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PHYSICS 2170: FOUNDATIONS OF MODERN PHYSICS

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  1. lecture 1 PHYSICS 2170: FOUNDATIONS OF MODERN PHYSICS • Instructor: Professor Leo Radzihovsky • Office: Duane Physics F623 (Gamow Tower) • Phone: 303-492-5436 • Email: radzihov@colorado.edu (best way to reach me) • Office Hours: Monday, Friday 2 - 3 pm (or by appointment) http://www.colorado.edu/physics/phys2170/

  2. “Last Time” recall “Lecture 0”: • Phys 1110 (Newton’s mechanics) and Phys 1120 (E&M) • do you have your Taylor Zafiratos Dubson (TZD) • text? …also “It’s About Time” • do you have the right clicker and know how to use it? • must be registered on CUconnect (once) • must be set to frequency CB (once)

  3. Today • course logistics • pedagogical comments • course overview • introduction to relativity

  4. Announcements • homework 1 is posted on the class website • due Wed, Jan 19 in class • solutions will be posted on the website or CULearn • reading for this week is: • Ch 1 in TZD • course syllabus details • remember to bring your clicker to every class • register it (once) • set it to frequency CB (once)

  5. Administrative details All course information can be found on the class website, that must be checked regularly (daily) http://www.colorado.edu/physics/phys2170

  6. Class rules • no use of laptops, cell phones, no texting, • no newspapers • you are responsible for all the material • assigned in the book even if it is not • covered in class • Lots of physics discussion (with nearby • “study group” of students) during clicker • questions is required before voting • it facilitates your learning and gives me valuable • feedback on your understanding

  7. Collective work vs. independent work • What is authorized: • working with others to make sense of questions • collectively sorting out the answer (explaining reasoning) • writing up your own solution in your own words • What is NOT authorized: • telling students answers • representing someone else’s work as your own The CU Honor Code

  8. Pedagogical comments Physics is difficult, but succeeding in this class is not; follow these suggestion and you willdo well: • Learning only comes as a result of your effort • Stay on top of it; that’s easier than playing catch-up • Attend class regularly, participate, ask questions • Read text and review notes before class; it will save you time • Do homework early (not last minute) • Working in study groups is OK, but be “careful” • (make sure you can do it on your own) • Think hard about concepts and solve many problems • …no pain, no gain • Come see me right away if you are having difficulties

  9. More on clickers • To set frequency, hold down on/off button until power • light starts flashing. Then enter CB and vote; light • should flash green and power light should be solid blue • Can only set frequency after the first question on the • class has started • If you turn off your clicker, repeat above procedure • You can vote as often as you like during the allowed • time, with only last vote counted • Only use your own clicker • Answering for someone else using their clicker is a • violation of the CU honor

  10. Top 5 reasons to take this course clicker question set frequency to CB • a. It is required for Physics majors • b. Much of the modern technology depends on covered material • c. To impress your friends with a casual “You mean you don’t know • how time dilation and energy quantization is important for • the Global Positioning Satelite (GPS) system?” • d. To better appreciation nerdy comments in the Big Bang • Theory and Star Trek TV series • e. This is just really cool stuff! What’s your reason for taking this course?

  11. Course overview • Modern Physics: (relativistic quantum field theory) • established during 1900-1920 • exotic and counter-intuitive • now common place in all modern technology, e.g., • GPS, electronics (cell phones, iPods, laptops…), and • throughout science, e.g., physics, chemistry, astronomy,… • (special) theory of relativity (mostly Einstein, 1905) • how does the world look when you are moving…fast? • quantum mechanics (Bohr, Heiseberg, Einstein, Schrodinger, …) • what are the laws of nature for very small things, • like electron, proton, photon,…a tiny electrical • circuits in you i-Pod?

  12. Big picture Basic properties of space-time Basic properties of light Basic properties of matter: atoms to solids How light and matter interact

  13. (Special) Theory of Relativity (mostly Einstein, 1905) How does the world look when you are moving…fast, …real fast ?

  14. Outline of Relativity part of the course • Relativity before Einstein (Galileo, Newton,…) • Simultaneity • Time slowing and length contraction • Lorentz transformation • Momentum, energy, and relativistic mechanics • We will not have time to cover: • effects on electricity and magnetism (light) • gravity (General Relativity)

  15. lecture 2 Relativity in nature Announcements: • lecture 1 is posted on the class website • homework 1 is posted on CULearn • due Wed, Jan 19 in class • solutions will be posted on CULearn • reading for this week is: • Ch 1 in TZD • course syllabus details • remember to bring your clicker to every class • register it (once) • set it to frequency CB (once)

  16. clicker question Recognize non-inertial reference frame • Q: Which of the following is not an inertial reference frame? • A car traveling at 100mph down a straight road • A car traveling at 10mph around a corner • Earth • A car in a process of crashing into a concrete barrier • More than one of the above • None of the above A: In b),c) and d) there is centripetal and linear accelerations, velocity not constant -> if released objects will accelerate even without a force acting on them; remember Earth is revolving around the Sun, etc.; we will ignore latter effect.

  17. Last Time recall lecture 1: • course logistics: http://www.colorado.edu/physics/phys2170 • modern physics overview: • Einstein’s theory of relativity: • description of fast (and slow) moving phenomena

  18. Today • relativity in nature • inertial reference frame • Galilean relativity • space-time event

  19. Looking at nature from different points of view y’ y R • changing coordinate systems: • rotate around origin • translate the origin • moving reference frames: x x’ x’= x-x0 R y y y' y' x’= x-vt R x x x’ x’

  20. Inertial reference frame v • inertial reference frame -> frame: • reference frame moving with constant velocity (not accelerating) • cannot tell there is motion without looking out the window • scope of Einstein’s special (as opposed general) theory of relativity • constant with respect to what? • philosophy: very subtle…with respect to distance stars (?) • pragmatic: frames in which juggling, playing pool, etc…requires • no adjustments, Newton’s laws satisfied,… y y' R x x’

  21. Intuition for inertial reference frame You are playing pool on a train moving with velocity v V • balls roll in straight lines on the table • (assuming you put no English on them) • usual Newtonian law of inertia still holds • The frame as a whole is not accelerating

  22. ... -3 -2 -1 0 1 2 3 ... ... -3 -2 -1 0 1 2 3 ... ... -3 -2 -1 0 1 2 3 ... ... -3 -2 -1 0 1 2 3 ... Comparing inertial frames • Two inertial reference frames, moving with • respect to one another: S S’ v • According to S, S′ is moving to the right, with v = 1 m/s S v • According to S′, S is moving to the right, with v = -1 m/s • (i.e., S is moving to the left, with v = 1 m/s) S’ Both S′ and S are correct: it’s a matter of reference frames

  23. Principle of relativity … even though description from different observers may be different Laws of nature are the same in all reference frames • special relativity: only inertial frames • general relativity: any (e.g., accelerating)frames • Galilean relativity: • satisfiedby Newton’s lawsof mechanics F = ma • violated by Maxwell’s laws description of light (E&M) • Choices: • change laws of light (Maxwell’s equations) • change transformation rules between frames  Lorentz transformations…later…

  24. clicker question Key ideas Q: Which of the following is a key idea from last lecture? • a) Relativity in nature: • physical phenomena are coordinate- and frame-invariant • b) Inertial reference frames: • non-accelerating … constant velocity (including zero) • c) Galilean relativity: • Newton’s laws (mechanics, Phys 1110) are invariant • Maxwell’s laws (E&M, light, Phys 1120) are not invariant • d) All of the above A: (d) all of the above.

  25. …before Einstein Galilean (“old”) relativity y y' v Galileo Galilei (1564—1642) If an object has velocity u in frame S, and its position, x(t), changes with time, t. And if frame S′ is moving with velocity v relative to frame S, then: x x’ positions and time: velocity (add): x’= x-vt y’= y z’ = z t’ = t r’= r-vt t’ = t eg: think about a car with velocity u relative to the ground and velocity u’= u - v relative to another car moving with v

  26. Newton’s law dynamics Galileo Galilei (1564—1642) y y' If an object has velocity u in frame S, and its position, x(t), changes with time, t. And if frame S′ is moving with velocity v relative to frame S, then: v positions: velocity add: x x’ acceleration unchanged: Newton’s law (F=ma) is therefore unchanged, i.e., Galilean invariant (all that you learned in Physics 1110 holds in S and S’)

  27. clicker question ... -3 -2 -1 0 1 2 3 ... ... -3 -2 -1 0 1 2 3 ... Galilean transformation coordinates t=0 x v=2m/s x’ • What is the coordinate of the green ball in two frames • after one second, i.e., at time t = 1? • 2 m in S and 2 m in S’ • 2 m in S and -1 m in S’ • 2 m in S and -3 m in S’ • 4 m in S and 4 m in S’ Two different observers measure two different coordinates for the same location of the ball And they are both correct!

  28. clicker question ... -3 -2 -1 0 1 2 3 ... ... -3 -2 -1 0 1 2 3 ... Galilean transformation t=0 x v=2m/s x’ • What is the distance between the green and black balls • in two frames at time t = 1 second? • 2 m in S and 2 m in S’ • 2 m in S and -1 m in S’ • 2 m in S and -3 m in S’ • 4 m in S and 4 m in S’ Both observers measure the same distance between two balls coordinates change but distance is a frame-invariant quantity

  29. x’= x-vt y’= y z’ = z t’ = t Galilean invariants y y' v distance (length of a vector) is an invariant i.e., independent of Galilean reference frame (many other quantities: mass, force,…) x x’ d’= x’2 - x’1 = (x2 - vt1) - (x1-vt2) = d x’1= x1-vt1 t’ 1= t1 why? x’2= x2-vt2 t’ 2= t2

  30. Invariance under Galilean transformation Galileo Galilei (1564—1642) y' y v Newton’s law (F=ma, mechanics) is therefore unchanged, i.e., Galilean invariant (all that you learned in Physics 1110 holds in S and S’) x x’ What about the physics of Electromagnetism? Does Electromagnetism depend on which inertial frame you are in ? YES according to Galileo!  “trouble” Einstein’s relativity

  31. lecture 3 EM and postulates of relativity Announcements: • lecture 2 is posted on the class website • homework 1 is posted on CULearn • due Wed, Jan 19 in class • solutions will be posted on CULearn • reading for this week is: • Ch 1 in TZD • course syllabus details • remember to bring your clicker to every class • register it (once), otherwise cannot get credit • set it to frequency CB (once)

  32. Last Time recall lecture 2: • Relativity in nature: • physical phenomena are coordinate- and frame-invariant • Inertial reference frames: • non-accelerating … constant velocity (including zero) • Galilean relativity: • Newton’s laws (mechanics, Phys 1110) are invariant • Maxwell’s laws (E&M, light, Phys 1120) are not invariant

  33. Today • Electromagnetic waves • Michelson-Morley experiment • Postulates of Einstein’s special theory of relativity

  34. Maxwell equations are not Galilean invariant • Galilean relativity: • satisfiedby Newton’s lawsof mechanics F = ma • violated by Maxwell’s laws description of light (E&M) James Clerk Maxwell 1831-1879 Maxwell’s equations: E&M waves: oscillating E and B fields Galileo says: c is speed of light in frame S c’ = c – v is speed of light in frame S’ … but c is with respect to what???

  35. Electromagnetic radiation and speed of light c = 300,000 km/s = 186,000 mi/s = 3 x 108 m/s ≈ 1 ft/nanosec James Clerk Maxwell 1831-1879 E&M waves: oscillating E and B fields

  36. EM-waves in what? • Sound wave propagates through air, with velocity (330 m/sec) relative to air • Water waves propagates through water, with velocity relative to water • “The wave” propagates through a crowd in a stadium, with velocity relative to the crowd • Electromagnetic wavepropagates through what??? What is “moving”/oscillating? Ether…so it was (incorrectly) thought in 19th century before Einstein

  37. clicker question Motion through ether • Q: Suppose earth is moving through ether with speed v in a direction • opposite to light, that moves with speed c relative to Ether. • According to Galilean relativity what is speed of light relative to earth? • a) c, b) c+v, c) c-v, d) none of the above v c * Assume the earth is not accelerating ether

  38. Measure earth’s motion through ether Earth goes around the sun at 30 km/s  must be going through ether v • light along earth’s motion: c-v c+v • light against earth’s motion: L L

  39. Michelson-Morley experiment, 1887 • measure speed of light in two • two perpendicular directions • interfere returned beams for • higher accuracy, > 1 km/s Michelson and Morley saw nothing !!! i.e., no difference in time between two paths

  40. View of experiment from Ether • We are moving with v relative to Ether, so from Ether we look like we are moving in the opposite direction, i.e., with -v Michelson and Morley saw nothing !!! i.e., no difference in time between two paths

  41. There is no ether Electromagnetic waves are special: A time-changing electric field induces a magnetic field, and vice-versa without any “ether”.

  42. Postulates of special relativity Postulates: 1.) All laws of nature are same in all frames 2.) Speed of light, c is same in all all inertial frames Albert Einstein, 1879-1955

  43. lecture 4 Simultaneity and relativity of time and length Announcements: • lecture 3 is posted • homework 2 (due Wed, Jan 26 in class) is posted • homework 1 solutions are posted • reading for this week is: • finish Ch 1, start Ch 2 in TZD

  44. Last Time recall lecture 3: • electromagnetic waves • Michelson-Morley experiment • c is indeed frame-independent, i.e., • there is no ether • postulates of Einstein’s special theory of relativity • laws of nature are frame-independent • speed of light, c is constant, i.e., same in all frames

  45. Today Time to talk about time: • space-time event • synchronization of clocks • simultaneity is frame dependent • relativity of time

  46. clicker question Speed of light in a moving frame • Q: Suppose earth is moving through space with speed v in a direction • opposite to light, that moves with speed c=3x108m/s with respect to • far away stars. • According to Einstein’s relativitywhat is speed of light as viewed from • the earth? • c, b) c+v, c) c-v, d) none of the above • A: There is no ether and light moves with the same speed, c in all • inertial reference frames v c * Assume the earth is not accelerating

  47. Space-time event location and time of events • “old” (non-relativistic) thinking: • 3D spatial coordinate (x,y,z) at time t • new (relativistic) thinking: • 4D space-time (x,y,z,t) labeling space-time events • same event has different coordinates in different • frames: • (x,y,z,t) v (x’,y’,z’,t’) • space-like and time-like events t t’ (3,2) x’ x

  48. Synchronization of clocks • need synchronized perfect clocks at different • locations • quite nontrivial at different x1 and x2, but doable: • synchronize at same point x1=x2, then move slowly • apart; if arbitrarily slowly do not screw up synchronization • positions via x = ctcreate space-time grid y x

  49. Summary of time dilation and length contraction

  50. Simultaneity is a relative concept S’ S’ c c S S S’ S’ L v vtL c v c tL tL ctL v t’R t’L S S tL c c ctR S’ t’L tR tR S D • S’: photons arrive simultaneously (at left/right ends) at t’L = t’R = L’/2c • S: photons arrive at right after left ends: • not simultaneous in S ! • front (right) clock on moving train lags behind back (left) one