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Jean-Pierre Zendri INFN- Padova

Jean-Pierre Zendri INFN- Padova. Planck Scale. Compton wavelength:. Quantum Field Theory. Schwarzschild radius:. General Relativity. Is the Planck scale accessible in earth based Experiments ? . Limits to distance (D) measurements. D. T:Round trip time. A. B. B ody A

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Jean-Pierre Zendri INFN- Padova

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  1. Jean-Pierre Zendri INFN-Padova

  2. Planck Scale Compton wavelength: Quantum Field Theory Schwarzschild radius: General Relativity Is the Planck scale accessible in earth based Experiments ?

  3. Limits to distance (D) measurements D T:Round trip time A B Body A Mass:M Size:<D Ligth Pulse Quantum Mechanics General Relativity Toavoid a Black-Holeformation Quantum mechanics + General Relativity

  4. Uncertainty Principle and Gravity Heisembeg Telescope Newtonian Gravity + Special Relativity +Equivalence principle E: photon energy Tint= Interaction time +Photon unknown direction (e)

  5. Uncertainty Principle and Gravity Different approaches to Quantum Gravity String Theory and loop quantum gravity Amati, D., Ciafaloni, M. & Veneziano, G. Superstring collisions at planckian energies. Phys. Lett. B 197, 81-88 (1987) Gross, D. J. & Mende, P. F. String theory beyond the Planck scale. Nucl. Phys. B 303, 407-454 (1988) Thought experiments Limits to the measurements of BH horizon area Maggiore, M. A generalized uncertainty principle in quantum gravity. Phys. Lett. B 304, 65-69 (1993). Scardigli, F. Generalized uncertainty principle in quantum gravity from micro-black hole gedanken experiment. Phys. Lett. B 452, 39-44 (1999). Jizba, P., Kleinert, H. & Scardigli, F. Uncertainty relation on a world crystal and its applications to micro black holes. Phys. Rev. D 81, 084030 (2010).

  6. Generalized Uncertainty Principle (GUP) The length uncertaincy should be larger than Lp • Including the clock wave function spread (quantum clock) • R.J.Adler, et all., Phys. Lett. B477, 424 (2000) . • W.A.Christiansen et all., Phys. Rev. Lett. 96, 051301 (2006). • Including clock rate in the Schwarzschild geometry and holographic principle E.Goklu, G. Lammerzhal Gen. Rel. and Grav. 43, 2065 (2011). • Y.J.Ng et all. Acad. Sci.755, 579 (1995). • String theory • S.Abel and J.Santiago, J.Phys. G30, 83 (2004) At the Planck scale

  7. GUP and harmonic oscillator ground state

  8. GUP and AURIGA Higher ground state energy for a quantum oscillator Test on low-temperature oscillators set limits GUP effects expected to scale with the mass m Massive cold oscillators AURIGA (Sub millikelvin cooling of ton-scale oscillator)

  9. The AURIGA detector • Strain sensitivity2 10-21<Shh<10-20 Hz-1/2 • over100 Hz band (FWHM ~ 26 Hz) • BurstSensitivityhrss ~ 10-20 Hz-1/2 • Duty-cycle ~ 96 % • ~ 20 outliers/day at SNR>6 • 3m long • Al5056 • 2200 kg • 4.5 K

  10. Effective mass vs reduced mass Readout measures the axial displacement of a bar face corresponding to the first longitudinal mode xcm1 xcm2 Meff depends on the modal shape and interrogation point of the readout (e.g. Meff∞ if the measurement is performed on a node of the vibration mode) Really moving mass 1) Modal motion implies an oscillation of each half-bar center-of-mass, to which is associated a reduced massM/2 2) The energy associated to the oscillation of the couple of c.m.’s, having a reduced mass Mred = M/2 is about 80% of that of the modal motion

  11. Active Cooling: principle (t) Equipartion theorem • FSigSignal Force • FThLangevin thermal force (

  12. () Not significant for GUT

  13. Active Cooling: principle (t) Equipartion theorem • FSigSignal Force • FThLangevin thermal force • FCD Feedback Force (

  14. Active Cooling: principle (t) / Equipartion theorem • FSigSignal Force • FThLangevin thermal force • FCD Feedback Force ( Cold damped distribution

  15. Cooling down to the ground state Active or passive feedback cooling of one (few) oscillator mode NO Displacementsensitivityimprovement YES Prepare oscillator in its fundamental state

  16. F Back-action force MB MT MLC • The bar resonator is coupled to a lighter resonator, with the same resonance • frequency to amplify signals • 2) A capacitive transducer, converts the differential motion between bar and the • ligher resonator into an electrical current, which isfinally detected by a • low noise dc SQUID amplifier • 3) Thetransducer efficiency is further increased by placing the • resonance frequency of the electrical LC circuit close tothe mechanical resonance • frequencies, at 930 Hz. KLC KT KB System ofthree coupled resonators: the bar and the transducer mechanical resonators and the LC electrical resonator

  17. System ofthree coupled resonators: the bar and the transducer mechanical resonators and the LC electrical resonator - At increasing feedback gain, the 3 modes of the detector reduce their vibration amplitude. - The equivalent temperature of the vibration was reduced down to Teff=0.17 mK

  18. AURIGA minimal energy

  19. Modified commutators I GUP can be associated to a deformed canonical commutator Planck scale modifications of the energy spectrum of quantum systems Lamb shift in hydrogen atoms 1S-2S level energy difference in hydrogen Lack of observed deviations from theory at the electroweak scale

  20. Active Cooling: Fundamental limit xn:Amplifier additive noise Fn: Amplifier back-action noise Amplifier Noise temperature Amplifier Noise Stiffness

  21. Auriga possible upgrading * P.Falferi et al. APS 88 062505 (2006) ** P.Falferiet al. APS 93 172506 (2008) Auriga just cooling down Auriga cooled down + New SQUID Further improvements expected decreasing the LC thermal noise (but never nt<1/2)

  22. Modified commutators II Modifications of commutators are not unique Experiments could distinguish between the various approaches M. Maggiore Phys. Lett. B 319, 83-86 (1993) μ0< 4 x 10 -13 ?

  23. Spacetime granularity (Quantum Foam) Vacuum energy Mass (energy) curves spacetime Energy of the virtual particles gives space time a "foamy" character at L ≈ Lp General Relativity Quantum mechanics (Wheeler, 1955) Property of the spacetime geometry and not of physical objects (Soccer ball problem ?) Apparatus independent (not based on a specific QG model)

  24. AURIGA: re-interpretation AURIGA is not the “coolest” oscillator, but is the most motionless Xrms= (kT/mω2)1/2 = (Eexp/mω2)1/2 ≈ 6 X 10-19 m

  25. Macroscopic oscillators in their quantum ground state (ω0= 1 GHz T ≈50 mK)

  26. Experimental proposals I/1 A sequence of 4 pulse is applied to the mechanical oscillator such that in the mechanical moves in the phase space around a loop: +Xm –Pm - Xm +Pm Quantum mechanics: [Xm,Pm]≠0

  27. Experimental proposals Ib Experimental set-up Critical Points • Classical phase rotation • Short cavity is chalangin (10-6 m !)

  28. Experimental proposals IIa 1) The photon has to discard momentum into the crystal 2) This momentum will be returned to the photon upon exit. 3) The crystal moves for a distance scaling with the energy of the incoming photon

  29. Experimental proposals IIb If the energy of the photon is so low that the crystal should move less than the Planck length, the photon cannot cross the crystal, leading to a decrease in the transmission Critical points Thermal noise Optical dissipations

  30. Experimental proposals III Space time is described with a wave function frequency limited (the Plank frequency). If one end point of the particle position is limited by an aperture with size D the uncertaincy of the other points at distance L is limited by diffraction to be lpL/D The possible orientation are minimized for DlpL/D thus D(LpL)1/2 There is an unavoidable transverse uncertaincy In a Michelsoninterferometertheeffectappears as noisethat resembles a randomPlanckianwalk of thebeamsplitterfordurations up tothe light-crossing time. Measurable (according to Hogan) using two cross-correlated two nearly coolacatedngMichelson interferometers with arms length of about L=40 meters

  31. Conclusions •The Auriga detector constrainedtheplankscalefor a macorscopicbody. Furtherimprovements are possiblebutstillfarfromthe “traditional” plankscale. •Recentexperimentsonmacroscopicmechanicaloscillatorsshowedthattheybehaves as quantum oscillator. •Put in prespective a new generation of experimentwithmacroscopicbodyshould be abbletoapproachtheplankscale. •Itisnotcleariftheseexperimentswould be abbletoconstrainthe quantum gravitybecausethedescribtionof the macroscopic objects in the framework of quantum gravity models is still lacking. •A INFN group is in charge to examine the feasibility of the new proposed experiments and in case to propose new and more realistic set-up HUMOR Heisenberg Uncertainty Measured with Opto-mechanical Resonator

  32. Soccer ball problem Minimal lengthProblems with standard special relativity (SR) Doubly Special Relativity Amelino-Camelia, G. Int. J. Mod. Phys. D 11, 1643-1669 (2002). Modified SR with two invariants: speed of light c, and minimal length Lp Possible (ad hoc) solutions 1) Effects scale as the number of constituent (Atoms, quarks... ?) Quesne, C. & Tkachuk, V. M. Phys. Rev. A 81, 012106 (2010). Hossenfelder, S. Phys. Rev. D 75, 105005 (2007) and Refs. therein Extremely huge for particles, but small for planets, stars and ... soccer balls Problem of macroscopic (multiparticle) bodies • Physical momenta sum nonlinearly • Correspondence principle 2) Decoherence ? Magueijo, J. Phys. Rev. D 73, 124020 (2006)

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