Yale Physics 120 4/9/2018 Quantum Physics and Beyond

Transcription

1 Physics 120 Quantum Physics and Beyond TODAY General Relativity and Black Holes Black Holes Approaching a Black Hole Watching You Approach a Black Hole Black Holes & the Information Paradox Radiation from a Black Hole Black Hole Complementarity Quantum Mechanics versus Gravity String Theory Intro String Theory to the Rescue John Harris 1

2 Physics 120 Reminder: the Rest of the Term Today Wed Apr 11 Mon Apr 16 Einstein s General Relativity and Black Holes Quantum Mechanics versus Gravity Bambi Meets Godzilla! Initial paper proposals (idea, topic, some references) due In-Class Quiz (40 minutes) Yale Science Librarian on Library Resources for Term Paper Guest speaker: Dr. Eliane Epple (Yale) Some Applications of Quantum Mechanics Mon Apr 23 Wed Apr 25 Fri Apr 27 Thurs May 3 String Theory to the Rescue Untangling the Problems Special Class (4 5:50 PM) String Theory & Extra Dimensions String Theory, Extra Dimensions, Multiverse What We ve Learned & Where Do We Go from Here? Paper approvals deadline READING WEEK (begins end of day) Final paper due John Harris 2

3 Physics 120 Quantum Physics and Beyond Announcements Quiz 2 next week at beginning of class Covers everything ~ since the midterm, specifically: Reading assignments (due on) 3/26, 4/2, 4/9 Homeworks 7, 8, 9 Lessons 9, 10, 11 (today s) Topics above cover Special Relativity, Quantum Erasure, Quantum Entanglement, General Relativity, Black Holes 40 minutes, 6 8 questions similar to those in homework Questions require short answers (no more than 2-3 sentences unless noted) Review Session Wednesday 4-5 PM Yale Physics 120 4/9/2018 Quantum Physics and Beyond John Harris 3

4 Reading Assignment for Next Week Reading Assignment for next week s class: Everyday Quantum Mechanics: 1) How Stuff Works the Laser 2) From Ray-gun to Blu-ray 3) How Does Quantum Computing Work? 4) Watch short video, a practical explanation: But No Written Homework Assignment for Next Week Quiz John Harris 4

5 Reading Assignment for April 23 & 25 Homework Assignment due on April 23 Reading for April 23 & 25 1) Imagining other Dimensions 2) "Universe's Unseen Dimensions", Arkani-Hamed 3) The String Theory Landscape, Bousso and Polchinski 4) "Illusion of Gravity", Maldacena 5) Looking for Life in the Multi-Verse, Jenkins and Perez 6) Does the Multiverse Really Exist? George F.R. Ellis For reference: String Theory Website - John Harris 5

6 Quick Review A few last words on Quantum Mechanics Some questions for you! Yale Physics 120 4/9/2018 Quantum Physics and Beyond John Harris 6

7 My Last Word on Quantum Mechanics Einstein Believed in objective reality independent of observation (required hidden variables that are encoded at creation) & QM theories must be deterministic to be complete! EPR To abandon Realism, we must abandon locality! Bohr and Copenhagen No reality without observation! Objects become real only upon observation. John Bell Bell s Inequalities If Einstein (EPR) is right and there are hidden variables, Bell predicted results. Bell s Inequalities were violated local realism was violated! Bell s Theorem proved that local hidden variables were not possible local hidden variables violate local realism! Bell forces us to give up either locality or realism but not both. It is realism that we have to give up. Entanglement preserves quantum uncertainty & is inherent in Quantum Mechanics! Yale Physics 120 4/9/2018 Quantum Physics and Beyond John Harris 7

8 Last Class Einstein s General Relativity (GR) Dynamics is replaced by geometry Space is warped by massive bodies Gravity affects time as well as a straight-line path. Principle of Equivalence: Impossible to distinguish an acceleration of a frame of reference from effects of gravity. In General Relativity, laws of physics are the same to all observers, whether inertial or accelerated. An accelerated clock (or in strong gravity) runs slower than a non-accelerated one Examples: gravitational red shift light (spectra) from sun (frequency ê wavelength (Λ) é shifts red) atomic clocks slowing down of electron vibrations (GR) John Harris 8

9 Warping of Space-time A mass like our Sun bends space. Path on left: the path of distant starlight is deflected (or gravitationally lensed) by curved space. Path on right: light loses energy as it climbs the gravitational potential, undergoing a gravitational redshift. The advance of the perihelion of the orbit of Mercury (in blue) is slightly altered by relativistic effects. John Harris 9

10 For Reference Classic Examples as Tests of GR 1) Mercury s precession of its perihelion - not elliptical - gravitation from other planets - gravitation from sun 2) Bending of light around sun British eclipse expedition gravitational lensing of a quasar by a massive galaxy (saw two images!) 3) Effect of gravity on clocks clocks 75 feet above/below - lower one loses 1 sec in 10 million yrs - γ-ray clocks GR correct to 1% accuracy (due to measurement error) atomic clock in rocket measured gravitational red shift to.02% John Harris 10

11 Black Holes John Harris 11

12 From Stars to Black Holes Spacetime geometry of a star: GR gravity replaced by spacetime curvature How is a Black Hole formed? Massive remnant of a collapsed star nuclear fueling of a star, burns out supernova collapse (1987a) black hole remnant Spacetime geometry of black hole: Light rays bend or do not pass through (depends on angle) absorbs light + matter Binary star (one is a black hole) motion of 1 star (must have a dark partner), matter attracted to unseen object candidate Cygnus X-1 (incredible rotation rate ~ 30 revolutions per second) stars? distances? energies? angular momenta? Recent Binary Black Hole merger gravitational waves! John Harris 12

13 Black Holes Do they exist? From your reading Central black hole in the Milky Way galaxy? Astronomers follow the motion of stars in the center of the galactic core The animation is based on observations made over 10 years Animation shows a region a few light days across, in the core region of the Milky Way that, as viewed from Earth, in the constellation Sagittarius. Region is roughly 25,000 light years away from Earth. The red cross in the center marks the position of "Sagittarius A*", a compact radio source. The astronomers have developed a detailed three-dimensional model to reconstruct the stars' motions; the orbits thus reconstructed are shown in yellow. John Harris 13

14 Black Holes John Harris 14

15 For reference - Data on previous slide Black Holes Slide contains images of the mammoth spiral galaxy M81 about 12 million light years away data from four different NASA satellites. 1 st infrared data from the Spitzer Space Telescope 2 nd optical data from the Hubble Space Telescope 3 rd UV data from Galex Satellite 4 th x-ray data from the Chandra X-ray Observatory reveals higher energies At the center of M81 supermassive black hole about 70 million times more massive than the sun John Harris 15

16 Animation of Elliptical Galaxy with Black Hole Black hole surrounded by hot gas shown in red and yellow, which acts as fuel for the black hole engine. Power generated by internal black hole engine flows away from the black hole via jets of high-energy particles. John Harris 16

17 Video Clip A Conflict is Building Quantum Mechanics and General Relativity From The Elegant Universe (find online, shown at Wednesday class): Part 1, Chap 7, (start at 41:00 to 51:10, 10 minutes) John Harris 17

18 Things to Know before Approaching a Black Hole What is escape velocity? Minimal velocity needed to escape the gravitational pull of an object What is the Event Horizon? Spherical boundary where the escape velocity = speed of light At a distance the event horizon appears static Up close the event horizon appears to move outward (grows rapidly) What is the Singularity? At the center of the black hole. What happens to spacetime? Once inside the horizon - spacetime so distorted radial distance from BH center (r) and time (t) switch roles - radial distance r becomes timelike and t becomes spacelike - approach smaller & smaller values of r, just as normally time moves into the future - you will move to smaller r & hit the singularity just as time moves forward normally Black Hole masses and sizes: Schwarzschild radius (horizon) ~ mass of Black Hole BH (mass = mass of Sun) has radius ~ 3 km BH (mass = 10 6 solar masses) has radius ~ 3 x 10 6 km (~ 4 R sun ) John Harris 18

19 Approaching a Black Hole What do you feel? No big changes until you get close enough to feel tidal gravitational forces (e.g. feet vs head, feel stretched,..ripped apart.) Large BH, large horizon radius must first cross horizon Small BH, small horizon radius torn apart before horizon What do you see? Far away objects distorted (BH bends light) Even crossing horizon, same How long do I last (starting at 10x BH radius) for large BH? Takes about 8 10 minutes to reach the horizon Then about 7 8 seconds to reach the singularity Time scales with the BH size John Harris 19

20 Watching You Approach a Black Hole What does my friend outside see? As you get closer, your friend sees you move more & more slowly You will never be seen to reach or cross the horizon Light you emit as you cross the horizon will linger there and never escape From the perspective of time? Time slows down as you approach the BH horizon Same twins problem! Light gets red-shifted as you approach you will no longer be recognizable John Harris 20

21 Black Holes and the Information Paradox What is the information paradox? Information entering a Black Hole appears to be lost In Classical Physics everything is reversible and time-reversal invariance results in energy conservation In QM all processes are microscopically reversible (e.g. particle reactions) Everything is not lost or QM and General Relativity are in conflict! The Debate - Hawking s view The Principle of Microreversibility is violated by Black Holes The Debate - t Hooft and Susskind s view No reversibility is a violation of QM and thus energy is NOT conserved! Although QM involves indeterminacy, QM (& particle motions) reversible Otherwise, energy can be created or destroyed in particle collisions The resolution - String Theory? Everything NOT lost but exists in extra dimensions, that we don t see. Yale Physics 120 4/9/2018 Quantum Physics and Beyond John Harris 21

22 More on Black Holes Bekenstein s Black Hole Thermodynamics Black hole horizon contains heat Black Hole can be described by a temperature (T) Temperature is minute from a large distance away becomes enormous very near horizon Black holes have entropy proportional to the surface area of the horizon Entropy is ~ number of degrees of freedom of system Entropy is ~ energy that cannot be used to do work Yale Physics 120 4/9/2018 Quantum Physics and Beyond John Harris 22

23 (Hawking) Radiation from a Black Hole Hawking again Microreversability is violated by Black Holes! Black holes, like all hot bodies, must radiate! Radiation from horizon, does not violate concept of nothing can escape Black holes will lose energy and mass, and over time vanish Yale Physics 120 4/9/2018 Quantum Physics and Beyond John Harris 23

24 (Hawking) Radiation from a Black Hole t Hooft and Susskind again Evaporated energy carries away all information that fell into the black hole Yale Physics 120 4/9/2018 Quantum Physics and Beyond John Harris 24

25 Black Hole Complementarity Susskind the two scenarios are not contradictory but complementary In special relativity: although lengths and times may vary - events take place at definite space-time locations Not so in Black Hole Complementarity As objects approach horizon two distinctly different scenarios! From outside view they slow down, snapshot resolution better From falling perspective not so, everything looks the same Strings Tiniest entities vibrate like a string with fundamental frequency and higher frequency modes Higher modes exist superimposed (freeze out for object falling into BH) Thus different space-time locations for different observers! Each a fundamental particle String size ~ 1/10 20 size of proton Each cm segment across a string acts as an information bit t Hooft and Susskind Strings can carry away all the evaporated energy and all information that falls into a black hole Yale Physics 120 4/9/2018 Quantum Physics and Beyond John Harris 25

26 Black Hole Complementarity Susskind the two scenarios are not contradictory but complementary In special relativity: although lengths and times may vary - events take place at definite space-time locations Not so in Black Hole Complementarity As objects approach horizon two distinctly different scenarios! From outside view they slow down, snapshot resolution better From falling perspective not so, everything looks the same Strings Tiniest entities vibrate like a string with fundamental frequency and higher frequency modes Higher modes exist superimposed (freeze out for object falling into BH) Thus different space-time locations for different observers! Each a fundamental particle String size ~ 1/10 20 size of proton Each cm segment across a string acts as an information bit t Hooft and Susskind Strings can carry away all the evaporated energy and all information that falls into a black hole Yale Physics 120 4/9/2018 Quantum Physics and Beyond John Harris 26

27 String Theory From The Elegant Universe (find online): Gravity - Einstein versus Newton Part 2, Chap 6-8 String Theory Intro (online) (start from 34:40 to 50 min total 14 min) John Harris 27