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 an all the geeky news when he stumbles upon one which states that an 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 he gave the excuse 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 was 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 Bat Man Cookie Jar. Devastated, Sheldon decides to form his own team. Meanwhile Leonard, Howard and Raj now need a forth for their team so they decided to recruit Leslie, she initially refuses but upon hearing they will be fighting Sheldon, she agrees as she bears a grudge for him.

On the day of the Physics Bowl, Sheldon arrives with his team which comprises of less than educated people who only serves to qualify him as the rules state each team must comprise of four people. Both teams rapidly increase their points and when the final question arrived the score stands at 1150 for AA (Sheldon's Group) and 1175 for PMS (Leonard, Howard, Raj and Leslie). The last question proved too difficult for PMS and in the end Leonard guessed 8.4 which was incorrect. But they soon notice that Sheldon also does not have an answer, suddenly one of his teammates who turned out to be a former Russian Physicist (credited as Dmitri and portrayed by Adam Gregor) provided an answer which was correct, but Sheldon denies that answer to be AA's official answer. 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 quizzed both Leonard and Sheldon about Pop Culture in which neither of them could 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 Season 4 as Amy Farrah Fowler.
 * 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."

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
 * (?) Pr&egrave;vost's theory of exchanges
 * (?) $$\lambda=\frac{1}{\pi r^2 N}$$
 * (What is the boiling point of potassium?) 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 since People awards a different man this award each year, it would date the show to have given the correct answer for that particular year)
 * 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

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