PHYS 248 C: Unraveling
the Dark Universe with
the Large Hadron Collider
Shih-Chieh Hsu
University of Washington Seattle
PHYS 248C - Lecture 3 Relativity I
PAA A 214
Tue/Wed/Thu/Fri: 9:30am-12:00pm
1
Relativity I
•
Reference from Tipler chapter 39-1 to 39-3
• Historical Remark
• Newtonian relativity
• Einstein’s postulates
• Lorentz transformation
• Time dilation
• Length contraction
• The relativistic Doppler effect
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Relativity
Einstein was far from being the only person who
contributed to the development of the theory of special
relativity. However, he was the one who put everything
together. Some important years:
1904 Lorentz transformation/Poincare
1905 Special Relativity - inertial frame
1915 General Relativity - non-inertial frame
(acceleration frame)
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Newton
1687
Sir Isaac Newton published his book Philosophiae naturalis principia mathematica (or just
Principia). In classical Newtonian mechanics, time was universal and absolute.
Isaac Newton
4
Maxwell
1873
James Clerk Maxwell completed his theory of electromagnetism. This theory turned out to be
compatible with special relativity, even though special relativity was not known at that time.
James Clark Maxwell
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Michelson-Morley
1887
The famous Michelson-Morley experiment was performed by Albert Abraham Michelson and
Edward Williams Morley. In the same year, during studies of the Doppler effect, Woldemar
Voigt wrote down what were later to be known as the Lorentz transformations.
The Nobel Prize in
Physics 1907 - Albert
Abraham Michelson
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Larmor and Lorentz
1898
The Lorentz transformations were also written down in 1898 by Joseph Larmor and in 1899 by
Hendrik Antoon Lorentz.
The Nobel Prize in Physics 1902 - Hendrik Antoon Lorentz
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Poincaré
1898
Jules Henri Poincaré said that "... we have no direct intuition about the equality of two time
intervals."
1904
Poincaré came very close to special relativity: "... as demanded by the relativity principle the
observer cannot know whether he is at rest or in absolute motion."
Jules Henri Poincaré
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Special Relativity
1905
On June 5, Poincaré finished an article in which he stated that there seems to be a general law
of Nature, that it is impossible to demonstrate absolute motion. On June 30, Einstein finished
his famous article On the Electrodynamics of Moving Bodies, where he formulated the two
postulates of special relativity. Furthermore, in September, Einstein published the short article
Does the Inertia of a Body Depend upon Its Energy-Content? In which he derived the formula
E0=mc2.
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Planck
1908
Max Planck wrote an article on special relativity. He was the second person after Einstein who
wrote an article about this theory. In the same year, Hermann Minkowski also published an
important article about special relativity.
The Nobel Prize in Physics 1918 - Max Karl Ernst Ludwig Planck »
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General Relativity
1915
On November 25, nearly ten years after the foundation of special relativity, Einstein submitted
his paper The Field Equations of Gravitation for publication, which gave the correct field
equations for the theory of general relativity (or general relativity for short). Actually, the
German mathematician David Hilbert submitted an article containing the correct field equations
for general relativity five days before Einstein. Hilbert never claimed priority for this theory.
The Nobel Prize in Physics 1921 - Albert Einstein »
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Wave theory of light
Is light a wave or a particle?
Huygens first proposed wave theory of light. (1678)
What is a wave?
an oscillation accompanied by a transfer of energy that travels through
space or mass.
Propagation in media. Interference
frequency
=1/T
Unit: [s-1]
Wave velocity =λ/T
=λf
Unit: [m/s]
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Diffraction
Particle theory of light
1660
Refraction Phenomenon
Hypothesis: Huygen’s wave
theory explains refraction due
to white light corruptions in
glass.
-> Experiment: The more glasses the more corruption.
Result: decomposed light depends on the
refraction angle but not amount of
materials passing through.
Conclusion: wave theory is wrong.
Newton's sketch of his crucial experiment. Image credit: Warden and Fellows.
New theory: white light is
composed of different
colored particle
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Wave theory returns
Young’s Double-slit experiment
Fresnel’s single-slit experiment
1801
1816
Interference
Diffraction
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Electromagnetic theory
15
Electric Field
Electric field’s SI units are newtons per coulomb (N⋅C−1) or, equivalently,
volts per metre (V⋅m−1)
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Magnetic field
B is measured in teslas
(symbol:T) and newtons per
meter per ampere (symbol:
N·m−1·A−1 or N/(m·A)) in the
SI.
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Electromagnetic theory
Gauss’s Law
Gauss’s Law for magnetism
1835
Absence of free magnetic poles
Faraday’s Law of Induction
Ampère's Circuital Law
1831
1826
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Gauss’s Law
Maxwell’s equation (Integral form)
Gauss’s Law for magnetism
1835
Absence of free magnetic poles
Faraday’s Law of Induction
Ampère's Circuital Law
1831
1826
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Gauss’s Law
Maxwell’s equation (Differential form)
Gauss’s Law for magnetism
1835
Absence of free magnetic poles
Faraday’s Law of Induction
Ampère's Circuital Law
1831
1826
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Maxwell’s EM wave equation
1861
c
=299792458 m/s
=3x108m/s
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Light is a Wave
c = constant in vaccum
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