RELATIVITY 1 Harrison B Prosper Florida State University

RELATIVITY 1 Harrison B. Prosper Florida State University Young Scholars Program

Where Do We Come From? What Are We? Where Are We Going? Paul Gauguin (1897) 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/PHY 232/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): 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 1870 s), the aether should be flowing past us at a speed close to 30 km/s, 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 b Speed of swimmer relative to water: w 5 ft/s Who wins the race? 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-Fitz. Gerald Theory Lorentz (1853 -1928) Fitz. Gerald (1851 -1901) http: //www-history. mcs. st-and. ac. uk/~history/Mathematicians

SPECIAL RELATIVITY 1905

14 March, 1879, Ulm, Germany Albert Pauline Einstein Hermann 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 – Postulates Principle of Relativity The laws of physics are the same in all inertial frames Principle of Constancy of Speed of Light The speed of light in vacuum is independent of the motion of its source The first principle implies that the speed of light is also independent of the motion of the observer

Experiment – At Rest A Measure time for a light ray to go from A to B to A in a frame of reference in which experiment is at rest relative to the observer t = 2 d / c B d t = distance between A and B = time to go from A to B to A c = speed of light in vacuum

Experiment – Moving A We now look at the same experiment from a reference frame in which the experiment is moving relative to that frame t = 2 d / c B The emission of the light ray at A and its arrival At B must also occur in the moving frame Why?

Because Events are Real ! An event is a physical occurrence: The birth of a baby The emission of a light pulse The explosion of a star, etc… Therefore, every observer will agree on the existence of events.

Experiment - Moving A (c. T/2)2 = (v. T/2)2 + d 2 v. T/2 d c. T/2 But, …. t = 2 d / c B T = time to go from A to B to A

Experiment - Conclusion The only way to avoid a contradiction is if where

Moving Clocks Run More Slowly… Therefore, if you move at a constant velocity relative to me, your clock runs slower than my clock. But this law of Nature most hold true in your inertial frame also according to the principle of relativity. Therefore, if I move at a constant velocity relative to you, my clock must also run slower than your clock!

Relativity of Simultaneity This paradoxical situation is resolved, as are almost all paradoxes in relativity, because of the relativity of simultaneity: Two events that are simultaneous in one inertial frame are not, in general, simultaneous in another inertial frame moving relative to the first

Relativity of Simultaneity A B C A flash of light at C, midway between A and B, will be detected at A and B simultaneously when viewed by an observer at rest relative C

Relativity of Simultaneity A B C A flash of light at C, midway between A and B, will be detected at A before B according to an observer moving relative to C

Length Contraction d=vt You: You D = v T v=d/t v=D/T d = D / (T / t) d=D/γ Prof

Space-Time Diagrams Events can be represented as points in a space-time diagram Those that have the same time values (in a given frame of reference) such as events A and B, are said to Time be simultaneous A B Space

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 3000 AD D C now B (t, x, y, z) 2500 AD A x O y 2000 AD

Cosmic Ray Muons ~ 20 km Time to the ground 20 km / 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

Summary l Michelson found no evidence of the Earth’s motion through an aether. l Lorentz and Fitzgerald proposed a clever, but ad hoc, theory to explain the result l Einstein proposed a different theory based on two postulates: l Principle of relativity: relativity The laws of physics are the same in all inertial frames of reference l The speed of light is independent of the motion of the light source