1 / 47

The Origin of Mass in Particle Physics

Lecture I: Concepts in Classical Physics. Lecture II: Concepts in Special Relativity and Quantum Mechanics. Lecture III: The World of the Small and the Fast. The Origin of Mass in Particle Physics. 60 th Compton Lectures Ambreesh Gupta.

violetta-michel
Download Presentation

The Origin of Mass in Particle Physics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture I: Concepts in Classical Physics Lecture II: Concepts in Special Relativity and Quantum Mechanics Lecture III: The World of the Small and the Fast. The Origin of Mass in Particle Physics 60th Compton Lectures Ambreesh Gupta

  2. Nobel Prize 2004 "for the discovery of asymptotic freedom in the theory of the strong interaction" David J. GrossUniversity of California, Santa Barbara H. David PolitzerCalifornia Institute of Technology, Pasadena Frank WilczekMassachusetts Institute of Technology, Cambridge http://mitworld.mit.edu/video/204/ Frank Wilczek’s Lecture Origin of Mass and Feebleness of Gravity

  3. x 0,0 0,1 10,0 10,1 z Getting Directions y

  4. Reference Frame 3 Space + 1 Time are sufficientto describe nature!

  5. But...Is it possible that there are extra space dimensions? We will get back to this in the seventh lecture

  6. Greek Science and Numerology Thales: The father of Greek mathematics. Pythagoras: Entire universe can be described in numbers. Aristotle: Systematized logic, which forms the basis of western science.

  7. Aristotelian Logic It is impossible for the same thing at the same time to belong and not belong to the same thing in the same respect . . . Not ( A )  A

  8. Earth at the Center: Geocentric Universe Aristotle: . Earth is at the center of the Universe . ‘Prime Movers’ responsible for movement of planets and stars. Ptolemy: . 100 A.D . Refined Aristotle’s model . Calculation devise for astronomical predictions. Dominant view for over 2000 years.

  9. Sun at the Center: Heliocentric Model Nicolaus Copernicus (1514) . Geocentric model too complicated . . . Ockham’s Razor? . First attempts resulted in worse predictions . “On the Revolutions”, published when he was on his deathbed.

  10. Galileo . Modified the telescope created in 1608 to magnify objects 30 times . He increasingly believed that the geocentric picture was wrong . Published “Dialogue Concerning the two world system: Ptolemaic and Copernican”

  11. Kepler . Used Tycho Brahe’s astronomical data to infer elliptical planetary orbits - 8 minute discrepancy . Gave three laws of planetary motion - elliptical planetary orbits - equal time sweeps equal area - relation between time period and average distance Why do planets follow these rules?

  12. Newton The laws of physics until the time of Newton’s, involved only space and time. Newton for the first time introduced the concept of mass in the laws of physics. Revolutionary implication: Same underlying law for all massive objects! The Mathematical Principles of Natural Philosophy: Principia …considered the most influential publication in the history of science.

  13. Principia : Definitions Principia defines three “Fundamental quantities” Length, Time, Mass Meter Second Kilogram as measurable and objective.

  14. m1 m2 r Principia: Newton’s Law Three laws of motion 1st Law of Inertia 2nd Law of Acceleration F=ma 3rd Law of Action and Reaction The Universal Law of Gravity F = G (m1m2 / r2) Two laws of Conservation 1st Law of conservation of Mass 2nd Law of Conservation of Momentum

  15. Unification With these laws, Newton could account for all types of motion: falling bodies on the surface of earth and heavenly bodies in the sky. Which body reaches the lower edge first?

  16. “I have seen farther, it is by standing on the shoulders of giants” - Newton in a letter to Robert Hooke “. . .Our understanding does not advance just by slow and steady building on previous work. Sometimes as with Copernicus and Einstein, we have to make a leap to new world picture. Maybe Newton should have said “I used the shoulders of giants as a springboard.” - Stephan Hawking in “On the Shoulder of Giants”

  17. A little more on the “Why’s” Q. Why do planets follow elliptical path? (Kepler) A. Because of the Nature of gravitational force. (Newton) Q. Why do massive bodies attract each other? (Newton) A. Because massive bodies curve space-time fabric. (Einstein) Q. Do the why’s ever end? A.I don’t know.

  18. mA mB r uA uB mA mB Newton’s Second Law: F=ma Defines Force or Mass? • Ernest Mach’s definition: • Use Newton’s second & third law • mA/mB = - (aB/A/aA/B) • Herman Weyl’s definition: • mA/mB = - (uB/uA)

  19. Inertial vs. Gravitational Mass Newton’s Gravitation Law Newton’s Second Law mi a = G(mgMg /r2) Mg mi, mg r Are mi and mg the same? Equivalence Principle

  20. Testing Equivalence Principle Newton - fractional accuracy of 1 part in 100 Loránd Eötvös (1848-1919 ) - fractional accuracy of 1 part in 100000000 Eöt-Wash Group - fractional accuracy of 1 part in 10000000000000 STEP: Satellite test of the equivalence principle - fractional accuracy of 1 part in 1000000000000000000

  21. Units: How do we define units of length, time and mass? Some early definitions, . The Kings arm or span of his foot . Weights convenient quantities carried in hand or back . Time followed astronomical variation of the Earth and Moon

  22. Average height of the crowd?!

  23. Natural Units Max Planck based the natural units on the “Fundamental Constants of Nature” Gravitational Constant G = 6.6742 x 10-11 m3 kg-1 s-2 Planck's Constant h = 6.626 0693 x 10-34 kg-m2/s Speed of Light c =299 792 458 m s-1 Electron Charge e = 1.602 176 53 x 10-19 C Are the fundamental constants of nature truly constant?

  24. +q1 -q2 r Fine Structure Constant:  Coulombs LawF  (q1q2)/r2 • = e2/ħc = 1./137.03559 Dimensionless Constant of Nature “…one of the greatest damn mysteries of physics: a magic number that comes to use with no understanding by man. You might say the ‘hand of God’ wrote that number, and ‘we don’t know how He pushed His pencil.’”– Richard P. Feynman, QED

  25. Realms of Physical Laws Small Classical Mechanics Quantum Mechanics Fast Quantum Field Theory Relativistic Mechanics How do we define length and time?

  26. Natural Units Max Planck based the natural units on the “Fundamental Constants of Nature” Gravitational Constant G = 6.6742 x 10-11 m3 kg-1 s-2 Planck's Constant h = 6.626 0693 x 10-34 kg-m2/s Speed of Light c =299 792 458 m s-1 Electron Charge e = 1.602 176 53 x 10-19 C Are the fundamental constants of nature truly constant?

  27. Fields The concept was introduced by Michael Faraday in 1844-46 Electric Field E = k Q /r2 Gravitational Field g= GM /r2 Scalar Field

  28. Electromagnetic Waves Until now we have dealt primarily with particles… - have mass, momentum, energy etc. Waves are disturbance that carry energy - without transporting matter - can refracts, reflect, interfere EM waves are disturbances in electric and magnetic field

  29. Ether & Michelson-Morley Experiment Successive experimentation Gave null result...no ether.

  30. Difficulties between Newtonian relativity and EM There is no reference frame in which an EM wave can be at rest…in conflict with Newtonian(Galilean) relativity

  31. Special Relativity In 1905, Albert Einstein postulated 1. Physical law’s invariant between reference frames. 2. Speed of light is same in all inertial frames. Solved Newtonian relativity conflict. …changed notion of space and time. Energy, momentum and mass E2 = p2 + m2c4

  32. v  + + + + ++ + + + + + + + + - - - - - - - - - - - - -  v r u q v+ + + + + + + + + + ++ + + + + + + + + + - - - - - -  v- r q Deriving magnetic field from EM and SR . We do not know about the existence of magnetic field . No electric force on ‘q’ in lab frame . Net force on ‘q’ in its rest frame . Transform force from ‘q’ rest frame to lab frame The form of this transformed force is like magnetic force!

  33. More on Units 1 eV ( electron Volt ) is the energy required to move an electron through a potential difference of 1 volt. 1 eV = 1.6  10-19 J (kg-m2/s2) In the rest frame of electron: E (=mc2) = 81.9  10-14 J Mass of electron: me = 0.511 MeV/c2 h/2=1, c=1 (Energy Units) 1 kg ~ 1027 GeV ; 1 m = 1016 GeV-1; 1 s = 1024 GeV-1 1 TeV = 1000 GeV = 1000000 MeV = 1012 eV Mass of a Proton: mp ~ 1 GeV

  34. Black Body Radiation Classical theory predicted that E()  2 In 1900 Max Planck proposed E() = h This was the first step toward Quantum Physics!

  35. De’Broglie, Schroedinger and Heisenberg De’Broglie relates particle and wave =h/p - provides a description for Bohr’s atomic model Schroedinger’s equation of matter wave - wave functions encapsulate probability…success with hydrogen atom. Heisenberg’s Uncertainty Principle - presence of probability implies uncertainty - xp  h/2 - tE  h/2

  36. 1 2 3 Electron source The Archetypical Double Slit Experiment Which of the three distributions should one expect in an experiment ?

  37. Feynman’s Path Formalism Consider all paths between two points Assign amplitude to each path Probability of event = |Sum of amplitude of all path|2 Classical Path For 1g particle: non classical path Probability zero. For electron 10-27 g: similar probability for either path. Non Classical

  38. A  1 2 B Identical Particle Collision The probability of observing particles at detectors 1 and 2 depends if the particles are Identical or not. If ‘p’ is the probability to observe A or B particle at 1 or 2…. Probability( particle at 1 or 2 ) = 2p (not identical) Probability( particle at 1 or 2 ) = 4p (identical in QM)

  39. Mass…A clarification Weight = mass  gravitational acceleration

  40. Energy and Mass The most famous equation of Physics E=mc2 Mass of 2 proton and 2 neutron separately is larger than the mass of helium nucleus Mass difference 28 MeV

  41. Mass of a Proton Proton is made of u u d quarks Mass of proton = Mass of u and d quarks + Kinetic Energy of quarks + Potential Energy between quarks Most of Proton mass comes from energy components! As far as we know, Quark, Lepton and Force carrying Bosons are fundamental Where does their mass comes from?

  42. A D ? B C Bubble of Ignorance A simplified view of particle physics experiment

  43. Dirac’s Equation Dirac combined Quantum Mechanics and Special Relativity in one equation Successes - spin of electron occurred naturally - prediction of anti-matter Failures - magnetic moment of electron - creation and annihilation of particles

  44. Quantum Mechanics of Fields A theory that can handle particle creation and annihilation. Quantum field theory describes the quantum mechanics of fields, such as the electromagnetic field and the electron field. In this setup, particles and waves, both are different faces of the same type of object: the quantum field. Feynman’s pictorial representation of possibilities in the bubble of ignorance

  45. Quantum Electrodynamics The quantum field theory of electric charge and photons was formulated by R.P Feynman, J. Schwinger and S. Tomonaga (1965 Nobel Prize) Crown jewel of its prediction, magnetic moment electron Dirac Theory 1.0 QED 1.00115965221(4) Experiments 1.00115965246(20) Deviation of these numbers, especially magnetic moment of muon could hint the presence of new physics beyond Standard Model.

More Related