Harrison B. Prosper Florida State University Young Scholars
Program
Slide 2
Where Do We Come From? What Are We? Paul Gauguin (1897) Where
Are We Going? Museum of Fine Arts, Boston
Slide 3
Topics A Glorious Failure Special Relativity Summary
Slide 4
Slide 5
James Clerk Maxwell (1831-1879)
http://www.pa.msu.edu/courses/1997/spring/PHY232/lectures/emwaves/maxwell.html
Maxwells Equations describing electric and magnetic fields in a
vacuum.
Slide 6
Electro + Magnetism = Light medium 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
aether300,000 km/s this medium (the aether): 300,000 km/s
Slide 7
The Aether Wind Taking the stars as our reference, the Earth 30
km/s 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 30 km/s to 30 km/s, since the aether is surely at
rest relative to the stars.
Slide 8
Swimming The Aether Sea ac b w Michelsons clever idea: Speed of
water relative to bank: 3 ft/s Speed of swimmer relative to water:
5 ft/s Who wins the race?
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!
Slide 11
The Lorentz-FitzGerald Theory FitzGerald (1851-1901) Lorentz
(1853-1928)
http://www-history.mcs.st-and.ac.uk/~history/Mathematicians
Slide 12
Slide 13
14 March, 1879, Ulm, Germany Hermann Einstein Pauline Einstein
Albert
Slide 14
Aarau Class of 1896 From 1896-1900, Einstein was enrolled at
the Eidgenssische Technische Hochschule, Zurich Marcel
Grossman
Slide 15
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
Slide 16
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
Slide 17
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
Slide 18
Experiment At Rest c t = 2d / c d= distance between A and B t=
time to go from A to B to A c c= speed of light in vacuum 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 A B
Slide 19
Experiment Moving We now look at the same experiment from a
reference frame in which the experiment is moving relative to that
frame B A c t = 2d / c The emission of the light ray at A and its
arrival At B must also occur in the moving frame Why?
Slide 20
Because Events are Real ! event 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.
Slide 21
Experiment - Moving c cT/2 vT/2 d T = time to go from A to B to
A A B c (cT/2) 2 = (vT/2) 2 + d 2 But,. c t = 2d / c
Slide 22
Experiment - Conclusion The only way to avoid a contradiction
is if where
Slide 23
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!
Slide 24
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
Slide 25
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
Slide 26
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
Slide 27
Length Contraction You You:D = v T d = v t v = d / t v = D / Td
= D / (T / t) d = D / Prof
Slide 28
Space-Time Diagrams Events can be represented as points in a
space-time diagram Time Space A B Those that have the same time
values (in a given frame of reference) such as events A and B, are
said to besimultaneous
Slide 29
Space + Time = Spacetime The distinction between past, present
and future is only an illusion, even if a stubborn one. Albert
Einstein
Slide 30
Earths Time Axis 3000 AD 2000 AD 2500 AD y x now Event: A place
at a given time Spacetime: The set of all events (t,x,y,z) A B CD
O
Slide 31
Cosmic Ray Muons ~ 20 km Muon lifetime 2 ~ 2 microsecond Time
to the ground 20km / 300,000 km/s 70 ~ 70 microsecond For every 35
microseconds of our clock, the muons clock advances only 1
microsecond!
Slide 32
Summary l Michelson found no evidence of the Earths 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
l Principle of 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