Physics 120 Quantum Physics and Beyond Today! General Relativity Accelerated Frames General Relativity Light in General Relativity Motion and Time in General Relativity Back to Quantum Entanglement? More examples EPR and Bell Theorem Threat to Special Relativity? John Harris 1
The Laws of Physics & Special Relativity are valid for all Inertial Frames of Reference! What about Non-inertial frames? Quantum Physics and Beyond Yale Physics 120 4/4/2018 John Harris 2
In special relativity, What about Accelerated Frames? Einstein postulated that the laws of physics (including c) are the same in all uniformly moving frames. What s so special about special relativity? Coordinate systems, their relative motion, & transformations are confusing! What about all the other possible coordinate systems? spinning, accelerating,. Einstein (in 1905) was not satisfied with special relativity! He sought a more general theory Totally independent of coordinate systems John Harris 3
Physics 120 Question 1 What if I were to fall (or jump) from a diving platform and at the same time I lost grip of my cell phone which then dropped from my hand? What would I observe? 1) My lighter cell phone would hit the water before me. 2) Being over 100 times more massive and heavier than my cell phone, I would hit the water first. 3) Cannot tell, it depends on if our wave functions were entangled. 4) None of the above John Harris 4
What Einstein Thought about Accelerated Frames Einstein recalled the happiest thought of his life (in 1907) if he were falling from a house accelerating downward and were to drop an object from his hand the object would appear to him as if it were at rest as in any other coordinate or reference frame Does the gravitational field have only a relative existence? As he falls from his roof, it seems not to exist! Relativity must extend to coordinate systems in non-uniform motion! John Harris 5
Einstein s General Relativity If you were in a sealed spaceship (or elevator ) in deep space (no local gravity) accelerating upward (relative to observer) at 9.8 m/s 2. You could not tell the difference between this constant acceleration and a constant gravitational force. a = g a = 0 g Elevator accelerating upward with g no gravity Elevator stopped, gravity g acceleration mimics gravity Principle of Equivalence: Impossible to distinguish an acceleration of a frame of reference from effects of gravity. In General Relativity, Einstein postulated that the laws of physics are the same to all observers, whether inertial or accelerated. John Harris 6
Motion of Objects in General Relativity In a sealed spaceship in deep space (no local gravity) accelerating upward (relative to observer project a ball horizontally: a a a a Outside observer sees ball travel in straight line. Inside observer sees ball s trajectory bend as if in gravitational field. John Harris 7
Physics 120 Question 2 What about light? If I were sitting still on earth in a rocket ship and a light beam shot horizontally across my rocket The light beam would: 1) bend downward along its trajectory across the ship (orange arrow). 2) shoot straight across the ship (green arrow). g 3) do neither of the above. Yale Physics 120 4/4/2018 Quantum Physics and Beyond John Harris 8
Light in General Relativity a By Equivalence Principle - if light is deflected by acceleration, then it must be deflected by gravity! Analogous situation for light! Inside observer sees light bend as if in a gravitational field. Newton - gravitational force is proportional to masses of objects! Light is massless, how can gravity affect it? Einstein s initial response? Einstein predicted that starlight would be deflected when passing by the sun This has been observed, measured consistent with GR. In earth s g field, light falls vertical distance of 4.9 m in 1 second! Travels horizontal distance of 300,000 km in that time. John Harris 9
Einstein s View of General Relativity (GR) Dynamics is replaced by geometry Space is warped by massive bodies (in 2d like a rubber sheet with heavy objects on it) Intrinsically curved 4-dimensional space-time universe uses tensor calculus + differential geometry difficult to intuit: e.g. make a flat map of the earth s surface! trajectories are treated in x, y, z, t Gravity must affect time as well as any straight-line motion. John Harris 10
Gravitational Fields & Time What is the impact of gravitational field or acceleration on time (clocks)? John Harris 11
Time Dilation due to Gravitational Fields Gravitational Fields & Time Consider a light beam (from a b and from c d) John Harris 12
Einstein s General Relativity A clock in a strong gravitational field runs more slowly than a clock in a weak gravitational field t 0 = time as measured in the gravitational potential (G) at distance r from mass M r decreases t f = time as measured in no gravitational potential (infinite distance from any mass) G = Newtonian gravitational constant M = mass of object (constant) r = distance from massive object s center c = speed of light (constant) Earth Executive working in Manhattan skyscraper ages more by a few micro-seconds per decade than twin! John Harris 13
Einstein s View of General Relativity (GR) By the principle of equivalence - An accelerated clock must run slower than non-accelerated one Gravity affects time as well as a straight-line path. ω John Harris 14
Einstein s General Relativity Observations that a clock in a strong gravitational field runs more slowly than a clock in a weak gravitational field Example - gravitational red shift atomic clocks slowing down of electron vibrations (GR) atomic spectra from sun lower frequency due to GR light (spectral lines) from sun frequency decreases Λ increases Λ shifts to red John Harris 15
Classic Examples as Tests of GR for notes 1) Mercury s precession of its perihelion - not elliptical - gravitation from other planets - gravitation from sun 2) Bending of light around sun 1919 - British eclipse expedition 1979 - gravitational lensing of a quasar by a massive galaxy (saw two images!) 3) Effect of gravity on clocks 1959-2 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) 1976 - atomic clock in rocket measured gravitational red shift to.02% John Harris 16
Video Clip A Conflict is Building Quantum Mechanics and General Relativity From The Elegant Universe (find online, shown in class): http://www.pbs.org/wgbh/nova/physics/elegant-universe.html#elegantuniverse-einstein Part 1, Chap 7, (start at 41:00 to 51:10, 10 minutes) John Harris 17
Back to Quantum Entanglement? John Harris 18
Quantum Eraser, Delayed Choice Eraser & Entanglement Videos assigned to view for this class: Quantum Eraser (10 min) https://www.youtube.com/watch?v=8orln_kwags Quantum Entanglement (11 min) https://www.youtube.com/watch?v=tafgl02euoa Suggest viewing, not assigned before this class, but good description pointing out philosophical implications: Delayed Choice Quantum Eraser (11 min) https://www.youtube.com/watch?v=h6hljpj4nt4 John Harris 19
Discussion of Delayed Choice Quantum Eraser! John Harris 20
Quantum Eraser Setup Quantum Eraser: https://www.youtube.com/watch?v=8orln_kwags Which-way information No interference pattern John Harris 21
Delayed Choice Quantum Erasure Quantum Eraser: https://www.youtube.com/watch?v=8orln_kwags Which-way information erased interference pattern returns John Harris 22