The Mysteries of Quantum Mechanics

Transcription

1 The Mysteries of Quantum Mechanics Class 4: History and the Quantum Atom Steve Bryson

2 QuesBons?

3 Class Outline 1) IntroducBon: ParBcles vs. Waves 2) Quantum Wave picture, uncertainty 3) ObservaBon and the Quantum Wave 4) History and the Quantum Atom 5) InterpretaBon, Entanglement 6) More Entanglements 7) InterpretaBons Revisited, Quantum Engineering 8) Quantum Everything?

4 What Is Quantum Mechanics? Quantum Mechanics describes the mobon of the smallest things Molecules, Atoms, electrons, It does not ma1er what those small things are

5 The Quantum Mechanical Answer: The Quantum Wave Quantum Mechanics says: A parbcle s behavior is described by a wave This wave is not the waving of physical things we re not sure what it is Where the wave is strong, the parbcle is most likely to be found Where the wave does not wiggle the parbcle will not be found The frequency of the wave is high the parbcle is moving fast, where the frequency is low the parbcle is slow But only if you look for the parbcle Otherwise the wave just keeps waving Quantum mechanics is wri\en enbrely in terms of this wave ParBcles do not appear in the mathemabcs

6 The Wavelike Behavior of Small ParBcles We see both parbcle and wave behavior in the double slit experiment Electron paths Slit These are real pictures of electrons hi^ng a detector over Bme Read about this actual experiment at h\p://

7 Wave Interference Requires two waves that are exactly synchronized

8 The Quantum Wave and the Double Slit The electron double slit experiment starts with an electron source What s really emi\ed by the electron source is electron quantum waves Those waves are what goes through the slits No electron here Electron quantum wave before the slit Electron quantum wave split by the slits Electron may be here

9 Describing Waves The Strength of the wave is how much it changes during one cycle Also called peak- to- peak amplitude The simple wave has the same strength everywhere Only such a simple wave has a well- defined frequency and strength Wavelength Strength

10 Complicated Waves Many waves are more complicated Most likely to be found here Will not be found here Small chance it will be found here This does not have an exact wavelength, and its locabon is approximately determined The parbcle described by this wave has an approximately determined posibon and speed

11 Adding Together Similar Waves What happens if we add two simple waves that differ only a li\le in frequency? + =

12 Visualizing the Components of a Complicated Wave We call the simple waves that add up to create a complicated wave the components of that wave Because the components are simple waves, they only have a frequency and a strength We draw the components with a bar graph Frequency Component view Component 1 Component 2 + Strength of the component Frequency of the component =

13 The Components of a Quantum Wave What does this quantum wave tell us about a parbcle described by this wave? If I look for a posibon the parbcle is more likely to be found where the wave is strong If I look for a speed, half the Bme I will measure one speed, half the Bme the other There are only two components, with the same strength and different frequency likely here not likely here

14 Localized in Space = Uncertain Frequency We get a wave with strength in a small region by adding together many simple waves of almost the same but spread out frequency Components farther from the average are lower strength This example has 100,000 components Wave view likely here Frequency Component view compare not likely here most likely speed less likely speed

15 More Localized in Space = More Uncertain Frequency We get a wave has strength in a smaller region if we add together components with a larger spread in frequency Components farther from the average are lower strength This example also has 100,000 components This is the only way to get wave strength in a smaller region Wave view likely here Frequency Component view compare not likely here maybe going the other way! most likely speed less likely speed (same scale as previous wave view) Much larger spread in frequencies!

16 The Quantum Uncertainty Principle A quantum wave cannot describe a parbcle with an exact posibon and an exact speed exact posibon means very very localized wave exact speed means only one frequency component No wave can have both A quantum wave can have an approximate posibon and speed Depends on the mass of the parbcle An tennis ball s posibon uncertainty of a trillionth of a meter (size of an atomic nucleus) has a speed uncertainty of 85 billion trillionths of a meter/second An electron s posibon uncertainty of 7.4 mm has a speed uncertainty of 7.4 meters/second Also called the Heisenberg Uncertainty Principle

17 The Quantum Rules Revisited If a quantum wave describes a parbcle, here is how to predict what you ll see in a measurement For a posibon measurement: You are most likely to find the parbcle where the wave is strongest, less likely where it is weak, and you will not find it where the wave is not waving For a speed measurement: First, decompose the wave into its component simple waves You will measure the speed determined by the frequency of one of those components, with stronger components being more likely You will only see a speed determined by a component

18 How a Measurement Changes the Quantum Wave Say I do a speed measurement on the parbcle described by this quantum wave So I decompose the wave into its two components Say I find the speed corresponding to the first component In this example I ll get that half the Bme I can say I found that speed exactly because the difference in speeds is smaller than the error in my measurement Now I know the speed of the parbcle If I measure it again I get the same speed So for the quantum wave to be correct, the quantum wave must now equal that first component The other component went away! Speed measurement Speed measurement

19 How a Measurement Changes the Quantum Wave Say I do a posibon measurement on the parbcle described by this quantum wave Much more difficult to do with high precision Say I find some posibon near the center With some small error Will I find it in the same posibon if I measure it again? same means aper accounbng for the mobon it had before the measurement No! A posibon measurement makes its speed uncertain, so it will move unpredictably between measurements So for the quantum wave to be correct just aper the measurement, the quantum wave must at that Bme be very well localized The rest of the wave went away! But now it has many more components But later on the wave is less localized But if I do another posibon measurement I ll localize it again PosiBon measurement No measurement PosiBon measurement

20 Measurement and the Quantum Wave So measurement changes the quantum wave to match the measurement result The type of measurement determines the type of collapse PosiBon: collapse to a well- localized wave Speed: collapse to one of the pre- measurement wave s simple sine wave components According to quantum mechanics, this is a real, physical change Important enough to have a name: Collapse of the quantum wave AKA Collapse of the wave funcbon But quantum mechanics does not explain how this collapse occurs We ll worry about what all this means next week Speed measurement PosiBon measurement

21 The Double Slit With a Detector Now we can understand why detecbng which slit the electron goes through destroys the interference The quantum wave collapses to a wave just at the slit with the detected electron Note: seeing no electron at one slit is the same as detecbng it at the other slit Only one wave means no interference! Detector Electron quantum wave split by the slits

22 What Does the Quantum Wave Do When We re Not Looking? Between observabons, the quantum wave changes according to a wave equa;on In the simplest version of quantum mechanics it s called the Schrödinger equabon It s technical, but given a wave at a specific Bme, the wave equabon tells you exactly what the wave will be at a later Bme So long as there are no observabons The change in the wave is completely determinisbc

23 How the Unmeasured Quantum Wave Evolves It depends on the starbng wave Well localized waves spread out Simple waves stay the same

24 Quantum EvoluBon SimulaBon From h\ps://phet.colorado.edu/en/ simulabon/quantum- tunneling

25 Two Kinds of EvoluBon of the Quantum Wave From the wave equabon When the parbcle is lep alone Completely determinisbc not random ObservaBon Causes instantaneous collapse of the wave to the wave that reflects the observabon Exactly which wave it collapses to is random But with exactly predicted stabsbcs based on the quantum wave before observabon

26 Where Did the Quantum Come From? The idea of the quantum was first suggested by Max Planck in 1901 To explain the behavior of glowing hot things Too technical for this class Planck got the right answer if he assumed that energy comes in li\le chunks Energy of a chunk of light is proporbonal to its frequency (color) But he did not believe this was actually the case: he though the quantum idea was just a mathemabcal trick He called it an act of despair

27 Big Hint that the Quantum is Real In 1905 Albert Einstein uses Planck s quanta to explain strange behavior of light Photoelectric effect, where light knocks electrons out of certain materials The energy of the knocked- out electron depends on the frequency, not brightness, of the light Exactly what Planck s quantum idea predicts Einstein proposes that light should be thought of as li\le parbcles Later called photons Planck s quantum idea is a real thing Very few people agreed at the Bme This is the work that got Einstein the Nobel Prize

28 Light from Atoms By 1900 it was also known that light from some gases (made from pure elements) have strange behavior Each element only emits certain colors The colors are unique to each element The pa\ern of colors seemed to be related to integers

29 Try Your Spectrum

30 The Rutherford Atom In 1911 Ernest Rutherford concludes that most of the mass of an atom is in a very small nucleus Based on observabons by Hans Geiger and Ernest Marsden Surrounded by electrons in orbits Light is emi\ed when an electron falls into a lower orbit The atom you learned in high school This raises several difficult quesbons How to the electrons remain in orbit Circling electrons should lose energy and fall into the atom Only certain colors means only certain orbits Why only certain orbits?

31 The Bohr Atom In 1913 Niels Bohr uses Planck s idea of quanbzed energy to explain the fixed colors of Hydrogen QuanBzed energy means electrons can only be in some orbits and not others Orbits determined by integers: the number of quanta of energy Prevents the electrons from falling into the nucleus But Bohr (and almost everyone else) sbll thinks quanta is probably a mathemabcal trick

32 The 1920s Quantum RevoluBon 1924: Louis de Broglie guesses that ma\er parbcles have wave aspects Inspired by light having both parbcle and wave aspects Confirmed by electron double- slit experiments in : Werner Heisenberg creates first systemabc framework to apply quanbzed energy Using observable quanbbes only: no statement about what is happening at the micro level Applies mainly to atoms, not to free parbcles Uncertainty principle in : Paul Dirac clarifies the relabonship between quantum and classical theory

33 1926: The Schrödinger Quantum Wave Inspired by de Broglie s ideas, Erwin Schrödinger proposes a wave equabon for ma\er quantum waves Completely different from Heisenberg s approach Later Schrödinger showed that his approach, Dirac s and Heisenberg s are mathemabcally equivalent Physicists know how to work with wave equabons, so this was very popular Describes both electrons in atoms and free electrons interacbng with each other Much more difficult with Heisenberg s approach

34 The Probability InterpretaBon of the Quantum Wave Schrödinger hoped that parbcles are really just ma\er waves The electron is a compact wave packet? But Schrödinger s equabon says an isolated electron s wave spreads out! Not a very good model of the electron In 1926, just aper Schrödinger published his wave equabon, Max Born interprets quantum waves in terms of probabilibes Establishes the quantum rules we are learning in this class The wave and the parbcle are disbnct

35 How the Quantum Wave Describes Electrons in Atoms The quanbzed orbits of electrons in atoms comes naturally from the idea of a quantum wave To see how, we start with an electron in a box Atoms are not boxes, but this is easier to think about and includes the most important idea According to the quantum rules, the wave can only wave in the box, not outside the box Wave cannot wave here Wave can wave here Wave cannot wave here

36 What Kind of Wave Waves Only in a Box? Look at only simple waves All other waves can be made from simple waves Wave cannot wave here Wave can wave here Wave cannot wave here The wave has to be zero at the boundary of the box Only mulbple of half- wavelengths are possible Just like a guitar string!

37 The Quantum Wave in a Box So the quantum wave in a box can only have certain, discrete frequencies By the quantum rules, frequency determines the speed of the electron Speed determines energy So the electron in a box can only have discrete energies If it has high energy (frequency), it can lose energy by emi^ng light to fall to a lower energy (frequency) The light s energy will be the difference in the electron s energy before and aper So an electron in a box would emit only specific energies = colors of light If an electron fell from the n=4 to the n=1 frequency, the emi\ed light will have energy E 4 E 1

38 Electrons in Atoms Atoms are not Boxes There are no walls The electron is held in the atom by a force from the nucleus But the quantum wave equabon can be solved for electrons with this force Hydrogen (one proton, one electron) is simplest The resulbng three- dimensional waves are complicated Depends on the energy of the electron But only a discrete set of waves with parbcular energies solve the wave equabon for an electron in an atom Like the electron in a box

39 Light Emi\ed by Atoms The light emi\ed by elements is completely explained by the quantum wave of electrons in atoms The colors exactly match the predicbons of quantum mechanics The Schrödinger equabon gets it almost right, later versions of quantum mechanics get it right to ¼ of one billionth (!!) of the value measured

40 Atom in a Box SimulaBon program for Macintosh/iPhone/ ipad only (atoms are not boxes, the box refers to the computer)

41 Next Week Strange behavior from the quantum wave What is the quantum wave? What does it tell us about reality? The closer we look, the weirder it gets