2. HOW PHYSICS LOOKS TO A BEGINNING STUDENT

3. A 21 st Century Approach to Introductory Physics Let’s start with a description of our current paradigm of the nature of the Universe Larry Curtis Distinguished University Professor of Physics and Astronomy University of Toledo

4. THE NATURE OF MATTER _________________________________________________________ All matter consists of little bits of positive and negative electricity: in perpetual motion; attract each other at short distances; repel each other when pressed too close together. ________________________________________________________ The most important discovery ever made. If all other scientific information we know were lost in some cataclysmic event, and only this information survived, all could be rediscovered in a very short time. - Richard P. Feynman ` ////

5. Iron atoms positioned on a carbon surface

6. Second Quantization - The Discrete Photon

7. 700 keV Li + beam (v=4.4 mm/ns) incident on a thin (3  g/cm 2 ) carbon foil. The blue light is H-like 4f-5g in Li 2+ ( 4500Å,  =3 ns,  x=1.3 cm). The green light is He-like 2s 3 S-2p 3 P in Li + ( 5485Å,  =44 ns,  x=19 cm).

8. Can we picture attractive and repulsive interactions without the force concept? Quantum Field Theory is conceptually easy!

9. ACTION-AT-A-DISTANCE Exchange of a ‘gauge boson’ Particle exchange can produce both attraction and repulsion. It is intermittent, like rain on the roof. The Force concept requires an average over a time interval.

10. Interactions between any two particles involves all the particles in the universe.

11. Intrinsic Action  Quantized: ħ /2 = building blocks  Odd#: 1 st quant. (inter. Part.) / Even#: 2 nd quant. (gauge bosons)  Odd #: FD stat. / Even #: BE stat. / Together: MB stat.  Least Action – gives conservation laws, dynamics  Energy = Action/Time; Momentum = Action/Length  Least Action + Quantization = Uncertainty Principle  A Lorentz Invariant  Mechanical action  parity

12. Conservation of Action http://www.youtube.com/watch?v=AQLtcEAG9v0

13. Strike a billiard ball so it rolls w/o slipping? If we use the line of action of the impulse as the fulcrum, there are NO torques ! The angular momentum is the same before and after the impulse.

14. Speed at which a sliding ball rolls w/o slipping ? Use conservation of angular momentum about the point-of contact with the floor, so there are no torques. at release alley exerts friction rolls w/o slipping

15. Action & Quantum Statistics

18. Least Action Action Quantization Minimum Uncertainty

19. LEAST ACTION – What is the path between (x 1,y 1,t 1 ) and (x 2,y 2,t 2 ) ? Total Energy = Kinetic Energy + Potential Energy “Action” = [Kinetic Energy – Potential Energy]  t The particle does whatever it wants, but we see the path where the Total “Action” summed over all points adds up to the smallest value. On this path the Total Energy is the SAME for each point

21. Nature chooses the space-time path of minimum action and that path must contain an integer number action “quanta” Action canonically welds: Momentum-to-Length Energy-to-Time This leads to an “Uncertainty Principle” between them

22. Principle of Least Action Interactive

23. THE SPACE-TIME CONTINUUM The Magnetic Field Zitterbewegung – Spin & magnetic moment of a point particle One unique electron The PET scan as a time traveler

24. TIME “Time is what keeps everything from happening at once.” - Attributed to John Archibald Wheeler Quoted by Woody Allen “Time flies like an arrow; fruit flies like a banana.” - Groucho Marx ‘Backward turn, turn backward, O time in your flight. Make me a child again, just for tonight.’ - Elizabeth Akers Allen

25. Nature has revealed a beautiful secret! The behavior of the Universe becomes very simple if it is described in a way in which space and time are symmetric. What makes it seem hard, is the fact the we must live our lives by standing at a point in space and watching time pass, but not the reverse. It’s like our perspective in riding the Earth around the Sun, which seems as if the Sun were going around us. However, the heliocentric equations are much simpler.

26. Model for a current in a wire Variously delayed photon arrivals make lengths appear shorter and charge appear denser. If q moves with the electron drift, the positive charge appears denser, giving a repulsion. If q moves opposite to the electron drift, the negative charge appears denser, giving an attraction. This is magnetism, and results from relativity at speed ~ 0.1 mm/sec ! Woldemar Voigt 1887

28. How can a point particle exhibit angular momentum and magnetic moment ? Zitterbewegung, averaged over time, has a finite extent commensurate with Compton wavelength. Virtual photons possess spin, cause Zitterbewegung region to precess, circulating mass and charge.

29. Electron-Positron Pair Creation and Annihilation Once created, e + and e - are stable until annihilated

30. Past Future Here-Now Are they all really the same electron? time space

31. PET scan: Ingest sugar with tagged positron-emitting Fluorine-18 (110 min. halflife). Sugar concentrates at high metabolism. On decay, positrons encounter electrons.

32. Ragnar Hellborg Lund University Positron Emission Tomography (PET) Scan

33. Laplacian Determinism – A Costly Mistake Pierre Simon Laplace - 1776: “An intelligence that knows all of the relations of the entities of the universe at one instant could state their positions, motions, and general effects any instant in the past of future. Henri Poincare – 1903: “Small differences in the initial conditions can produce very great ones in the final phenomena – prediction Then becomes impossible (1st recognition of chaos). Werner Heisenberg – 1924: There is a fundamental limit on the accuracy to which position and velocity can be co-determined. Stephen Hawking –1988: In the cosmology of the Big Bang and Black Holes, space and time themselves break down.

34. Position Probability Density Dwell Time

35. Why didn’t Isaac Newton think about the possibility of getting hit on the head when he sat under the apple tree?   x 

36. Where does the pendulum spend the most time? The least time?

37. Dwell time: High: many / slow Low: Few / fast Time exposure

38. Equal time inside No time outside Most time at end points Least time at center Most time at aphelion and perihelion

41. The secret of life, computers, & transitors

42. 1-D Periodic Motion Non-relativistic conservative potential Periodic motion with turning points Distribution (x m  x  x m ) Box: SHO:

43. So in general Where V(x) can be any algebraic or numerical function.

44. Solve Numerically : First normalize Then evaluate

45. Einstein-Brillouin-Keller Action Quantization (1917) (1926) (1958) Bohr-Sommerfeld-Wilson quantization used fuzzy math, neglecting caustics at turning points in librations. The correct semiclassical action quantization condition is: where  i = 0 (rotations) = 2 (librations) Topological Maslov Index It yields astonishingly accurate results !!!

46. Average Values of Powers of the Coordinate