Lecture 2 Einstein Asserts Relativity July 31, 2017 Where We Are Now... Ruled out the possibility that Earth is at rest relative to the ether Earth alone at rest? Violates Copernicus! Ether Drag? Ruled out by aberration of starlight So Earth is moving relative to ether From Earth s point of view, there s an ether wind We should be able to detect that wind and thus determine Earth s motion through ether How? Because the speed of light should be different in different directions Faster when light is going with the wind Slower when light is going against the wind 1
Wave speed depends on wind speed and direction Wave speed relative to me Speed of medium relative to me Michelson-Morley Experiment An attempt to detect Earth s motion relative to the ether Compared speed of light in two perpendicular directions Did not measure the actual speed in two directions Michelson first performed in 1880-82, Europe Improved experiment by Michelson & Morley, 1887, Case School of Applied Science, Cleveland 10 times more sensitive than needed to detect Earth s orbital motion Used wave interference to achieve high sensitivity 2
A Boat Analogy for the M-M Experiment Which river paddle takes longer? Across & back Upstream/downstream Answer: Upstream/downstream Michelson-Morley Experiment MIRROR LIGHT SOURCE MIRROR VIEWER BEAM SPLITTER 3
Michelson-Morley Experiment The real thing Modern version using a laser pointer Michelson-Morley Experiment Ether wind MIRROR LIGHT SOURCE MIRROR VIEWER BEAM SPLITTER 4
Michelson-Morley Experiment Ether wind Michelson-Morley Experiment Ether wind 5
Michelson Reports the Results: The experiments on relative motion of earth and ether have been completed and the result is decidedly negative. The expected deviation of the interference fringes should have been 0.40 of a fringe the average [was] much less than 0.01 Michelson to Lord Rayleigh, August 17, 1887; quoted in Livingston, The Master of Light (Scribner s, 1973) The expected shift: 0.40 fringe Contradiction! Earth is not at rest with respect to the ether Copernican principle, aberration of starlight So Earth is moving with respect Ether wind to the ether MIRROR But it isn t!!! Michelson-Morley experiment LIGHT SOURCE VIEWER MIRROR BEAM SPLITTER 6
How We Got Here Asked: Speed c relative to what? Answer: Ether Asked: Is Earth moving relative to the ether? Answer (Copernican paradigm, aberration of starlight): It is Asked: How is Earth moving relative to the ether? Answer (Michelson-Morley experiment): It isn t CONTRADICTION! Also remember: that dichotomy in physics Mechanics obeys a relativity principle Electromagnetism doesn t An Unsuccessful Attempt to Resolve the Contradiction Lorentz-Fitzgerald contraction hypothesis (1892) All objects contract in the direction of their motion through the ether Michelson-Morley apparatus shrinks on the upstream/downsteam arm by just the right amount to make the travel times equal This explains the null result of the experiment But ad hoc hypothesis with no physical justification or theoretical basis 7
Resolved in 1905 by Albert Einstein Source (both photos), Einstein: A Portrait (Pomegranate Artbooks, 1984) 1905 Einstein s Miracle Year April 30: Doctoral dissertation A New Determination of Molecular Dimensions June 9: Quantum nature of light On a Heuristic Point of View Concerning the Production and Transformation of Light July 18: Convincing proof that atoms exist On the Movement of Small Particles Suspended in Stationary Liquids September 26: Special Theory of Relativity On the Electrodynamics of Moving Bodies November 21: E=mc 2 Does the Inertia of a Body Depend on Its Energy Content? 8
The Resolution (Einstein, 1905) There is no ether But then with respect to what does light go at speed c? With respect to any observer in uniform motion Principle of Relativity holds in all of physics, electromagnetism as well as mechanics No experiment can answer the question Am I moving? Microwaving a cup of tea: A Physics Experiment On Earth 9
Microwaving a cup of tea: A Physics Experiment On a Cruise Ship Microwaving a cup of tea: A Physics Experiment On Venus 10
Microwaving a cup of tea: A Physics Experiment On an Earthlike planet in a distant galaxy, moving rapidly away from Earth On the Electrodynamics of Moving Bodies A. Einstein (Ann. Physik, 17, 891, 1905) It is known that Maxwell s electrodynamics when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. Take, for example, the reciprocal action of a magnet and a conductor. The observable phenomenon here depends only on the relative motion of the conductor and the magnet Examples of this sort, together with the unsuccessful attempts to discover any motion of the earth relative to the light medium, suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good 11
Special Theory of Relativity The laws of physics are the same for all observers in uniform motion This includes electromagnetism, with its prediction of electromagnetic waves (light) that travel at speed c Therefore all observers in uniform motion will measure the same value for the speed of light even if they re moving relative to each other! Speed of Light c = 299,792,458 meters per second Exact value, used since 1982 to define the meter Approximate values 186,000 miles/second 300,000 km/second 1 foot/nanosecond 1,000 feet/microsecond 12
Measuring the Speed of Light 1 2 c 600 mph c 70 mph Measuring the Speed of Light 1 2 c c 13
Measuring the Speed of Light c 1 2 c Space & Time in Special Relativity Laws of physics are the same for all observers in uniform motion That includes electromagnetism, with its statement that light propagates at speed c But then measures of space and time can t be the same! Space and time are relative 14
Special Theory of Relativity The laws of physics are the same for all observers in uniform motion (Einstein, 1905) Simple: Physics is the same for everyone as long as they re in uniform motion; here on Earth, on Venus, on a planet in a distant galaxy moving rapidly with respect to Earth. The universe couldn t be simpler! Conservative: Asserts for all of physics what was already true for mechanics that your state of motion doesn t matter. Radical: Alters profoundly our common-sense notions of space and time. Common Sense? Common sense is that layer of prejudice laid down in the mind before the age of 18 - A. Einstein 15
Being Relativistically Correct (RC) What s wrong with these statements? Alice: Bob s clock and meter stick must be wrong, and his measures of time and space are therefore different, because he s moving Bob: Alice s clock and meter stick must be wrong, and her measures of time and space are therefore different, because she s moving Correct: Alice or Bob: The other s clock and meter stick read different quantities than mine, because we re in relative motion Ending Quiz State Einstein s Special Theory of Relativity in a single English sentence The laws of physics are the same for all observers in uniform motion 16