Chapters 1 and 2 What we’ve derived from first principles •
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Galilean transforma:ons Time dila:on Length contrac:on Lorentz transforma:ons Invariant quan:ty, Δs2 –  Δs2 = (cΔt)2 –(Δr)2, where r2 = x2 + y2 + z2 •  How S frame sees S’ on space-­‐:me diagrams •  Velocity transforma:ons between frames •
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Rela:vis:c momentum Rela:vis:c energy Lorentz transforms of p and E Invariant quan:ty, (Δmc2)2 –  (Δmc2)2 = (ΔE)2 –(Δpc)2, where p2 = px2 + py2 + pz2 •  Useful rela:onship: u = (pc / E) * c Chapters 1 and 2 Examples done in class Time contrac:on Par:cle decay using half life Length contrac:on Par:cle decay using mean life:me Space:me diagram Rocket shoo:ng par:cles, how seen by another frame •  Snake chopped up paradox •  Pole-­‐barn paradox •
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Rela:vis:c p Rela:vis:c treatment of elas:c collision Cons of rel E in inelas:c collision CR muons, rela:vis:c E System of par:cles & extra E, invariants Unstable nuclei/par:cle decay e+e-­‐ annihila:on (mass to E conversion) Pair produc:on (E to mass conversion) Par:cle decay at rest/decay in flight, as seen by COM and lab frame •  Threshold energy of protons in beam for par:cle produc:on •
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Chapters 1 and 2 Suggested problems from book that overlap material covered in class •
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Thought experiment for rela:vity & light What is an invariant quan:ty Coordinates of an event in moving frames Speed of moving frames rela:ve to each other/
Earth Rela:ve speed differences for Δt of 1% Speed of objects in frames Lengths :lted wrt moving axis Moving frames and :me differences Simultaneity and moving frames, Δs Paradox of ruler and steel plate with circular hole •  Change in mass of system wrt change in E of system •  Speed, p, E of nuclei in collisions in different frames •  E, KE, p of rela:vis:c par:cle in it’s own frame •  E required to remove n from atom •  Threshold energy of protons in beam for par:cle produc:on •  Invariant mass/rest energy of a system •  Decay of individual par:cles How to solve collision problems •  For problems where two things are colliding and producing more things, there is a common algorithm to sebng up the problem, regardless of what things are involved. –  Write down ini:al and final E and p, in COM and LAB frames (4 sets of equa:ons) –  Goal: to solve for minimum beam energy required or mass of par:cles produced you want to construct invariant masses (mc2)2, and set them equal to each other –  Make sure the invariant masses you form have •  the energy of the incident beam of par:cles in the ini:al state •  the rest masses of the par:cles produced in the final state. –  You MUST have these two terms present to properly solve the problem. This will dictate which invariant mass terms you use and set equal to each other. Chapters 1-­‐2 Possible Theory-­‐esque Ques:ons ** All contained material comes 100% from the lecture notes •
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Difference between conserved and invariant How do you know you’re in an iner:al frame What are the 4 postulates of special rela:vity What is the rela:vity of simultaneity When is non-­‐rela:vis:c good enough –  5 reasons, covered in ch 2 lectures, not the 3 reasons from ch 1 lectures •  What are the 3 rela:vis:c par:cles •  How does PET work? Describe in words and through the calcula:on of the physical process that is involved –  answer: e+e-­‐ annihila:on to 2 photons, the e+ and e-­‐ are at rest. Calculate E of photons produced and the p of the photons. They are produced back to back with the same E, so look for this signature in your detector. –  e-­‐ are naturally present in your body. You get the e+ from injec:on of a radio-­‐isotope that decays via beta+ (ie e+ emission) decay Chapters 1-­‐2 Possible Deriva:ons ** All contained material comes 100% from the lecture notes •  Time and length contrac:ons •  Lorentz transforma:on equa:ons •  Draw a space:me diagram with S and S’ (not an explicit deriva:on but need to know how to find the slopes of ct’ and x’ as seen by S) •  Velocity transforma:ons •  Prove invariant rest E of system ≠ sum of rest energy of par:cles in system if par:cles move rela:ve to each other