Q W u e. c t o u m m e P h B. B e. s c i k c s 2. John Harris 1
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1 Q W u e a l n c t o u m m e P h B y a s c i k c s 2 & B e y o n d! Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 1
2 Physics 120 Reminder: the Rest of the Term Today - Mar 26 Mon Apr 2 Mon Apr 9 Wed Apr 11 Mon Apr 16 Mon Apr 23 Wed Apr 25 Fri Apr 27 Einstein s Relativity Traveling at the Cosmic Speed Limit More on Special Relativity The Threat of Quantum Mechanics, More on Quantum Entanglement Intro to Einstein s General Relativity Warped Space-time 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 Some Applications of Quantum Mechanics 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) Thurs May 3 Final paper due Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 2
3 Paper Proposals: Physics 120 Final Paper Guidelines Due Wednesday, 11 April Title, short abstract and ideas about references (any articles or books identified already) Due Wednesday, 23 April Final paper approvals with most references identified Final Paper due Thursday, 3 May Topic: Must be related to or motivated by material we ve covered in class this term Can be experimental or theoretical Must use references beyond those assigned in class Can be expository, descriptive, persuasive can even be narrative. But remember this is a paper for a science class so it should be based on facts not opinions! Wikipedia not a valid reference! Length 2,000 5,000 words Typically 2,500 3,500 words Remember a picture is worth 1,000 words, figures are encouraged! Examples (next slide) Some titles of past papers Questions? Yale Physics 120 for 3/26/2018 Quantum Physics and Beyond John Harris 3
4 Physics 120 Examples of Titles of Past Papers A Brief History of Quantum Entanglement On Uncertainty and Emptiness The Cosmological Constant: Einstein s Biggest Blunder or Finest Foresight? Time and Time Travel: Problems and Possibilities The Infinite Loneliness of Quantum Immortality The Mixed-Up Files of Quantum Computing Everything s a Hologram, The Startling Conclusion of Black Hole Complementarity Moving Up Well Not Really Up: Exploring Physics in Higher Dimensions The Conception and Development of String Theory Leibniz Goes Quantum Black Holes, White Holes, and Wormholes Quantum Cryptography: too "spooky" to be true? The Search for Dark Matter The physics of LASIK surgery The Search for the Unseen: The History or Dark Energy Theories Superconductors: Remarkable properties and Elusive Applications Misanthropic Argument? Evaluating the Anthropic Principle's Applications in String Theory Symmetry in Nature and the Formation of the Fundamental Forces The Hunt for the Higgs Quantum Computing Inflation or Not? Yale Physics 120 for 3/26/2018 Quantum Physics and Beyond John Harris 4
5 Reading Assignment for Next Week (1) 1) Spacetime 2) A Quantum Threat to Special Relativity, article by David Z Albert and Rivka Galchen 3) S. Hawking's "A Briefer History of Time, Chap. 6" (linked on web) 4) The Equivalence Principle 5) Gravity: Weightlessness to Curvature 6) Mass and More on Gravity 7) Gravitational Deflection of Light 8) Equivalence Principle and Deflection of Light 9) General Relativity (all sections from Geometric gravity through Light side of gravity ) Optional Reading see any of the other topics of interest on special relativity in: Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 5
6 Reading Assignment for Next Week (2) View two short video clips Delayed Choice Quantum Eraser (10 min.): Quantum Entanglement (11 min.): Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 6
7 Physics 120 Today Special Relativity Principle of Relativity (Galileo, Newton and Einstein) Michelson-Morley Experiment Special Relativity Travelling at the speed of light Spacetime Simultaneity Time Dilation Length Contraction Spacetime Diagrams (Minkowski Diagrams) Quantum Physics and Beyond Yale Physics 120 3/26/2018 John Harris 7
8 Relativity Galilean Physics - Motion is Relative frame of reference inertial frames (i.e. velocity is constant) Velocities add: 1d V person on train V tr V tr train relative to earth V person relative to earth = V person + V tr 2d v water V boat in water V boat rel to earth V boat relative to earth = V boat in water + V water 3d etc. Is there an absolute reference frame an inertial frame at rest? Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 8
9 1880 s The Michelson-Morley Experiment Luminiferous Ether Is there an absolute frame of reference? If earth moving relative to the ether, light velocity also affected by earth's motion! Michelson-Morley Experiment Should see differences in light one arm (e.g. parallel to the ether) vs. other arm (perpendicular to the ether) v motion through ether? Or, see differences at different times of year. V light = V light rel. to ether + V ether rel. to space Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 9
10 Relativity and the Michelson-Morley Experiment Remember? Galilean Physics - Motion is Relative 2d v water V boat in water V boat rel to earth V boat relative to earth = V boat in water + V water How is the MM Experiment analogous to this? see How is the MM Experiment different from this? see Michelson-Morley experiment - did not detect any motion relative to ether or motion of the ether. - observed no difference in the speed of light in their experiment! Einstein knew about these results as a kid! Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 10
11 Relativity and Special Relativity Einstein in his 1905 paper Velocity of light is NOT affected by motion of the source or frame of reference. Postulate 1: Laws of physics are the same in any inertial frame of reference. [This is the Galilean/Newtonian Principle of Relativity] ex) inside moving trains, jetliner Postulate 2: Speed of light in a vacuum is the same in any inertial frame of reference, regardless of relative motion of the source and observer (c = 300,000 km/s) i.e.) light (EM waves) does not behave like most waves or moving objects! For light: no Galilean invariance & no velocity addition Contradicted classical ideas of the independence of space & time. Einstein - space and time are linked! No need for an ether No absolute rest frame All motion is relative Today speed of light is measured as constant to better than 6 parts in No one has shown the speed of light to be anything but the constant c in vacuum! Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 11
12 Motion in Special Relativity We know: Throw a ball on a train, velocity of the ball relative to the earth is V ball relative to earth = V ball + V train What if you do the same experiment with light..with a flashlight on a train? Einstein Einstein s Special Relativity: Reshapes concepts of space & time! Velocity addition does not work! Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 12
13 How Radical Was this Idea? Inspiration for the special theory of relativity came from Einstein asking himself: What would the world look like, if I rode on a beam of light? Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 13
14 Hypothetical Thought Experiment Travelling at the Speed of Light? Quantum Physics and Beyond Yale Physics 120 3/26/2018 John Harris 14
15 And if Time Stops.. There is no such thing as slowing down! Slowing down requires a sense of time. If no slowing down, then there is no such thing as stopped! There is no stopped for light, it either moves or doesn t exist. Light is the cosmic speed limit Things with mass go slower than light. Space and time must change as massive objects approach c! Quantum Physics and Beyond Yale Physics 120 3/26/2018 John Harris 15
16 Spacetime Three dimensions a valid description at a certain point in time e.g. imagine a box or can described by a length, height, width crush it! A complete description requires another coordinate time spacetime Two observers at rest with each other: Agree on measurements of space and time and intervals between events Two observers in (relativistic) motion relative to one another: Do not agree on measurements or intervals All measurements are unified by: space time SPACE = = c TIME one rest frame Yale Physics 120 3/26/2018 Quantum Physics and Beyond ANOTHER REST FRAME John Harris 16
17 Simultaneity Two events are simultaneous if they occur at the same time! If speed of light is same in all inertial frames (i.e. for all observers) then space & time not same for all observers! Two events that are simultaneous in one frame need not be simultaneous in another frame moving relative to the first. Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 17
18 Concept of Time Dilation Time is not absolute but is relative! Light clock distance distance distance space DISTANCE SPACE = = c c = constant time time TIME Thus DISTANCE > distance TIME > time This is time dilation moving clocks appear to run slower tick to the rhythm of a different time! Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 18
19 Concept of Time Dilation time dilation moving clocks appear to run slower distance distance distance space time SPACE DISTANCE = = = = c TIME ct o /2 t o = proper time d = ct o /2 t = 1 (1 - v 2 / c 2 ) t o vt/2 2 events occur at same place in the rest frame Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 19
20 t = 1 (1 - v 2 / c 2 ) t o More on Time Dilation observer in t = γ t 0 inertial proper time t o frame γ 5 1 Time dilation γ 1 t t 0 v ~ c necessary for effect! If c = constant, t t 0 time passes differently v c All processes - physical, chemical, biological slow down heartbeat aging A moving clock runs more slowly than a stationary clock! proven Cesium clocks on flights around earth s time diff. Global positioning satellites require relativistic corrections! experimentally Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 20
21 Concept of Length Contraction v v L L o In moving frame: L = vt 0 To observer on earth: L o = vt (note t > t 0 ) L 0 = rest length (or proper length) measured by observer at rest relative to distance being measured. Since: t > t 0 L 0 > L L L Know v = = 0 t 0 t And since t = γ t 0 L is contracted relative to rest length L 0 t 0 L = L t 0 1 L = L γ 0 Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 21
22 Basics of Space-time Diagrams Shown at right is a general space-time diagram: The primed axes are moving relative to the unprimed axes. The time axes are in units of ct, where c is the speed of light. A few notes: - The light cone (not drawn) is the path of light relative to a rest frame and would correspond to a time axis (ct ) at 45 degrees relative to the ct axis. - The axes shown at right are allowed as the primed ct axis is < 45 degrees from the ct axis. - Here the x axis is & must be different from x as it represents the space axis of the moving frame. (Often - The Twin paradox space-time diagram is drawn with axes in the earth s rest frame only!) - The primed coordinate axes are not and must not be perpendicular to each other, only one frame defined as at rest can have orthogonal coordinates in special relativity (see detail and ref. below)!* Events that are simultaneous for one observer are not for the other. - Observers see events parallel to his/her space axis as simultaneous. - The primed coordinates are not orthogonal! lines parallel to the ct axes are fixed in x space just as lines parallel to ct axis are fixed in x space! *for reference angle α is given by tan(α) = v/c, where v is the speed of the prime frame relative to light speed c. for more details see the first few sections of: Quantum Physics and Beyond Yale Physics 120 3/26/2018 John Harris 22
23 Simultaneity and Causality Space-time diagrams (Minkowski space) Time on the y axis Distance on the x axis Light cone Interval AB is time-like There is a frame of reference in which events A and B occur at the same location in space, separated only by time. If A precedes B then A precedes B in ALL frames Information can travel from A to B - there s a causal relationship. Interval AC is space-like There is a frame of reference in which events A and C occur at the same time (simultaneously), separated only by space. In some frames A precedes C and in others C precedes A. A and C are not causally connected. Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 23
24 Understanding the Space-time Diagram Quantum Physics and Beyond Yale Physics 120 3/26/2018 John Harris 24
25 Physics 120 Question Event B is simultaneous with event A in which reference frame? 1) ct 2) ct 3) ct Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 25
26 Physics 120 Question Event B is simultaneous with event A in which reference frame? 1) ct 2) ct 3) ct Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 26
27 Physics 120 Question Event A occurs before event B in which reference frame? 1) ct 2) ct 3) ct Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 27
28 Physics 120 Question Event A occurs before event B in which reference frame? 1) ct 2) ct 3) ct Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 28
29 Physics 120 Question Event B occurs before event A in which reference frame? 1) ct 2) ct 3) ct Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 29
30 Physics 120 Question Event B occurs before event A in which reference frame? 1) ct 2) ct 3) ct Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 30
31 Twins Paradox! D H G C F B A E Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 31
32 Twins Paradox! Bob sends signals to Alice. Alice sends signals to Bob. D H G C F B A E See video for an easy-to-understand perspective with some additional information: Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 32
33 Problem - Train in Tunnel Paradox! When both at rest, train longer than tunnel. Train moving at v =0.8c Tunnel at rest. Train length contracted Train fits in tunnel. Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 33
34 Problem - Train in Tunnel Paradox! Train at rest Tunnel moving at v =0.8c. Tunnel length contracted Train does not fit in tunnel! Events no longer simultaneous! We re now in a different frame. Clocks simultaneous in one frame Not in another! Right clock reads earlier time! Left clock s time is behind (according to observers on train)! Note: train sees tunnel clocks ticking slowly. Left clock reaches 0 after right clock does. So, the end of the train will be in the tunnel when the left clock reads 0! Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 34
35 ct Problem - Train in Tunnel Paradox! Trajectory of tunnel entrance ct B ct (trajectory of earth) C A F D Trajectory of tunnel exit E G H J x (space axis of earth) Yale Physics 120 3/26/2018 Quantum Physics and Beyond John Harris 35
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