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Niels Bohr “Gott Würfelt Nicht (God Does Not Play Dice).” - Albert Einstein ”Einstein, Stop Telling God What to Do!” - Niels Bohr Key Persons of Quantum Mechanics 5

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Niels Bohr “Gott Würfelt Nicht (God Does Not Play Dice).” - Albert Einstein ”Einstein, Stop Telling God What to Do!” - Niels Bohr Key Persons of Quantum Mechanics 5 The Relativistic Quantum World A lecture series on Relativity Theory and Quantum Mechanics Marcel Merk University of Maastricht, Sept 16 – Oct 14, 2020 The Relativistic Quantum World 1 Lecture 1: The Principle of Relativity and the Speed of Light Sept. 16: Lecture 2: Time Dilation and Lorentz Contraction Lecture 3: The Lorentz Transformation and Paradoxes Relativity Sept. 23: Lecture 4: General Relativity and Gravitational Waves Lecture 5: The Early Quantum Theory Sept. 30: Lecture 6: Feynman’s Double Slit Experiment Oct. 7: Lecture 7: Wheeler’s Delayed Choice and Schrodinger’s Cat Quantum Mechanics Lecture 8: Quantum Reality and the EPR Paradox Lecture 9: The Standard Model and Antimatter Oct. 14: Lecture 10: The Large Hadron Collider Model Standard Lecture notes, written for this course, are available: www.nikhef.nl/~i93/Teaching/ Prerequisite for the course: High school level physics & mathematics. Relativity Theory 2 Special Relativity General Relativity All observers moving in inertial frames: • A free falling person is also inertial frame, • Have identical laws of physics, • Acceleration and gravitation are equivalent: • Observe the same speed of light: c. Inertial mass = gravitational mass Consequences: Consequences: • Simultaneity is not the same for everyone, Space-time is curved: • Distances shrink, time slows down at • Light bends around a massive object, high speed, • Time slows down and space shrinks • Velocities do not add-up as expected. in gravitational fields, • Gravitational radiation exists. Relativity and Quantum Mechanics 3 Classical Mechanics Quantum Mechanics Smaller Sizes (ħ) Higher Speed Newton Bohr Classical mechanics is not “wrong”. It is limited to macroscopic objects and moderate velocities. ( c ) Dirac Feynman Einstein Relativity Theory Quantum Field Theory 4 Lecture 5 The Early Quantum Theory “If Quantum Mechanics hasn’t profoundly shocked you, you haven’t understood it yet.” - Niels Bohr “Gott würfelt nicht (God does not play dice).” - Albert Einstein ”Einstein, stop telling God what to do!” - Niels Bohr Key Persons of Quantum Mechanics 5 Niels Bohr Erwin Schrodinger Werner Heisenberg Paul Dirac Max Born Niels Bohr: Nestor of the ”Copenhagen Interpretation” Erwin Schrödinger: Inventor of the quantum mechanical wave equation Werner Heisenberg: Inventor of the uncertainty relation and “matrix mechanics” Paul Dirac: Inventor of relativistic wave equation: Antimatter! Max Born: Inventor of the probability interpretation of the wave function We will focus of the Copenhagen Interpretation and work with the concept of Schrödinger’s wave-function: � Deterministic Universe 6 Mechanics Laws of Newton: 1. The law of inertia: a body in rest moves with a constant speed 2. The law of force and acceleration: F= m a 3. The law: Action = - Reaction “Principia” (1687) Isaac Newton (1642 – 1727) • Classical Mechanics leads to a deterministic universe. - From exact initial conditions future can be predicted. • Quantum mechanics introduces a fundamental element of chance in the laws of nature: Planck’s constant: ℎ. - Quantum mechanics only makes statistical predictions. The Nature of Light 7 Isaac Newton (1642 – 1727): Light is a stream of particles. Christiaan Huygens (1629 – 1695): Light consists of waves. Thomas Young (1773 – 1829): Interference observed: Light is waves! Isaac Newton Christiaan Huygens Newton Huygens Thomas Young Waves & Interference : water, sound, light 8 Principle of a wave Water: Interference pattern: � = �⁄� � = 1⁄� Sound: Active noise cancellation: Light: Thomas Young experiment: light + light can give darkness! Interference with Water Waves 9 Interfering Waves 10 Double slit experiment: 11 Particle nature: Quantized Light Max Planck (1858 – 1947) “UV catastrophe” in Black Body radiation spectrum: If you heat a body it emits radiation. Classical thermodynamics predicts the amount of light at very short wavelength to be infinite! Paul Ehrenfest Planck invented an ad-hoc solution: For some reason material emitted light in “packages”. h = 6.62 ×10-34 Js Nobel prize 1918 Classical theory: There are more short wavelength “oscillation modes” of atoms than large wavelength “oscillation modes”. Quantum theory: Light of high frequency (small wavelength) requires more energy: E = h f (h = Planck’s constant) Photoelectric Effect 12 Photoelectric effect: light Light kicks out electron with E = h f (Independent on light intensity!) electrons Light consists of quanta. (Nobelprize 1921) Wave: � = ℎ� = ℎ�⁄� à � = ℎ�⁄� Albert Einstein Momentum: � = �� = �� = �⁄� à � = �� It follows that: � = ℎ⁄� ℎ �* − � = 1 − cos � �-� Compton Scattering: “Playing billiards” with light quanta and electron electrons. light Light behaves as a particle with: λ = h / p (Nobelprize 1927) Arthur Compton Photoelectric Effect 13 Photoelectric effect: light Light kicks out electron with E = h f (Independent on light intensity!) electrons Light consists of quanta. (Nobelprize 1921) Wave: � = ℎ� = ℎ�⁄� à � = ℎ�⁄� Albert Einstein Momentum: � = �� = �� = �⁄� à � = �� It follows that: � = ℎ⁄� ℎ �* − � = 1 − cos � �-� Compton Scattering: “Playing billiards” with light quanta and electron electrons. light Light behaves as a particle with: λ = h / p (Nobelprize 1927) Arthur Compton 14 Matter Waves 15 Louis de Broglie - PhD Thesis(!) 1924 (Nobel prize 1929): If light are particles incorporated in a wave, it suggests that particles (electrons) “are carried” by waves. Original idea: a physical wave è Quantum mechanics: probability wave! Particle wavelength: � = ℎ⁄� à � = ℎ⁄ �� Louis de Broglie Wavelength visible light: graphene 400 – 700 nm Use h= 6.62 × 10-34 Js to calculate: • Wavelength electron with v = 0.1 c: 0.024 nm • Wavelength of a fly (m = 0.01 gram, v = 10 m/s): 0.0000000000000000000062 nm Matter Waves 16 Louis de Broglie - PhD Thesis(!) 1924 (Nobel prize 1929): If light are particles incorporated in a wave, it suggests that particles (electrons) “are carried” by waves. Original idea: a physical wave è Quantum mechanics: probability wave! Particle wavelength: ELECTRON� = ℎ⁄� à � = ℎ⁄ �� Louis de Broglie Wavelength visible light: graphene 400 – 700 nm Use h= 6.62 × 10-34 Js to calculate: • Wavelength electron with v = 0.1 c: 0.024 nm • Wavelength of a fly (m = 0.01 gram, v = 10 m/s): 0.0000000000000000000062 nm 17 The Quantum Atom of Niels Bohr 18 The classical Atom is unstable! Expect: t < 10-10 s Niels Bohr: Atom is only stable for specific orbits: “energy levels”. An electron can jump from a high to Niels Bohr lower level by emitting a light quantum 1885 - 1962 with corresponding energy difference. Balmer spectrum of wavelengths: Schrödinger: Bohr atom and de Broglie waves 19 If orbit length “fits”: 2π r = n λ with n = 1, 2, 3, … The wave positively interferes with itself! n = 1 è Stable orbits! Erwin Schrödinger Periodic Table of the Elements de Broglie: λ = h / p L = r p Energy levels explained L = r h/ λ à atom explained L = r n h/ (2 π r) Outer shell electrons L = n h/(2π) = n ħ à “chemistry explained” (L = angular momentum) Not yet explained 20 !"#$%#&'()'*$!+,-#$./$0*(1*"$2"'345 !"#" $%%& .89#&3 6+ ' 7" $ ;'+A#( !(%% %(!$ 6-#9$6+&'(*" 7'-*"(@+9 %#&9()$K'*+&) !)"& !)#! !)"* :+-1$2"'345$;'31'--#&'#3$<=*1'>#? $%%) !)!& F+*+&)' 6" $ 0& + 63 * =) $ =& $ !(!% $('% !()% ,-.( %(%$ !(!& 2@$6&+91$V$0(93 6-#9A-+33+BA" 01&+1"@'-- 6-#9-(33'# 21-6( =,"+'99$;#+&A =&),#A !)$& !")* !)#" !)") !)#) !)'* !#"* ;' /.011- $%%+ !##' !))! 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