Lecture 2: Quantum Mechanics & Uncertainty. Today s song: I Know But I Don t Know- Blondie

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1 Lecture 2: Quantum Mechanics & Uncertainty Today s song: I Know But I Don t Know- Blondie 1

2 Practicalities Substantial draft for blog assignment due next Monday. (See rubric for details on grading) Homework pick-up after class Monday reading: Chapter 3 of lecture notes 2

3 In the mechanical worldview, which of the following do you need to making for making accurate predictions? A. An understanding of the laws of Nature B. Mathematical tools to analyse these laws C. A good measurement of the starting conditions D. All of the above E. Only A and C 3

4 In the mechanical worldview, which of the following do you need to making for making accurate predictions? A. An understanding of the laws of Nature B. Mathematical tools to analyse these laws C. A good measurement of the starting conditions D. All of the above E. Only A and C 4

5 Coarse graining... A.... always results in statistical uncertainty B.... always results in systematic uncertainty C.... always results in both statistical and systematic uncertainty D.... can be done without introducing uncertainties, when done carefully E.... can result in a beach vacation 5

6 Coarse graining... A.... always results in statistical uncertainty B.... always results in systematic uncertainty C.... always results in both statistical and systematic uncertainty D.... can be done without introducing uncertainties, when done carefully E.... can result in a beach vacation 6

7 The plan of action Lecture 1: Intro to Quantum Mechanics Lecture 2: Quantum Mechanics & Uncertainty Lecture 3: E=mc 2 & the atomic bomb Workshop: Radioactivity Lecture 4: The Fukushima disaster Lecture 5: Intro to modern Particle Physics 7

8 Last time you learned... 8

9 Waves Frequency = amount of cycles per second (measured in Hz) Wavelength = length over which the wave repeats itself once (measured in meters) What is the wavelength? A. C. B. 9

10 Waves Frequency = amount of cycles per second (measured in Hz) Wavelength = length over which the wave repeats itself once (measured in meters) What is the wavelength? A. C. B. 10

11 Waves Frequency = amount of cycles per second (measured in Hz) Wavelength = length over which the wave repeats itself once (measured in meters) speed = frequency x wavelength Examples: The speed of a wave is constant! (But depends on type of wave and its environment) Wave Sound Light Speed 340 m/s 3 x 10 8 m/s 11

12 If the frequency of a wave is increased to 4 times its original frequency, what happens to its wavelength? speed = frequency x wavelength A. The wavelength becomes 4 times larger B. The wavelength becomes 4 times smaller C. The wavelength stays the same D. The wavelength stays the same, but the speed becomes 4 times larger E. Waves are for surfing only 12

13 If the frequency of a wave is increased to 4 times its original frequency, what happens to its wavelength? speed = frequency x wavelength A. The wavelength becomes 4 times larger B. The wavelength becomes 4 times smaller C. The wavelength stays the same D. The wavelength stays the same, but the speed becomes 4 times larger E. Waves are for surfing only 13

$Diffraction = the bending of$ $Mooo! Diffraction!$

14 Diffraction = the bending of a wave around an obstacle Mooo! Diffraction!?! It pretty much works for any obstacle! 14

15 Constructive Interference Displacement of the individual waves is in the same direction Displacement of both waves combined is larger 15

16 Destructive Interference Displacement of the individual waves is in the opposite direction Displacement of both waves combined is smaller 16

17 Interference on water waves 17

18 Interference! Diffraction! 18

19 different wavelengths 19

20 The double slit experiment with light with electrons constructive interference destructive interference constructive interference destructive interference 20

21 The double slit experiment without detector with detector Wave-like behavior! Particle-like behavior! 21

22 A measurement problem???? The act of observing changes the properties of the electron! 22

Wave-Particle duality and so are electrons, protons, neutrons,... http://www.empiricalzeal.

23 Wave-Particle duality and so are electrons, protons, neutrons,

24 Quantum Mechanics & Uncertainty 24

25 Making predictions Must understand cause and effect 25

26 Projectile Motion Galileo Galilei ( ) 26

27 How to make accurate predictions? We need: 1. An understanding of the relevant laws of Nature 2. A set of appropriate mathematical tools 3. An accurate measurement of the initial conditions 1. Laws of gravity 2. Calculus Isaac Newton ( ) 27

28 Succes with solar system Predict planetary orbits, moon phases, seasons etc 28

29 Mechanism (Determinism) We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes. Pierre Simon Laplace A Philosophical Essay on Probabilities 29

30 Mechanism (Determinism) We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes. Pierre Simon Laplace A Philosophical Essay on Probabilities 30

31 Nice, but still a long shot from predicting THIS! we need a better tool Coarse Graining 31

32 Coarse Graining A number of details are ignored The system is described by a small number of quantities Always results in some loss of information Man made uncertainty! From our inability to Measure stuff to arbitrary precision Calculate stuff to arbitrary precision 32

33 An example Unimportant: Movement of air atoms Atomic structure of the airplane Important: Weight of the aircraft Shape of the aircraft Airflow / wind direction etc 33

34 Last Friday s Asteroid 34

35 Will the asteroid hit the earth? What are all the ingredients for this problem? Which of these are unimportant? What quantities ARE important? What measurements should we make? How to check our assumptions? 35

36 How does a physicist determine the volume of this cow? Mooo! Volume = 4/3 π Radius 3 DONE! 36

37 SCIENCE = KNOWING WHAT TO IGNORE + estimate the error/uncertainty you introduced (you can do so by assigning probabilities, see Module 4) 37

38 Error or uncertainty You did it wrong = The measurement / calculation was not fully precise No measurement / calculation is ever 100% precise! A prediction is USELESS without an estimate of its error / uncertainty! 38

39 Types of uncertainty / error Statistical Uncertainty Systematic Uncertainty / Bias Decreases with sample size or amount of experiments Example: polling 500 people will be less accurate than polling people Results from your coarse graining procedure Cannot be reduced by more experiments, only by a BETTER experiment Example: You only interview people over , which reaches mostly young people 39

40 Intermezzo: It s just a theory... Scientific Term Public Meaning Scientific Meaning Theory hunch, speculation established scientific paradigm Positive/Negative good/bad bigger/smaller than zero Uncertainty Ignorance difference from true number Error mistake, wrong, incorrect difference from true number Bias distortion, political motive offset due to coarse graining Values ethics, monetairy value numbers, quantity Manipulation illicit tampering data processing Scheme devious plot systematic plan 40

41 Recap: What would good old Isaac have said? Nature knows exactly what it wants to do but us humans are just not smart enough to predict stuff without introducing uncertainties! 41

42 Rolling the dice: In principle, can we know the answer in advance? A. No, because it always random B. Yes, but only if we knew exactly under what angle and with what speed you rolled the dice C. Yes, but only if we could calculate the motion of the dice very precisely D. Yes, but only if we had both B and C E. I am heading to Atlantic City right now 42

43 Rolling the dice: In principle, can we know the answer in advance? A. No, because it always random B. Yes, but only if we knew exactly under what angle and with what speed you rolled the dice C. Yes, but only if we could calculate the motion of the dice very precisely D. Yes, but only if we had both B and C E. I am heading to Atlantic City right now 43

44 Now back to the double slit experiment! We could not predict the position of each individual electron but we can get the average pattern right! 44

45 The electrons appear to behave randomly Coarse Graining? Experimental uncertainty? Weird experimental result Apply new grant Build better experiment 45

46 The random behavior of the electron cannot be attributed to experimental uncertainties! Nature ITSELF is inherently random!... but it does produce a predictable pattern when there are a lot of particles involved! 46

47 What would good old Isaac have said NOW? WTF?!?!? 47

48 The indeterministic world view Certain events are not caused by prior events, but instead happen randomly. 48

49 Early controversy God does not play dice. - A. Einstein Individual events can happen randomly. - N. Bohr Remember, our everyday intuition is not necessarily a good measure of what must happen at atomic length scales! 49

50 Could it be that Quantum Mechanics is just unfinished, and that the finished theory will be once again deterministic? or in other words Could there be yet undiscovered laws of Nature that account for the uncertainty? This hypothesis is experimentally testable and was proven FALSE! John Steward Bell ( ) 50

51 If Nature behaves randomly, how can we predict anything all? Quantum Mechanics is not totally random... It does a superb job in predicting the average behavior of a large number of particles! 51

52 Recap Uncertainties limit our ability to predict stuff From coarse graining: From quantum mechanics: man made uncertainties, due to imperfect experiments/ computers Hard wired into Nature itself (Much more about coarse graining in Module 4!) Both types of uncertainties can and must be controlled to estimate the accuracy of our predictions 52

53 Atomic structure (lightning review) Protons (charge +1) Neutrons (charge 0) Electrons (charge -1) Electrically Neutral 53

54 The element Oxygen has atomic number 8, which means its nucleus has 8 protons. Which of these statements about Oxygen is true? A. The nucleus is electrically neutral B. The total electric charge of the nucleus is positive 8 C. The total charge of the nucleus depends on the amount of neutrons in the nucleus D. The total charge of the nucleus depends on the amount of electrons in the atom E. Oxygen, who needs that anyways? 54

55 The element Oxygen has atomic number 8, which means its nucleus has 8 protons. Which of these statements about Oxygen is true? A. The nucleus is electrically neutral B. The total electric charge of the nucleus is positive 8 C. The total charge of the nucleus depends on the amount of neutrons in the nucleus D. The total charge of the nucleus depends on the amount of electrons in the atom E. Oxygen, who needs that anyways? 55

56 Amount of protons Elements with the same amount of protons but a different amount of neutrons are called isotopes. Some isotopes are radioactive. Example: 235 U 235 = # protons + # neutrons 56

57 electron nucleus 57

58 On Thursday: E=mc 2 & The atomic bomb 58

Introduction. Prediction MATH February 2017

Introduction. Prediction MATH February 2017 21 February 2017 Predicting the future is very difficult, especially if it s about the future. Niels Bohr Can we say what is going to happen: in the next minute? tomorrow? next year? Predicting the future