Report

N Head for Understandable Description of Matter and Forces at the Most Fundamental Level June 2001 Frank Sciulli - Lecture I Page 1 Particles and Forces tell us about the beginning of the Universe June 2001 Frank Sciulli - Lecture I Page 2 N Is this a Belief System? NO! Science does use the beauty of ideas, but ultimately relies on EXPERIMENT!! June 2001 Frank Sciulli - Lecture I Page 3 Four Lectures Leading to the Standard Model of Particle Physics - A Paradigm • Particles, Light, and Special Relativity • Quantum Mechanics, Atoms and Particles • Particles, Forces, and the Electroweak Interaction • Hadrons, Strong Force and the Standard Model Illustrate, hopefully, that Physics (Science) has as ultimate arbitrator NATURE ! ! ! ! June 2001 Frank Sciulli - Lecture I Page 4 Approach to the Subjects Eclectic: factual, historical, experimental, … Lets start with pre-20th Century Particles and Forces: June 2001 • Newton’s Laws (Galileo,…) • Energy and Work • Thermodynamics • Chemistry … atoms? • Optics, fluids, waves, ... Frank Sciulli - Lecture I Page 5 Classical particles and waves Classical particle scattering (balls) June 2001 Water waves hit slits Frank Sciulli - Lecture I Page 6 Newton’s Laws for Particles Forces from elsewhere Gravity, electricity, magnetism, …. Get acceleration from F ma For no acceleration, its simple x x 0 vt (Even Galileo knew the last one!) June 2001 Frank Sciulli - Lecture I Page 7 Consolidation of Established clear rules for fields as the Electricity and origin of EM force. Magnetism by Maxwell Made rules consistent! They read (1864) Q Source of E is charge (Gauss Law) E 1 0 2 B 0 No magnetic charge Faraday’s Law of Induction Source of B is charge motion + Maxwell’s new Displacement Current June 2001 c B E t E B 0J 0 0 t Frank Sciulli - Lecture I Page 8 Implications: Electromagnetic Waves c June 2001 1 0 0 Frank Sciulli - Lecture I 3 10 m/s 8 Page 9 Michaelson Interferometer Observer sees fringes (light and dark pattern), corresponding to constructive and destructive interference: For example, if 2d2 -2d1 changes by /2, fringe pattern shifts Became important element in central problem of 100 yrs ago: why is c 1/ 0 0 const?? June 2001 Frank Sciulli - Lecture I Page 10 But the velocity of the PROBLEM mechanical wave relative to Velocity of a mechanical the observer obeys the same rules wave depends only on the as a travelling particle: medium, not the velocity relative velocities of the source (even though frequency and wavelength change - Doppler shift) c 2 B Light also has velocity independent of source speed June 2001 Example, it is possible for a “listener” to travel faster than a sound wave. In this case, the sound will never catch up to the listener. Sound wave in “A” never catches “B” if v>c But MEs state EM waves have v=c Frank Sciulli - Lecture I Page 11 Most obvious resolution: Luminiferous Ether • Provides transmission medium, in analogy with that required by mechanical waves • Provides a “special” frame of motion … where the laws of E&M (Maxwell’s Equations) are valid - All other frames of reference (in motion relative to the special one), Maxwell’s Equations are only approximately true! • Essential element of scientific hypothesis: provides a possibility for testing! June 2001 Frank Sciulli - Lecture I V=30km/s Earth motion around sun Page 12 1887: Michaelson-Morley idea June 2001 Frank Sciulli - Lecture I Page 13 Michaelson - Morley Expt Use velocity of Earth around the sun v =30km/s Rotate apparatus by 90 deg… change in relative phase of the two light rays by is expected 2 L 2dv c 2 2 Apparatus on bed of liquid mercury, rotate by 90 degrees June 2001 Frank Sciulli - Lecture I Page 14 Michaelson Morley Experiment “Big” Physics of 1887 V=30km/s Earth motion around sun 5 10-7 m Make d as large as possible June 2001 2 L 2dv 2 v2 8 4 10 c2 d 2 107 0.1 rad c 2 CONCLUDE: No phase shift was observed NO ETHER … ?!%* Frank Sciulli - Lecture I Page 15 Einstein’s Reasoning Maxwell’s Equations (eg Law of Induction at left) do not depend on which is moving relative to what. So it is reasonable that the value of c coming out of the equations should not depend on state of motion of anyone! Sound a bit crazy? Not to Albert Einstein! Newtonian mechanics with objects or (mechanical) waves: velocity is relative to motion of observer! OLDTHINK… Plane shoots rocket June 2001 Frank Sciulli - Lecture I Plane shoots laser Page 16 Conundrum EITHER light is like mechanical waves: E&M only valid in one frame!? OR light is NOT like mechanical waves; E&M valid in all frames, independent of their motion Einstein chose the latter Einstein “Laws of Physics the same in all inertial frames” MEANS Maxwell’s equations valid in all non-accelerating coord. systs BUT this implies that velocity of light = c in vacuum no matter where the light comes from and how fast you are moving c 1/ 0 0 June 2001 Frank Sciulli - Lecture I Page 17 Einstein Postulates (1905) require (a) speed of light (in vacuum) same in all inertial frames (b) speed of light (in vacuum) independent of the motion of source CARRY MANY IMPLICATIONS + June 2001 Frank Sciulli - Lecture I Lorentz Contraction + Time Dilation Page 18 Transformations of Position and Time Galilean (Newton) x x ' vt ' y y' z z' t t' June 2001 c 3 10 m/s 8 1 Lorentz (Einstein) x ( x ' vt ') v/c 0 1 y y' z z' v/c 0 1 t (t ' vx '/ c 2 ) 1 (v / c)2 Frank Sciulli - Lecture I Page 19 Reversible 1 1 ( v / c) 2 x ( x ' vt ') y y' z z' t (t ' vx '/ c 2 ) Check if these equations give correct answer: For x’=ct’ ….. x=ct ? June 2001 Frank Sciulli - Lecture I x ' ( x vt ) y' y z' z t ' (t vx / c ) 2 Page 20 v << c Limiting cases 2 1v 1 ... So this is 2 2c 1 (v / c) essentially ONE unless the object is near the velocity of light… where it rises very rapidly. 1 June 2001 = v/c Frank Sciulli - Lecture I Page 21 Time Dilation and Lorentz Contraction t (t ' v x '/ c ) 2 Happening in S’ at x’=0 over t’ t t ' x ' (x vt ) Rod at rest in S’, with length L0 Length in S is L, measure ends at same time: t=0 L June 2001 Frank Sciulli - Lecture I L0 Page 22 Relativistic Invariants 1 1 ( v / c) 2 x ( x ' vt ') y y' z z' t (t ' vx '/ c 2 ) x y z c t invariant 2 2 2 2 2 (x ') ( y ') (z ') c (t ') 2 June 2001 2 Frank Sciulli - Lecture I 2 2 Page 23 2 Implications of Relativity for Particle Momentum and Energy Nonrelativistic p mv 1 2 K mv 2 Relativistic 1 1 ( v / c) 2 K ( 1)mc Implication: Matter is a form of energy. At v=0, E=mc2. E p c m c 2 June 2001 p mv 2 2 2 4 Frank Sciulli - Lecture I E K mc E mc 2 2 Prove it! Page 24 2 Transformation of Momenta/Energy 1 1 ( v / c) 2 x ( x ' vt ') y y' z z' t (t ' vx '/ c ) 2 p x ( px vE / c 2 ) p y py pz pz E ( E vpx ) June 2001 Frank Sciulli - Lecture I Page 25 Energy/Momentum/Mass and Units Universal energy units are joules (traditionally); but a much simpler one for dealing with particles: E pX c m X c 2 eV MeV GeV 2 eV/c MeV/c GeV/c 2 2 4 eV/c2 MeV/c2 GeV/c2 Sensible units for discussion (with electric of atoms and subatomic particles charges that is the electron volt = eV are multiples of 1 eV = energy gained by electron the electron) (or proton) by acceleration through q 1.6 1019 Coulomb precisely V = one volt. 1 ev = q V 1.6 1019 joules June 2001 Frank Sciulli - Lecture I Page 26 Mass is Energy and vice versa N • Macroscopic systems, mass stays essentially the same and kinetic energies small compared to rest mass energy: separate! • Microscopic systems (atoms), energies of electrons are small compared to mass of system: in hydrogen atom, U=13.6 eV but M~109 eV/c2 Note that mass of proton is ~ 1 GeV/c2 • Ultra - microscopic systems (nuclei and smaller), energies of constituents get comparable or larger than their rest mass What about EM fields? June 2001 Photons have no rest mass E p c Frank Sciulli - Lecture I Page 27 Mass Disappears-Energy Appears FUSION Mass difference of .0304u = 28.3 MeV/c2 becomes energy June 2001 Frank Sciulli - Lecture I Page 28 N Relativity is the way the world works Example: NAVSTAR Satellite system to track velocity of airplanes uses Doppler shifts. If non-relativistic Doppler formula were used, precision on velocity would be about 21 cm/s. If relativistic Doppler formula used, precision 1.4 cm/s Examples: Real-life everyday observations in particle and nuclear physics, where new matter is made and it spontaneously decays June 2001 Frank Sciulli - Lecture I Page 29 Metastable Matter (Radioactive Decay makes a clock) Characterized by lifetime () or half-life (T1/2 = ln2 = 0.7 ) 1000 100 10 1 June 2001 Example 128I nuclide with T1/2 = 25 minutes. Compare: 14C has T 1/2 = 5730 yrs. has T1/2= 3.75 10-8 sec N N0e R R0e Frank Sciulli - Lecture I t t Page 30 N Working with Unstable Matter Can Make for Problems! Just kidding … It’s actually not that hard! Here we use pions, unstable particles with mass of 140 Mev and lifetimes of ~ 3 10-8 sec June 2001 Frank Sciulli - Lecture I Page 31 Real World Test of Relativity: Fermilab Complex Four mile circumference Tevatron Ring June 2001 Frank Sciulli - Lecture I 15 story high rise Page 32 Accelerators Raise Kinetic Energy using Electric Fields Each loop, the energy of protons are raised by increment determined by electric potential: E =eV = E/m Proton total Energy versus velocity measure velocity = v/c June 2001 Frank Sciulli - Lecture I Page 33 Accelerated protons have very large energy Beam protons hit stationary target (Et=m) with very large kinetic energy = Eb/m What happens???? June 2001 Extracted protons have energy E 800 GeV Frank Sciulli - Lecture I Page 34 Collision of 300 GeV proton with stationary nucleon New kinds of particles made out of kinetic energy: mesons (pions) with mass of 140 MeV each. p p p p 28 Total Energy available for mass M 2 (E mp )2 p 2 with E mp M 2mpE 2(1 GeV )(300 GeV ) 2 M 24.5 GeV 28 m 3.9 GeV June 2001 Frank Sciulli - Lecture I Page 35 Beams of pions made from collisions of high energy protons L0 780 m 2.6 10 8 sec v 3 108 m / sec & t L0 /v t 2.6 10 6 sec t Nonrelativistic, 100 so fraction left e 100 3.7 10 44 WRONG!! June 2001 Beam line, 0.78 km long, transports 140 GeV ’s made at tgt Frank Sciulli - Lecture I Page 36 Right answer: Lab perspective E 140 GeV 1000 m 140 MeV v Observer: Time dilation lab 1000 2.6 10 8 lab 2.6 10 5 sec t 2.6 10 6 sec t 0.1 so lab Right!!! fraction left e 0.1 0.90 June 2001 Frank Sciulli - Lecture I Page 37 Right answer: pion perspective E 140 GeV 1000 m 140 MeV Pion sees: Lorentz Contraction v L 780 m L 0.78 m 1000 t June 2001 L c 2.6 10 7 sec 2.6 10 8 t Right!!! 0.1 so fraction left e 0.1 0.90 Frank Sciulli - Lecture I Page 38 Conclusions - Special Relativity • Relativity was required by experimental information at the time it was invented (1905) • It is essential now to describe the world, especially since we can directly observe objects travelling near the speed of light • The rules are, in fact, simple - see handout or website! • Do the problems and prove the simplicity! June 2001 Frank Sciulli - Lecture I Page 39