning to the initial state approaches zero. This is strange. The process appears to be reversible when n = 5 but becomes irreversible as n increases—something the old saying “There’s no use crying over spilled milk” alludes to.* *In the above process, when n is large, the number of balls in the two urns is known to eventually approach n/2 and stabilize. For example, when n = 1,000, we reach a near steady-state with 500 balls in the left urn and 500 in the right, even after repeating the procedure of moving the balls randomly. This implies the creation of a time irreversible state in which a state of equilibrium with the same number of balls in the two urns is reached from the initial state of all balls in one of the urns. Theoretically, the system can return to its initial state where 1,000 balls are in the left urn and 0 balls are in the right urn. But to enable such a state, we have to repeat the procedure around 2n times. Based on calculations, this means that returning to the initial state when n = 1,000, assuming we can transfer balls at a rate of 1012 moves per second, will take 10281 years. The story illustrates how irreversibility becomes manifest in practice as n increases. The reasoning is simple: There are many patterns for having approximately the same number of balls in each urn; there’s only one pattern in which all the balls are in the left urn and none in the right. In other words, having all balls in the left urn is a unique state, while having nearly the same number of balls in each urn (a total of 1,000 balls) is a common state. It’s normal for a unique state to transition into a common state, but quite rare for a common state to transition to a unique state. It requires an incredibly long time for this to happen naturally.* *I once again nd myself being fascinated by the Ehrenfest urn story. My duties lie in the eld of technological development. I believe Rion’s job is to explore the phenomena we encounter in the world in search of those that may be reversible under certain conditions. Once a phenomenon is found to be reversible, we must nd out what forces we need to apply to return it to the initial state and realize this reversal. For example, we could regard extracting just the target sound from a background of various sounds as the process of reversing the sound to its initial state at its source, thereby proving its reversibility. It’s not easy to determine whether a process is reversible or irreversible. But I nd the challenge fascinating.001The Ehrenfest Urn ModelFascinating IrreversibilityPaul EhrenfestAustrian physicist born in 1880, a friend of Einstein and Bohr, and known for the Ehrenfest classication of phase transi-tions, Ehrenfest theorem, and contributions to establishing the relationship between statistical mechanics and quantum mechanics.Yasutaka NakajimaNew Business Development Group, R&D Depart ment of the Technical Development Center. Since joining Rion he’s worked on developing sound level meters, frequen-cy analyzers, data recorders, aircraft noise monitoring system, and microphone ar-rays. Since 2019, he’s been a member of the R&D Department, where he’s currently focusing on marketing strategies and new business development from an engineering perspective.41723685Balls with numbers 1, 2, …, M are placed in two urns.The essence of irreversibilityEhrenfest’s urnsThere’s only one pattern for a unique stateThere are countless patterns for the state of equilibrium A transition occurs naturally from the few “unique states” to the countless “states of equilibrium” A transition occurs naturally from the few “unique states” A transition occurs naturally from the few “unique states” A transition occurs naturally from the few “unique states” A transition occurs naturally from the few “unique states” A transition occurs naturally from the few “unique states” A transition occurs naturally from the few “unique states” A transition occurs naturally from the few “unique states” A transition occurs naturally from the few “unique states” A transition occurs naturally from the few “unique 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