Simply Einstein A Mini-Course in Relativity

Transcription

1 Simply Einstein A Mini-Course in Relativity Rich Wolfson Prof of Physics Middlebury College Scientific American Travel Bright Horizons 32 July-August 2017 Simply Einstein A Mini-Course in Relativity Rich Wolfson Prof of Physics Middlebury College Scientific American Travel Bright Horizons 32 July-August

2 Simply Einstein A Mini-Course in Relativity Physics 101 Rich Wolfson Prof of Physics Middlebury College Scientific American Travel Bright Horizons 32 July-August 2017 Simply Einstein A Mini-Course in Relativity 1) A Brief History of Physics 2) Einstein Asserts Relativity 3) Time & Space in Relativity 4) Space, Time, & Causality 5) Black Holes & Gravitational Waves: The General Theory 2

3 A Brief History of Physics ~ : Galileo, Newton, and others develop a mechanical understanding of physical reality, based in laws of motion ~ : Maxwell and others develop an understanding of electromagnetic phenomena, including light ~1900 Einstein, Bohr, and others develop modern understanding of physical reality Motion! Why study motion? Because without motion nothing would happen Because to move is to move through space Because to move takes time 3

4 Questions about Motion What causes motion? Is there a natural state of motion? Aristotle s Answers What causes motion? On Earth, pushes and pulls (forces) In the heavens, a prime mover Is there a natural state of motion? On Earth, at rest as close as possible to Earth s center In the heavens, motion in perfect circles Different laws for different realms! 4

5 The Universe According to Aristotle & Ptolemy Sun Planet Earth The Universe According to Aristotle & Ptolemy Sun Planet Earth 5

6 The Universe According to Copernicus (~1540) Earth now less special! Earth Sun Planet Kepler & Galileo (~1600) Imperfection in the Heavens! Orbits not circular Orbit (highly exaggerated) Sun Planet Blemished Sun Jupiter s moons Phases of Venus 6

7 Galileo: Thoughts on Motion Galileo: Thoughts on Motion 7

8 Galileo: Thoughts on Motion Galileo s Answers What causes motion? No cause needed! Force causes change in motion Is there a natural state of motion? Uniform motion (straight line, constant speed) 8

9 Isaac Newton (b. 1643) 3 laws of motion: predictability! How forces cause change in motion Universal gravitation Every object in the universe attracts every other object Celestial motion explained But first invent calculus! One set of laws for all realms! And a relativity principle Galilean/Newtonian Principle of Relativity The laws of motion are the same for anyone in uniform motion You can play tennis on a cruise ship Only relative motion matters You can eat dinner on an airplane I am moving is a meaningless statement You can juggle on a moving cart There is no experiment involving the laws of motion that will answer the question Am I moving? 9

10 Relativity Principle at the Palace Hotel, Copenhagen Tennis: A Physics Experiment On Earth 10

11 Tennis: A Physics Experiment On a Cruise Ship Tennis: A Physics Experiment On Venus 11

12 Tennis: A Physics Experiment On an Earthlike planet in a distant galaxy, moving rapidly away from Earth History of Physics So Far Newtonian Physics (~ ) Unites the celestial and terrestrial realms under a common set of physical laws Newton s laws of motion Universal gravitation Natural state of motion is uniform motion Obeys a relativity principle: The laws of Newtonian physics (the laws governing motion) are the same for anyone who s in uniform motion. Statements like I am moving and I am at rest are meaningless. 12

13 What about Light? Newton (1600s): Light consists of Particles Huygens (1678): Light consists of Waves Young (1801): Experimental proof: It s Waves Something Waves Do That Particles Don t They undergo interference Constructive interference (Waves reinforce) 13

14 Something Waves Do That Particles Don t They undergo interference Destructive interference (Waves cancel) Young s Proof that Light Consists of Waves Passed light through two slits to create two light sources Observed interference of light from the two slits, thus proving conclusively that light consists of waves 14

15 What about Light? Newton (1600s): Light consists of Particles Huygens (1678): Light consists of Waves Young (1801): Experimental proof: It s Waves But waves of what? A New Realm of Physics Electricity Magnetism 15

16 Electric Charge A fundamental property of matter Comes in two kinds (B. Franklin) Positive (+) Negative ( ) Likes repel, opposites attract Force weakens with distance + Strong force (attractive) + + Weaker force (repulsive) A New Realm of Physics Electricity Magnetism 16

17 Magnetism Originates from moving electric charge Results in forces on other moving charges The Field Concept The old view: action at a distance Earth reaches out across empty space, pulls on Moon The new view: Earth creates a gravitational field throughout space Moon responds to the gravitational field at its location 17

18 Electric and Magnetic Fields Electric field Proton creates electric field electron responds to field Electric and Magnetic Fields Electric field Proton creates electric field Electron responds to field Magnetic field Magnet or moving charge creates magnetic field Magnet or moving charge responds to the field 18

19 Electricity and Magnetism So Far Electricity Electric charges produce electric fields Other charges respond to those fields Magnetism Moving electric charges produce magnetic fields Other moving charges respond to those fields With both electricity and magnetism Electric charge is the source of the fields (so far ) Changing E&M Fields Faraday (1831): Changing magnetic field creates electric field Basis of electric generators, computer disks, credit cards Electromagnetic induction 19

20 Electric & Magnetic Fields Changing magnetic field creates electric field Question: Does changing electric field create magnetic field? Maxwell (1860s): It should! Then each field is a source of the other! Maxwell s Insight Changing magnetic field creates electric field Changing electric field creates magnetic field So: Changing electric and magnetic fields regenerate each other and propagate through space electromagnetic waves 20

21 How Fast? How fast do electromagnetic waves go? Maxwell s theory says: 186,000 miles/second, 300,000 km/s the speed of light So What is Light? Light consists of electromagnetic waves Includes not only visible light but also radio waves, microwaves, infrared, ultraviolet, x-rays, gamma rays All these waves are essentially the same; they differ only in wavelength All propagate (in vacuum) at c, the speed of light 21

22 So What is Light? Light consists of electromagnetic waves Includes not only visible light but also radio waves, microwaves, infrared, ultraviolet, x-rays, gamma rays All these waves are essentially the same; they differ only in wavelength Maxwell s Equations And God said Equation E = ρ / ε 0 B = 0 E = B t B = µ 0 J + µ0 ε 0 E t What it says How charges attract/repel No isolated magnetic poles Changing magnetic field produces electric field Changing electric field produces magnetic field and there was light 22

23 A Brief History of Physics ~ : Galileo, Newton, and others develop a mechanical understanding of physical reality, based in laws of motion ~ : Maxwell and others develop an understanding of electromagnetic phenomena, including light A Nagging Question With respect to what does light go at speed c? Possible answer: With respect to its source Ruled out by observations, especially of double stars 23

24 A Nagging Question With respect to what does light go at speed c? Possible answer: With respect to its source Ruled out by observations, especially of double stars Equivalent question: In what frame of reference are the laws of electromagnetism (Maxwell s equations) valid? Corresponding Answers for Newtonian Physics With respect to what does a wave (sound, etc.) go at its characteristic speed? Answer: with respect to the medium in which the wave is a disturbance air, for sound waves water, for water waves etc. In what frame of reference are the laws of motion valid? Answer: In any uniformly moving frame of reference (Principle of Galilean relativity) 24

25 Light & Electromagnetism: 19 th Century Answers With respect to what does light go at speed c? Answer: With respect to the ether, a substance that permeates the universe and which is the medium in which electromagnetic waves (light) are disturbances Equivalent question: In what frame of reference are the laws of electromagnetism (Maxwell s equations) valid? Answer: in a frame of reference at rest with respect to the ether Properties of the Ether Very tenuous Planets move through it without resistance Able to penetrate everywhere Light propagates through otherwise empty space Very stiff Speed of light is fast! Not a gas or liquid; more like Jello Electromagnetic waves are transverse (disturbance is perpendicular to the wave s motion) 25

26 Don t like the Ether concept? Then you answer the question: With respect to what does light go at speed c? A Dichotomy in Physics Laws of motion (mechanics; Newtonian physics) obey a relativity principle The laws of mechanics work just the same in all uniformly moving frames of reference Absolute motion and absolute rest are meaningless in mechanics Laws of electromagnetism (Maxwell s equations, including the prediction of EM waves with speed c) are valid only in one frame of reference: the ether frame Absolute motion and absolute rest are meaningful in electromagnetism 26

27 Is Earth Moving Relative to the Ether? One possibility: IT ISN T The other possibility: IT IS Is Earth Moving Relative to the Ether? One possibility: IT ISN T. Then either: Earth alone among the cosmos is at rest relative to the ether Or, Earth drags with it the ether in its vicinity (and so do other astronomical bodies) 27

28 Aberration of Starlight: Umbrella Analogy (a) Stand still (b) Run (c) In runner's frame (d) With "air drag" Aberration of Starlight: The Real Thing With ether drag March 28

29 Aberration of Starlight: The Real Thing With ether drag September Aberration of Starlight: The Real Thing No ether drag September James Bradley,1727: angular position of star g-draconis March 29

30 Is Earth Moving Relative to the Ether? One possibility: IT ISN T. Then either: (Copernican paradigm) Earth alone among the cosmos is at rest relative to the ether (Aberration of starlight) Or, Earth drags with it the ether in its vicinity The other possibility: IT IS Then there should be an ether wind blowing past Earth We should be able to detect this wind and determine the speed and direction of Earth s motion through the ether Where We Are Now (late 1800s) Two branches of knowledge that describe all known physical reality Newtonian mechanics Phenomena involving motion Relativity principle holds Electromagnetism Phenomena involving electricity & magnetism Includes light Seems not to obey a relativity principle Valid in ether frame only Question: What s Earth s motion relative to ether? 30