Half-life Simulation - EMERGENT Exponential Decay
2Half-life Simulation.
Note that the exponential decay rate is EMERGENT. It is not coded in. Every particle has an equal chance to decay at every moment in time, independent of its time-of-life, as per real-world measurements described by quantum mechanics. The only mathematics being performed is the equal and linearly consistent chance for each particle to decay, independent of time and each other. The overall exponential decay of the mass is emergent, not programmed into the system. It also explains the often unintuitive idea that somehow a mass of radioactive particles somehow "knows" to decay faster when it is larger, as if somehow the particles know how big they are collectively. This is explained by particle physics in that when the mass is larger, there are more particles and therefore more chances for particles to decay (more rolls of the dice, one per each particle) although not more chance for any individual particle to decay. Makes sense?
Purpose:
To explore why half-life decay is exponential and not linear. Why does decay depend on quantity or mass? Why doesn't 100g of substance decay by 50g, and then by another 50g in the same amount of time? Etc.
Inspiration:
A good friend of mine from Acadia University, mentioned half-life as an analogy to aggregated data, and it piqued my interest.
Research:
I read on reddit that a chemistry class teacher could not explain why half-life was exponential decay rather than linear, and I was stuck at the same place. Although the answer given was correct, I did not intuitively understand it. Hence, I explored it more.
- https://www.reddit.com/r/askscience/comments/3rdt2n/why_is_radioactive_decay_exponential_not_linear/
Links:
- https://en.wikipedia.org/wiki/Half-life
- http://xona.com/simulations/ (more of our simulation work)
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Matthew Doucette (Xonatron)
http://matthewdoucette.com/