1. E = mc2 The most well-known yet misunderstood scientific equation
“E” is energy
“m” is mass
“c” is the speed of light = 186,000 mps = 3108 m/s
Gregory R. Snow
UNL Department of Physics and Astronomy

2. UNL High Energy Physics Group
Faculty members: G. Snow (1993), D. Claes (1996),
K. Bloom (2004), A. Dominguez (2004)
Main research area is experiments at particle accelerator
laboratories:
Fermilab in Batavia, Illinois
CERN in Geneva, Switzerland
Plus secondary activities in Ultra-High Energy Cosmic
Ray physics (Pierre Auger Observatory) and an associated
cosmic ray education/outreach experiment (CROP)
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3. Fermilab in Batavia, Illinois
Feynman Computing
Center
Wilson Hall DØ
CDF
Lederman Education
Center + new
Visitor Center
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4. High Energy Physics is the study of the smallest pieces of matter
Discovery of the “Top Quark”
in 1995
Particle Detector at Fermilab
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5. The Large Hadron Collider at CERN in Geneva
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6. CMS Experiment at CERN in Geneva
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7. UNESCO declared it as the International Year of Physics
2005 was declared the World Year of Physics by the IUPAP (International Union of Pure and Applied Physics)
UNESCO declared it as the International Year of Physics
(UNESCO: United Nations Education, Scientific,
and Cultural Organization)
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8. Why ?
The year 1905 was marked by the publications of Einstein in Annalen der Physik (one of the most important physics journals of the time).
Regularly only three papers are mentioned, but like the The Three Musketeers, there were four.
Annalen der Physik 17, (1905)
Annalen der Physik 17, (1905)
Annalen der Physik 17, (1905)
Annalen der Physik 18, (1905)
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9. Einstein was 26 years old in 1905 !
Albert Einstein
Einstein was 26 years old in 1905 !
Young Einstein, Swiss patent office
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10. Albert Einstein
Elder Einstein
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11. Albert Einstein
Elder Einstein
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12. Über einen die Erzeugung und Verwandelung des Lichtes betreffenden heuristischen Gesichtspunkt.
Annalen der Physik 17, (1905)
(On an heuristic aspect concerning the production and transformation of light)
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13. The Photoelectric Effect
The effect was discovered by
Heinrich Hertz in 1887 and
explained by Albert Einstein
in 1905.
According to Einstein's theory,
light is composed of discrete
particles of energy, or quanta,
called PHOTONS. When photons
with enough energy strike a metallic
surface, they liberate electrons that have
a kinetic energy equal to the energy of the photons less
the “work function” (the energy required to free the
electrons from a particular material).
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14. The first paper of the miraculous year is about the birth of the photon. Light as a stream of individual particles, complementary to the idea that light behaves as a wave.
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15. The existence of the light quanta, later named photon, was not immediately accepted by the physicists of the time.
Only after the discovering of the Compton effect, the photon was accepted. The Compton paper appears in 1923.
Curiously, Einstein got the Noble Prize for the photoelectric effect two years earlier
(in 1921).
Among other consequences it gives the way to the Quantum Mechanics, a theory that Einstein never liked.
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16. April
On 30 April, Einstein completed the work for his doctoral thesis, accepted by the University of Zurich.
Concerned “osmotic pressure”, developed a statistical theory of liquid behaviour based on the existence of molecules.
He showed how to calculate Avogadro's number and the size of molecules by studying their motion in a solution.
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17. Über die von der molekularkinetischen Theorie der Wärne geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen.
Annalen der Physik 17, (1905)
(On the Movement of Small Particles suspended in a Stationary Liquid Demanded by the Molecular Theory of Heat)
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18. This paper refers to Brownian motion.
The botanist Robert Brown (1827) observed that pollen grains suspended in water jiggled about under the lens of the microscope, following a zigzag path like.
Einstein combined kinetic theory and classical hydrodynamics to derive an equation that showed that the displacement of Brownian particles varies as the square root of time.
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19. Einstein showed that the movement of the particles was due to the thermal agitation of the molecules in the surrounding liquid.
The theory was confirmed experimentally by Jean Perrin three years later, proving once and for all that atoms do exist.
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20. Brownian motion Explanation: visible particles move due to
collisions with invisible
atoms in fluid
What we observe
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21. Despite often being obscured by the fame of his papers on special relativity and the photoelectric effect, Einstein's thesis on Brownian Motion became one of his most quoted works.
It was a strong support for the development of the Statistical Mechanics
The influence on the Hydrodynamics, Physical Chemistry, and Biology is remarkable.
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22. Zur Elektrodynamik bewegte. Annalen der Physik 17, 891-921 (1905)
(On the electrodynamics of moving bodies)
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23. Einstein develops the theory of special relativity in this paper.
It has about 30 pages long and containing no references.
He had an idea about synchronizing clocks that were spatially separated. It changed all our understanding of space and time.
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24. Einstein built a completely new theory of motion that revealed Newtonian Mechanics to be an approximation that only holds at low, everyday speeds.
The theory later became known as the theory of special relativity - special because it applies only to non-accelerating frames - and led to the realization that space and time are intimately linked to one another. “We live in a 4-dimensional world.”
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25. The AXIOMS of SPECIAL RELATIVITY
The speed of light is constant no matter what.
The laws of physics don’t change from one inertial reference frame to another.
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26. Some consequences of special relativity
Velocity addition
Time dilation
Length contraction
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27. Laser beam shot from moving cart
v = c
Laser beam
“c” is the
speed of light
v = c (!)
v = c/2
Laser beam shot from moving cart
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28. Length contraction Stationary ruler
Same ruler moving fast with respect to us
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29. Special relativistic effects only measurable
for speeds that approach c
Length contraction factor
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30. Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?
Annalen der Physik (1905).
(Does the inertia of a body depend on its energy content?)
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31. This equation was to become the most famous in all of science.
Written as a brief follow-up to the special relativity paper, this short note derives the inertia of energy: all energy E also has an inertia equal to E/c2, i.e. that E = mc2
This equation was to become the most famous in all of science.
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32. 11/10/2018

33. We now write
this as
E = mc2
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34. A closer look at E = mc2 E = mc2 is a special case of a formula that
relates an object’s total energy to its momentum
and mass:
E2 = p2c2 + m2c4
“E” is energy, “p” is momentum (measure of impact
in a collision, for example), and “m” is mass.
When an object is stationary, its momentum p = 0.
Then the above formula becomes E = mc2
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35. A closer look at E = mc2 E = mc2 describes the inter-convertibility of
energy and mass
c2 is like a currency exchange rate between
the U.S. Dollar and the Euro. The energy exchange
rate is very favorable. A small amount of mass
can be converted to a tremendous amount of
energy.
Let’s see some examples of E = mc2 in action,
2 examples of mass into energy, 2 examples of
energy into mass
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36. The atomic bomb dropped on Hiroshima August 6, 1945
0.6 gram of 235U converted to energy
(Nuclear “fission” process)
0.6  10-3 kg x (3 x 108 m/s) x (3 x 108 m/s)
= 5.4 x 1013 Joules of energy
(heat, light, kinetic energy)
Equivalent of 15,000 tons of TNT
140,000 fatalities,
city destroyed
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37. Energy from the Sun
In a multi-step “fusion” process, 4 protons (Hydrogen nuclei) combine
to make one Helium-4 nucleus.
The Helium nucleus is 0.7% less massive than the original 4 protons
– the mass converted to the energy of gamma rays and neutrinos.
26.73 MeV of energy released in the multi-step fusion process.
3.4  1038 protons converted to Helium each second,
equivalent to 4 x 109 kg/s or 4 million metric tons per second
About 100 earth masses have been converted to energy in the
Sun’s 4 billion year lifetime
This results in 1000 Watts/m2 reaching the earth’s surface in the form
of light and heat.
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38. “Top quark” Production in proton-proton Collisions at Fermilab
Protons and antiprotons, each with
a mass of about 1 GeV energy
equivalent, collide with a total energy
(mass + kinetic energy) of 2000 GeV.
A top quark and its antiquark partner
are produced, each of which have
a mass of 170 GeV. The original
proton and antiproton are destroyed,
converting 12% of their total energy
into the mass of the top quarks.
Higher and higher energy particle
accelerators exploit E = mc2 to
produce more and more massive
particles.
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39. Extensive Cosmic Ray Air Showers
The most impressive conversion of energy to mass
that I know of occurs when a high-energy cosmic
ray particle from outer space converts its energy
into the mass of billions of secondary particles
through collisions with molecules in the Earth’s
atmosphere.
Astrophysicists measure properties of the original
cosmic ray particle by detecting the secondary
particles on the Earth’s surface.
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40. Development of an extensive air shower in the Earth’s atmosphere
Primary cosmic ray
Development of an extensive air
shower in the Earth’s
atmosphere
Mostly muons, electrons and photons at Earth’s surface
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41. A 1019 eV Extensive Air Shower
100 billion particles
at sea level
Mostly muons, photons,
and electrons
Note the large ground area
hit by shower particles
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42. How a cosmic-ray air shower is formed and detected
Primary cosmic rays (mostly protons or light nuclei)
impinge on earth’s atmosphere from outer space
“Air shower”
of secondary
particles
formed by collisions
with air molecules
Grid of particle detectors
intercept and sample
portion of secondaries
Number of secondaries
related to energy of primary
Relative arrival time
reveals incident direction
3. Depth of shower maximum
related to primary particle
type
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43. The Pierre Auger Observatory
Auger north is planned in Colorado
The Pierre Auger Observatory
Auger south is here.
Malargue is a small town on the high plains not far from a ski area in the Andes.
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44. Installation nearly complete
As of October 20, 2007, 1500 of 1600 SD stations
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45. The Detectors
Let me focus a bit more on the power of the hybrid design.
Remark on each of the features of the hybrid design. I will illustrate these features of the hybrid design as I go along.
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46. Event timing and direction determination
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47. Major result from the Observatory will be
featured in the November 9 issue of Science (cover story)
Super-galactic
plane
Galactic
coordinates
“Correlation of the highest energy cosmic rays with
nearby extragalactic objects”
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48. This presentation ignores Einstein’s other contributions to Physics, like the theory of “General Relativity” in 1948
And his many contributions to the promotion of peace, like his warnings about the dangers of developing nuclear weapons
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