1 Electricity and Magnetism II12.1 Electricity and Magnetism II Griffiths Chapter 12 Relativity Clicker Questions

2 12.3 A rocket is moving to the right at speed v = (3/4)c, relative to Earth. On the front of the rocket is a headlight which emits a flash of light. v = 3/4c v = 0 light beam v = (3/4) c In the reference frame of a passenger on the rocket, the speed of the light flash is A) c B) 7/4 c C) 1/4 c D) None of these According to a person at rest on the earth, the speed of the light flash is A) c B) 7/4 c C) 1/4 c D) None of these Class: MATH/PHYSICS Correct Answer(s) A, A, A ______________________________ Physics 3320 Sp12 (MD) Lecture 31 Top Question: [[85]], 4, 11, 0 Middle Question [[96]], 0, 4 Bottom Question [[85]], 4, 0, 11 _____________________________ Spring 2012 Comments Think this is a case where students know what the correct answer is, but don’t necessarily believe it, or understand completely why they should believe it other than it is the authoritative answer. =========================== Written by M Dubson 3320 Sp12 According to a person moving toward the rocket at speed (3/4)c, relative to earth, the speed of the light flash is A) c B) 7/4 c C) 1/4 c D) None of these

3 12.4 A light bulb flashes in the center of a train car that is moving at speed v with respect to the ground. In the frame of reference of the train car, light wave from the flash strikes the front and back of the train simultaneously. In the frame of reference of the ground, the light strikes the back of the train ___________ (fill in the blank) the light strikes the front of the train. A) before B) after C) at the same time as Class: CONCEPTUAL Correct Answer: A _______________________________ Physics 3320 Sp12 (MD) Lecture 31 [[85]], 4, 11 ______________________________ Spring 2012 Comments Confusion (as expected) about how two observers can watch the same system and see two different things. Note that the slide is animated. ============================ Written by M Dubson 3320 Sp12 Events that are simultaneous in one frame are not simultaneous in other frames. There is no such a thing as “now”. The time “now” in the Andromeda galaxy, depends on whether we are in the Earth rest frame or the Andromeda rest frame, or…

4 Light clock v Rest frame of clock Δt0 Moving frame Δt12.5 Light clock v Rest frame of clock Δt0 Moving frame Δt Class: CONCEPTUAL Correct Answer: B _______________________________ Physics 3320 Sp12 (MD) Lecture 32 5, [[90]], 5 Spring 2012 Comments Some confusion about representation – needed to be very explicit about the mirrors being the same, and that the one on the right is in motion (the dashed lines show it at an earlier and a later time). Note that this slide is animated. ============================= Written by M Dubson 3320 Sp12 In which frame of reference is the time between tics of the clock longer? A) Rest frame of clock B) moving frame C) no difference “Moving clocks run slower”:

5 A long train was passing (speed v) during this experiment. 12.7 I flash a lightbulb (event 1). The light reaches a mirror, and returns to me (event 2) I measure the time Δt =t2-t1 for the complete trip of the light. A long train was passing (speed v) during this experiment. In the reference frame of the train, what is the interval Δt’ between those two events? (As usual, ) D) I’m sure it’s either B or C, but I’m NOT sure which one! E) I’m pretty sure it’s “none of the above” Class: CONCEPTUAL Correct Answer: B _______________________________ Physics 3320 Fa11 (SJP) Lecture 39 Pre-class: 0, [68]], 27, 0, 5 After discussion: 5, [[85]], 10 Fall 2011 Comments Pre-class: We didn’t discuss this too much, I told them we would come back to it after having derived and discussed the Lorentz Transformations. It turns out that some students chose B because of linguistics: it’s “time dilation”, so they look for the formula with the gamma in the numerator! After discussion: Back to the same question, with Lorentz transformations (rewritten in terms of deltas) on the board. Students are struggling with interpretation, I think one student is asking if delta t mean the SAME thing as delta t-prime as measured in different frames, or can the two “observers” choose different methods to decide what delta t they should be using to “get the right answer”? Another student invoked “proper time” to get B. (Not wrong, but might be worth changing up the equation to make the answer less obviously “dilation”) Notes Baily: Steve points out that he could have switched which frame was primed, so that gamma in the numerator isn’t automatically correct. LA: Students knew it had to be either B or C and were pretty divided between them. Some students were concerned about the direction of the light but Steve tried to argue it wouldn't matter. ============================== Written by SJP in PHYS 3320 Fa11

6 12.10 Can one change the order of events in time by measuring them in a different inertial reference frame? Always Sometimes Never Class: CONCEPTUAL Correct Answer: B ________________________________ Physics 3320 Fa11 (SJP) Lecture 40 5, [[53]], 42. Physics 3320 Sp12 (MD) Lecture 42 50, [[25]], 25 AND Physics 3320 Sp12 (MD) Lecture 43 4, [[88]], 8 Fall 2011 Comments Answer is “sometimes”. We haven’t yet gotten to “invariants”, so I had to leave this question by showing one case where the answer is YES (the canonical bulb at the center of a train car, 2 events are the two simultaneous detections in the train frame) and another where it is NO (like two claps at the same point, the time ordering could be causal, NO frame can reverse those events. But we don’t quite have the tools today to decide a priori whether two events can have their time ordering reversed, need invariant interval to get at that) Good discussion, students are still confused about this. My homework (due today) had some “FTL neutrino” physics in it, so I was careful to distinguish from that, here we’re talking good old “straight” special relativity. One student pointed out that in the homework, the LIGHT beam went from event 1 to event 2 and no observer could change the time ordering, so they wanted to argue “never”. (But finding one “no” situation doesn’t prove it’s ALWAYS no) Another student remembered the “light signal at center of train car is detected at two ends, which are simultaneous events in THAT frame, but not in relatively moving ones. You can make delta t be either sign) Notes LA: It was like pulling teeth to get students nearby to talk. I basically got no data from them, but once we started discussing this as a class, one said that he was able to eliminate "Always" as an answer because from the homework, they had just seen that it isn't possible. After that, another referred to the typical "flash a bulb in a train" problem, and said that you see different times in different reference frames, so he was apparently choosing B. ============================== Written by SJP in PHYS 3320 Fa11

7 C) Answer depends on the frame of reference12.11 The interval between two particular events is positive: Could these events be causally connected? That is, could one of these events have caused the other? Yes B) No C) Answer depends on the frame of reference Class: CONCEPTUAL Correct Answer: B _____________________________ Physics 3320 Sp12 (MD) Lecture 42 52, [[26]], 22 Spring 2012 Comments Good follow up to previous question on time-ordering, now that we’ve talked about invariant quantities, like the spacetime interval. ============================ Written by Dubson 3320 Sp12

8 12.12 A clock flies over a town at high speed (constant velocity). In the rest frame of the town, the clock reads 0 when it is over the church steeple and it reads 2 when it is over the Old Watch Tower. So according the townsfolk, the flying clock face advanced 2 units between these two events. Do observers in all other references frames agree that the flying clock face advanced 2 units between these two events? A) Yes B) No Class: CONCEPTUAL Correct Answer: A _____________________________ Physics 3320 Sp12 (MD) Lecture 42 Before Discussion: [[11]], 89 After Discussion: [[90]], 10 Spring 2012 Comments Again, some issues of representation – have to be very explicit that this is the same clock shown at two different times. ============================ Written by Dubson 3320 Sp12

9 Displacement is a defined quantity:12.16 Displacement is a defined quantity: Is displacement a 4-vector? Yes No Ummm… don’t know how to tell None of these. Class: CONCEPTUAL Correct Answer: A ________________________________ Physics 3320 Fa11 (SJP) Lecture 40 [95], 5, 0,0,0 Physics 3320 Sp12 (MD) Lecture 42 [[95]], 5, 0, 0 Fall 2011 Comments This vote was much more split in the silent period, but they eventually got to it. I was careful to point out that just writing the superscript mu is not “proof” that it’s a contravariant vector – I’m asking them to convince me! We had already written the x’ = lambda x formula on the board, and one student clearly articulated the argument that you can write that twice (for xA and xB), subtract, and you’ve proven it. Perfect. Notes Baily: Discussion nearby focused on the linearity of the transformations, that performing the transformations and then adding the subsequent vectors is the same as adding the vectors and then doing the transformation. LA: Students were very hesitant in answering, even though they did know the answer to this one (I think they thought it was a trick). Their reasoning was that if you subtract a vector from a vector, you get back a vector. ====================================== From Charles Rogers. Be ready to explain your answer.

10 4-velocity? Imagine this quantity: Is this quantity a 4-vector?12.19 4-velocity? Imagine this quantity: Is this quantity a 4-vector? Yes, and I can say why. No, and I can say why. None of the above. Class: MATH Correct Answer: B ________________________________ Physics 3320 Fa11 (SJP) Lecture 41 48, [[48]], 4,0,0 Fall 2011 Comments Even though we had effectively answered this question at the end of last class, it’s a good one, and confronts students with what I *mean* by 4-vector. (Note that there’s a “hint” slide coming up next, though it’s a little too abstract to really help them much). The one student who voted C said “I think it’s no but cannot say why”  The next slide (and one coming up 2 further) are my explanations – but a student mostly came up with it in class. He pointed to the Lorentz transformations, and focused his attention on the 0 component. He couldn’t articulate it clearly, but he was noticing that “c” in one frame was turning into something more complicated in another frame, yet from the form in THIS slide, it really looks like the 0th component would need to be some sort of frame invariant?! The answer is a clear no – one way to see it is that this beast here is delta x^mu / delta t, it’s a contravariant 4-fector divided by something which is NOT frame invariant. Another is to think about what we KNOW about u in other frames (we worked out velocity addition last class), and it certainly is NOT what the Lorentz transformation would give us. Notes LA: Lots of students were confused on how a 3-component object could be a four-vector. Other were confused how it couldn't be, since position is. (2nd part) Few students knew the right approach here, i.e. check the transformation. When they were pushed in that direction, some students immediately tried to expand everything out in v's (as opposed to leaving gammas and betas), and got bogged down in algebra. ================================ Written by SJP in PHYS 3320 Fa11

11 This object does not Lorentz Transform. NOT a a 4-vector.12.20 4-velocity? Imagine this quantity: Is this quantity a 4-vector? Yes, and I can say why. No, and I can say why. None of the above. Answer to previous slide Fall 2011 Comments SJP: I wanted to emphasize the answer, and the “x through the mu” is to explicitly point out that you should not just label any arbitrary collection of 4-things AS THOUGH it were a contravariant 4-vector. The “superscript mu” notation should be reserved for things we know are contravariant! So e.g. I mentioned that I can write a column vector of c, my age, the price of gas, and the speed of an object. This is a column with 4 entries, but that doesn’t make it a 4-vector, because another inertial observer will not measure different components based on the Lorentz transformation matrix! This object does not Lorentz Transform. NOT a a 4-vector.

12 4-velocity? Imagine this quantity: Is this quantity a 4-vector?12.21 4-velocity? Imagine this quantity: Is this quantity a 4-vector? Proper time Yes, and I can say why. No, and I can say why. None of the above. Class: CONCEPTUAL Correct Answer: A _______________________________ Physics 3320 Fa11 (SJP) Lecture 41 [[100]], 0, 0, 0, 0 Looks good, students were pretty comfortable with this. I pushed them to define “delta tau”, and got the usual “it’s the time interval measured in a frame where you can use just one clock”, which led to the next question…. Notes Baily: Think the order of presentation (that it immediately follows the trick question and an incorrect expression) might have been too suggestive. LA: Most students near me thought "The last one was wrong, so this one should be correct" and didn't put too much effort into it. Others remarked it seemed reasonable because delta_tau invariant, until delta_t. ============================== Written by SJP in PHYS 3320 Fa11

13 The 4-velocity ημ is defined as12.25 The 4-velocity ημ is defined as What is the invariant length squared of the 4-velocity, ημημ? c2 -c2 -c2 + u2 c2 – u2 None of the above Class: MATH/PHYSICS Correct Answer: B _________________________________ Physics 3320 Fa11 (SJP) Lecture #42 10, [[45]], 20, 0, 25 Physics 3320 Sp12 (MD) Lecture 44 Before Discussion: 12, [[6]], 59, 12, 12 After Discussion: , [[91]], 0, 4, 4 Fall 2011 Comments Good question, glad I let them work on it. Some students were confused by the complicated language, I clarified that the words “invariant length squared of the 4-velocity” LITERALLY MEANS eta(mu) eta(mu) I animated this and set them working, and only showed the answers after they’d been working for a minute. Many got “E”, some with explicit “gamma’s” out front that had not canceled. You can do this by explicitly multiplying it out (remember that the zero component gets a minus sign), and the u^2-c^2 cancels the gamma^2 (mostly) OR you can shift to the REST FRAME of the object, where u=0, and you’re just squaring (c,0,0,0) That’s an important idea, that you can make your life easier by picking a “good” frame to compute in! I pointed out that this is a bit of a surprise. Normally you think of v^2 as carrying lots of information (kinetic energy!), but the 4-velocity squared seems to carry NO information about the particle at all, EVERY particle has the same 4-velocity squared. ================================ From ERK Spring 2011

14 12.28 The rest mass m of an object is the mass measured in the rest frame of the object. Is a 4-vector ? A) Yes B) No C) Sometimes Class: CONCEPTUAL Correct Answer: A _______________________________ Physics 3320 Sp12 (MD) Lecture 44 [[91]], 0, 0 Spring 2012 Comments ============================= Written by M Dubson 3320 Sp12

15 Is 4-momentum invariant ?12.27 For isolated systems, the total 4-momentum is CONSERVED (this is an experimental fact). Is 4-momentum invariant ? Yes, and I can say why. No, and I can say why. None of the above. Class: CONCEPTUAL Correct Answer: B ________________________________ Physics 3320 Fa11 (SJP) Lecture 43 29, [[65]], 6 Fall 2011 Comments It’s a question of language, but “contravariant” or “covariant” is NOT the same as “invariant”. We talked about examples of invariants, students came up with proper time, c, mass, E dot B, …. But I pointed out that neither p, nor E, are in this list, and the 4-vector DOES change when you Lorentz boost. Admittedly in a simple and definite way, but it is not Invariant. =============================== Written by SJP in PHYS 3320 Fa11

16 Are energy and rest mass Lorentz invariants?12.31 Are energy and rest mass Lorentz invariants? Both energy and mass are invariants Only energy is an invariant Only rest mass is an invariant Neither energy or mass are invariants Class: CONCEPTUAL Correct Answer: C _______________________________ Physics 3320 Fa11 (SJP) Lecture 44 0, 6, [[94]], 0 Physics 3320 Sp12 (MD) Lecture 44 9, 0, [[91]], 0, 0 AND Physics 3320 Sp12 (MD) Lecture 45 0, 0, [[93]], 7, 0 Fall 2011 Comments Preclass question. They seemed to be doing fine on this, but I think there are “false positives here”. The discussion is partly about semantics, energy is part of a 4-vector, which is “covariant”, and they’re still a little unclear on the distinction between that word and “invariant”, but people were explaining that energy depends on observer (which is correct) - although, later in class we uncovered that some students are confused about the difference between kinetic energy and relativistic energy. On this one, someone answered C, but as an explanation for why energy wasn’t invariant, said “because the zero of potential energy is arbitrary”, which is mixing up a different idea. So I think the high score on this isn’t necessarily a sign that this is all cleared up. ============================== From ERK Spring 2011

17 12.30 A row of positive charges is stationary on the ground. A person with a gauss-meter is running to the right along the row of charges, at the same height as the charges and in front of them. What is the direction of the B-field which the observer measures? A) Right B) left C) up D) down E) B = 0 Class: CONCEPTUAL Correct Answer: C _______________________________ Physics 3320 Sp12 (MD) Lecture 34 0, 4, [[96]], 0, 0 Spring 2012 Comments Students could see this easily by thinking of the row of charges as a current in the moving frame. ============================= Written by M Dubson 3320 Sp12

18 Switch from frame S to frame S-bar:12.35 Switch from frame S to frame S-bar: S v +s -s Frame S (at rest) Frame S v Class: CONCEPTUAL Correct Answer: A _______________________________ Physics 3320 Sp12 (MD) Lecture 36 Before Discussion: [[21]], 46, 32 After Discussion: [[43]], 46, 11 Spring 2012 Comments Important point is that the magnitude of the field between the plates doesn’t depend on their separation distance. Students had trouble seeing this. ============================= Written by M Dubson 3320 Sp12 How does Ex compare to Ex ?

19 Switch from frame S to S-bar. Things change:12.36 Switch from frame S to S-bar. Things change: S v Do Maxwell’s Equations look the same in S-bar? Class: CONCEPTUAL Correct Answer: A _______________________________ Physics 3320 Sp12 (MD) Lecture 36 [[86]], 14 Spring 2012 Comments We’ve seen some confusion on what we mean when we say the laws of physics are the same in all inertial frames (have the same form), meaning the quantities may be different but the relationships between them are the same. ============================= Written by M Dubson 3320 Sp12 A) Yes B) No

20 Can we define a 4-force via the 4-momentum?12.37 Can we define a 4-force via the 4-momentum? Proper time Is K, so defined, a 4-vector? Yes, and I can say why. No, and I can say why. None of the above. Class: CONCEPTUAL Correct Answer: A _________________________________ Physics 3320 Fa11 (SJP) Lecture 44 [[64]], 23, 14 Fall 2011 Comments I thought this was a gimme, but people struggled and argued. On the blackboard, I had written F = dp/dt, and then K(vec) = dp(vec)/dtau, thinking this would help them. I tried hard to get students to explain why they didn’t all vote A, but it was pulling teeth. One student said he was uncomfortable with the 0 component, he wasn’t sure if dE/dtau would give zero, that didn’t seem like it would transform… I think the “C” answers were because they couldn’t really defend their reasoning. The answer is A, same reason as we’ve used in several previous instances! (Next slide) =============================== Written by SJP in PHYS 3320 Fa11

21 How many ordinary equations is that, really? 1 4 6 16 ????12.39 Consider the equation How many ordinary equations is that, really? 1 4 6 16 ???? Class: CONCEPTUAL Correct Answer: _____________________________ Fall 2011 Comments (No time to click, students looked at it for ~30 seconds or a minute, and I heard “1”, and “16” and “4”. I asked why 4, and they said “I don’t know, it’s a 4 vector?” which seemed like a lovely insight! It’s a little ambiguous, but that’s what I had in mind: mu can be 0, 1, 2, or 3, and each of those is an “ordinary” equation. (Although you might argue, once you know the result, that’s it’s “2”: div(B)=0 and curl(E)+dB/dt=0… But anyway, the point here was that this notation is all very new, the Einstein summation convention is new, and I wanted them to wrestle with interpretation rather than simply being “shown” the lovely result that these are the homogeneous Maxwell equations in covariant form. ============================ Written by SJP in PHYS 3320 Fa11