particles - a library and utility for simulating a simple particle universe
particles implements a simulation of a toy-universe.
This universe contains particles which have 2 quarks. Quarks exist in either an up state (up-quarks) or a down state (down-quarks). Particles with one up and and one down quark are called 'calm' particles. Particles with two up-quarks are called 'happy' particles. Particles with two down-quarks would be called 'sad' particles, but such particles have never been observed. In nature, the ratio of 'calm' particles to 'happy' particles is 2:1.
Only one quark of a particle is directly observable in a given observation and the only observable quarks are up-quarks. An observation can be "confirmed" to determine the state of the unobserved quark. Once this happens the associated particle disappears and it is replaced by a particle with the same quark-state somewhere else close by - the replacement particle has no other discernible relationship to the replaced particle. This behaviour has annoyed physicists for a long time, because they haven't been able to isolate a pool of pure 'happy' particles to understand how they behave in an environment that is unconstrained by neighbouring 'calm' particles.
Particles can be pooled. Pools can be sampled by random sampling processes. Sampling processes choose a particle or quark at random and then emit an observation which encodes details of the particle and one related up-quark (sample-particle) or the quark and its related particle (sample-quark) in an observation.
The observation also records the probability that the observation is of a 'happy' particle. The sample-particle process generates observations that have a 1/3 chance of identifying a 'happy' particle. The sample-quark process generates observations that have a 1/2 chance of identifying a 'happy' particle.
Different observations of the same particle generated by the same or different processes can be matched. Matching can occur in one of two ways - matching by particle or matching by quark.
Matching must be done by sensitive equipment that does not reveal the identity of either the quark or particle being matched but, if matching is successful, does emit a new observation for the matched particle and one of its up-quarks.
Q1. Suppose you match two observations of the same particle, one from the sample-quark process, one from the sample-particle process, each asserting a different probability, 1/2 and 1/3 respectively, that the observed particle is a 'happy' particle.
Given the contradictory assertions made by the matching observations, which observation, if any, do you believe?
Q2. Now you repeat the experiment in Q1 many times with matching observations of many different particles. What is the probability that the observations emitted by the matching equipment are observations of 'happy' particles?
The simulator command (called particles) generates a simulated pool of particles and then observes that pool with two different sampling processes. The pools are comprised of 'calm' and 'happy' particles in the natural occuring ratio of 2:1. The observations generated by these processes are matched with a matching process. The resulting stream of matched observations is confirmed to count the number of particles and the number of 'happy' particles. This number is reported on stderr.
The options that can be passed to the command are:
Usage of particles:
-match-type string
Type of match: particle or quark (default "particle")
-max-matches int
Maximum number of matches (default 1000)
-pool-size int
Size of the particle pool. (default 10000)
-process-A string
Sampling process A: particle or quark (default "quark")
-process-B string
Sampling process B: particle or quark (default "particle")
-verbose
Be verbose about statistics
The expected probabilities and resulting matching process for each combination of parameters are:
process-A process-B match-type probability resulting-matching-process
----------------------------------------------- -----------------------------------------
particle particle quark 1/5 U1u2 U3d dU4 U3d dU4 u1U2 U3d dU4 U3d dU4
particle particle particle 1/3 U1u2 U3d dU4 u1U2 U3d dU4 # also, sample-particle
particle quark quark 1/3 U1u2 U3d dU4 u1U2 U3d dU4
quark particle particle 1/2 U1u2 U3d dU4 u1U2
quark quark quark 1/2 U1u2 U3d dU4 u1U2 # also, sample-quark
quark quark particle 2/3 U1u2 u1U2 U3d U1u2 u1U2 dU4
U - observed up-quark
u - unobserved up-quark
d - unobserved down-quark
u1U2 U1u2 - two different observations of a single happy particle
dU4 U3d - two different observations of two different calm particles
U3d U3d - two different observations the same particle
This simulation was inspired in part by a variant of the Boy-Girl paradox and ultimately by the well-known Boy or Girl paradox. The analogy between those problems and this system is:
- mother/family <=> particle
- girl <=> up-quark
- boy <=> down-quark
- boy-girl family <=> calm particle
- girl-girl family <=> happy particle
The amusing thing about the linked problem and the simulated universe is that you one can have two sampling processes which accurately describe the world as they have sampled it yet when the outputs of two different processes make conflicting probabilistic statements about the state of a given object, it isn't clear which (if either) is to be believed. It turns out that the means by which observations from different processes are matched is extremely relevant to the characteristation of the probability of observations emerging from the matching process - in this example, the probability can range from 20% to 67% depending on what combination of sampling and matching processes are used.