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anybody knows about Einstein: E mc2 . This means energy, E, and mass, m,are equivalent up to a factor of the speed of light, c, squared. To study fundamental particles, physicists collide protons or electrons at high enegies, causingthem to produce new particles. In order to produce heavy, exotic particles, oneneeds to collide the protons or electrons at very high energies. Hence the name‘high energy physics.’ In the latter half of the twentieth century, national laboratories such as Fermilab and the Stanford Linear Accelerator Center pioneeredthe search for even more elementary particles. The particles and patterns ofinteractions they discovered have laid the groundwork for what is now calledthe Standard Model of particle physics.Quantum physics, further, has challenged our ideas of what ‘particles’ reallyare. This is something we’ll discuss later on. I will briefly talk about stringtheory and the physics of the twenty-first century towards the end of this document.2.4The Twenty-First CenturyBy the 1980s, particle physicists had developed a theory of elementary particles that was so successful and accurate in its predictions that they called itthe Standard Model of particle physics. The Standard Model accurately described the behavior of the weird quarks that made up protons and neutrons,the elusive neutrinos that pass through your body at a rate of about ten trillionper second, and the exotic composite particles discovered in accelerators. By theend of the century, nearly all of the particles that the theory predicted had beendiscovered exactly as the theory had predicted. The two notable exceptions arethe discovery that neutrinos have mass in the 1990s and the expected discovery of the Higgs boson at the Large Hadron Collider–the largest particlecollider to date (expected to turn on in 2007).2.5Modern Physics and Eastern Philosophy?I should note one more thing. I said above that Western scholars developed theframework for modern science. By and large this is true beginning, perhaps,around the Renaissance. However, this is not to say that Eastern thought hasnot contributed significantly to physics. In fact, many of the foundations ofmathematics were developed in the Middle East. In more recent times, manyhave tried to draw parallels between Eastern mysticism and modern physics.The quintessential book for this is the Tao of Physics [4]. However, books suchas this and more speculative works such as the recent movie What the Bleep DoWe Know tend not to be taken very seriously by most scientists and tend todiscuss qualitative and metaphorical connections rather than scientific fact.6

References[1] “physics, 2” The Oxford English Dictionary. 2nd ed. 1989. OED Online.Oxford University Press. 13 Jan. 2006 http://dictionary.oed.com/.[2] For a fantastic introduction to philosophy, I recommend Jostein Gaarder’sbook Sophie’s World. Democritus is described in the fifth chapter. For moreformal descriptions, I refer you to any beginning philosophy text.[3] And here I’m really skipping over some fascinating science and history thatI encourage you to look into. Your high school physics and chemistry booksmight be a good place to start. Just how did these clever scientists discoverthese things, anyway? In this section I paraphrase the relevant articlesfrom Wikipedia, http://en.wikipedia.org as of January 21, 2006. Pleasenote that this is not a rigorous nor comprehensive source, and I recommendindependent encyclopedic research on your own part if you intend to usethis information in your own scholarly work.[4] Capra, Fritjof. The Tao of Physics. Fritjof Capra also cowrote the screenplay for a film called Mindwalk, which I recommend to any young scholar.3ScaleIn the previous section, we discussed how physicists studying ‘fundamental’physics kept looking for ‘elementary’ particles: the “stuff” that ultimately makesup all other stuff. Implicit in this is the idea that ‘elementary’ particles aresmaller than the non-elementary stuff it makes up. This is just like saying thatindividual Lego blocks are smaller than the model of the Death Star that youmade out of them.3.1The Importance of ScaleScale turns out to be an incredibly important idea in physics for detailed reasonsthat are generally outside the scope of this seminar[1]. The gist of the idea,however, is that physics is different at different scales! That is to say that naturebehaves differently depending on how ‘big’ or how ‘small’ you’re examining it.This is both very surprising and very obvious. This is surprising because many ofus have been trained to read ‘facts’ out of textbooks and accept them as ‘truths’(this is not science, even though one might be learning about science6 ). Whyshould these ‘truths’ be any different depending on whether you’re looking at amicrometer or a kilometer? Who is to say what ‘big’ or ‘small’ is? (Certainlyatoms and galaxies would have different opinions on this, if they have opinionsat all.)6 Thedifference is the scientific method. I point this out only because recent events dealingwith science education have made it clear that a distressingly large number of Americancitizens do not have a clear understanding of what science is and why it is important.7

However, it is actually very obvious that physics should be different at different scales because we deal with situations every day where big things behavedifferently from small things. We know that giant ants from cheesy 1950s horror films cannot exist because their legs wouldn’t be able to support their bodyweight[2]. We know that little water beetles can float on a pond through surfacetension alone, but a battleship floats because of buoyancy (so they both float,but for very different reasons–i.e. because of different physics). More extremely,we know that atoms behave very differently from anything on a human scale(though curiously enough we believed for a long time that atoms looked verymuch like the solar system).The best example, perhaps, is Newton’s theory of gravity. Every high schoolphysics student knows how to calculate the gravitational pull of the moon bythe Earth. But every college physics student knows that Newton’s theory isonly an approximation to a more accurate theory, namely Einstein’s theoryof gravity (general relativity). Why, then, do we ‘waste time’ teaching highschool students theories that are ‘incorrect’ ? Because at the scales that highschool physics cares about (something between the scale of the solar system andsmall ball bearings) the predictions of Newton’s theory is pretty darn close tothose of the ‘correct’ theory. In fact, the difference is imperceptibly small. Fora student, however, the difference is significant: the Newtonian calculation ismuch easier and shorter than that the complicated general relativity calculation.The lesson of this, then, is that at different scales there are different effectivetheories, which we can think of as “really, really good approximations.” Ofcourse, if we were to do a calculation of the gravitational effects of a very massivegalaxy, Einstein’s approach is significantly more accurate than Newton’s–so theNewtonian approximation is not useful outside of its regime of effectiveness.It turns out that there’s a little more to this than just the fact that onetheory is a simpler “approximation” of another, and this leads to the idea ofeffective field theories, which we’ll discuss very briefly in the section on quantummechanics below.3.2Scales and SciencesWith all that in mind, I’d like to get the ball rolling with an overview of scalesand associated sciences to put particle physics in proper perspective. Todaymodern physics deals with nature both at the largest (cosmology) and smallest known scales (particle physics). The classic introduction to scale, which Irecommend highly, is Charles and Ray Eames’ famous short film, The Powersof Ten, where the Eames discuss objects from 1025 to 10 18 meters[3]. Muchof the material here, however, is motivated by lectures by Savas Dimopoulos7 ,who begins many his courses (even graduate courses) with a lecture on scale.In the following, everything is given to the nearest power of ten. When you’recomparing the size of a galaxy and the size of an ant, it’s ok if you’re off by a7 A professor theoretical physics at Stanford and the 2006 recipient of the American PhysicalSociety’s Sakurai Prize for lifelong contributions to theoretical physics.8

factor or two of ten8 .Length10 35 mScienceString Theory (?)10 15 mParticlePhysics,Nuclear Physics10 10 mAtomic and SolidState PhysicsChemistryMicrobiologyBiology10 8,9 m10 5 m1m3.3102,6 mEcology,ogy, etc.107 mEarth Science1012 mAstronomy, Astrophysics1018 m1026 mCosmologyCosmologyPsychol-ExamplesApprox. width of a hypotheticalstring. At distances smaller thanthis, the act of making a measurement might create a little black hole.Approx. scale of subatomic particles such as quarks. However, at thisscale, the ‘width’ of a particle is illdefined due to quantum uncertainty.This is about the width of a hydrogen or helium atom.The width of a molecule, like DNAThe width of a eukaryotic cell.The scale of everyday things, like agolden retriever.We have all sorts of “-ologies” at thisscale because this is the scale relevant to humans and groups of humans on an every day basis.The width of the Earth. (This isprobably a little larger than whatgeologists actually study.)The width of the solar system,though this is somewhat of an illdefined quantity depending on whatyou include in the solar system9 .The width of a globular cluster.The size of the observable universe.We don’t know if the universe is infinite beyond this.Scales and PhysicsMuch of science (and especially particle physics) has been driven by a paradigmof reductionism, the idea that in order to really understand something, one needsto understand its separate parts[5]. Implicit in this is the idea that there is somefundamental part that makes up everything, which is why many physicists aredrawn to the study of elementary particles.The lesson of all of this talk about scales can be summarized in the followingstatement:8 This is related to many jokes about cosmologists, who, if they can predict something towithin a factor of 100, are very excited that they’ve proved something.9

Figure 1: My own sketch of the scales of science.10

Figure 2: An example of insensitivity to different scales: a car driving on a long,straight road feels a smooth ride. The relevant scale is the width of the car’stire; so, for example, when the driver sees a rock that is about half the size ofhis tires on the road, he has to swerve to avoid it. At scales much smaller thanthis, say the scale of a pebble, the road is actually very bumpy (take a closelook at asphalt sometime). At scales much larger, such as the scale of a planet,the Earth itself is just one big bump. Despite these ‘bumps’ at different scales,the driver feels a smooth ride because he’s only sensitive to his own scale.A cook does not need to know string theory10 .This means that for the most part, you only care about what nature is doingat the scale you’re considering. A cook does not need to know how the atomsthat make up the molecules that make up the cells that make up the eggs that(s)he is cooking for breakfast–(s)he already has an understanding and a setof rules for how to make a meal (namely a recipe and whatever you learn atculinary school). The cook effectively has an understanding of what’s going on:when one puts eggs on a hot pan, they eventually coagulate into sunny side upeggs that one can eat. Of course, there’s a lot of good science in understandingwhat is actually going on there[6], but as far as what the cook needs to know,it doesn’t matter what’s going on at an atomic scale (it can be “magic” for allthe cook cares). Another example is seen in figure 2For physicists, this means that the results of particle physics 30, 60, 90 yearsago are (mostly) still valid today–even if we didn’t quite understand them correctly the first time around. In fact, we know that the Standard Model (whichwe’ll get to) is not a complete theory–for one, it does not explain gravity. Gravity, however, is an extremely weak force, which means–for reasons we won’t getinto–it becomes “relevant” (in some sense) at very small scales around 10 30 m.From the argument above, whatever the form of the quantum theory of gravitytakes (perhaps string theory), it won’t make the predictions of the StandardModel irrelevant.10 SavasDimopoulos11

In fancy language, this concept is referred to as an effective theory. Newton’s theory of gravity isn’t wrong just because Einstein’s theory of gravityappears to be correct. It’s just a theory that is effectively correct (very, very,very close to the result of Einstein’s theory) on the scale of everyday things(between about 10 2 m and 1010 m). In fact, we believe that even Einstein’stheory is only an effective theory of a more fundamental theory (perhaps stringtheory) that unifies gravity and the Standard Model.References[1] This is formally an idea called the renormalization group and is best described in the paper The renormalization group and the ² expansion byWilson and Kogut (Phys. Rep, 1974). This is, however, a graduate-leveltopic.[2] I wrote a short “just for fun” essay on this a few years ago, it is currentlyavailable at http://www.stanford.edu/ flipt/files/SoCo/them.pdf[3] The Films of Charles and Ray Eames – The Powers of 10 (Vol. 1), ImageEntertainment (1968). There is also a book by the same name.[4] In particular, this is motivated by his course Physics 351 given Autumn2005. Additional information came from a section from the website of JohnBaez (http://math.ucr.edu/home/baez/distances.html), a mathematical physicist at UC Riverside.[5] There are some eccentrics in physics who are challenging this idea of reductionism, the main stalwart being Nobel Prize winning physicist RobertLaughlin, who proposes a new paradigm in emergence–that many physicalphenomena are only explainable in terms of the joint behavior of a largenumber of parts that would otherwise be unexpected by studying only asingle part. That is, “the sum is greater than its parts.” Many of Laughlin’scomments haven’t been received particularly well by the particle physicscommunity (though is better received in the condensed matter physics community, in which his points of view are just facts of life). He has writtena popular-level book explaining his insights: A Different Universe, BasicBooks (2005). Check out the comments on Amazon.com for a sample of thedebate. Additionally, he prepared a more technical manifesto for the National Academy of Sciences (Proceedings of., 97, 28 (2000)), which is available at: m.[6] See,for ://www.bbc.co.uk/science/hottopics/cooking/, and a bookby Peter Barham, The Science of Cooking (Springer, 2001).12

4Special RelativityThe United Nations designated 2005 as the World Year of Physics in commemoration of Albert Einstein’s “Miraculous Year” in which he published groundbreaking papers on special relativity, Brownian Motion, and the photoelectriceffect. Over the course of his lifetime, he became an international pop iconknown for his famous equation, E mc2 . Here I’ll very briefly discuss the ideasof Special Relativity, but I’ll leave most of the details to your own reading.4.1A Note: Special versus General RelativityFirst a short note on nomenclature. Special relativity refers to Einstein’stheory of light objects that travel at very fast velocities. Special relativity isone of the standard pillars of modern physics that every undergraduate physicsstudent learns in college and, in it’s most minimal form, requires nothing morethan algebra to learn[1]. General relativity refers to Einstein’s theory of veryheavy objects and how they bend “the fabric of spacetime.” This was developedabout ten years after special relativity (and includes special relativity) and ismore mathematically involved[2]. It is usually a graduate-level subject that isclosely linked with a branch of mathematics called differential geometry. Herewe will talk about special relativity. Note that you’ll hear lots of people talkabout ‘grand unified theories’ that unite quantum mechanics and relativity.Statements like these refer to general relativity, as quantum mechanics andspecial relativity have already been successfully unified (this is called quantumfield theory).4.2The Idea of RelativityThere are two major pillars to the theory of special relativity. If you intend tounderstand anything about relativity, you have to understand these first.4.2.1The Principle of RelativityThe Principle of Relativity is, at the end of the day, an unremarkably obviousstatement.The Principle of Relativity. The laws of physics (nature) are thesame in every inertial frame of reference.What is this saying? An inertial frame of reference is one that is atconstant velocity. That is to say, you are in an inertial frame of reference (or“inertial frame” for short) if you can close your eyes and you can’t tell whetheror not you’re moving. In fact, this is exactly the statement of the Principle ofRelativity. Imagine you were in a closed box floating in space. In your inertialframe, you think that you and your box is stationary. However, suppose yourbest friend is also in a box floating in space, say at some fixed velocity. As hefloats by you, you think, “oh, poor bloke. he’s drifting away while I’m sitting13

here not moving.” Your friend, however, sees things slightly differently. Tohim/her, it is you that are drifting away while he/she is stationary.Who is ‘right?’ Both of course. This is because the laws of nature are thesame for each of you. Each of you can run little physics experiments in yourboxes and determine that the laws of physics are exactly the same as those inyour physics textbooks, so long as you remain in the inertial frame.What is not an inertial frame? One where the reference point is acceleratingrelative to another inertial frame. So a car that is speeding up is not an inertialframe. This is obvious–when we’re sitting in the car with our eyes closed, we feela backwards force when the car accelerates. The laws of physics are differentfrom when you’re just sitting in your living room.4.2.2The Speed of Light is ConstantThe second pillar of special relativity is the observation that the speed of lightis constant. This is something that has been confirmed experimentally, to

The Allure of Particle Physics: Neutrinos, Quarks, and the Higgs Boson Philip Tanedo V.2: January 21, 2006 Contents . 4For you SAT junkies, the roots of this word are a-, meaning not, and tomos, meaning cut. For example, PET (a way doctors image the brain) stands for Positron Emission Tomography