Spacetime and the Quantum World Questions Fall 2010

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1 Spetime nd the Quntum World Questions Fll Cliker Questions from Clss: (1) In toss of two die, wht is the proility tht the sum of the outomes is 6? () P (x 1 + x 2 = 6) = out 3% () P (x 1 + x 2 = 6) = out 6% () P (x 1 + x 2 = 6) = out 14% (d) P (x 1 + x 2 = 6) = out 11% (e) This n t e determined from the info given (2) As forest on Mondy (Novemer 1) morning, suppose tht the likelihood of preipittion on Eletion Dy, Tuesdy Novemer 2, is 10 % for eh 3 hour intervl. For instne, the proility of preipittion from 10 AM to 1 PM is 10 %. Similrly for the rest of the dy. So for the entire 24 hour period, wht is the proility of preipittion? () You multiply the hourly forests so you get = so % of the time. Essentilly, it will not rin tody. () You dd the hourly forests so you get = 2.4 so 240 % of the time. Essentilly, it is rining! () You tke one hourly intervl nd use tht. There is 10 % hne of rin for the 24 hour period. (d) The hne it will not rin in one 3 hour intervl is 90% so for the whole dy we hve 1 (0.9) Roughly, there is 60% hne of rin. d (3) Wht hppens to urrent-rrying loop in uniform mgneti field? () Not muh. It stys where it is. () It osilltes. () It preesses ut otherwise stys put. (d) It preesses nd elertes into the stronger prt of the field. (e) We need more informtion efore it is possile to determine the orret nswer. (4) Wht hppens to urrent-rrying loop in non-uniform mgneti field? () Not muh. It stys where it is. () It osilltes. () It preesses nd otherwise stys put. (d) It preesses nd elertes in the diretion determined y the projetion of its mgneti rrow. (e) It preesses nd elertes into the weker prt of the field. d (5) If eh eletron ehved like urrent-rrying loop, wht would the Stern-Gerlh dt look like? () Just wht they sw in () A ump with tils - most would lnd ner the enter of the em. () A uniform even spred from the ottom-most defletion to the top-most (d) Three, seprte umps. 1

2 2 (6) If eh eletron hd tiket telling it whether its projetion ws + or -, nd the tikets were distriuted rndomly, wht would the Stern-Gerlh dt look like? () Just wht they sw in () One entrl ump, most would lnd ner the enter of he em. () A uniform even spred from the ottom-most defletion to the top-most (d) Three, seprte umps. (e) We need more informtion efore it is possile to determine the orret nswer. (i.e. lol deterministi sheme would work for this experiment) (7) Is it possile to onstrut projetions +m B or m B of one rrow for ll xes? () Yes, they re t right ngles. () Yes, ut it is hrd to drw () No wy. (d) No, I n prove it geometrilly (e) We need more informtion efore it is possile to determine the orret nswer. or d (8) Wht would e outome of the repeted Stern-Gerlh experiment 4.1? () +m B 100 % of the time () m B 100 % of the time (d) +m B 75 % of the time nd m B 25 % of the time (9) Wht would e outome of the repeted Stern-Gerlh experiment 4.2? () +m B 100 % of the time () m B 100 % of the time (d) +m B 75 % of the time nd m B 25 % of the time (10) Wht would e outome of the repeted Stern-Gerlh experiment 4.3? () +m B 100 % of the time () m B 100 % of the time (d) +m B 75 % of the time nd m B 25 % of the time (11) Wht would e outome of the -30 to +60 degree repeted Stern-Gerlh experiment? () +m B 100 % of the time () m B 100 % of the time (d) +m B 25 % of the time nd m B 75 % of the time (e) +m B 75 % of the time nd m B 25 % of the time (12) Referring to the hrt of proility s funtion of ngle θ, wht would e outome of the θ = 45 degrees repeted Stern-Gerlh experiment? () +m B 100 % of the time

3 3 () m B 100 % of the time (d) +m B 15 % of the time nd m B 85 % of the time (e) +m B 85 % of the time nd m B 15 % of the time e (13) Referring to the hrt of proility s funtion of ngle θ, wht would e outome of the θ = 37 degrees repeted Stern-Gerlh experiment? () +m B 100 % of the time () m B 100 % of the time () +m B 90 % of the time nd m B 10 % of the time (d) +m B 10 % of the time nd m B 90 % of the time (14) For the initil stte m z = +m B going into the swithing Stern-Gerlh pprtus, wht is the proility of the +m B outome, given the setting? () P (+ ) = 1 4 () P (+ ) = 1 () P (+ ) = 1 2 (d) P (+ ) = 3 4 (e) This n t e determined from the info given (15) For the initil stte m z = +m B going into the swithing Stern-Gerlh pprtus, wht is the proility of the +m B outome, given the setting? () P (+ ) = 1 4 () P (+ ) = 1 () P (+ ) = 1 2 (d) P (+ ) = 3 4 (e) This n t e determined from the info given (16) For the swithing Stern-Gerlh pprtus, wht is the proility of the +m B outome, given eh of the settings,, re eqully likely? () P (+m B ) = 1 4 () P (+m B ) = 1 () P (+m B ) = 1 2 (d) P (+m B ) = 1 3 (e) P (+m B ) = 1 6 ( = 1 2 ) (17) You hve friend who gives two of you oxes to tke to Phoenix nd Chigo. She tells you tht the oxes ontin gint pumpkin 6 seeds. One you re in Chigo you open the ox nd see 2 seeds. How mny re in the ox in Phoenix? () 4 () 4 () 4 hmmm (18) Instntneously nd ertinly your know the numer of these gint pumpkin seeds in Phoenix. Does this men tht there is fster-thn-light signls etween Chigo nd Phoenix? () Yes, otherwise the stte in Phoenix would not determined. () No, the only thing tht hnged ws your knowledge of previously existing sitution.

4 4 (19) In the originl EPRB experiment does Alie know the results of Bo s experiments with ertinty (proility of 1)? () Yes. () No. () Yes, ut only fter she hs tken her mesurements. (d) No, sine she does hve ess to Bo s distnt nlyzer. (20) Cn the EPR experiment e used to ommunite? () Yes. () No. (21) Are these EPR experiments onsistent with speil reltivity? () Yes. () No. (22) We hve tht the proility P (m m = +m B m = +m B ) = 1 4 Wht is the proility P (m m = m B m = +m B )? () 1 sine it is the sme outome. () 0 sine it never ours. () 3/4 sine 1 1/4 = 3/4. (d) 1/2 sine eh outome is eqully likely. (e) 1/4 sine it is the sme s the one ove. (f) None of the ove. (23) Wht is the proility of the + or R outome, given stte prepred in the m = +m B stte, for ll possile settings? () 1 sine is my fvorite numer tody. () 0 sine it never ours. () 1/2 sine 1/3 + 1/12 + 1/12 = 1/2 (d) 1/2 sine 1/4 + 1/4 = 1/2. (e) 1/4 sine it is the sme s the one ove. (f) None of the ove. (24) Wht is the proility of the or G outome, given stte prepred in the m = +m B stte, for ll possile settings? () 1 sine is my fvorite numer tody. () 0 sine it never ours. () 1/2 sine 1/3 + 1/12 + 1/12 = 1/2 (d) 1/2 sine 1/4 + 1/4 = 1/2. (e) 1/2 sine 1 1/2 = 1/2. d or e (25) It turns out tht P (m m = m B m = m B ) lso equls 1 4. Wht then hppens to our predition for the proilities of the R nd G outomes for rndom settings in the EPRB experiment? () Not muh. The proilities re unhnged, 50/50 s efore. () Oh der, we etter re-do this to find out.

5 () I m just not sure. (26) In the lol deterministi hypothesis, wht is the proility of different outomes for rndom settings? () 4/9 () 1/2 () 5/9 (27) Wht is the proility for se VIII? () 1 () 1/2 () 5/9 (d) 0 (e) 1/4 (f) None of the ove (28) Cn the lol deterministi hypothesis explin the EPRB experiment? () No () Yes (29) Using the Stern-Gerlh interferometer of hpter 9 nd shown on the ord, we lok off the m x = m B pth through the devie. Wht is the proility tht n tom mkes it to point C, given we stred with the stte m z = +m B t A? () P (C m z = +m B, A) = 1 2 () P (C m z = +m B, A) = 1 4 () P (C m z = +m B, A) = 1 8 (30) Using the Stern-Gerlh interferometer, we lok off the m x = +m B pth through the devie. Wht is the proility tht n tom mkes it to point C, given we stred with the stte m z = +m B t A? () P (C m z = +m B, A) = 1 2 () P (C m z = +m B, A) = 1 4 () P (C m z = +m B, A) = 1 8 (31) Using the Stern-Gerlh interferometer, leve oth pths open. Wht is the proility tht n tom mkes it to point C, given we stred with the stte m z = +m B t A? () P (C m z = +m B, A) = 1 2 () P (C m z = +m B, A) = 1 4 () P (C m z = +m B, A) = 1 8 d Sine the stte t C is m z = +m B nd sine the interferometer doesn t hnge the stte, P (C m z = +m B, A) = 1. 5

6 6 (32) Wills sks, In this setup...if the reltive ngle etween the oxes is 90 degrees, shouldn t the proilities e 50% / 50%? () No. Tht result holds only when we know the stte. () No. The interferometer in this se does nothing so the stte is unhnged. () Yes. It must hve gone through one of nd so its stte must e either m x = +m B or m x = m B. or (33) With right light we n see every tom tht psses through the interferometer wht result do we find? Wht is the proility tht n tom mkes it to point C? () P (C m z = +m B, A) = 1 8 () P (C m z = +m B, A) = 1 4 () P (C m z = +m B, A) = 1 2 e P (C m z = +m B, A) = 1 2 if there is glint nd P (C m z = +m B, A) = 0 if there is no glint. (34) With relly dim light so there re too few photons to stter off the toms, wht result do you find?wht is the proility tht n tom mkes it to point C? () P (C m z = +m B, A) = 1 4 () Two ses: P (C m z = +m B, A) = 1 4 if there is glint nd P (C m z = +m B, A) = 1 if there is no glint. () Two ses: P (C m z = +m B, A) = 1 2 if there is glint nd P (C m z = +m B, A) = 1 if there is no glint. e P (C m z = +m B, A) = 1 2 if there is glint nd P (C m z = +m B, A) = 0 if there is no glint. (35) You sk whle to wth the pths, using light tht will llow the whle to see the glint of light (or the shdow) from the tom pssing through one pth or the other. Wht is the proility tht n tom mkes it to point C, given we stred with the stte m z = +m B t A? () P (C m z = +m B, A) = 1 2 () P (C m z = +m B, A) = 1 4 () P (C m z = +m B, A) = 1 8 (36) Luren sks, How does oserving hnge the outome?? Chrley sks, Does eletron ehvior depend on n oserver? Is it only nd solely the t of oservtion tht determines the outome? () Yes. It is when folks (tht s us) eome wre of the result. () No. It is the physis tht tells us; if it is possile, in priniple, to determine whih wy informtion then then the tom ts s if nd is known euse it is knowle. (37) Brndon sks, Is it enough to know tht it hd n m x stte or do we hve to know whih one in order for the m z informtion to e lost? () It is not enough. If it is possile, in priniple, to determine whih wy informtion then then the tom ts s if it is in the m x = +m B stte or in the m x = m B stte. () It is not enough. We need to tully mesure the m x stte. () It is enough. The tom pssed through the field in the x diretion nd so is hnged.

7 (38) Curren sks, Why ould the proility hnge if we re looking t it or not? () Beuse we hnge the system when we lern the result of n experiment. () It doesn t. The proility only depends on wht goes on in the experiment. 7

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