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June 2001Frank Sciulli - Lecture IPage 1 Head for Understandable Description of Matter and Forces at the Most Fundamental Level N.

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Presentation on theme: "June 2001Frank Sciulli - Lecture IPage 1 Head for Understandable Description of Matter and Forces at the Most Fundamental Level N."— Presentation transcript:

1 June 2001Frank Sciulli - Lecture IPage 1 Head for Understandable Description of Matter and Forces at the Most Fundamental Level N

2 June 2001Frank Sciulli - Lecture IPage 2 Particles and Forces tell us about the beginning of the Universe N

3 June 2001Frank Sciulli - Lecture IPage 3 Is this a Belief System? NO! Science does use the beauty of ideas, but ultimately relies on EXPERIMENT!!

4 June 2001Frank Sciulli - Lecture IPage 4 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 ! ! ! !

5 June 2001Frank Sciulli - Lecture IPage 5 Approach to the Subjects Eclectic: factual, historical, experimental, … Lets start with pre-20th Century Particles and Forces : Newton’s Laws (Galileo,…) Energy and Work Thermodynamics Chemistry … atoms? Optics, fluids, waves,...

6 June 2001Frank Sciulli - Lecture IPage 6 Classical particles and waves Classical particle scattering (balls) Water waves hit slits Double slit Single slit

7 June 2001Frank Sciulli - Lecture IPage 7 Newton’s Laws for Particles Forces from elsewhere Gravity, electricity, magnetism, ….

8 June 2001Frank Sciulli - Lecture IPage 8 Consolidation of Electricity and Magnetism by Maxwell (1864) Source of E is charge (Gauss Law) Established clear rules for fields as the origin of EM force. Made rules consistent! They read No magnetic charge Faraday’s Law of Induction Source of B is charge motion + Maxwell’s new Displacement Current

9 June 2001Frank Sciulli - Lecture IPage 9 Implications: Electromagnetic Waves

10 June 2001Frank Sciulli - Lecture IPage 10 Michaelson Interferometer Observer sees fringes (light and dark pattern), corresponding to constructive and destructive interference: For example, if 2d 2 -2d 1 changes by /2, fringe pattern shifts Became important element in central problem of 100 yrs ago: why is

11 June 2001Frank Sciulli - Lecture IPage 11 PROBLEM Velocity of a mechanical wave depends only on the medium, not the velocity of the source (even though frequency and wavelength change - Doppler shift) 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 the velocity of the mechanical wave relative to the observer obeys the same rules as a travelling particle: relative velocities Light also has velocity independent of source speed But MEs state EM waves have v=c

12 June 2001Frank Sciulli - Lecture IPage 12 Most obvious resolution: Luminiferous Ether V =30km/s Earth motion around sun 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!

13 June 2001Frank Sciulli - Lecture IPage : Michaelson-Morley idea

14 June 2001Frank Sciulli - Lecture IPage 14 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 Apparatus on bed of liquid mercury, rotate by 90 degrees

15 June 2001Frank Sciulli - Lecture IPage 15 Michaelson Morley Experiment - “Big” Physics of 1887 V =30km/s Earth motion around sun  m Make d as large as possible CONCLUDE: No phase shift was observed NO ETHER … ?!%*

16 June 2001Frank Sciulli - Lecture IPage 16 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 rocketPlane shoots laser

17 June 2001Frank Sciulli - Lecture IPage 17 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

18 June 2001Frank Sciulli - Lecture IPage 18 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 + Lorentz Contraction + Time Dilation

19 June 2001Frank Sciulli - Lecture IPage 19 Transformations of Position and Time

20 June 2001Frank Sciulli - Lecture IPage 20 Reversible Check if these equations give correct answer: For x’=ct’ ….. x=ct ?

21 June 2001Frank Sciulli - Lecture IPage 21 Limiting cases = v/c So this  is essentially ONE unless the object is near the velocity of light… where it rises very rapidly. v << c

22 June 2001Frank Sciulli - Lecture IPage 22 Time Dilation and Lorentz Contraction Happening in S’ at x’=0 over  t’ Rod at rest in S’, with length L 0 Length in S is L, measure ends at same time:  t=0

23 June 2001Frank Sciulli - Lecture IPage 23 Relativistic Invariants

24 June 2001Frank Sciulli - Lecture IPage 24 Implications of Relativity for Particle Momentum and Energy Nonrelativistic Relativistic Implication: Matter is a form of energy. At v=0, E=mc 2.

25 June 2001Frank Sciulli - Lecture IPage 25 Transformation of Momenta/Energy

26 June 2001Frank Sciulli - Lecture IPage 26 Energy/Momentum/Mass and Units Universal energy units are joules (traditionally); but a much simpler one for dealing with particles: eV eV/c eV/c 2 MeV MeV/c MeV/c 2 GeV GeV/c GeV/c 2 XX (with electric charges that are multiples of the electron)

27 June 2001Frank Sciulli - Lecture IPage 27 Mass is Energy and vice versa 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~10 9 eV/c 2 Note that mass of proton is ~ 1 GeV/c 2 Ultra - microscopic systems (nuclei and smaller), energies of constituents get comparable or larger than their rest mass What about EM fields? N

28 June 2001Frank Sciulli - Lecture IPage 28 Mass Disappears-Energy Appears FUSION Mass difference of.0304u = 28.3 MeV/c 2 becomes energy N

29 June 2001Frank Sciulli - Lecture IPage 29 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

30 June 2001Frank Sciulli - Lecture IPage 30 Metastable Matter (Radioactive Decay makes a clock) Example 128 I nuclide with T 1/2 = 25 minutes. Compare: 14 C has T 1/2 = 5730 yrs.  has T 1/2 = 3.75  sec Characterized by lifetime (  ) or half-life (T 1/2 =  ln2 = 0.7  )

31 June 2001Frank Sciulli - Lecture IPage 31 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 ~ sec N

32 June 2001Frank Sciulli - Lecture IPage 32 Real World Test of Relativity: Fermilab Complex Four mile circumference Tevatron Ring 15 story high rise

33 June 2001Frank Sciulli - Lecture IPage 33 Accelerators Raise Kinetic Energy using Electric Fields = v/c Each loop, the energy of protons are raised by increment determined by electric potential:  E =e  V  = E/m Proton total Energy versus velocity measure velocity

34 June 2001Frank Sciulli - Lecture IPage 34 Accelerated protons have very large energy Extracted protons have energy E  800 GeV Beam protons hit stationary target (E t =m) with very large kinetic energy  = E b /m What happens????

35 June 2001Frank Sciulli - Lecture IPage 35 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.

36 June 2001Frank Sciulli - Lecture IPage 36 Beams of pions made from collisions of high energy protons Beam line, 0.78 km long, transports 140 GeV  ’s made at tgt  WRONG!!

37 June 2001Frank Sciulli - Lecture IPage 37 Right answer: Lab perspective Right!!!  v

38 June 2001Frank Sciulli - Lecture IPage 38 Right answer: pion perspective Right!!!  v

39 June 2001Frank Sciulli - Lecture IPage 39 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!


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