# Double-slit logic experiment

A double-slit logic experiment is the use of probability to determine of there is an underlying logical basis for the surprising effect observed in the double-slit experiment in physics.

The logical essence of the double-slit experiment is to have two levels of uncertainty in sequence. First, there is uncertainty about which of the two slits a "particle" passes through, and then there is uncertainty about where it lands on the distant screen. Resolving the uncertainty at the first level through observation then affects the outcome at the second level.

A logic or thought experiment could model this phenomenon by setting up a random variable at the first level, and then another random variable at the second level that is a function of the first random variable.

## Simple case

Consider a double-slit experiment where a particle has a 50% chance of being found, if observed, to be passing through one of the slits. When it ends up on a distant background screen could then be one of three places for each slit: further left, straight ahead, or further right, each with a probability of one third. Assume that the placement on the distant screen of "further right" for the left slit is the same as "further left" for the right slit. 'What is the pattern observed on the distant screen when the double slits remain unobserved?

Answer: The five locations on the distant screen have these probabilities:

position probability
far left $\frac{1}{2} \cdot \frac{1}{3} = \frac{1}{6}$
center left $\frac{1}{2} \cdot \frac{1}{3} = \frac{1}{6}$
center $\frac{1}{2} \cdot \frac{1}{3} \cdot 2= \frac{1}{3}$
center right $\frac{1}{2} \cdot \frac{1}{3} = \frac{1}{6}$
far right $\frac{1}{2} \cdot \frac{1}{3} = \frac{1}{6}$
total 1