Reversing the Irreversible in Puella Magi Madoka Magica – Future Predictions Using Physics

Lately I have been fascinated with Puella Magi Madoka Magica. Madoka Magica takes a darker approach to the classically fluffy Mahou Shoujo genre. Each episode of this Faustian story is incredibly intense and thought-provoking. In particular, I found Kyubey and Madoka’s discussion on reversing entropy particularly interesting.

For those not following the series, here is a (relatively) brief synopsis of what has happened so far (in not so definite terms). Madoka meets a cute animal Kyubey, who wants to contract her to become a magical girl and protect the world from cursed witches. While this sounds typical of the genre, the real agenda of Kyubey is actually to subject young girls to cycles of hope and despair as they turn from magical girls into witches. Kyubey then harvests and transforms those emotions into usable energy to balance the loss of free energy in the universe. Kyubey claims this as a noble cause to reverse the entropic effects defined by the second law of thermodynamic.

The second law of thermodynamic states that entropy, or disorder, of an isolated macroscopic physical system –such as our universe– always increases irreversibly. For example, gas in a room will always diffuse to fill the entire space; glass fallen off a table will shatter into pieces. It does not happen the other way around naturally. In both cases, the molecules in the gas and pieces of glass are now in much more random motion. This irreversible increase in entropy has huge implications both physically and philosophically.

Embedded in the second law is perhaps a somewhat pessimistic view of the universe. The increasing disorder has oft been compared to Murphy’s law: things that can go wrong always tends go wrong. That idea is certainly core to how Madoka Magica has been developing. The story seems to be headed for a bleak ending. However, perhaps magical girls can not only reverse entropic effects, but also fix all that have gone wrong with the girls’ lives.

Now let us delve into the physics beyond basic general chemistry, and discuss the other major theme of Madoka Magica –time. Since Einstein’s relativity, we now recognize that time is not absolute, but instead dependent on the observer. Further, the laws of science do not distinguish between going forward and going backward in time. So then, how do we know the past from the future?

Though the laws of science are unchanged for both time directions, there does exist an arrow of time to denote past and future. Interestingly, entropy is the only physical quantity with a  specific direction in time. The irreversibility stated by the second law gives an initial and an ending state, and thus a past and a future. We observe gas diffusing in a room instead of gathering in a corner, or pieces of glass scattering rather than gathering together, because in both cases, we perceive an increase in entropy.

If the role of magical girls in Madoka Magica is to reverse the effects of irreversibly increasing entropy, then perhaps inherent in that role is also reversing the effects of time or the events that have transpired. By loose extension, the girls represent a reversal of Murphy’s Law in a sort of Poincaré way.

And if we do reach such an ending, that would make a really neat parallel to the physical ideas underlying the story. I have hope that things will end well.

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Side Notes:

1. A further elaboration and continuation from the comments:
   

   Assuming there are infinite parallel universes, there is a possibility one exists where the current entropy is still at essentially zero and only increases ever so slightly with time.
   Now if the events that transpire in Madoka Magica symbolizes entropy, and an increase in entropy represents the girls’ lives falling apart, then there is a non-zero probability that Homura ends up in a timeline, where we start with all the girls not yet mahou shoujos, and that in the span of the girls’ timelines, they never come into contact with Kyubee or avoid contracted (possibly because of Homura’s actions – inputting work).

   […]

   Entropy only increases in time because of our definition of time. Regarding the arrow of time, Stephen Hawking argues that the reason we feel time passing from past to future is because we have that’s the direction entropy increases. Assume today that we could reverse either time or entropy (via Homura’s ability for time or Kyubee’s technology for entropy), does that then mean we could indeed have a mass reset to before all of this -including the first Homura timeline that sparks all the other timelines- happen? And more importantly, does the ability to reverse time/ entropy represent a possible timeline that moves toward less chaos?

   If we were to continue with the symbolism set up between entropy and the events, then it seems a good ending can happen.

2. I should make this clear. I make no claims that magical girls have to abide by the laws of physics. I am merely noting a possible entropy-like plot development. A reset ending would make some fun parallels between the story and physics.
3. Stephen Hawking’s A Brief History of Time and A Briefer History of Time are both good further light readings, especially for those non-physics majors (like me).
4. Poincaré Recurrence Theorem states that systems will return very closely to the initial state with enough time.
5. I am way over-thinking this.

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A moment of silence, kind thoughts, and a link for those affected by the earthquake and tsunami. Mar. 11. 2011.