Series writers Cheryl Heuton and Nicolas Falacci wanted to explore the emotional effects of the case on Dr. Charlie Eppes (David Krumholtz).
During production, CBS requested that the producers tone down slightly the level of violence in the opening action sequence and that one additional narrative element involving FBI Agent David Sinclair be removed for the sake of clarity.
Following a lead, FBI Special Agents Don Eppes (Rob Morrow), Terry Lake (Sabrina Lloyd), and David Sinclair (Alimi Ballard) stake out two banks which are possibly the Charm School Boys' next target.
The agents' lead comes from their math consultant and Don's younger brother, Dr. Charlie Eppes (David Krumholtz), who used probability theory and statistical analysis to predict the targets.
Charlie arrives at the scene and finds Don being treated for a minor gunshot wound to his arm.
Charlie, horrified by the sight of the crime scene, withdraws himself from the investigation since one of his model's assumptions was that the robbers were nonviolent.
Don returns to the house and learns about Charlie's actions from their father, Alan Eppes (Judd Hirsch).
At the office, the team uncovers evidence which confirms Don's suspicion that one of the bank robbers was military-trained.
This time, the robbers fatally shoot a bank president who attempted to confront them, and video surveillance footage shows that Don's gun is present at the scene.
The team assumes that the bank robbers need the computer programmer's knowledge to access the data.
After being diverted under an expressway, David and Terry are confronted by the bank robbers, one of whom has an RPG aimed at them, allowing the leader to escape.
"Uncertainty Principle" is based on a series of bank robberies, solved with the assistance of an Arkansas mathematician, that occurred in Maryland in 2004.
When writing "Uncertainty Principle", Heuton and Falacci wanted to show Charlie's reaction to the violent nature of Don's work.
Heuton and Falacci decided to incorporate into the episode elements, including an opening shootout, from their earlier feature writing.
While discussing the episode in "Uncertainty Principle"'s commentary, Heuton and Falacci mentioned that Charlie could not tolerate Don being shot shortly after their mother's death.
[4] The cast and crew delayed production of "Uncertainty Principle" until director Davis Guggenheim could film the episode.
[4] David Grynkiewicz, a graduate student of Dr. Rick Wilson's who was working with the series producers,[7] developed the mathematics within one-half hour without any guidance.
Heuton and Falacci insisted on keeping it in the script, and series regular Rob Morrow also liked the idea of Don losing his gun.
In spite of earlier protests during production about the violent nature of the episode, the executives felt that "Uncertainty Principle" was a strong story to follow the "Pilot".
Raazesh Sainudiin, a mathematics professor at the University of Canterbury in New Zealand, disliked the emphasis on Charlie's reaction to the case.
Richard Penny, a statistics professor in New Zealand, believed that Charlie confused the observer effect with the Heisenberg uncertainty principle.
[9] In contrast, Cynthia Boris, a reviewer for DVD Verdict, called "Uncertainty Principle" "likely the best episode ever".
[10] Todd Douglass, Jr., a reviewer for DVD Talk, called the episode "solid...to make the payoff worth it".