E = mc 2 The most well-known yet misunderstood scientific equation

1. E = mc2The 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)

3. Feynman Computing Center CDF DØ Wilson Hall Lederman Education Center + new Visitor Center Fermilab in Batavia, Illinois

4. High Energy Physics is the study of the smallest pieces of matter Discovery of the “Top Quark” in 1995 Particle Detector at Fermilab

5. The Large Hadron Collider at CERN in Geneva

6. CMS Experiment at CERN in Geneva

7. 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)

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 Physik17, 132-148 (1905) • Annalen der Physik17, 549-560 (1905) • Annalen der Physik17, 891-921 (1905) • Annalen der Physik 18, 639-641 (1905)

9. Albert Einstein 1879 - 1955 Einstein was 26 years old in 1905 ! Young Einstein, Swiss patent office

10. Albert Einstein 1879 - 1955 Elder Einstein

11. Albert Einstein 1879 - 1955 Elder Einstein

12. Über einen die Erzeugung und Verwandelung des Lichtes betreffenden heuristischen Gesichtspunkt. Annalen der Physik17, 132-148 (1905) (On an heuristic aspect concerning the production and transformation of light)

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).

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 ideathat light behaves as a wave.

15. The existence of the lightquanta, 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.

16. 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. April

17. Über die von der molekularkinetischen Theorie der Wärne geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Annalen der Physik17, 549-560 (1905) (On the Movement of Small Particles suspended in a Stationary Liquid Demanded by the Molecular Theory of Heat)

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.

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.

20. Brownian motion Explanation: visible particles move due to collisions with invisible atoms in fluid What we observe

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.

22. Zur Elektrodynamik bewegte. Annalen der Physik17, 891-921 (1905) (On the electrodynamics of moving bodies)

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.

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.”

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.

26. Some consequences of special relativity • Velocity addition • Time dilation • Length contraction

27. v = c Laser beam “c” is the speed of light v = c (!) v = c/2 Laser beam shot from moving cart

28. Length contraction Stationary ruler Same ruler moving fast with respect to us

29. Special relativistic effects only measurable for speeds that approach c Length contraction factor

30. Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig? Annalen der Physik 18639-641 (1905). (Does the inertia of a body depend on its energy content?)

31. 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.

33. We now write this as E = mc2

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

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

36. The atomic bomb dropped on HiroshimaAugust 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

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.

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 = mc2to produce more and more massive particles.

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.

40. Primary cosmic ray Development of an extensive air shower in the Earth’s atmosphere Mostly muons, electrons and photons at Earth’s surface

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

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

43. 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.

44. Installation nearly complete As of October 20, 2007, 1500 of 1600 SD stations

45. The Detectors

46. Event timing and direction determination

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”

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