The Relativistic Quantum World

Transcription

1 The Relativistic Quantum World A lecture series on Relativity Theory and Quantum Mechanics Marcel Merk University of Maastricht, Sept 14 Oct 12, 2017

2 Relativity Quantum Mechanics The Relativistic Quantum World Sept 14: Lecture 1: The Principle of Relativity and the Speed of Light Lecture 2: Time Dilation and Lorentz Contraction Sept 21: Lecture 3: The Lorentz Transformation and Paradoxes Lecture 4: General Relativity and Gravitational Waves Sept 28: Lecture 5: The Early Quantum Theory Lecture 6: Feynman s Double Slit Experiment Oct 5: Lecture 7: The Delayed Choice and Schrodinger s Cat Lecture 8: Quantum Reality and the EPR Paradox Standard Model Oct 12: Lecture 9: The Standard Model and Antimatter Lecture 10: The Large Hadron Collider Lecture notes, written for this course, are available: Prerequisite for the course: High school level mathematics.

3 Lecture 4 General Relativity and Gravitational Waves Do not worry about your difficulties in mathematics. I can assure you mine are still greater. -Albert Einstein

4 Ehrenfest Paradox Rotating disk with ruler on the edge: Circumference: C = 2 p r 2p r Paul Ehrenfest

5 Ehrenfest Paradox Rotating disk with ruler on the edge: Circumference: C = 2 p r 2p r Alice stands next to the disk and sees rulers on disk Lorentz contracted: C = 2 p r / g è Circumference is smaller! Bob moves on the disk and sees rulers next to disk contracted: C = 2 p r g è Circumference is larger! A rotating object is not an inertial frame: Postulate of relativity only worked for inertial frames Need to adapt the postulates: special relativity à general relativity

6 The Equivalence Principle (Inertial Frame) Einstein happiest thought : There is no way to determine whether you are standing on the earth or accelerating upwards in a rocket in space.

7 The Equivalence Principle (Inertial Frame) There is no difference between acceleration force and gravitation. Gravitational mass = inertial mass

8 The Eötvös Experiment Direction of gravity and Centrifugal force on earth Small (m 1 ) and big (m 2 ) mass on a rod suspended by a thin fiber Loránd Eötvös Gravity force G depends on Newton s law of gravity: gravitational mass Centrifugal force F depends on Newton s law of motion inertial mass: inertial mass The system did not rotate. è F 1 /F 2 = G 1 /G 2 èexperimental proof that indeed gravitational mass is equivalent to inertial mass.

9 Bending of light Consequence if acceleration and gravity are identical: A B Outside view Inside view Gravity view A: Lightbeam in accelerating rocket B: Lightbeam in gravitational field Prediction of Einstein: light beam bends under gravity!

10 Bending of light in gravitation field of the Sun Light wants to go straight but space is curved! Confirmed during solar eclipse on November !

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12 Einstein s thought experiment Particle with mass m falling from tower: m E = mc 2 ) E = hf From quantum mechanics we know: Energy of light is related to frequency (and wavelength): E = hf = hc/ h hf 0 >hf?? èno! Photon loses energy as it travels up the gravitational field! E 0 = mc mv2 = mc 2 + mgh = mc 2 1+gh/c 2 ) E 0 = hf 0

13 The Harvard Tower Experiment Harvard Tower Experiment (Pound-Rebka) at Jefferson lab in Harvard: Measure red-shift of photons in earth gravitational field. h = 22.5 m Df/f = DE/E = gh/c 2 = 2.5 x as expected!

14 Gravitational Time Dilation The photon loses energy as it climbs the gravitational field. ètime ticks faster at higher altitude.

15 Accelerating Rocket From special relativity we know that space contracts at high velocity velocity : 0 < v 1 < v 2 < v 3 s s s l 1 v 2 1 c 2 l 1 v 2 2 c 2 l 1 v 2 3 c 2 l Space is seen to shrink further and further with increasing velocity! 1/ = s 1 v 2 c 2

16 Falling apple: E pot = G mm R Free falling object Newton s Constant G Compare an to accelerating rocket: 1 E kin = E pot 2 mv2 = G mm R l v 2 =2 GM R s 1 v 2 c 2 = Lorentz factor r 1 2 GM Rc 2 l 0 Space shrinkage ( curvature ): l 0 = r 1 2 GM Rc 2 l

17 Space-Time curvature A falling apple accelerates and units of space get more and more contracted: An apple falls into the gravitational field and time runs slower and slower: l t Space Time l 0 t 0 l 0 =1/ l = r 1 2 GM Rc 2 l t 0 = t = 1 t q1 2 GMRc2 Space contracts near mass and dilates away from it. Time slows near mass and Speeds up away from it. Space-time is curved in the presence of mass

18 Mass causes curvature in space-time

19 Relativity and GPS Two effects: Time speeds up at the satellite in comparison to earth surface due to gravity Time slows down at the satellite due to high velocity compared to person on earth è Clocks in satellite and on earth de-synchronize with ~ 40 msec per day!

20 Black Hole Gravitational time slowdown near a star with mass M: r t 0 2GM = t 1 Rc 2 Schwarzschild radius: R s = 2GM c 2 r t 0 = t 1 R s R R

21 Black Hole Gravitational time slowdown near a star with mass M: r t 0 2GM = t 1 Rc 2 Schwarzschild radius: R s = 2GM c 2 r t 0 = t 1 R s R R s Time stand-still: if R = R s then t 0 =0 (Time stands still at the horizon of a black-hole) Example our Sun: G = 6.67 x m 3 /kg s 2 (Newton s gravitation constant) M sun = 2 x kg è R s = 3 km for a black hole.

22 Black hole requires ~ 3 x Msun

23 What is a black hole? Purely curved space-time!

24 What is a black hole? What happens when black holes meet?

25 Electric vs Gravitational Fields Electric field of positive and negative charged particle: Gravitational field of the earth: F e = qe = 1 qq 4 " 0 r 2 F g = mg = G mm R 2 Einstein spent most of his life looking for a unified theory of electromagnetism and general relativity.

26 Waves and Radiation Electromagnetic waves: Caused by accelerating electric particles electrons, eg.: radio-emission Maxwell µ F µ = 4 c J E and B fields Electric charge and currents Gravitational Waves: Caused by moving masses. Requires very heavy masses àblack holes. (Einstein thought these couldn t be observed) Einstein equations: G µ + g µ = 8 G c 4 T µ Space-time fields Mass and mass-flow

27 Electromagnetic and Gravitational Waves Electromagnetic wave Electromagnetic wave: Changing electric and magnetic field propagating through space. Caused by moving (accelerating!) electric charges. Gravitational wave Gravitational wave: Changing space-time field. Caused by moving (accelerating!) masses. y x

28 Remember the interferometer!

29 Detection of Gravitational Waves

30 Which precision is needed? Seismic proton Laser noise (f,p) atom Laser Beamsplitter Mirror hair Radiation Pressure noise Photodetector Interference

31 Current Facilities

32 Two merging black holes Two massive colliding/merging black holes: B.H.1 = 36 x mass of the sun B.H.2 = 29 x mass of the sun New BH: 62 solar masses Distance: 1.3 billion lightyears Relative change of space (strain) % Rotation speed increasing to half the light speed! More energy emitted in grav waves than the visible light of all stars in the universe!

33 Ligo Hanford and Livingston Consistent signals seen in the Washington and Louisiana detectors! (GW150914) observation observation Expectation GR Expectation GR

34 Numerical relativity simulation for GW Parameters measured by matching millions of trial waveforms in 15-dimensional parameter space

35 The Virgo Experiment in Pisa

36 Ultrahigh Vacuüm Largest vacuüm vessel in Europe Pressure ~ mbar

37 Seismic dampingsystem

38 Seismic Damping Table

39 Input mode cleaner end mirror

40 Beam splitter Example #1: advanced optical systems

41 Example #2: Cavity control

42 Einstein Telescope Possible future facility Een observatorium voor zwaartekrachtsgolven van 2 Hz tot 10 khz

43 Possible future facility Einstein Telescope The next gravitational wave observatory

44 Possible future facility Einstein Telescope The next gravitational wave observatory

45 Fundamental Black hole physics Wat happens at the edge of a black hole (quantum effects)? Is Einstein s theory still valid under these extreme conditions?

46 Looking into the Big Bang What happened the first moments of the Big Bang? Search for gravitational waves originating from the very first moment! Inflatie (Big Bang plus seconden) Neutrino s 1 seconde Big Bang plus jaar zwaartekrachtsgolven Licht Nu Big Bang plus 14 miljard jaar

47 Next Lecture Quantum mechanics developed by Bohr and Heisenberg leads to absurd thought experiments of Feynman and Wheeler. Einstein and Schrödinger did not like it. Even today people are debating its interpretation. Richard Feynman

48 Some extra slides

49 Einstein Quotes Imagination is more important than knowledge Education is what remains after one has forgotten what one has learned at school. I fear the day that technology will surpass our human interaction. The world will have a generation of idiots. A person who never made a mistake never tried anything new.

50 Gravitatie golven Detectie methode (dutch)

51 The Gravitational Wave Spectrum