Relativity part 1
Where Do We Come From? What Are We? Paul Gauguin (1897) Where Are We Going? Museum of Fine Arts, Boston
Topics • A Glorious “Failure” • Special Relativity • Summary
A Glorious “Failure”
James Clerk Maxwell (1831-1879) Maxwell’s Equations describing electric and magnetic fields in a vacuum. http://www.pa.msu.edu/courses/1997/spring/PHY232/lectures/emwaves/maxwell.html
Electro + Magnetism = Light ”We can scarcely avoid the conclusion that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena.” Maxwell (1866) Moreover, light travels at a specific speed in this medium (the aether): 300,000 km/s
The Aether Wind Taking the stars as our reference, the Earth travels at about 30 km/s around the Sun. Therefore, it was argued (in the late 1870s), the aether should be flowing past us at a speed close to 30 km/s, since the aether is surely at rest relative to the stars.
Swimming The Aether Sea Michelson’s clever idea: Speed of water relative to bank: 3 ft/s Speed of swimmer relative to water: 5 ft/s Who wins the race? b w a c
Measuring The Aether Wind Michelson Experiment (1881) Michelson-Morley Experiment (1887) http://erwin.phys.virginia.edu/classes/109/lectures/michelson.html
A Glorious “Failure” “The interpretation of these results is that there is no displacement of the interference bands. … The result of the hypothesis of a stationary aether is thus shown to be incorrect.” A. A. Michelson, Am. J. Sci., 122, 120 (1881) Nobel Prize 1907!
The Lorentz-FitzGerald Theory FitzGerald (1851-1901) Lorentz (1853-1928) http://www-history.mcs.st-and.ac.uk/~history/Mathematicians
Special Relativity1905
Hermann Einstein 14 March, 1879, Ulm, Germany Albert Pauline Einstein
Aarau Class of 1896 Marcel Grossman From 1896-1900, Einstein was enrolled at the Eidgenössische Technische Hochschule, Zurich
Technical Expert, Third Class Einstein got a job at the Swiss Patent Office in Bern, on the 23 June 1902 Six months later, he married his Serbian girlfriend, Mileva
1905 – Annus Mirabilis • 17 March • A new theory of light • 30 April • A new method to infer the size of molecules • 11 May • A new theory of Brownian motion • 30 June • A new theory of space and time
Special Relativity Principles • The Principle of Relativity: The laws of physics are the same in all inertial frames of reference • The speed of light, in vacuum, is independent of the motion of its source It follows from the above that the speed of light must be independent of the motion of the observer, also.
v T c T d Time Dilation (cT)2 = (vT)2 + d2 T = time in frame in which clock is moving
Time Dilation – II Moving clock frame (cT)2 = (vT)2 + d2 t =T / g Stationary clock frame d = c t t = time in frame in which clock is stationary
Prof Length Contraction d = v t You: D = v T d / t= v = D / Td = D / (T / t) d = D / g
Time Dilation and Length Contraction Moving clocks tick more slowly Moving lengths contract T is time in moving clock frame t is time in stationary clock frame D is length in stationary object frame d is length in moving object frame
Moving clocks run more slowly! Moving objects shorten! But, what Einstein recognized is that this effect must, by the principle of relativity, be perfectly symmetrical between different frames of reference.
Cosmic Ray Muons ~ 20 km Time to the ground 20km / 300,000 km/s ~ 70 microsecond For every 35 microseconds of our clock, the muon’s “clock” advances only 1 microsecond! Muon lifetime ~ 2 microsecond
Space + Time = Spacetime The distinction between past, present and future is only an illusion, even if a stubborn one. Albert Einstein
Event: A place at a given time Spacetime: The set of all events Earth’s Time Axis 3007 AD now D C B (t,x,y,z) 2507 AD A 2007 AD y x O
Summary • Michelson found no evidence of motion through an aether. • Lorentz and Fitzgerald proposed a clever, but ad hoc, theory to explain the result • Einstein’s theory is based on two principles: • Principle of relativity: The laws of physics are the same in all inertial frames of reference • The speed of light is independent of the motion of the light source
