**Quantum World**

Imagine you need to do a massive project for Social Studies and an essay for Language Arts. Being the procrastinator that you are, you waited till the last day. Today is the season finally of your favorite television series; you can't miss it. Don't you just wish you could split into 3 people, get a 100% in your essay and project, and watch the season finally. Sadly, this can't happen in real life, right? Wrong. In quantum mechanics, this is possible. Even though this may seem counter-intuitive, at the subatomic level, this phenomenon does occur.

**Quantum Mechanics**

Quantum mechanics is the theory of the interactions that occur at the subatomic level. It states that a particle is in a superposition of states: the most famous example is Schrodinger's cat. The experiment consists of putting a cat inside a box with a radioactive isotope, such as uranium. If the radioactive isotope decays, a deadly poison will be released, killing the cat. However, it is just as likely that the radioactive isotope will no decay, and the cat will survive. From outside, the cat could be dead or alive, so it is in a superposition of the two states. Opening the box, however, stops the effect (Quantum Mechanics, Gale Encyclopedia of Science).

Quantum chromodynamics, or QCD for short, deals with the interactions of the strong force, which is transmitted by the gluon. In QCD, gluons not only respond to color charge, but also change one color charge to another, so, for example, if a quark absorbs a gluon, which changes its color charge from red to green, the gluon must have carried one unit green charge and minus one unit red charge. The calculations of QCD begin with the QCD Lagrangian, with various methods (Wilczek 1; "Quantum Chromodynamics" World of Scientific Discovery).

Physics 101

The standard model is the best theory mankind has that mathematically describes how the universe works. It describes electromagnetism, the strong force, and the weak force, but does not describe gravity, which has yet to be quantized. The theory predicts the existence of 6 leptons, 6 quarks, and force carriers.

Quantum Chromodynamics

Fermions

Quarks

Leptons

Colors:

Red

,

green

, and

blue

.

Up

Down

Top

Bottom

Charm

Strange

Tau

Tau Neutrino

Muon

Muon Neutrino

Electron

Electron Neutrino

The Four Bosons

The Higgs Boson: The force carrier of gravity. (It was discovered recently in the Large Hadron Collider!!!)

The Photon: The force carrier of the electromagnetic force.

The Gluon: The force carrier of the weak force.

: The force carriers of the weak force.

Switzerland, Geneva, Large Hadron Collider In CERN.

The limit: the basis of calculus. To calculate, plug the value x is going to into the function. If it is undefined, factor, and try to solve again. If this doesn't work, use L'Hopital's rule, or take the derivative until only the constant is left. It is useful to calculate instantaneous rates, and especially to find the y output for functions that have asymptotes. However, limits are rarely used after learning differentiation and integration.

The derivative: Think slope. The derivative of a function is primarily used to calculate the slope of a curved line, even though it can be used on linear functions. It was derived by using limits to calculate the slope of a tangent line touching a curve. To calculate the derivative of a function, multiply the coefficient of the variable's by their exponent, and then subtract one from the exponent. Voila! Done. For example, to calculate the slope of the function y=2x+3, do the following, and you get 2, the slope. For example in the equation y=3x^2+4x+1, do the following steps, and the answer appears quickly and easily: y'=6x+4. To calculate the slope of a line at any point, merely plug in the value of x and solve. The derivative stems from the difference quotient, which is derived from the limit of the slope as the run of x goes to zero for a secant line crossing a function. For example, a function like y=sinx+x^3-3x^2, to find the derivative of sinx you will have to use the difference quotient or know the value, and you get y=cosx+3x^2-6x.

Evidence

The integral: one of the most important parts of calculus. The integral basically calculates the area under a curve, and is sometimes called the anti-derivative because to find one, you do a derivative in reverse. The long "skinny" S is the integral. It looks like this because the integral's definition is calculating the sum of infinitely small rectangles under the curve. First, you place the function in front of the integral. The b and a are two points on the x-axis from which you are calculating the area underneath the function. First find the integral of the function, then plug in b for x and a for x. Find the difference, and this will be the area under the two points.

In science, everything is questioned. That's how science started, and thus, a hypothesis is nothing if it cannot correctly predict something that can be tested. To prove and study quantum chromodynamics, scientists use advanced equations to predict the results of collisions between particles like quarks. Experimental data obtained from the Large Hadron Collider is then compared with the theoretical particles physicist's calculations to see the accuracy with which they predicted the result of the collisions. So far, top scientists work nearly perfectly matches the results of the LHC, which is to be expected since the accuracy of the LHC is imperfect. The accuracy of the physicist's results are limited to the amount of math they do, plus the predictions can never be perfect do to the fact that the world is quantum, so only the probabilities of some result occurring can be produced (Agashe et al. LHC).

Yikes!

**A quick summary of math skills**

learned from middle school to college

to prep you for any physics equations

that might appear.

learned from middle school to college

to prep you for any physics equations

that might appear.

**Rudimentary Math Skills Necessary to Know**

"Blank open book template | PSDGraphics."

Photoshop backgrounds, textures

Ryan, Mark.

Calculus for Dummies

. Hoboken, NJ: Wiley Pub, 2003. Print.

Wiley, the Wiley Publishing logo, For Dummies, the Dummies Man logo, A Reference for the Rest of Us!, The Dummies Way, Dummies Daily, The Fun and Easy Way, Dummies.com, and related trade dress are trademarks or registered trademarks of John Wiley & Sons, Inc. and/or its affiliates in the United States.

Virtual Particles

Virtual particles are a major cornerstone of

QCD. They are particles which briefly pop into and out of existence using borrowed energy. They consist of a particle and its antiparticle, which nearly instantly annihilate, with a total net energy usage of 0. They cannot be detected, and the only reason we know they exist is by the interactions they mediate. Feynman diagrams are used to predict the interactions that they will make, with the simplest requiring relatively simpler math, and with the hardest requiring billions of calculations, nearly impossible to do by hand, requiring cutting edge computers (an advantage of being a physicist) and for methods like the lattice, supercomputers ("Feynman Diagrams", the Gale Encyclopedia of Science).

"Quantum mechanics."

The Gale Encyclopedia of Science

. Ed. K. Lee Lerner and

LHC

In the LHC, the Large Hadron Collider, theoretical particle physicist's calculations are put to the test. Protons and anti-protons are accelerated around the LHC by super powerful magnets in a ring several miles in circumference. In the end of their journey, the protons achieve speeds of 99.99997% of the speed of light, and smash together. Massive detectors then record the events that occur during the collisions of the protons, with four in the LHC to weed out any false results. Computers in the detectors get rid of more than 99% of the data recorded which doesn't match what physicists are looking at, yet the remaining 1% take petabytes of space. This data is then examined, sometimes taking several years to determine certain characteristics (Agashe et al. LHC). Fun fact: Tim Berners-Lee was a theoretical particle physicist that wanted to effectively communicate data collected from the LHC with colleagues that were in other cities, or even over seas. Eventually, to solve the problem, he invented what would come to be called the world wide web (Tim Burners-Lee Internet Hall of Fame).

Perturbative QCD

This method of QCD has been thoroughly tested with spectacular accuracy in colliders. It uses the theory of asymptotic freedom to allow perturbation theory to be used. Asymptotic freedom states that the interactions between quarks diminish at high energies. Therefore, at high energies, gluon emissions can be treated as small perturbations. At next-to-leading order, there is one gluon emission. At next-to-next-to-leading order, there are two gluons emitted. At higher orders, one encounters infinities, and to deal with them, one has to renormalize the theory by including counterterms in the Lagrangian, which renormalize the mass, the charge, and the wave function of the quarks. In this manner, the divergences disappear. A technical method to perform the renormalization is via integrating over the momenta of the virtual particles in n spacetime dimensions, with n=4-(Epsilon), where epsilon eventually is allowed to go to zero (Kidonakis).

Lattice QCD

Unlike perturbative QCD, lattice QCD is a non-pertubative method of solving QCD. In it, spacetime is approximated by a discrete set of lattice points, with finite distance between them, where quark and gluon quantum fields take values. Upon solving QCD equations for these quantum fields, one can determine the values of the hadrons, such as protons and pions. Lattice QCD is an excellent method for solving these equations in low energy environments, which is primarily why lattice QCD and perturbative QCD are complementary branches of QCD (Kidonakis).

In the Lagrangian of QCD theory, F represents the gluon field tensor, A represents the gluon, psi is the quark field with mass m, g denotes the strength of the coupling between quark and gluon, and gamma is the Dirac matrix (Wilczek 3).

Feynman Diagrams

Feynman diagrams provide an intuitive graphical approach that allows one to easily picture the interactions between elementary particles ("Feynman Diagrams", the Gale Encyclopedia of Science).

Key

g is the gluon

t is the top quark

t bar is the anti top quark

Curly lines are the gluons

"Quantum chromodynamics."

World of Scientific Discovery.

Gale, 2007.

Student Resources in Context.

Web.26 Mar. 2014.

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The Gale Encyclopedia of Science.

Ed. K. Lee Lerner

Colored Quarks and QCD”.

Joint Institute for Nuclear Research (JINR). Inru.ru, January 19-20, 2006. April 6, 2014. http://www.inr.troitsk.ru/quantum.html

Matveev, V. A. and Tavkhelidze, A. N.

“The Quantum Number Color,

Pich, A.

"Quantum Chromodynamics."

Inspire Hep (1995): n. pag. Print.

Eidemüller, M., H. G. Dosch, and M. Jamin.

"The field strength

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Lim x^2+2

x

3

f(x+h)-f(x)

h

The Difference Quotient

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