The Bat Jar Conjecture

The Bat Jar Conjecture is the thirteenth episode of the first season of the CBS sitcom The Big Bang Theory. It aired on April 21st, 2008.

Plot Summary
It’s the annual Physics Bowl and the the usual competition isn't going to be competing (they got a gig as a barbershop quartet playing Knotts Berry Farm), so the four guys form a team, but end up booting Sheldon off their team because he is being a pain. They recruit Leslie Winkle and Sheldon takes them all on alone.



Expanded Plot
Howard is checking up on all the geeky news, when he stumbles upon information that the almighty team which always won the Physics Bowl will not compete this year. Leonard, Howard and Raj are eager to compete, but Sheldon isn't and offers the explanation that his talents are too good for the Physics Bowl. But after they quote Spock's dying words, Sheldon agrees to join their team.

Howard suggests they should name their team the Perpetual Motion Squad (PMS), although Sheldon suggests the Army Ants, as it is the most powerful animal gram for gram. Because Sheldon threatens to quit if he doesn't get his way, the team is named Army Ants (AA). Later, during team practice, Sheldon takes it upon himself to answer every question. Eventually, he even promotes himself to team captain. Sheldon's insufferable attitude is becoming too much for the team to handle, and as a result, they kick Sheldon off the team with a consolation Batman cookie jar. Devastated, Sheldon decides to form his own team. Meanwhile, Leonard, Howard and Raj now need a fourth member for their team and decide to recruit Leslie, who initially refuses. Upon hearing they will be fighting Sheldon, she agrees, as she bears a grudge against him.

On the day of the Physics Bowl, Sheldon arrives with his team, which is comprised of poorly educated people (presumably) who only serve to qualify him, as the rules state that each team must consist of four people. Both teams rapidly increase their points and, when the final question arrives, the score stands at 1150 for AA (Sheldon's Group) and 1175 for PMS (Leonard, Howard, Raj and Leslie). The last question proves too difficult for PMS, and, in the end, Leonard guesses 8.4, which is incorrect. However, they soon notice that Sheldon also does not have an answer, when suddenly the third floor janitor (one of his teammates) turns out to be a former Soviet physicist (credited as Dmitri and portrayed by Adam Gregor) from Leningrad Polytechnika and states the correct answer. In disbelief, Sheldon denies that answer to be AA's official answer and declines to provide one. Before the winner is announced, Leonard offers Sheldon a chance at redemption, asking if he'd rather lose by himself or win as part of a team. Sheldon simply replies that he doesn't understand the question. PMS is declared the winners.

In the final scene, Penny quizzes both Leonard and Sheldon about Pop Culture, in which neither of them can answer a single question.

Trivia

 * Raj speaks to Penny, though inadvertently, by agreeing with Howard that the the story of Zod is a good one.
 * Although he does not speak to (or in front of) Penny, he laughs his "Cruella de Ville" laugh at Sheldon when he, Leonard and Howard confront Sheldon just before the start of the Physics Bowl.
 * Sheldon at first doesn't agree to join the team, citing "Would you ask Picasso (a famous artist) to play Pictionary? Would you ask Noah Webster (a famous linguist) to play Boggle? Would you ask Jacques Cousteau (a famous naval explorer) to play 'Go Fish'?". While the last is a stretch to imply that the card game 'Go Fish' requires actual skill at sailing, all three imply that those famous men would have no difficulty winning at those games.
 * Spock's dying words ("The needs of the many outweigh the needs of the few, or the one."), which inspires Sheldon to join the team are from the movie Star Trek II: The Wrath of Khan.
 * Sheldon designs uniforms that are emblazoned with the initials "AA", which he designed to mean "Army Ants", though Leonard points out it could imply something else (likely implying "Alcoholics Anonymous"), though Sheldon misses the point and guesses "Anodized Aluminum" as the next most likely acronym expansion. Though the other team's name is no better; 'Perpetual Motion Squad' abbreviates to PMS, more commonly associated with "Premenstrual syndrome".
 * Raj suggests "the actress who played TV's Blossom" for their physics bowl team to replace Sheldon. That actress would be Mayim Bialik, and she does have a Ph.D in neuroscience. Coinicidentally, Bialik joins the show in the Season 3 finale and becomes a regular cast member in Season 4 as Amy Farrah Fowler. Raj also says, "How about the girl from the Wonder Years?" He is referring to Danica McKellar, who has a degree in mathematics, and appears in the Season 3 episode "The Psychic Vortex" as Abby.
 * Sheldon's spanish is really bad. Apparently, he could not differentiate the spanish words hijo and carnicero to ascertain if his third teammate was the son or butcher of his second.
 * Sheldon's long-winded insult of "I'm polymerized tree sap and you're an inorganic adhesive so whatever verbal projectile you launch in my direction is reflected off of me, returns on it's original trajectory and adheres to you." is a much longer (and detailed) version of "I'm rubber and you're glue; whatever you say bounces off me and sticks onto you."
 * Howard's checkerboard belt buckle is the same design as the 'Jaunting belt' used in Series 3 and 4 of the 1970's UK TV series The Tomorrow People.
 * "Leningrad Polytechnika" most likely refers to the Saint Petersburg Polytechnical University in St. Petersburg, Russia (formerly, Leningrad, U.S.S.R.).

Physics questions
Here's more information about the questions asked during the Physics Bowl and during the practice round with Penny:

Penny's

 * What is the shortest light pulse ever produced? 130 attoseconds (billionths of a billionth of a second)
 * What is the quantum mechanical effect used to encode data on hard disk drives? Giant magnetoresistance
 * What artificial satellite has seen Einstein's predicted frame-dragging? Gravity Probe B

Physics Bowl

 * What is the isospin singlet partner of the pi-zero meson? Eta meson
 * What is the lightest element on earth, with no stable isotopes? Technetium
 * What is the force between two uncharged plates due to quantum vacuum fluctuation? The Casimir Effect
 * How does a quantum computer factor large numbers? Shor's Algorithm
 * (What is the mechanical work necessary to produce 1 cal of heat?) 4.1855&times;107 ergs/cal
 * (What theory proposed that the temperatures of two adjacent bodies will equalize due to the transfer of heat energy by radiation and absorption?) Pr&egrave;vost's theory of exchanges
 * (?) $$\lambda=\frac{1}{\pi r^2 N}$$
 * (What is the Curie temperature of iron?) 760&deg; Celsius

The final question asks to solve what looks to be the following equation: $$\left ( 2 \pi \right )^4 \int \left [ \bar{v}^{(s_2)} \left ( p _3 \right ) \left (i \sqrt{4 \pi \alpha}\gamma^\mu \right ) v^{(s_1)} \left ( p _1 \right ) \right ] \frac{i g_{\mu\nu}}{q^2} \left [ \bar{v}^{(s_4)} \left ( p _4 \right ) \left ( i \sqrt{4 \pi \alpha}\gamma^\mu \right ) v^{(s_2)} \left ( p _2 \right ) \right ] \times \delta ^{(4)} \left (p _1 - p _3 - q \right ) \delta ^{(4)} \left ( p _2 + q - p _4 \right ) d^4 q$$



PMS guesses 8.4, which is incorrect, while AA has no official answer, one of Sheldon's teammates suggests $$-8\pi\alpha$$, which turns out to be the correct answer.

Actually $$-8\pi\alpha$$ is not really the correct solution of the equation shown above, but it would take some effort to get the right answer, which surely won't be as simple as given in the show. Additionaly, there's an error in this equation; if it should correspond to the Feynman-Diagram standing above it and if the answers should not have an open index $$\nu$$, because $$\nu$$ isn't contracted, then the second gammamatrix needs to have the index $$\nu$$. Even if one corrects that, one has to square this Matrixelement (expression) and sum over the Spins $$s_1,s_2,s_3,s_4$$ to get a better result than just the whole expression, or something. And even then the answer depends on some kinematic variables. If someone is really interested in calculating that, look in Peskin Schröder "An Introduction to Quantum Field Theory" pages 131ff, if you're into that sort of thing.

Penny's quiz
Penny brings in what looks to be cards from a Trivial Pursuit game, to settle once and for all, who's smarter between Sheldon and Leonard. She asks them:

After her questions, it turns out that Leonard and Sheldon have trouble understanding pop culture and seem to be mainly smart in their comfort zone of Science and other general knowledge. Like, when Penny asks the Tweety Bird question, Sheldon struggles to know the answer and comes up with Romulan, which Penny with her attitude of sarcasm sarcastically says yes. When Leonard hooks up with Penny in season 3, however, he has a much better understanding of it.
 * Marsha, Jan, and Cindy were the three daughters in what TV family? The Brady Bunch
 * Sammy Hagar replaced David Lee Roth as the lead singer in what group? Van Halen
 * Madonna was married to this Ridgemont High alum? Sean Penn
 * What actor holds the record for being named People magazine's Sexiest Man Alive? (Penny doesn't give the answer, but the answer would be between either Brad Pitt, George Clooney, Johnny Depp or Richard Gere; Brad Pitt was given the award in 1995 and 2000, while George Clooney was given the award in 1997 and 2006. They have all been named sexiest man alive at least twice)
 * Singer who sang "Oops!... I Did It Again"? (Britney Spears)
 * Tweety Bird t'awt he t'aw a what? ('Puddy tat')

Critics
"A straightforward sit com plot without the straightforward sitcom jokes. The show is losing its way but hopefully it is not terminal." - The TV Critic's Review