Physics 2130 Foundations of Modern Physics Special Relativity

Physics 2130 Foundations of Modern Physics Special Relativity Clicker Questions Lecture Slides Professor John Price, Spring 2019

Clickers • You MUST register your clicker. • Every day: set your clicker code to AB • Hold down On/Off Switch 4 seconds • Flashing blue light: hit AB • Do not turn off your clicker during class (otherwise, repeat) 2

Do you have your clicker here today? a) yes b) no c) 1492 d) The Gettysburg Address e) I think so, but where are we going to get an octopus this time of night? Clicker Slide 1 Physics 2130, Spring 2019 3

My major is (or is most likely) a) Astronomy/Astrophysics b) Mechanical Engineering c) Electrical Engineering d) Other Engineering e) Other A&S Clicker Slide 2 Physics 2130, Spring 2019 4

Special Relativity is important for understanding… a) b) c) d) e) The color of metals Gravity waves emitted by collisions of black holes The global positioning system The lifetime of muons All of the above Clicker Slide 3 Physics 2130, Spring 2019 5

Quantum mechanics is needed to understand…. a) b) c) d) e) Medical imaging Lasers Combustion Thermal conductivity of metals All of the above Clicker Slide 4 Physics 2130, Spring 2019 6

Galilean Relativity x t=0. . . -3 -2 -1 0 1 2 3. . . x’ v=2 m/s What is the coordinate of the green ball in each frame at time t = 2? a) 1 m in S and 2 m in S’ b) 3 m in S and -1 m in S’ c) 3 m in S and 1 m in S’ d) 4 m in S and 4 m in S’ Clicker Slide 5 Physics 2130, Spring 2019

Galilean Relativity x t=0. . . -3 -2 -1 0 1 2 3. . . x’ v=2 m/s What is the coordinate of the black ball in each frame at time t = 2? a) -2 m in S and -4 m in S’ b) -4 m in S and -1 m in S’ c) -2 m in S and -6 m in S’ d) 4 m in S and 4 m in S’ Clicker Slide 6 Physics 2130, Spring 2019

The Ether c v Suppose the earth moves through the fixed ether with speed v. A light wave traveling at speed c with respect to the ether is heading in the opposite direction. According to Galilean relativity, what is the speed of the light wave as viewed from the earth? a) c Clicker Slide 7 b) c+v c) c-v Physics 2130, Spring 2019

M&M 1887 results with theory (sine functions) shown 1/8 predicted amplitude

The speed of light in vacuum is 3. 0 108 m/s. About how long does it take light to move the length of your arm? a) 2 ms b) 2 ms c) 2 ns d) 2 ps Clicker Slide 8 Physics 2130, Spring 2019

The Ether c v Suppose the earth moves through space with speed v. A light wave traveling at speed c with respect to faraway stars is heading in the opposite direction. According to Einstein’s relativity, what is the speed of the light wave as viewed from the earth? a) c Clicker Slide 9 b) c+v c) c-v Physics 2130, Spring 2019

Events and Time Measurement in Special Relativity Bang! That’s an “event” with a location and a time measured locally Reference Frame with Synchronized Clocks

Time Measurements In a given reference frame, the time of an event is given by a) The time the observer at the origin sees it. b) The time that any observer anywhere in the frame sees it. c) The time according to the clock nearest the event when it happens. d) The time according to a properly synchronized clock nearest the event when it happens. Clicker Slide 10 Physics 2130, Spring 2019

Light Clock v S’ S • Clicker Slide 11 Physics 2130, Spring 2019

Light Clock v S’ S • Clicker Slide 12 Physics 2130, Spring 2019

Balance wheel clock Robert Downey Jr. is wearing a $600, 000 Greubel Forsey balance wheel watch. When he is at rest, the second hand moves forward once every 1. 000000 s. When he flies by at v = (3/5) c, it moves every how many seconds? a) 0. 750000 s b) 1. 000000 s c) 1. 250000 s d) 2. 000000 s Clicker Slide 13 Physics 2130, Spring 2019

Another Light Clock v S’ Clicker Slide 14 S Physics 2130, Spring 2019

Simultaneity S S’ event 1 v S’ L S’ event 2 light ray event 3

How does this appear in the S frame? S’ v S event 1 S L/ Are events 2 & 3 simultaneous? A) yes B) no, 2 happens first C) no, 3 happens first Clicker Slide 15 Physics 2130, Spring 2019 v

How does this appear in the S frame? S’ v S S event 1 L/ v event 2 v

How does this appear in the S frame? S’ v S S event 1 L/ v S event 3 v events 2 & 3 are simultaneous in S’ but not in S

Lorentz Transformations S S’ v

Lorentz Transformations S S’ v These terms are needed to get time dilation correct

A clock in the S’ frame S’ S’ tick How does this appear in the S frame? S S tick Clicker Slide 16 Physics 2130, Spring 2019 A) B)

A clock in the S’ frame S’ S’ tick How does this appear in the S frame? S S tick Clicker Slide 16 Physics 2130, Spring 2019 tick time dilation

Lorentz Transformations v S S’ These terms are needed to get length contraction correct

Length contraction from Lorentz transformation S’ event 2 event 1 S S event 2 event 1 v v

Length contraction from Lorentz transformation S’ event 2 event 1 S S event 2 event 1 v v What is the x coord. of this point? A) Clicker Slide 17 Physics 2130, Spring 2019 B) C)

Length contraction from Lorentz transformation S’ event 2 event 1 S S event 2 event 1 v Contracted length = v