Harrison B. Prosper Florida State University Young Scholars Program
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- Slide 1
- 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
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- Topics A Glorious Failure Special Relativity Summary
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- 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.
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- 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
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- 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.
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- 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?
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- Measuring The Aether Wind Michelson Experiment (1881)
Michelson-Morley Experiment (1887)
http://erwin.phys.virginia.edu/classes/109/lectures/michelson.html
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- 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!
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- The Lorentz-FitzGerald Theory FitzGerald (1851-1901) Lorentz
(1853-1928)
http://www-history.mcs.st-and.ac.uk/~history/Mathematicians
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- 14 March, 1879, Ulm, Germany Hermann Einstein Pauline Einstein
Albert
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- Aarau Class of 1896 From 1896-1900, Einstein was enrolled at
the Eidgenssische Technische Hochschule, Zurich Marcel
Grossman
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- 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
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- 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
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- 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
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- 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
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- 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?
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- 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.
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- 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
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- Experiment - Conclusion The only way to avoid a contradiction
is if where
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- 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!
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- 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
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- 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
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- 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
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- Length Contraction You You:D = v T d = v t v = d / t v = D / Td
= D / (T / t) d = D / Prof
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- 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
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- Space + Time = Spacetime The distinction between past, present
and future is only an illusion, even if a stubborn one. Albert
Einstein
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- 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
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- 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!
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- 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