1. A lecture series on Relativity Theory and Quantum Mechanics The Relativistic Quantum World University of Maastricht, Sept 24 – Oct 15, 2014 Marcel Merk

2. The Relativistic Quantum World Relativity Quantum Mechanics Standard Model Lecture notes, written for this course, are available: www.nikhef.nl/~i93/Teaching/www.nikhef.nl/~i93/Teaching/ Literature used: see lecture notes. Prerequisite for the course: High school level mathematics. Sept 24: Lecture 1: The Principle of Relativity and the Speed of Light Lecture 2: Time Dilation and Lorentz Contraction Oct 1: Lecture 3: The Lorentz Transformation Lecture 4: The Early Quantum Theory Oct 8: Lecture 5: The Double Slit Experiment Lecture 6: Quantum Reality Oct 15: Lecture 7: The Standard Model Lecture 8: The Large Hadron Collider

3. Lecture 6 Quantum Reality “Your theory is crazy, but not crazy enough to be true.” -Niels Bohr “I don’t like it, and I’m sorry I ever had anything to do with it.” -Erwin Schrödinger

4. The Double Slit Experiment Case 5: The Delayed Choice Experiment

5. Case 4: Watch the Electrons Consider again the double slit experiment in which we watch the electrons. D1D1 D2D2 Can we try to fool the electron?

6. Wheeler’s Suggestion (1978) John Wheeler (1911 – 2008): Famous for work on gravitation (Black holes – quantum gravity) Replace detectors D 1 and D 2 with telescopes T 1 and T 2 which are focused on slits 1 and 2 What happens if we afterwards would reconstruct whether the electron went through slit 1 or slit 2? T1T1 T2T2

7. Wheeler’s Delayed Choice Experiment We can suddenly decide to make the back-screen transparent to electrons. We decide whether or not to make it transparent after the electrons passed the slits! What will we see? An wave interference pattern or a bullet-like non-interference pattern? T1T1 T2T2 Answer: “Bullets”. We still have killed the interference.

8. Wheeler’s idea What if we make the distance from slits to screen very long? Then, either: Project image of T 1 and T 2 on separate screens, Or: Combine the image of T 1 and T 2 on one screen Galaxy Star One screen or two screens T1T1 T2T2 Crucial point: it must be impossible to know which path the photon took to see interference!  QM: no interference!  QM: interference! The double slit experiment can also be done replacing electrons by photons. In this case Wheeler uses “gravitational lensing” as a “double slit”.

9. Delayed Choice…?

10. The Experiment of Aspect (2007). Alain Aspect and his team have done the experiment in yet another way: using photons in the lab. They used beam-splitters to create two alternative routes For a photon to the same place. Path 1 = Path 2 = 48 m Beam-splitter: Photon has 50% chance to pass through and 50% chance to reflect. Like 2-slits: the quantum can do both!

11. Three Equivalent Experiments T1T1 T2T2

12. The Experiment of Aspect (2007) Situation 1: “Are you a particle?” (open BS output ) Situation 2: “Are you a wave?” (closed BS output ) Answer: “Yes!” (Photon never on 2 paths) Answer: “Yes!” (Photon on 2 paths) Make the choice to open or close BS output well after the photon has passed BS input !

13. The Experiment of Aspect (2007) Situation 1: “Are you a particle?” (open BS output ) Situation 2: “Are you a wave?” (closed BS output ) Answer: “Yes!” (Photon never on 2 paths) Answer: “Yes!” (Photon on 2 paths) Make the choice to open or close BS output well after the photon has passed BS input !

14. The Experiment of Aspect (2007) Situation 1: “Are you a particle?” (open BS output ) Situation 2: “Are you a wave?” (closed BS output ) Answer: “Yes!” (Photon never on 2 paths) Answer: “Yes!” (Photon on 2 paths) “Thus one decides the photon shall have come by one route or by both routes after it has already done its travel” - John A. Wheeler Apparently the quantum wave function includes both possibilities. The observation makes one of them a reality via the collapse of the wave function.

15. Schrödinger’s Cat

16. The Copenhagen Interpretation Particle-Wave duality: one of the great mysteries of quantum mechanics. Complementarity: A quantum object is both a particle and a wave. A measurement can illustrate either particle or wave nature but not both at the same time, because the object is affected by the act of measurement. Niels Bohr: Uncertainty relation Complementary, collapse of the wave function. Niels Bohr and Albert Einstein debates at Solvay conf. Albert Einstein: “God does not play dice” Objective Reality Photo: Paul Ehrenfest (December 1925) 1927

17. Schrodinger’s Cat Paradox (thought experiment) invented by Erwin Schrödinger in 1935 to demonstrate that the Copenhagen interpretation makes no sense. In a radioactive source, a single random quantum event has 50% probability to trigger a lever arm and break a flask containing deadly poison. Is the cat both dead and alive before we open the box to observe? Who is observer? When does the wave function collapse? Does it require consciousness? Is it the cat? The Experimenter? The press reporter? Or you when you hear the news? Compare quantum choice with double slit situation.

18. Schrodinger’s Cat Paradox (though experiment) invented by Erwin Schrödinger in 1935 to demonstrate that the Copenhagen interpretation makes no sense. In a radioactive source, a single random quantum event has 50% probability to trigger a lever arm and break a flask containing deadly poison. Is the cat both dead and alive before we open the box to observe? Who is observer? When does the wave function collapse? Does it require consciousness? Is it the cat? The Experimenter? The press reporter? Or you when you hear the news?

19. The EPR Paradox

20. The EPR Paradox (1935) EPR = Albert Einstein, Boris Podolsky, Nathan Rosen Bohr et al.: Quantum Mechanics: The wave function can be precisely calculated, but a measurement of mutually exclusive quantities is driven by pure chance. Einstein et al.: Local Reality: There must exist hidden variables (hidden to us) in which the outcome of the measurement is encoded such that effectively it only looks as if it is driven by chance. Local Realism vs Quantum Entanglement: EPR: What if the wave function is very large and a measurement at one end can influence the other end via some “unreasonable spooky interaction”. Propose a measurement to test quantum entanglement of particles

21. The EPR Paradox Two particles produced with known total momentum P total, and fly far away. Alice can not measure at the same time position (x 1 ) and momentum (p 1 ) of particle 1. Bob can not measure at the same time position (x 2 ) and momentum (p 2 ) of particle 2. But: If Alice measures p 1, then automatically p 2 is known, since p 1 +p 2 = p total If Alice measures x 1, then p 1 is unknown and therefore also p 2 is unknown. How can a decision of Alice to measure x 1 or p 1 affect the quantum state of Bob’s particle (x 2 or p 2 ) at the same time over a long distance? Communication with speed faster than the speed of light? Contradiction with causality? Is there “local realism” or “spooky action at a distance”?

22. An EPR Experiment 2: z-Spin= – + 1: z-Spin= + – Produce two particle with an opposite spin quantum state. Quantum wave function: total spin = 0. If Alice measures spin of her particle along the z-direction, Then also Bob’s particle’s spin points (oppositely) along the z-direction! Heisenberg uncertainty: an electron cannot have well defined spin along two different directions, eg. z and x

23. An EPR Experiment 2: x-Spin= – + 1: x-Spin= + – Produce two particle with an opposite spin quantum state. Heisenberg uncertainty: an electron cannot have well defined spin along two different directions, eg. z and x Quantum wave function: total spin = 0. If Alice measures spin of her particle along the x-direction, Then also Bob’s particle’s spin points (oppositely) along the x-direction!

24. An EPR Experiment Produce two particle with an opposite spin quantum state. Heisenberg uncertainty: an electron cannot have well defined spin along two different directions, eg. z and x Quantum wave function: total spin = 0. But how does Bob’s particle know that Alice measures x-spin or z-spin? 2: x-Spin= – + 1: x-Spin= + – 2: z-Spin= – + 1: z-Spin= + – Either the particles are linked because of some hidden variable (objective reality) or they are QM “entangled” and a measurement “collapses” the wave function. AliceBobAliceBob

25. An EPR Experiment Produce two particle with an opposite spin quantum state. 2: x-Spin= – + 1: x-Spin= + – 2: z-Spin= – + 1: z-Spin= + – Either the particles are linked because of some hidden variable (objective reality) or they are QM “entangled” and a measurement “collapses” the wave function. AliceBobAliceBob John Bell: ”inequality equation” (1964): Measure many times (“n”) spin along 3 different axes “A-B-C”. Then local reality (hidden variable) requires: n(A + B + ) ≤ n(B + C + ) + n(A + C + ) Quantum Mechanics should violate this equation.

26. Alain Aspect 1982 Observations agree with quantum mechanics and not with local reality! (A slightly different version (CHSH) of Bells inequality with coincidences is tested) (CHSH = John Clauser, Michael Horne, Abner Shimony, Richard Holt)

27. Philosophical? Hugh Everett (PhD Student of John Wheeler) formulated the Many Worlds Interpretation of quantum mechanics in 1957 The wave function does not collapse, but at each quantum decision both states continue to exist is a decoupled world. A tree of quantum worlds for each quantum decision. Triggered science fiction stories with “parallel universes” Still a topic of debate (and theoretical calculations). Several alternatives (“Many Minds”). Personal opinion: Quantum coherence is related to complexity of the wave-function.

28. Application 1: Quantum Cryptography Quantum Key Distribution (QKD): 1. Public Channel (Internet, email): send an encrypted message. 2. Quantum Channel (Laser + fiber optics) send key to decode the public message 3. Eve cannot secretly eavesdrop. She destroys quantum information and is detected. Alice sends a secret message to Bob and prevents Eve to eavesdrop. First idea by Stephen Wiesner (1970s) Worked out by Bennet (IBM) and Brassard (1980s) Physicsworld.com Sept 2, 2013 “Quantum cryptography coming to mobile phones”

29. Application2: Quantum Computer Idea: Yuri Manin and Richard Feynman: Use superposition and entanglement of quantum states to make a super-fast computer. Normal computer: bits are either 0 or 1 Quantum computer: qbits are super-positions of two states: 0 and 1 (Eg. spin up and spin down) Compute with quantum logic. With 2 bits it can do 4 calculations simultaneously. With 3 bits 8 calculations, with n bits 2 n ! Difficulty: prevent “decoherence”. Recently, “D-wave systems”: Claim the first commercial quantum computer based on 128 qbits. Not generally accepted by the community that it really uses quantum mechanics.

30. Food for thought Relativity theory: The finite speed of light means that there is no sharp separation between space and time. (Think of different observers) Universal constant: c = 300 000 km/s Quantum Mechanics: The finite value of the quantum of action means that there is no sharp separation between a system and an observer Universal constant: ħ = 6.6262 × 10 -34 Js John Wheeler: “Bohr’s principle of complementarity is the most revolutionary scientific concept of the century.”

31. Next Week Next week: Quantum Field Theory and Antimatter The Standard Model The Large Hadron Collider The Origin of Mass: Higgs Peter HiggsFrancois Englert Paul Dirac Richard Feynman

32. The origin of mass and “Higgs” The particle associated to the origin with mass is predicted by Peter Higgs The corresponding quantum field is the Brout-Englert-Higgs field The mechanism that describes the origin of mass is the Englert-Brout-Higgs-Guralnik-Hagen-Kibble mechanism. Robert Brout (1928 – 2011) Peter Higgs (1929) Francois Englert (1932 )

33. Nobel Prize in Physics 2013 “for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles, and which was recently confirmed through the discovery of the predicted fundamental particle, by the Atlas and CMS experiments at CERN’s Large Hadron Collider.”

34. Perhaps time for…