Everything comes unglued

Transcription

1 Blackbody Radiation Potoelectric Effect Wave-Particle Duality SPH4U Everyting comes unglued Te predictions of classical pysics (Newton s laws and Maxwell s equations) are sometimes completely, utterly WRONG. classical pysics says tat an atom s electrons sould fall into te nucleus and STAY THERE. No cemistry, no biology can appen. classical pysics says tat toaster coils radiate an infinite amount of energy: radio waves, visible ligt, X-rays, gamma rays, Te source of te problem It s not possible, even in teory to know everyting about a pysical system. knowing te approximate position of a particle corrupts our ability to know its precise velocity ( Heisenberg uncertainty principle ) Particles exibit wave-like properties. interference effects! Te scale of te problem Let s say we know an object s position to an accuracy Dx. How muc does tis mess up our ability to know its speed? Here s te connection between Dx and Dv (Dp = mdv): DpDx 4 Tat s te Heisenberg uncertainty principle J s It is pysically impossible to predict simultaneously te exact position and exact momentum of a particle. 1

2 Atomic scale effects Small Dx means large Dv since Dv 4mDx Example: an electron (m = kg) in an atom is confined to a region of size x ~ m. How is te minimum uncertainty in its velocity? Plug in, using = to find v > m/sec Example Te speed of an electron (m = kg) is measured to ave a value of 5 x 10 3 m/s to an accuracy of percent. Determine te uncertainty in determining its position. p mv 31 3 m kg s 7 kg m s Dp p 7 kg m s 31 kg m s DxDp Js Dx 4Dp 31 kg m s m 0.385mm Example Te speed of an bullet (m = 0.00 kg) is measured to ave a value of 300 m/s to an accuracy of percent. Determine te uncertainty in determining its position. p mv m 0.00kg 300 s kg m 6 DxDp s 4 34 Dp p Js Dx 4Dp 4 kg m kg m s s m 4 kg m s Example A proton as a mass of 1.67 x 10-7 kg and is close to motionless as possible. Wat minimum uncertainty in its momentum and in its kinetic energy must it ave if it is confined to a region : (a) 1.0 mm (b) An atom lengt 5.0 x m (c) About te nucleus of lengt 5.0 x m

3 Example A proton as a mass of 1.67 x 10-7 kg and is close to motionless as possible. Wat minimum uncertainty in its momentum and in its kinetic energy must it ave if it is confined to a region : (a) 1.0 mm DxDp 4 3 s J Dp 3 4Dx m kg m s 1 KE mv DpmDv Js Dv 4 mdx kg m m s m kg 10 s J Example A proton as a mass of 1.67 x 10-7 kg and is close to motionless as possible. Wat minimum uncertainty in its momentum and in its kinetic energy must it ave if it is confined to a region : (b) An atom lengt 5.0 x m DxDp Js Dp 10 4Dx m kg m s 1 KE mv DpmDv Js 34 kg 0 m 7 10 Dv 4 mdx m 63. s kg J m s Example A proton as a mass of 1.67 x 10-7 kg and is close to motionless as possible. Wat minimum uncertainty in its momentum Notice and in tat its wen kinetic we energy consider must a it particle ave if it is confined to (say a region a proton), : tat is confined to a small (c) About region, te nucleus te Quantum of lengt Mecanics 5.0 x m requires tat suc a particle cannot ave a precise DxDp momentum (or even Dpmomentum mdv of zero) Tis means 34 tat even at absolute Js zero, 6.63tis 10 Js Dv Dp proton must ave kinetic menergy. Dx 4 4Dx m 1. Tis 6710 kg m energy is called te zero point 6 m energy, 0 kg m and 0 tere is no way to avoid tis. s s 1 KE mv m kg s mj Quantum Mecanics! At very small sizes te world is VERY different! Energy can come in discrete packets Everyting is probability; very little is absolutely certain. Particles can seem to be in two places at same time. Looking at someting canges ow it beaves. 3

4 Anoter Consequence of Heisenberg s Uncertainty Principle A quantum particle can never be in a state of rest, as tis would mean we know bot its position and momentum precisely Tus, te carriage will be jiggling around te bottom of te valley forever Blackbody Motivation Te black body is importance in termal radiation teory and practice. Te ideal black body notion is importance in studying termal radiation and electromagnetic radiation transfer in all wavelengt bands. Te black body is used as a standard wit wic te absorption of real bodies is compared. Blackbody Radiation Hot objects glow (toaster coils, ligt bulbs, te sun). As te temperature increases te color sifts from Red to Blue. Te classical pysics prediction was completely wrong! (It said tat an infinite amount of energy sould be radiated by an object at finite temperature.) Definition of a black body A black body is an ideal body wic allows te wole of te incident radiation to pass into itself ( witout reflecting te energy ) and absorbs witin itself tis wole incident radiation. Tis propety is valid for radiation corresponding to all wavelengts and to all angels of incidence. Terefore, te black body is an ideal absorber and emitter of radaition. Te blackbody will ten radiate at a wavelengt tat is related to its absolute temperature. One sould picture a ot oven wit an open door emitting radiation into its cooler surroundings or, if te surroundings are otter, one pictures a cool oven wit an open door taking in radiation from its surroundings. It is te open oven door, wic is meant to look black and ence absorbs all colours or frequencies tat gives rise to te term black body. 4

5 Maxwell s Classical Teory Te Ultraviolet Catastrope Rayleig-Jeans Law Tis formula also ad a problem. Te problem was te term in te denominator. For large wavelengts it fitted te experimental data but it ad major problems at sorter wavelengts. ckt I(, T) 4 Planck Law Blackbody Radiation: First evidence for Q.M. c 1 I(, T) 5 c ekt 1 Max Planck found e could explain tese curves if e assumed tat electromagnetic energy was radiated in discrete cunks, rater tan continuously. Te quanta of electromagnetic energy is called te poton. Energy carried by a single poton is E = f = c/ Planck s constant: = 6.66 X Joule sec Higer temperature: peak intensity at sorter E = nf, n=1,, 3, 4 5

6 Blackbody Radiation: First evidence for Q.M. It was more difficult for atoms to absorb very ig energy potons (sort wave lengts tus ig frequency). E = nf, n=1,, 3, 4 Planck imself matced matematics to te data. He used matematics as a device to obtain te correct answer wic e initially believed was still in classical Newtonian pysics. Questions A series of ligt bulbs are glowing red, yellow, and blue. Wic bulb emits potons wit te most energy? Blue! Lowest wavelengt is igest energy. Red! Te least energy? E = f = c/ Higest wavelengt is lowest energy. Wic is otter? (1) stove burner glowing red () stove burner glowing orange Hotter stove emits iger-energy potons (sorter wavelengt = orange) Colored Ligt Wic coloured bulb s filament is ottest? 1) Red ) Green 3) Blue 4) Same Visible Ligt Coloured bulbs are identical on te inside te glass is tinted to absorb all of te ligt, except te color you see. max Poton A red and green laser are eac rated at.5mw. Wic one produces more potons/second? 1) Red ) Green 3) Same # potons Energy/second second Energy/poton Power Energy/poton Power f Red ligt as less energy/poton so if tey bot ave te same total energy, red as to ave more potons! 6

7 Wein s Law b max T Wein Displacement Law - It tells us as we eat an object up, its color canges from red to orange to wite ot. - You can use tis to calculate te temperature of stars. Te surface temperature of te Sun is 5778 K, tis temperature corresponds to a peak emission = 50 nm = about 5000 Å. Wien s Displacement Law (nice to know) To calculate te peak wavelengt produced at any particular temperature, use Wien s Displacement Law: T peak = 0.898*10 - m K temperature in Kelvin! Te Wave Particle Duality OR Ligt Waves Until about 1900, te classical wave teory of ligt described most observed penomenon. Ligt waves: Caracterized by: Amplitude (A) Frequency (n) Wavelengt () Energy of wave is a A 7

8 Waves or Particles? Pysical Objects: Ball, Car, cow, or point like objects called particles. Tey can be located at a location at a given time. Tey can be at rest, moving or accelerating. Falling Ball Waves or Particles? Common types of waves: Ripples, surf, ocean waves, sound waves, radio waves. Need to see crests and trougs to define tem. Waves are oscillations in space and time. Direction of travel, velocity Up-down oscillations Ground level Wavelengt,frequency, velocity and amplitude defines waves Particles and Waves: Basic difference in beaviour Wen particles collide tey cannot pass troug eac oter! Tey can bounce or tey can satter Waves and Particles Basic difference: Waves can pass troug eac oter! As tey pass troug eac oter tey can enance or cancel eac oter Later tey regain teir original form! 8

9 And ten tere was a problem In te early 0 t century, several effects were observed wic could not be understood using te wave teory of ligt. Two of te more influential observations were: 1) Te Poto-Electric Effect ) Te Compton Effect Potoelectric Effect Electrons are attracted to te (positively carged) nucleus by te electrical force In metals, te outermost electrons are not tigtly bound, and can be easily liberated from te sackles of its atom. It just takes sufficient energy Classically, we increase te energy of an EM wave by increasing te intensity (e.g. brigtness) Energy a A But tis doesn t work?? PotoElectric Effect Nobel Trivia An alternate view is tat ligt is acting like a particle Te ligt particle must ave sufficient energy to free te electron from te atom. Increasing te Intensity is simply increasing te number of ligt particles, but its NOT increasing te energy of eac one! Increasing te Intensity does diddly-squat! For wic work did Einstein receive te Nobel Prize? 1) Special Relativity E = mc ) General Relativity Gravity bends Ligt 3) Potoelectric Effect Potons 4) Einstein didn t receive a Nobel prize. However, if te energy of tese ligt particle is related to teir frequency, tis would explain wy iger frequency ligt can knock te electrons out of teir atoms, but low frequency ligt cannot 9

10 Potoelectric Effect Te Apparatus Ligt sining on a metal can knock electrons out of atoms. Ligt must provide energy to overcome Coulomb attraction of electron to nucleus Wen te emission of potoelectrons from te catode occurs, tey travel across te vacuum tube toward te anode, due to te applied potential. Even wen te variable potential is dropped to zero, te current does not drop to zero, because te kinetic energy of te electrons is still adequate enoug to allow some to cross te gas (tus creating a current). If we make te variable source of electrical potential negative ten tis as te effect of reducing te electron flow. If te anode is made more negative, relative to te catode, a potential difference, te cutoff potential, V 0, is reaced wen te electrons are all turned back. Te cutoff potential corresponds to te maximum kinetic energy of te potoelectrons. Tey do not ave te KE to make it across te gap. Classical pysics prediction Electrons can be emitted regardless of te incident frequency, toug it will take longer time for smaller incident wave amplitude. Tere sould be a time delay between te wave illumination and te emission of electrons. Modern pysics explanation Te electromagnetic wave consists of many lumped energy particles called potons. Te energy of eac individual poton is given by te Joule Te iger te wave intensity, te iger electron energy, and tus te iger te stopping voltage. 1 f E f 10

11 Modern pysics explanation If N is te total number of potons incident during time interval T, ten te total incident optical energy in Joules is: E Nf Te incident energy per second (power) is given by: N P f Watt = J/Sec. T Modern pysics explanation Interaction (absorption / emission) between te electromagnetic wave and matter occurs troug anniilation/creation of a quantized energy (poton). In te potoelectric effect, eac single absorbed poton gives its total energy (f) to one single electron. Tis energy is used by te electron to: Overcome te attraction force of te material. Gain kinetic energy wen freed from te material. n=n/t is te number of incident potons per second. Modern pysics explanation Work function (): It is te minimum required energy required by an electron to be free from te attraction force of te metal ions. Some of te electrons may need more energy tan te work function to be freed. +ve -ve Zero Total Energy Te most energetic electrons in te material Modern pysics explanation +ve -ve Total Energy Zero f f Te most energetic electrons in te material 11

12 Modern pysics explanation Total Energy f +ve -ve Zero 1 Te most energetic electron outside te material mv max f Modern pysics explanation Te electrons tat need only te work function to be freed, will ave te greatest kinetic energy outside te metal. 1 f mvmax Te electrons requiring iger energy to be freed, will ave lower kinetic energy. Modern pysics explanation Tus, tere is a minimum required poton energy (f o ) to overcome te work function of te material (note f 0 is called te cutoff frequency). f o If te incident poton energy is less tan te work function, te electron will not be freed from te surface, and no potoelectric effect will be observed. If f< = If f< f o No potoelectric current Modern pysics explanation Te most energetic electrons are stopped by te reverse biased stopping potential V o. K f max 1 mv max evo 1

13 Modern pysics explanation 1 f mv max f ev o f o ev f o f o Vo f f e o Slope = /e Te stopping potential doesn t depend on te incident ligt intensity. Te stopping potential depends on te incident frequency. Potoelectric Equation Since te cutoff potential is related to te maximum kinetic energy wit wic te potoelectrons are emitted: for a potoelectron of carge e and kinetic energy E k, and retarding potential V 0. Ten we ave (loss is KE = gain in PE) : E k =ev 0. E poton (f)=φ+e k (Φ, te work function, is energy wit wic te electron is bound to te surface, E k is te kinetic energy of te ejected potoelectron) E k =f-φ : Tis tells us tat if f is small suc tat f=φ, no electrons will be ejected. Tresold Frequency Potoelectrons are emitted from te potoelectric surface wen te incident ligt is above a certain frequency f 0, called te tresold frequency. Above te tresold frequency, te more intense te ligt, te greater te current of potoelectrons Tresold frequency Te intensity (brigtness) of te ligt as no effect on te tresold frequency. No matter ow intense te incident ligt, if it is below te tresold frequency, not a single potoelectron is emitted. 13

14 Potoelectric Effect Summary Eac metal as Work Function (Φ) wic is te minimum energy needed to free electron from atom. Ligt comes in packets called Potons E = f =6.66 X Joule sec Maximum kinetic energy of released electrons K.E. = f Φ Potoelectrons are emitted from te potoelectric surface wen te incident ligt is above a certain frequency f 0, called te tresold frequency. Potoelectric Effect (Summary) Classical Metod Increase energy by increasing amplitude electrons emitted? No No No No Wat if we try tis? Vary wavelengt, fixed amplitude electrons emitted? No electrons were emitted until te frequency of te ligt Anoter exceeded a critical frequency, at wic point electrons were emitted symbol from for te surface! (Recall: small large n) frequency No Yes, wit low KE Yes, wit ig KE Poto-Electric Effect (Summary) In tis quantum-mecanical picture, te energy of te ligt particle (poton) must overcome te binding energy (work function, Φ) of te electron to te nucleus. If te energy of te poton does exceed te binding energy, te electron is emitted wit a KE = E poton E binding. Te energy of te poton is given by E=n, were te constant = 6.6x10-34 [J s] is Planck s constant. Summary If ligt is under your control: You can set te frequency (wavelengt, colour) and intensity. Your apparatus can count any ejected electrons. You create a iger potential relative to te metal plate, ten te ejected electrons will be pulled into te collector and forced into te ammeter circuit. If you are interested in te energy of te ejected electrons, you would make te potential of te collector for and more negative wit respect to te surface and eventually you will reac a voltage level were te ejected electrons can no longer reac te collector. Tis potential is called te Stopping potential, V o. Te maximum kinetic energy of te ejected electrons will ten be: KEelectron qv 0 Ligt particle By te definition of te ev, te Stopping Potential expressed in volts will ave te same numerical value as te electron energy expressed in ev. Tat is a Stopping Potential of.7 V implies a maximum electron energy of.7 ev Before Collision After Collision 14

15 Summary How does tis explain te potoelectric effect? For our metal wit.7 ev work function, ten a single poton would need an energy of.7 ev to eject an electron. If you used red ligt (650 nm), ten te potons in te beam would ave energy c Epoton f eV eV=1.60x10-19 J Tese potons will be absorbed, but tey do not ave enoug energy to eject electrons. Often te potoelectric equation is illustrated on a grap of KE vs frequency. On tis grap, te slope ALWAYS equals Planck's constant, 6.63 x J sec. It NEVER canges. All lines on tis type of grap will be parallel, only differing in teir y-axis intercept (-f) and teir x-axis intercept (te tresold frequency). Te tresold frequency is te lowest frequency, or longest wavelengt, tat permits potoelectrons to be ejected from te surface. At tis frequency te potoelectrons ave no extra KE (KE = 0) resulting in 0 = f Φ f =Φ E poton =Φ Energy (ev) f o (material 1) Φ (material 1) Curve for material 1 Slope= Planck s constant, f o (material ) Curve for material Frequency (Hz) Φ (material ) Note tat red ligt as suc a low frequency (energy) tat it will never eject potoelectrons - tat is, te energy of a red poton is less tan te work function of te metal. Review Question Wat appens to te rate electrons are emitted wen increase te brigtness? more potons/sec so more electrons are emitted. Rate goes up. Te If Te suitable negative Minimum ligt potential is amount allowed of of te to energy fall plate on wic 'C' plate wic is 'P', necessary it will te give poto out start electric poto poto current electrons electric becomes as emission sown in zero is te called is figure. called Work Te Stopping Function. poto Potential electrons If te amount or are cut-off attracted potential. energy by te of Stopping incident collector radiation potential 'C' connected is is less tat to tan value te te Tresold +ve of work retarding terminal function frequency potential of of a battery. metal, is difference defined no Te poto glass between te electrons tube minimum is two evacuated. are plates frequency emitted. wic Wen of is incident just te sufficient collector ligt wic to 'C' alt is kept can te cause at most It +ve is energetic poto denoted potential, electric by poto te Φ. emission poto Work electrons function electrons i.e. emitted. tis of are frequency a material attracted is just by given it able and by to a Φ=f current eject 0. electrons flows in wit te out circuit It It is giving is denoted a wic property tem by is additional indicated "Vo" of material. by energy. te Different galvanometer. It is denoted materials by ave f 0. different values of work function. Wat appens to max kinetic energy wen increase brigtness? no cange: eac poton carries te same energy as long as we don t cange te color of te ligt 15

16 Potoelectric Effect: Ligt Frequency Wat appens to rate electrons are emitted wen increase te frequency of te ligt? as long te number of potons/sec doesn t cange, te rate won t cange. Question Wic drawing of te atom is more correct? Wat appens to max kinetic energy wen increase te frequency of te ligt? eac poton carries more energy, so eac electron receives more energy. Tis is a drawing of an electron s p-orbital probability distribution. At wic location is te electron most likely to exist? 1 3 Question You observe tat for a certain metal surface illuminated wit decreasing wavelengts of ligt, electrons are first ejected wen te ligt as a wavelengt of 550 nm. a) Determine te work function for te material. b) Determine te Tresold Potential wen ligt of wavelengt 400 nm is incident on te surface Question You observe tat for a certain metal surface illuminated wit decreasing wavelengts of ligt, electrons are first ejected wen te ligt as a wavelengt of 550 nm. a) Determine te work function for te material. c 34 8 m J s310 s m J.5eV It is quicker is we use c=140ev nm c 140eV nm 550nm.5eV 16

17 Question You observe tat for a certain metal surface illuminated wit decreasing wavelengts of ligt, electrons are first ejected wen te ligt as a wavelengt of 550 nm. b) Determine te Tresold Potential wen ligt of wavelengt 400 nm is incident on te surface KE E potons c 140eV nm.5ev 400nm 0.85eV Question Suppose you find tat te electric potential needed to sut down a potoelectric current is 3 volts. Wat is te maximum kinetic energy of te potoelectrons. Te given potential is te stopping potential V 0 U qvo C3V J 3eV Tis is te maximum kinetic energy of te potoelectron Question If te work function of te material is known to be ev, wat is te cut-off frequency of te potons for tis material. Te cutt-off frequency is te frequency above wic electrons can be freed from te material. Tat is, te frequency of radiation wose energy is equal to te work function So is ligt a wave or a particle? E f c fc ev ev s Hz or E f c fc J Js Hz On macroscopic scales, we can treat a large number of potons as a wave. Wen dealing wit subatomic penomenon, we are often dealing wit a single poton, or a few. In tis case, you cannot use te wave description of ligt. It doesn t work! 17

18 Is Ligt a Wave or a Particle? Wave Electric and Magnetic fields act like waves Superposition, Interference and Diffraction Particle Potons Collision wit electrons in poto-electric effect Bot Particle and Wave! Are Electrons Particles or Waves? Particles, definitely particles. You can see tem. You can bounce tings off tem. You can put tem on an electroscope. How would know if electron was a wave? Look for interference! Young s Double Slit w/ electron Electrons are Waves? Source of monoenergetic electrons d slitsseparated by d L Screen a distance L from slits Electrons produce interference pattern just like ligt waves. Need electrons to go troug bot slits. Wat if we send 1 electron at a time? Does a single electron go troug bot slits? 18

19 Electrons are Particles If we sine a brigt ligt, we can see wic ole te electron goes troug. (1) Bot Slits () Only 1 Slit Electrons are Particles and Waves! Depending on te experiment electron can beave like wave (interference) particle (localized mass and carge) If we don t look, electron goes troug bot slits. If we do look it cooses 1. But now te interference is gone! Electrons are Particles and Waves! Depending on te experiment electron can beave like wave (interference) particle (localized mass and carge) If we don t look, electron goes troug bot slits. If we do look it cooses 1. I m not kidding it s true! Scroedinger s Cat Place cat in box wit some poison. If we don t look at te cat it will be bot dead and alive! Poison Here Kitty, Kitty! 19

20 Momentum of a Poton Compton found tat te conservation of momentum did old for X-ray scattering collisions at an angle (Compton effect) p mv E p v c E c f c f f Te Compton Effect In 194, A. H. Compton performed an experiment were X-rays impinged on matter, and e measured te scattered radiation. Incident X-ray wavelengt M A T T E R 1 Scattered X-ray wavelengt > 1 e Louis de Broglie Electron comes flying out Problem: According to te wave picture of ligt, te incident X-ray gives up energy to te electron, and emerges wit a lower energy (ie., te amplitude is lower), but must ave 1. Quantum Picture to te Rescue If we treat te X-ray as a particle wit zero mass, and momentum p = E / c, everyting works! Incident X-ray p 1 = / 1 Electron initially at rest e e p e Scattered X-ray p = / > 1 Compton found tat if te poton was treated like a particle wit mometum p=e/c, e could fully account for te energy & momentum (direction also) of te scattered electron and poton! Just as if billiard balls colliding! Compton Scattering (nice to know) Compton assumed te potons acted like oter particles in collisions Energy and momentum were conserved Te sift in wavelengt is D o (1 cos ) mc Compton wavelengt e 0

21 DeBroglie s Relation p = / Te smaller te wavelengt te larger te poton s momentum! Te energy of a poton is simply related to te momentum by: E = pc (or, p = E / c ) Te wavelengt is related to te momentum by: = /p Te poton as momentum, and its momentum is given by simply p = /. Quantum Summary Particles act as waves and waves act as particles Pysics is NOT deterministic Observations affect te experiment Paradox 1 (non-locality): Einstein s Bubble Four Quantum Paradoxes Situation: A poton is emitted from an isotropic source. 1

22 Paradox 1 (non-locality): Einstein s Bubble Situation: A poton is emitted from an isotropic source. Its sperical wave function Y expands like an inflating bubble. Paradox 1 (non-locality): Einstein s Bubble Situation: A poton is emitted from an isotropic source. Its sperical wave function Y expands like an inflating bubble. Question (Albert Einstein): If a poton is detected at Detector A, ow does te poton s wave function Y at te location of Detectors B & C know tat it sould vanis? Paradox 1 (non-locality): Einstein s Bubble It is as if one trows a beer bottle into Lake Ontario. It disappears, and its quantum ripples spread all over te Atlantic. Ten in Copenagen, te beer bottle suddenly jumps onto te dock, and te ripples disappear everywere else. Tat s wat quantum mecanics says appens to electrons and potons wen tey move from place to place. Paradox (Y collapse): Scrödinger s Cat Experiment: A cat is placed in a sealed box containing a device tat as a 50% cance of killing te cat. Question 1: Wat is te wave function of te cat just before te box is opened? Wen does te wave function collapse? 1 1 ( Y dead + alive?) Question : If we observe Scrödinger, wat is is wave function during te experiment? Wen does it collapse? Te question is, wen and ow does te wave function collapse. Wat event collapses it? How does te collapse spread to remote locations?

23 Paradox 3 (wave vs. particle): Weeler s Delayed Coice A source emits one poton. Its wave function passes troug slits 1 and, making interference beyond te slits. Te observer can coose to eiter: (a) measure te interference pattern at * * plane s 1, requiring tat te poton travels troug bot slits. or (b) measure at plane s wic slit image it appears in, indicating tat it as passed only troug slit. Te observer waits until after te poton as passed te slits to decide wic measurement to do. Paradox 3 (wave vs. particle): Weeler s Delayed Coice Tus, te poton does not decide if it is a particle or a wave until after it passes te slits, even toug a particle must pass troug only one slit and a wave must pass troug bot slits. Apparently te measurement coice determines weter te poton is a particle or a wave retroactively! Paradox 4 (non-locality): EPR Experiments Malus and Furry An EPR (einstein Poldalsky Rosen) Experiment measures te correlated polarizations of a pair of entangled potons, obeying Malus Law [P( rel ) = Cos rel ] Paradox 4 (non-locality): EPR Experiments Malus and Furry An EPR Experiment measures te correlated polarizations of a pair of entangled potons, obeying Malus Law [P( rel ) = Cos rel ] Te measurement gives te same result as if bot filters were in te same arm. 3

24 Paradox 4 (non-locality): EPR Experiments Malus and Furry An EPR Experiment measures te correlated polarizations of a pair of entangled potons, obeying Malus Law [P( rel ) = Cos rel ] Te measurement gives te same result as if bot filters were in te same arm. Furry proposed to place bot potons in te same random polarization state. Tis gives a different and weaker correlation. Paradox 4 (non-locality): EPR Experiments Malus and Furry Apparently, te measurement on te rigt side of te apparatus causes (in some sense of te word cause) te poton on te left side to be in te same quantum mecanical state, and tis does not appen until well after tey ave left te source. Tis EPR influence across space time works even if te measurements are ligt years apart. Could tat be used for FTL signaling? Sorry, SF fans, te answer is No! Four Interpretations of Quantum Mecanics Te Collapse Interpretation Scientists wo subscribe to te Collapse interpretation make a coice. Tey believe tat wen you accept te electron s wave nature, you must give up on te electron s particle nature. In tis interpretation, te electron leaves te source as a particle tat is governed by one set of laws, but ten expands into a spread-out wave as it passes troug te slits. Te electron is now governed by new laws. However, before we can measure tis wavy, spread-out quantum electron it collapses back into a particle and arrives at only one of te many possible places on te screen. Te consequence of coosing te Collapse interpretation line of tinking is tat you must accept tat an electron pysically canges from particle to wave and back again. Tese two realities, including te laws tat describe tem, alternate uncontrollably 4

25 Te Pilot Wave Interpretation Te Pilot Wave interpretation avoids tis unexplained collapse altogeter. Scientists wo subscribe to tis interpretation coose to believe tat te electron always exists as a classical particle and is only ever governed by one kind of pysical law, for bot te familiar classical as well as quantum penomena. However, to account for te electron s wave beaviour tis description requires te introduction of an invisible guiding wave. In tis interpretation, wave-particle duality is explained by assuming tat electrons are real particles all of te time, and are guided by an invisible wave. Te electron s wave nature is attributed to tis abstract wave, called a Pilot Wave, wic tells te electron ow to move. To obtain te interference pattern in te double-slit experiment, tis wave must be everywere and know about everyting in te universe, including wat conditions will exist in te future. For example, it knows if one or two slits are open, or if a detector is iding beind te slits. Te Pilot Wave interpretation embodies all of te quantum beaviour, including all te interactions between classical objects like te electron, te two-slit barrier, and te measuring devices. In contrast to te Collapse interpretation were te collapsing electron wave was considered real, in te Pilot Wave interpretation te wave is an abstract matematical tool. Tis interpretation as a consequence. Te Pilot Wave interpretation, wic was invented to deal wit an electron as a real pysical object, suffers te fate of being permanently beyond detection Te Many-Worlds Interpretation Supporters of te Many Worlds interpretation, similar to te Pilot Wave idea, coose to accept tat electrons are classical particles. Ten tey go even furter, demanding tat all elements of te teory must correspond to real objects unlike te collapsing electron or te Pilot Wave. Supporters insist on only measurable, pysical objects witin te world. Tis world is constantly splitting into many copies of itself. Wen electrons demonstrate wave beaviour tey exist in a superposition of many different states. To Many Worlds supporters, wo maintain te idea of an electron as a classical particle, a parallel universe must exist for eac of te electron s possible states. Wen te electron reaces te slits, it as to coose wic slit to go troug. At tat moment, te entire universe splits into two. In one universe, te electron passes troug te left slit as a real particle. In te oter universe it passes troug te rigt slit as a real particle. Te consequence of accepting te Many Worlds interpretation, wit many quantum particles constantly facing similar coices, is te requirement tat our universe must be constantly splitting into an almost infinite number of parallel universes, eac aving its own copy of every one of us Te Copenagen Interpretation Advocates of te Copenagen interpretation coose to limit teir discussion directly to te experiment and to te measurements on pysical objects. Questions are restricted to wat can be seen and to wat we actually do. Tey try to tink about experiments in a very onest way, witout invoking extra teoretical ideas like te on-off switcing of te Collapse idea, or te guidance supplied by te invisible Pilot Wave, or te proposed splitting into Many Worlds. Let s Compare It is tempting to come up wit mental pictures about wat is appening tat go beyond te results of an experiment, and to try to interpret wat is appening by means of tose idden teoretical mecanisms. Te previous interpretations attributed te mysterious wave particle duality to imaginative matematics. In te Copenagen interpretation muc of tis mystery is attributed to wat appens wen an experimenter enters te lab and interacts wit te quantum mecanical system. Wit te Copenagen perspective, te matematics only deals wit te experimenter s information about measurement interactions wit te quantum mecanical system. Te consequence of accepting te Copenagen interpretation is a fundamental restriction on ow muc you can read into experimental results. We know tat electrons are particles wen tey are fired from te source, and we know tat tey are particles wen tey it te screen. Wat appens to electrons in te middle, wat tey are doing, or wat tey really are is not possible to know. In te Copenagen interpretation tese are unfounded questions. We may call an electron a wave or a particle, but ultimately tose names are no more tan suitable models. 5