Quantum time                            Is time quantized in the same way that space is                                   ...
`Clearly, the Time Traveller                            proceeded, `any                            real body must have ext...
Block universe                            Evolving universeSunday, November 29, 2009
Relativity                      “Henceforth space by itself, and time by itself, are                      doomed to fade a...
Quantum mechanics                   • space is fuzzy                   • time is a parameter                   • we build ...
How to combine?                   • Strings                   • Loop quantum gravity                   • Lots of others   ...
This is often the way it is in physics - our             mistake is not that we take our theories too             seriousl...
Laboratory time                 What clocks measureSunday, November 29, 2009
Quantum wave function                                    1                                 0.75                          ...
Train from Berne to                                   Zurich                   • measure in time: t hours to Zurich       ...
double slit experimentSunday, November 29, 2009
small & large                                    dimensions                   • trip measured in kilometers               ...
Postulate wave function                  in four dimensions                            t                                 x...
how to evolve                                                                  t                                          ...
path integralsSunday, November 29, 2009
Feynman diagrams                                  t                                        xSunday, November 29, 2009
almost no change                   • path integrals add sum over paths in time                            to sum over path...
did you break anything                   • internal contradictions?                   • consistent in appropriate limits? ...
• thanks to a subtlety of relativistic mechanics,                    the average trajectory is identical for both         ...
beam & apparatus must                       change                   • have to send a beam which is changing in           ...
why bound states?                   • Bohr rule: fits evenly around the atom                   • what is “fits evenly” in ti...
mass is measure of                               width in time                   • larger is wider                   • for...
coherent interferenceSunday, November 29, 2009
lamb shift                            E                                             τSunday, November 29, 2009
same answer, no infinity                     E                                  τSunday, November 29, 2009
one gate                            t                                              D                                    T2...
two gates                                             G1                            G2                            t       ...
aharonov bohm                              experimentSunday, November 29, 2009
AB in time                                                            ∆t                            t                     ...
pauli exclusion principleSunday, November 29, 2009
symmetric fermions                            τ pa                               ′                   ′                    ...
Lindner’s double slit in                            timeSunday, November 29, 2009
Short photon pulse acts                   like two gatesSunday, November 29, 2009
review of requirements                   • well-defined                   • symmetric between time and space               ...
uses                   • fun with time                   • 300+ experiments                   • starting point for quantum...
thanks!               • Miriam Kelly               • Jonathan Smith               • Ferne Welch               • Graham & G...
• The End of Time - Julian Barbour                     • Time Travel in Einstein’s Universe - J.                          ...
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Time & Quantum Mechanics

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Time & Quantum Mechanics

  1. 1. Quantum time Is time quantized in the same way that space is quantized? John Ashmead john.ashmead@timeandquantummechanics.com 2008Sunday, November 29, 2009
  2. 2. `Clearly, the Time Traveller proceeded, `any real body must have extension in four directions: it must have Length, Breadth, Thickness, and--Duration. But through a natural infirmity of the flesh, which I will explain to you in a moment, we incline to overlook this fact. There are really four dimensions, three which we call the three planes of Space, and a fourth, Time. There is, however, a tendency to draw an unreal distinction between the former three dimensions and the latter, because it happens that our consciousness moves intermittently in one direction along the latter from the beginning to the end of our lives.Sunday, November 29, 2009
  3. 3. Block universe Evolving universeSunday, November 29, 2009
  4. 4. Relativity “Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.” -- Minkowski • time and space mix’d: on way into a black hole, they even change places • block universe naturally static: 80+ pages to define an evolving time.Sunday, November 29, 2009
  5. 5. Quantum mechanics • space is fuzzy • time is a parameter • we build the wave function at the next time instant based on the wave function at the currentSunday, November 29, 2009
  6. 6. How to combine? • Strings • Loop quantum gravity • Lots of others All are new physicsSunday, November 29, 2009
  7. 7. This is often the way it is in physics - our mistake is not that we take our theories too seriously, but that we do not take them seriously enough. It is always hard to realize that these numbers and equations we play with at our desks have something to do with the real world. Even worse, there often seems to be a general agreement that certain phenomena are just not fit subjects for respectable theoretical and experimental effort. -- Steven WeinbergSunday, November 29, 2009
  8. 8. Laboratory time What clocks measureSunday, November 29, 2009
  9. 9. Quantum wave function 1 0.75  − it 1  − 1 t2 ϕ (t ) =  e − e 2  e 0.5 0.25 rea l -4 -2 2 4 -0.25 -0.5 ry na agi -0.75 im -1Sunday, November 29, 2009
  10. 10. Train from Berne to Zurich • measure in time: t hours to Zurich • measure in distance: x kilometers to ZurichSunday, November 29, 2009
  11. 11. double slit experimentSunday, November 29, 2009
  12. 12. small & large dimensions • trip measured in kilometers • wave function measured in nanometers • “real” x is total of large and small • Now, what happens if we take this position for time???Sunday, November 29, 2009
  13. 13. Postulate wave function in four dimensions t xSunday, November 29, 2009
  14. 14. how to evolve t x t lab time = 2 x t lab time = 1 x lab time = 0Sunday, November 29, 2009
  15. 15. path integralsSunday, November 29, 2009
  16. 16. Feynman diagrams t xSunday, November 29, 2009
  17. 17. almost no change • path integrals add sum over paths in time to sum over paths in space • just 4/3 more algebra • and a few technical complications which I will not distress you withSunday, November 29, 2009
  18. 18. did you break anything • internal contradictions? • consistent in appropriate limits? • should it have been seen already?Sunday, November 29, 2009
  19. 19. • thanks to a subtlety of relativistic mechanics, the average trajectory is identical for both quantum time & regular time • quantum time packets do spread more in timeSunday, November 29, 2009
  20. 20. beam & apparatus must change • have to send a beam which is changing in time • through a gate which is open and closed • normally, we let beams settle down, but now it is fiddly bits at the ends we are interested inSunday, November 29, 2009
  21. 21. why bound states? • Bohr rule: fits evenly around the atom • what is “fits evenly” in time? • But only those orbits which “fit evenly” add coherentlySunday, November 29, 2009
  22. 22. mass is measure of width in time • larger is wider • for electrons, is 10 to the -21st seconds (zeptoseconds) • for photons is zero (so you can’t find effect using only photons)Sunday, November 29, 2009
  23. 23. coherent interferenceSunday, November 29, 2009
  24. 24. lamb shift E τSunday, November 29, 2009
  25. 25. same answer, no infinity E τSunday, November 29, 2009
  26. 26. one gate t D T2 T1 S L G xSunday, November 29, 2009
  27. 27. two gates G1 G2 t D T4( 2 ) T3( 2 ) (1 ) T2 T2( 2 ) T1( 2 ) S T1(1) L1 L 21 L2 xSunday, November 29, 2009
  28. 28. aharonov bohm experimentSunday, November 29, 2009
  29. 29. AB in time ∆t t B D D′ ∆Φ V =0 V =Φ C C′ A xSunday, November 29, 2009
  30. 30. pauli exclusion principleSunday, November 29, 2009
  31. 31. symmetric fermions τ pa ′ ′ pb ′ pa ′ pb k k 1 1 1 1 ! ! 2 2 2 2 x pa pb pa pbSunday, November 29, 2009
  32. 32. Lindner’s double slit in timeSunday, November 29, 2009
  33. 33. Short photon pulse acts like two gatesSunday, November 29, 2009
  34. 34. review of requirements • well-defined • symmetric between time and space • consistent with known • testable • reasonably simpleSunday, November 29, 2009
  35. 35. uses • fun with time • 300+ experiments • starting point for quantum gravity • covert transmissions • quantum computersSunday, November 29, 2009
  36. 36. thanks! • Miriam Kelly • Jonathan Smith • Ferne Welch • Graham & Gaylord Ashmead • Linda Kalb • Stewart Personick • Fred Herz • Host of quasi-willing earsSunday, November 29, 2009
  37. 37. • The End of Time - Julian Barbour • Time Travel in Einstein’s Universe - J. Richard Gott • Physics of the Impossible - Michio Kaku • Time Traveler - Ronald L. Mallett • Time’s Arrow & Archimedes’ Point - Huw Price • Timeless Reality - Victor J. Stenger • The New Time Travelers - David ToomeySunday, November 29, 2009

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