Today. Wave-Matter Duality. Quantum Non-Locality. What is waving for matter waves?

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1 Today Wav-Mattr Duality HW 7 and Exam 2 du Thurs. 8pm 0 min rcap from last lctur on QM Finish QM odds and nds from ch.4 Th Standard Modl 4 forcs of Natur Fundamntal particls of Natur Fynman diagrams EM wavs ar wavs in EM filds EM wavs intrfr EM wavs ar quantizd E fild = 0,hf, 2hf, 3hf, quanta ar photons E photon = hf Mattr wavs ar wavs in mattr filds Mattr wavs intrfr Mattr wavs ar quantizd E fild = 0, mc 2, 2mc 2, quanta ar th particls (.g., lctrons) ISP209s9 Lctur 8 -- Quantum non-locality Quantum non-locality ISP209s9 Lctur 8-2- Quantum Non-Locality What is waving for mattr wavs? Einstin was troubld! Spooky action at a distanc Probability all particls dscribd by a wav function!. Th squar of! givs th probability dnsity of finding a particl pr unit volum. Th! xtnds ovr all spac, which givs wird consquncs. Sprad out EM fild instantanously knows it has lost hf of nrgy whn th photon impacts th scrn at a distant point. = prob. of finding particl in a small volum V cntrd at th point r. ISP209s9 Lctur 8-3- ISP209s9 Lctur 8-4-

2 Obsrvation can altr th outcom in QM Elctrons show an intrfrnc pattrn in th doubl slit xprimnt. Now try to watch which path th - took A watchd lctron dosn t show intrfrnc! If you try to find out Which slit th lctron Gos thru, th wav faturs Go away An lctron Dtctor ISP209s9 Lctur 8-5- Many mor wird xampls ISP209s9 Lctur 8-6- Quantum Tunnling Classically: A low nrgy particl dos not Escap th box. It is always insid. Quantum Thory: Th! function xtnds ovr all spac, vn outsid th box. Thr Is a finit probability th particl will tunnl thru th box and found outsid. Quantization of Enrgy Lvls in Atoms Elctrons in atoms can only assum discrt, quantizd valus of Enrgy. 2nd xcitd stat st xcitd stat Particl bouncing around in a box This is why som nucli can radioactivly dcay. Ground stat ISP209s9 Lctur 8-7- ISP209s9 Lctur 8-8-

3 E 2 E Lasrs Etc Say you hav many idntical atoms that ar all in th xcitd stat. You can st off a chain raction whr many of thm d-xcit togthr, and th mittd photons stimulat th d-xcitation in th othr atoms that rlass still mor photons. Light Amplifid Stimulatd Emission ISP209s9 Lctur 8-9- Bosons and Frmions Particls com in two typs Bosons hav th proprty that thy can ovrlap. Exampls ar photons and crtain atoms (hlium). Thy ar social. Frmions can not xist in th sam stat. Thy ar anti-social. Exampls lctrons, protons. Th frmion natur of lctrons xplains atomic structur (priodic tabl and all that) ISP209s9 Lctur 8-0- Hisnbrg s Uncrtainty Principl Uncrtainty dpnds on mass Uncrtainty Principl: It is not possibl to know xactly th position and momntum of a particl at th sam tim. vlocity lctron basball, highly xaggratd (by 0 25 ) Thr is no absolut knowldg. Th Nwtonian viw of th world (if vrything wr known, vrything could b prdictd) in not attainabl. proton position ISP209s9 Lctur 8 -- ISP209s9 Lctur 8-2-

4 Sampl Problm Thr ar two vrsions h h # x # p " # E # t " 4! 4! If th position of a proton, mass.67e-27 kg, is known to E-9 m th momntum and vlocity could hav a rang of $ 34 h 6.625! 0 Js $ 26 " p # = = 5.27! 0 kg! m $ 9 4 %" x 4%.00! 0 m s # 26 " p = m" v = 5.27! 0 kg! m s # ! 0 kg! m " v = s = 3.6 m # 27.67! 0 kg s ISP209s9 Lctur Intraction Quantum Nonlocality Aftr intraction th wav functions ar ntangld. If w masur and 2 at th sam tim th diffrnc in position forms an intrfrnc pattrn. If w masur 2 bfor, th masurmnt of 2 dfins whr must hit. This information travls fastr than th spd of light. This has bn confirmd xprimntally. ISP209s9 Lctur 8-4- From larg to small Thr ar two mor forcs in natur Strong Forc Atoms Atomic Nuclus A proton (uud) Strong forc A forc that xists btwn quarks, which hav a proprty calld color charg. Th carrir of th forc is th gluon (th gluon also has color charg) No isolatd quarks ar found in natur Th forc btwn protons-proton, protons-nutrons, and nutronsnutrons is th rsult of th xchang of pairs of quarks. Pairs of quarks ar calld msons (th pion is th lightst mson) Th Strong forc is rsponsibl for binding atomic nucli. Mad of nucli and lctrons. Siz: 0-9 m Mad of nutrons and proton. Siz 0-4 m Mad of quarks: Siz 0-5 m A nutron has ISP209s9 Lctur 8-5- ddu ISP209s9 Lctur 8-6-

5 Th Wak Forc Wak forc A forc btwn lctrons, nutrinos and protons (or nutrons), du to a proprty of mattr calld wak charg. Th carrir of th forc ar calld wak vctor bosons W+ or W-, Z. Th + or tlls th lctric charg of th boson. This forc allows a nutron to chang into a proton and is rsponsibl for most radioactiv dcays. Wak Potntial Wak Potntial quark distanc Th wak forc falls off fastr than /r 2. quark Rmmbr, th slop givs th magnitud of th fild (forc). DistancHamL Elctric potntial shap - /r ISP209s9 Lctur 8-7- Wak potntial ISP209s9 Lctur 8-8- A big pictur Forcs com about bcaus of som proprty of mattr (charg, mass, wak charg, color charg) Th forc is du to th xchang of forc carrir particls (photon, graviton, vctor boson, gluon) ISP209s9 Lctur 8-9- T. Kondo Th particls of natur Typ " u Quantum Numbrs Charg () - +2/3 d -/3 0 /3 W ISP209s9 Lctur Lpton numbr 0 Baryon numbr 0 0 /3

6 Antiparticls Evry particl has a corrsponding antiparticl. Whn a particl and an anti particl mt thy annihilat giving off nrgy. Th fraction of mass convrtd to nrgy in a mattr anti-mattr annihilation is, that is, all th mass is convrtd to nrgy. A particl and its antiparticl hav opposit valus for all quantum numbrs xcpt spin and mass. Exampl: Th antiparticl of an lctron is a positron. In all othr cass, th nam of th antiparticl is anti- in front of th nam of th particl, such as proton and anti-proton. Antiparticls ar writtn with a lin ovr th top: p vs p (th antiproton) ISP209s9 Lctur 8-2- Antimattr Antimattr (mattr mad of anti-particls) is vry difficult to mak. It can artificially b producd only at larg particl acclrators ( atom smashrs ). Mattr and anti-mattr ar cratd naturally in pairs So far th total amount of antimattr vr producd by humankind is a fw grams, and that almost immdiatly annihilatd with mattr. Th total nrgy in g of anti-mattr is: E=mc 2 = 0.00kg (3E8) 2 =9E4 J = 9E5 GJ nough to run a normal powr plant for day. ISP209s9 Lctur Nutrinos Obsrvatoris for nutrinos Subatomic particls that do not hav charg, but intract via th wak forc. Ths ar vry unusual particls and w still don t know much about thir proprtis. Thy hav a mass, but it is so small w hav not bn abl to masur it. Thy com in thr typs, but th typs mix. Thy account for about 2% of th univrs but intract wakly. On light-yar of lad would hav only a 50% chanc of stopping on. ISP209s9 Lctur Sudbury solar nutrino dtctor ISP209s9 Lctur 8-24-

7 A way to pictur forcs Fynman Diagrams Altrnativ vrsion of th uncrtainty principl Tim and nrgy also also rlatd. # E # t " h 4! # x # p " h 4! g It is possibl for a short tim to gt somthing for nothing. But, it has to b paid back. quark quark On th vry small scal, mpty spac is aliv with fluctuations. Particls can pop into and out of xistnc. ISP209s9 Lctur ISP209s9 Lctur Quantum Chromo Dynamics - QCD Th problm with QCD tim spac Fynman Diagram for th Strong forc Looks lik This is calld an xchang forc. Th probability of an intraction dcrass xponntially with th mass of th xchangs particl. Exponntially mans, twic th mass is 2 =7.3 tims lss Th mor massiv th particl xchangd, th shortr th rang of th forc. ISP209s9 Lctur Gluons thmslvs hav color charg! normal This is also possibl. ISP209s9 Lctur 8-28-

8 Equations sort of A summary of th forcs of natur Ruls for Fynman Diagrams: Forc Strngth Carrir Rang (m) ). Th numbr of lptons and baryons must b consrvd. allowd 2). Charg must b consrvd. Not allowd sinc lpton numbr not consrvd Strong Elctromagntic Wak Gravity / x0-39 Gluon, g, btwn quarks Msons-protons/nutrons photon Vctor Bosons W +, W -, Z 0 Graviton (?) 0-5 siz of a proton infinit 0-8 Only 0.00 width of proton infinit ISP209s9 Lctur ISP209s9 Lctur Back to th wak and lctromagntic forcs proton (udu) W - lctron (udd) " nutron nutrino Transformation of a nutron into a proton by an intraction with a nutrino via th Wak forc. photon Rpulsiv forc btwn two lctrons. In th procss: Enrgy (including mass); momntum, charg, baryon numbr, lpton numbr, ar consrvd. ISP209s9 Lctur 8-3- Quantum Elctrodynamics - QED Th dscription of th forcs on th prvious pag is basd on a thory calld quantum lctrodynamics. Most succssful thory vry dvisd it has at th momnt no known problms and dscribs all lctric, magntic and wak intractions. Strngth of th EM forc:! = thory (56)! = (32) xprimnt Unification of EM and Wak Forcs is calld Elctrowak thory Thory of th strong forc is calld Quantum Chromodynamics ISP209s9 Lctur 8-32-