Why is a E&M nature of light not sufficient to explain experiments?

Transcription

1 1 Th wird world of photons Why is a E&M natur of light not sufficint to xplain xprimnts? Do photons xist? Som quantum proprtis of photons

2 2 Black body radiation Stfan s law: Enrgy/ ara/ tim = Win s displacmnt law: R T R T ( ) / T ( ) 3 only dpnds on T=5500 K T=5000 K T=4500 K T4000 K J RT ( ) d = T σ, σ = K m s 0 4 RT ( ) d = T f ( T ) d( T ), f ( T ) d( T ) = 0 / T=6000 K T visibl σ 0 THz 430 THz 750 THz 700 nm 400 nm 1000 THz

3 3 Drivation of black body radiation Th first quantum proprty discussd was that of light by Max Plank (1900). By proposing light quanta h drivd th function Drivation: 1. Rprsnt th black body as a black body box. 2. In ordr to find what radiation scaps from th hol, comput th nrgy in th box in th frquncy intrval from to +d. 3. Driv th numbr of radiation mods for this intrval in th black body box: 4. Us th fact from statistical mchanics that for a tmpratur T, th probability for systm to hav nrgy E is givn by xp(-e/kt). 5a. Initially: Each radiation mod can hav arbitrary intnsity 5b. Plank: Assum th ach mod can only hav an nrgy that is a multipl of som dpndnt quantum ε(). 6. Comput th avrag nrgy pr mod and sum ovr all mods. f ( T ) dz = g( ) d Win s displacmnt law and Stfan s law R c 3 2π h ( / T ) T ( ) = 4 u = T 2 xp( h c ) 1 k T 3

4 4 Intrprtation A lctromagntic wav with frquncy contains light quanta (photons) with th nrgy h. Th nrgy of th wav dtrmins th numbr of such photons that mak up th wav. 01/28/2005 For small, th wav can hav narly all nrgis nh and on obtains th classical limit R T ( ) T=6000 K visibl max = THz K T 0 THz 430 THz 750 THz 700 nm 400 nm 1.8 V 3.1 V 1000 THz

5 5 Furthr vidnc for photons 01/31/2005 Th photolctric ffct: 1) Th maximum lctron nrgy dpnds only on and incrass linarly with : E max = h - W (Millikan 1916) 2) Thr is a minimum indpndnt of intnsity. It is th Work function W dividd by h. K max = h( ) 0 3) Th first mission happns fastr than a wav would dposit nrgy (Lawrnc and Bams 1928) 4) Diffrnt mtals lad to th sam valu for h

6 6 Furthr vidnc for photons 01/31/2005 Brmsstrahlung Th maximum mittd frquncy dpnds only on th lctron nrgy, not on th -bam intnsity. Highst frquncy is linar in lctron nrgy. Typical lctron nrgis ar kv, and th work function of a fw V can thrfor b nglctd. (Duan and Hunt 1915) max = K h Th Compton ffct: Scattring of light with fr lctrons follows th formulas of classical scattring of fr particls whn on assums an nrgy E=h and momntum p=e/c=h/λ for th photons. (Compton )

7 7 Stimulatd mission for balck-body radiation u(ω) Einstin s xplanation from 1917 for th nrgy dnsity in a black body box. Th light in a black body is mittd by lctrons that chang thir nrgy lvl: N j B ji u(ω) Spontanous mission 02/04/2005 Lvl j Absorption N i j = N B i ij u(ω) Stimulatd mission N j A ji Lvl i Equilibrium: Ni j = N j i NiBiju( ω) = N j[ Aji + B jiu( ω)] u( ω) = Thrmodynamic population of lctron nrgy stats: N i = C Ei kt, N j = C E j kt N N i j = E j E kt i = ω kt B B ij ji A ji N N i / B j ji 1 To obtain Plank s black-body radiation formula: u( ω) Probability for stimulatd mission = probability of absorbtion, Probability of spontanous mission incrass with ω 3 : ω kt ω 3 1 B ij = B ji 3 A ji / B ji ω

8 8 Formation of optical imags At low xposur, th fw photons that lad to a raction in a photographic plat ar statistically distributd. Hits of individual photons can b obsrvd. With incrasing xposur, th intrfrncs of lctromagntic wavs that rfract in th lns of th camra and form th imag bcom apparnt. Th imag formd by many photons forms corrsponds to th imag formd by intrfring lctromagntic wavs.

9 9 Non-particl lik proprtis of photons Photons mov into shadowd rgions by diffraction On cannot associat a fild vctor to an individual photon. Wav proprtis of light can only b found whn vry larg numbrs of photons ar invstigatd. Particl wav duality: Wav proprtis ar an xprssion of th probabilistic or statistical bhavior of larg numbrs of idntically prpard quantum particls. Intrfrnc frings

10 10 Wav function and probability amplitud Particl wav duality: Wav proprtis ar an xprssion of th probabilistic or statistical bhavior of larg numbrs of idntically prpard quantum particls. Th paths of a photon: Information about th photon must hav travld through both slots. Othrwis th intnsity distribution du to th two opnings would b addd.

11 11 Photons and quantum stats A lctromagntic plain wav can b uniquly dfind by spcifying four things: 1. Frquncy 2. Dirction of propagation 3. Polarization 4. Amplitud of th lctric fild (and thrby th nrgy in th fild) Similarly th stat of a photon is uniquly dfind by spcifying thr things: 1. Frquncy (and thrfor th nrgy of th photon h) 2. Dirction of motion 3. Polarization stat Th nrgy in th wav is thn dtrmind by th numbr of photons. Th stat of a photon compltly dtrmins a photon in th following sns: Evrything that can b known about a photon is spcifid.

12 12 Probability or hiddn variabls Hiddn variabls: To avoid th introduction of probability into th propagation of compltly dtrmind particls, som popl hav trid to introduc hiddn variabls, that distinguish th photons that bhav diffrntly at th scrn. This would not b satisfying, sinc th wav is compltly dtrmind bfor th slids and th photons should thrfor all b qually dtrmind. It has bn shown that this approach cannot work.

13 13 Not on th xistnc of photons K = h ) max ( 0

14 14 Altrnat xplanation of th photolctric ffct

15 15 Exprimntal vrification of photons Ψ = A + A A3 +

16 16 Photons and wavs What is lft: Th probability intrprtation of quantum mchanics.

17 17 Th uncrtainty of birth Lasr 1 Lasr 2 Light from two lasrs can intrfr, vn whn light is mrging with vry low intnsity: Th photon wav function intrfrs as if th photon could hav bn born in ithr lasr. Thr is quantum uncrtainty of th birth plac of th photon. Ψ born at 1 + born at 2