5/21/06 1Physics 801: Instrumentations and Methods inAstroparticle PhysicsProf. Teresa MontaruliChamberlin Hall, Room [email protected]://www.icecube.wisc.edu/~tmontaruliLectures: Tue-Thu 11:00-12:15Office Hours: send me an email to fix a time or after lectures5/21/06 2Course ContentsIntroduction to Special Relativity and Particle PhysicsInteraction of radiation with MatterParticle DetectorsCosmic Rays (examples of detectors)Gamma Astronomy (example of detectors)Neutrino Astronomy and Neutrino TelescopesCosmology: Dark Matter and Gravitational Waves5/21/06 3Why Astroparticle?Astroparticle: cross-disciplinary area (astrophysics, high energy particlephysics, plasma physics) . Meeting point betweenPhysicists: extended understanding of matter down to quark level thatcompose neutrons and protons and leptons (electrons, muons, taus andtheir neutrinos partners) and described how forces shape matterAstronomers: observed Expansion of the Universe Cosmic Microwave Background Radiation: the echo of the big bang thatprovides a snapshot of the universe when it was 1/2 million yrs old measured the relative abundance of light elements in the Universe (H, Li, 2H,He) produced in nuclear reactions in the first seconds of the universe life in the quantity predicted by the Big Bang globular clusters and some radioactive isotopes do not seem to exceed anage 13-14 billion of yrs from now5/21/06 4Open questionsAll questions address to the understanding of the Universe.Existing models describe its evolution down to 10-43 secondsPhysicists are building the largest collider LHC at CERN (1011 particles/bunch,600 million collisions/s at 7 TeV in CM, 10 times more powerful thanTevatron and LEP) which will bring protons/ions in head on collisionsreproducing the conditions of the early universe 10-11 s after the Big Bang.They will discover new particles, possibly composing the dark matter andcomplete the understanding of building blocks of matter. Otherfundamental questions: neutrino mass and Majorana/Dirac. Still onefamiliar interaction, gravitation, that is not formulated as a relativisticquantum field theoryAstronomers have found that the Universe is speeding up in its expansion afterthe Big Bang due to the mysterious Dark Energy. What is it? Why there ismuch less antimatter than matter? What is the Dark matter?You are lucky! Will see the re-birth of Physics5/21/06 5The building blocks of Matter andinteracting Forces5/21/06 6Notions of Special RelativityInertial frames: a body not subject to any force remains at rest or in steadyrectilinear motionTwo postulates:1) The laws of physics have the same form in any inertial frame2) The velocity of light in vacuum c = 2.99793 × 108 m/s has the samevalue in all inertial framesSpace-time coordinates: xµ = (ct,x,y,z) = (ct,r) (4-vectors)From 2) if we consider the same light ray in the 2 ref systems K and K’ and look at the time difference Δt, Δt’ of its passage through the distance |Δr|, |Δr’|, thevelocity of light must be the sameHence the combination (the line element)is invariant in 2 different reference framesIn analogy to rotations that leave invariant the length of a vector x, namely alsoits square x2+y2+z2, the quantity s2 = c2t2 - x2 - y2 - z2 is an invariant.This suggests that x,y,z,t can form a 4 vector in this 4-dimensional space thattransforms according to Lorentz transformations withx0 = ct, x1 = x, x2 = y, x3 = z'ttcΔΔ=ΔΔ=r'r€ Δs2= c2Δt2− Δr2= c2Δt2− Δx2− Δy2− Δz25/21/06 7Casual structure of space-timeFor a light ray: Δs2 = 0 light-like separationA system in which 2 events happen at the same time (Δt=0) can be found only ifΔs2<0 space-like separationA system in which 2 events happen at the same place can be found only ifΔs2>0 time-like separationThe light cone respect to an event A in theorigin of an inertial ref frame at time t=0is defined by Δs2 = 0 (Δs is thedistance respect to another event)Points in the light cone (B) haveΔs2 > 0 and are casually connectedto the observer since cΔt>|Δr|so that they can be connectedby signals traveling at speed <cEvents outside (C ) the light coneΔs2<0 are casually disconnectedand cΔt<|Δr|€ Δs2= c2Δt2− Δr2= c2Δt2− Δx2− Δy2− Δz25/21/06 8Galilean transformations5/21/06 9Lorentz transformations)''''()(222222222ττΔ+Δ+Δ+Δ−=Δ+Δ+Δ+Δ−=Δ zyxzyxsTransformations leaving Δs2 invariant are rotations (let’s consider the rotation inxτ plane – y,z stay constant). The transformation must be of the form+=−=αταταταcos'sin'sin'cos'xxxTo determine α: we are in K and observe the origin of K’ (x’=0) moving atvelocity v along x (x = vt)βγββαααγβααββαταττατiiciicxx≡−=+=≡−=+==⇒−≡−==⇒=−=22221tan1tansin11tan11cosvtanvcos'sin'+=⇒+=+=−=)''('')''()'('βγγβγβγβγγxctctictixictctxictixxLorentz transformations=''''100001000000zyxctzyxctγβγβγγwith τ = ict with i2 = -1Transformations between reference systems: K’ moves at velocity v = constrespect to K. Due to its invariance:)''''()(22222222222tczyxtczyxs Δ−Δ+Δ+Δ−=Δ−Δ+Δ+Δ−=Δ5/21/06 10Lorentz transformations=''''100001000000zyxctzyxctγβγβγγThe primed frame moves withvelocity v in the x direction withrespect to the fixed referenceframe. The reference framescoincide at t=t'=0. The point x' ismoving with the primed frame.Lorentz contraction: given a rod of a length Δx in the frame at rest its length in themoving frame Δx’ looks contractedSimilarly, time dilation: in the equation for t’, t is multiplied by γ in the comoving frame:this is interpreted as time proceeding slower when an object is moving relative toanother frame of reference (the twin paradox: 1 of 2 twin brothers undertakes a longspace journey with a high speed rocket at almost the spped of light while the other stayson Earth. When the traveler returns to hearth he is younger than the twin who stayed. AEinstein 1911)5/21/06 11Length ContractionLet us measure the length of the rod Δx’ in the moving frame K’:The simultaneous observation takes place in S’ where Δt’ = 0. We caneliminate Δt from€ tanθ =sinθ'γ(cosθ'+v / c)=cγvΔt'= 0
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