10520EE Modern Physics Instructor: 陳明彰 LAs:??

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Opal Dennis
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10520EE 211000 Modern Physics http://mx.nthu.edu.

1 10520EE Modern Physics Instructor: 陳明彰 LAs:??

2 Today s class Why are we here? What s this class about? What do we need to do? How do we plan on doing it? Lots of information posted on the web. Check frequently for changes!

3 What is modern physics? Classical Physics (prior ~1900): Two Giants : Newton & Maxwell They invented classical mechanics and E&M Around 1900: three crises in physics: Michelson-Morley experiment (speed of light) Photoelectric effect (quantization of energy of light) Black body radiation (UV catastrophe) Modern physics (after ~1900): THIS COURSE! Relativity theory & quantum mechanics ( QM )

4 What will be covered in 10520EE ? Special Relativity What happens when things go really fast Quantum Mechanics Describes the properties of really small things

5 Topics in Relativity * Relativity before Einstein * Simultaneity * Time dilation and length contraction * Geometry of spacetime * Momentum, energy, and E = mc 2 We will not study: * effect on electromagnetism * gravity (general relativity) (both are very interesting, but mathematically too hard for this course!)

6 What is Quantum Mechanics? Pre quantum - understood how stuff falls (gravity) & a little about properties of electric and magnetic fields, gases. Quantum - understand underlying behavior of everything you are likely to see or experience in your lifetime! properties of light and other EM radiation how light interacts with matter basis for all modern technology, etc. properties of materials

7 Properties of materials: e.g. color Chlorophyll: QM explains how electrons & atoms behave. Predicts properties, such as color and function of material. Photonic crystal: a clever mechanical structure leads to light interference

8 Topics in quantum mechanics * Historical perspective about Atoms * Key experimental results that gave rise to the ideas of quantum mechanics * Apply these ideas to simple systems such as simple atoms and model situations * Apply these ideas to real world situations

9 Trad l Model of Education Content Instruction via transmission Individual (you!)

10 Teach by actively engaging students based on what they know...

11 Course Transformation with LAs Otero et al, Science

12 Engagement Improves Learning FCI I traditional lecture <g> = post-pre 100-pre <g> <g>

13 Engagement Improves Learning traditional lecture interactive engagement Fraction of Courses CU - IE & trad recitations <g> = post-pre 100-pre CU - IE & Tutorials learning gain <g> Pollock & Finkelstein, Physical Review, 4, (2008).

14 Guiding principles: (basis for how course is run) 1. People understand concepts by seeing, discussing, and applying them, not by passively listening to explanations. 2. Understanding physics (& solving problems that develop understanding) is a learned skill, like golf or playing basketball or violin. Takes time, effort, and practice. Research says better retention if sustained effort rather than cramming. 3. People learn best by sharing and getting feedback on their thinking-- Student-student more often than student-faculty. Physics is not collection of facts (it s magic ) ((just kidding it s better than magic)) It is way of thinking. Only you can teach yourself to think! Analyzing, applying concepts, solving problems.

15 Great! Does that mean that I only have to learn what I think is important? No! Course Goal: Every student learns everything! If not important to learn, we took it out. (Trust me on this one!)

16 We provide you with opportunities to help you learn. Content, problems, simulations, guidance, organization. (But we can t do the learning for you!) Reward activities and efforts conducive to your learning (grade) Learning only comes as result of your effort! Model for learning 10520EE Reading before class- introduce ideas and terms. 2. Analysis and discussion in class- explore, develop basic ideas and understanding. 3. Master and retain ideas through use in extensive HW (4-6 hrs/wk) (collaboration good, but submit own work)

17 Learning only comes as result of your effort! Constant efforts (Homework, reading, disussions ) degrade Patient:T.R.Schibli

18 Homework Reading assignments: For every class (typically 2 assignments per week). Quizzes on reading assignments will be part of your final grades Written Homework: Weekly. (Usually due in the class on Thursday.) See class and course homepage for assignments! Late HW will not be accepted! I will drop your lowest (one) HW score, but no other freebies.

19 Grading In-class participation (5%) Participation only Graded (Reading quizzes, occasional graded clicker question) Homework (35%) (most of learning, collaboration helps but you need to write your own solutions) Late HW will not be accepted, but I will drop your lowest one HW. No other freebies! Exams (60%) Two midterm exams (15% each): 1. March 20: 1pm- 3:20pm. 2. May 8: 1pm 3:20 pm. Final (30%): Jun. 12: 12:30pm 3:30 pm Note: In-class participation and weekly homework make up 40% of final grade. Grade strongly depends on showing up for class, doing reading, and doing homework every week. You must be able to make these dates so reserve this time on your calendar! If you need special accommodations: See me!

21 You just woke up inside a train without windows. The train is magnetically levitated, so you cannot hear if the train is moving or if it is standing still. How can you determine if the train is moving at a constant speed on a straight track or if it is standing still? A Use a pendulum that is attached to the ceiling of the rail car B Use a gyro compass C Drop a ball and see which direction it goes D Use a glass of water and look at the water surface. E You can t tell.

22 Announcements Reading Beiser 1.1, 1.2, 1.3, and Michelson Morley experimet (wikipedia) Morley_experiment

23 Today All about Galilean relativity Inertial frames in classical physics and other important vocabulary. Motivation for special relativity Strange things about Speed of light.

24 Galilean relativity Explore how things move with respect to things that are also moving. Galileo Father of modern science. ( )

25 Reference frames y A reference frame is a set of coordinate axes that never move with respect to each other. x Think about laying out a set of meter sticks in a pattern like this one, and never moving them again relative to each other. And it goes on forever because you might want to measure things far away.

26 Reference frames Q: Where do I put the origin, (0,0)? A: Anywhere you like! There is no preferred place. (0,0) I could choose it to be where I m standing.

27 Reference frames y (3,2) Now I locate an object in my frame, at, say, (x,y) = (3m,2m). (0,0) x In principle, somebody standing there yells out the coordinate. If I go myself to check, I m moving in this reference frame!

28 Reference frames (3,2) The blue ball is at (3m,2m). The red ball is at (0m, -2m). Distance from red ball to blue ball is (0,-2) 2 2 (3m) + (4m) = 25m = 5m

29 Reference frames (2,0) In a different reference frame, the blue ball could be at (2m,0m) and the red ball is at (-1m,-4m). The balls are still 5m apart! (-1,-4) Where I stand doesn t affect physical facts like distance.

30 Remark (2,0) The distance between two objects that are not moving in a reference frame is a constant. (-1,-4) We say this distance is an invariant. Q

31 Compare two reference frames (now in one-dimension only) Frame S has origin here x x Frame S has origin here, at x=3m according to reference frame S. (The frame S is drawn below S so you can read both axes.)

32 Compare two reference frames (now in one-dimension only) x x Observer in S measures ball at x = 2m. Observer in S measures ball at x = -1m.

33 Important conclusion Observer in S finds the ball at x = 2 m Observer in S finds the ball at x = -1 m Q: Who is right? a) Observer in S b) Observer in S c) Both are right d) Neither is right e) It depends Two observers in different reference frames can give a different description of the same physical fact (in this case, the location of the ball.) And they re both right! This is relativity!

34 Inertial reference frames An inertial reference frame is one: a) that is not moving b) that is not accelerating c) in which objects are a fixed distance apart d) in which observers are a fixed distance apart e) in which nothing is moving

35 Inertial reference frames V Imagine a train car (it s always a train!) moving on a straight track with constant velocity with respect to the ground. The train runs smoothly, so that you can t tell it s moving by feeling the bumps on the track. Would you expect the laws of Physics to be different inside this train compared to the labs here at NTHU? What if I put an atomic clock in there?

36 Inertial reference frames V Now, you re playing pool on the train. The balls roll in straight lines on the table. In other words, the usual Newtonian law of inertia still holds. The frame as a whole is not accelerating.

37 Which of these is an inertial reference frame (in good approximation)? A. My car without brakes rolling down a steep hill B. A rocket being launched C.A sky diver falling at terminal speed D. None of the above

40 Inertial reference frames V As I m lining up my shot, the train slows and approaches the station. I have not touched the cue ball. What does it do? a) Rolls to the front of the train b) Rolls to the back of the train c) Remains motionless (Is this still an inertial reference frame?) This frame is no longer inertial! (Accelerated frame)

41 Summary An inertial reference frame is one that is not accelerating. Einstein s special theory of relativity is about measurements in different inertial frames of reference. Note: There is no absolute state of rest! All motion is relative. FYI: Einstein s general theory of relativity is about measurements in any frame of reference (accelerating or not, including gravity etc.).

42 Comparing inertial frames x v x Here are two inertial reference frames, moving relative to one another. According to S, S is moving to the right, with v = 1 m/s.

43 Comparing inertial frames v x x Here are two inertial reference frames, moving with respect to one another. According to S, S is moving to the left, with v = -1 m/s. But again: Both observers are right.

44 Important conclusion Observer in S measures velocity of S to be +1 m/s Observer in S measures velocity of S to be -1 m/s Q: Who is right? a) Observer in S b) Observer in S c) Both are right d) Neither is right e) It depends! Two observers in different reference frames can give a different description of the same physical fact (in this case, the relative velocity of the other reference frame.) And they re both right! The two frames are moving relative to each other.

45 Comparing inertial frames v At time t = 0, the two frames coincide. A ball is at rest in frame S. Its position is x = 2 m in S x = 2 m in S

46 Comparing inertial frames v Frame S is moving to the right (relative to S) at v=1m/s. At time t = 3 sec, the position of the ball is x = 2 m in S x = -1 m in S

47 Important conclusion Where something is depends on when you check on it and on the movement of your own reference frame. Time and space are not independent quantities; they are related by rel. velocity. Definition: An event is a measurement of where something is and when it is there. ( x, y, z, t)

48 Comparing inertial frames v At time t=0, the ball was at x = x = 2. At time t>0, the ball is still at x=2 in S but where is it in S at the time t>0? a) x = x b) x = x + vt c) x = x-vt

49 Galilean position transformation If S is moving with speed v in the positive x direction relative to S, then its coordinates in S are x y = z = t = x = t y z vt Note: In Galilean relativity, time t=t is the same in both reference frames; why wouldn t it be?!

50 Galilean velocity transformation u v Same thing as before, but now the ball is moving in S, too, with velocity u = 1 m/s. Is the ball faster or slower, as measured in Frame S? A faster B slower C same speed

51 Galilean velocity transformation u If an object has velocity u in frame S, and if frame S is moving with velocity v along the x-axes of frame S, then the position of object in S is: x v x x' ( t) = x( t) vt The velocity u of the object in frame S is therefore: A) u + v B) u - v C) v - u D) u E) -v

52 Galilean velocity transformation u If an object has velocity u in frame S, and if frame S is moving with velocity v along the x-axes of frame S, then the position of object in S is: x v x x' ( t) = x( t) vt The velocity of the object in frame S is therefore: u' = dx ( t) dt = d dt dx( t) ( x( t) vt) = v = u v dt

53 Important conclusion Two observers in different reference frames can give a different description of the same physical fact (in this case, the velocity of the ball.) And they re both right!

54 So far we have talked about how observers from different reference frames describe the location (x) and the velocity (v) of objects. What other quantities did we talk about in Fundamental Physics? F = m a

55 Dynamics F S F F v S

56 Dynamics In inertial frame S, we have (in x-direction, say) F = ma How about in inertial frame S? Well, F' = F since you re still applying the same forces, and du' d du a ' = = ( u v) = = dt dt dt a à no additional acceleration in an inertial frame.

57 Galilean relativity The laws of mechanics (good old F = ma) are the same in any inertial frame of reference.

58 Einstein s First Postulate of Relativity The laws of physics (including electromagnetism) are the same in all inertial frames of reference.

59 Huston, we have a problem!! From Fundamental Physics you might recall that Mr. Maxwell told us the speed of light c would be: 1 8 c = = m / ε µ 0 0 s Now, Mr. Einstein tells us that ε 0 and µ 0 are the same in any inertial frame of reference. But Mr. Galileo just told us that c = c - v What gives??

Galilean velocity transformation

Galilean velocity transformation... -3-2 -1 0 1 2 3... u... -3-2 -1 0 1 2 3... If an object has velocity u in frame S (note: velocities have a direction!), and if frame S is moving with velocity v along