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ECT* Trento Aug. 2011

ECT* Trento Aug. 2011. I. Internal clock (L.de Broglie) II. Dirac equation and Zitterbewegung III. Experiments in crystals - ALS (Saclay) - RICCE experiment (Frascati). I.Internal clock.

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ECT* Trento Aug. 2011

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  1. ECT* Trento Aug. 2011 • I. Internal clock (L.de Broglie) • II. Dirac equation and Zitterbewegung • III. Experiments in crystals - ALS (Saclay) - RICCE experiment (Frascati) M.Gouanère Trento Aug.2011

  2. I.Internalclock • Quantum Mechanics can be interpreted in several ways (J.S.Bell “Speakable and Unspeakable in Q.M”.Chap 20: Six possible worlds in Q.M.). With the internal clock, we go in the geometrical interpretation of Q.M. There is a particle AND there is a wave. ->beyond Q.M. M.Gouanère Trento Aug.2011

  3. L. de Broglie (Thesis 1924): • A particle is surrounded by a wave Y • In its rest frame Y= a0 exp(2pin0t) E= m0c2 = hn0 ->n0 = m0c2/h • In the Lab. • t = gt’ – bgx’/c (Lorentz transformation) • Y’= a0 exp[2pi(n0gt’ - n0 bgx’/c)] or • Y’= a0 exp[2pi(nt’ - x’/l)] M.Gouanère Trento Aug.2011

  4. Therefore a new wave frequency: nwave=n0g and a wave length l =c/ (n0 bg) = c h/ (m0c2 bg)= h/p But ! nparticle=n0 /g relativistic slow down of clocks. “clock length”->a length that the particle travels during one period of the clockl = cbg/n0 l l = lc2 M.Gouanère Trento Aug.2011

  5. But the internal clock could be observed only if there are additional non linearity terms in the function Y at the particle coordinates. M.Gouanère Trento Aug.2011

  6. But from where comes this wave? A simple speculation: particle oscillates along a further dimensional space. Wave speed could be >> c. No electromagnetic radiation. Only the mass oscillates. M.Gouanère Trento Aug.2011

  7. II. Dirac equation and Zitterbewegung • The Principles of Q.M. P.A.M.Dirac Oxford Science Publications 1957 Fourth Edition • Schrödinger (1930). Gravity centre motion of a free wave Y. M.Gouanère Trento Aug.2011

  8. x(t)= v.t + “Zitterbewegung” -”v.t” is the classical motion of a particle. -the “Zitterbewegung” term is roughly: o(lc) cos(wzt/g) lc = ~10-10 cm for e- . wz = 2 wB =2 m0c2/ħ. M.Gouanère Trento Aug.2011

  9. D.Hestenes. Zitterbewegung in Quantum Mechanics. Foundations of Physics, 40:1-54, 2010. A reformulation of the Dirac equation in terms of Spacetime Algebra. An helical motion with a radius lc = ~10-10 cm for e- . Frequency is twice the de Broglie frequency, like the “Schrödinger” Zitterbewegung : wz = 2 wB =2 m0c2/ħ M.Gouanère Trento Aug.2011

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  11. III. An early experiment in crystals to detect this very high frequency: (ALS Saclay 1980) P.Catillon, N.Cue, M.J.Gaillard, R.Genre, M.Gouanère, R.G.Kirsch, J.C.Poizat, J.Remillieux, L.Roussel and M.Spighel. Found.Physics 38 (2008) 659. • n0= m0c2/h (~1020 s for e-). Si <110> 1 m d= 3.84 Å e- ~80 MeV/c l ~ 15 fermi M.Gouanère Trento Aug.2011

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  14. Why the resonance is so narrow? • At each atomic step, the deviation is ~10-2 mrad. The deviation needs to be ~1 mrad to be detected. If the energy is close to the resonant energy by less than 1%, the deviations add COHERENTLY. If the energy is different from the resonant energy by more than 1%, the deviations cannot add coherently, and the final deviation is less than 1 mrad. M.Gouanère Trento Aug.2011

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  19. Other explanations? • e- 81 Mev/c -> l ~ 15 fermi. • “Okorokov” effect in rosette motion? No • Diffraction in pair production (trident)? Unlikely. See magnet M. • 1m Si = 10-5 X0. • … M.Gouanère Trento Aug.2011

  20. RICCE experiment: Research of Internal Clock by Channeling of Electrons. Preliminary results at the LNF-BTF (Frascati) • C.Raya, M.Bajarda, R.Chehaba, M.Chevalliera, C.Curceanub, S.Dabagovb , D.Dauvergnea, M.Gouanèrea, R.Kirscha, J.C.Poizata, J.Remillieuxa , and E.Testaa • a Université de Lyon, F-69003 Lyon; Université Lyon 1 and IN2P3/CNRS, UMR 5822, Institut de Physique Nucléaire de Lyon, F-69622 Villeurbanne, France • b LNF-INFN, Via E. Fermi 40, 00044 Frascati (Roma), Italia M.Gouanère Trento Aug.2011

  21. Experimental conditions • Ge crystal (0.85 m) <110> d= 4.0 Å n0 = 2m0c2/h (-> e- 168 MeV/c) M.Gouanère Trento Aug.2011

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  25. CONCLUSION Two theoretical issues (at least) give a possible internal motion at w0= m0c2/ħ (~1021 s for e-). Or a multiple or fraction of it. Experiments with e- in crystals allow to observe such a high frequency. An early experiment gave a signal for Si <110> at 81 MeV/c. An experiment is under way at DAFNE-BTF (Frascati) to confirm it. M.Gouanère Trento Aug.2011

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  27. Trident hypothesis: • The wave length of a 80.874 MeV/c electron is 15.3288 fermi. • The wave length of a trident of the same energy is 15.3312 fermi. (with E2=p2+m2c4, me=0.511 MeV/c2, and mtrident=1.533 MeV/c ( h= 12.397 keV-Å). • The total energy is conserved, the missing momentum is given by the crystal (The missing energy given by the crystal is negligible). • In order to overcome the small difference in the wave lengths, it needs 6262 times the wave length, i.e. 0.96 Å. This is 2 times the distance between 2 planes <110> (1.92 Å). M.Gouanère Trento Aug.2011

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