1. Probing deformed commutators with macroscopic harmonic oscillators Francesco Marin

2. HUMOR Heisenberg Uncertainty Measured with Opto-mechanical Resonators

3. Morning Session (2): Strong field tests of General Relativity (Pulsars, Black holes,...)

4. Phenomenological quantum gravity  General ‘remark’: one cannot determine a position with an accuracy better than the Planck length L P =  hG/c 3 = 1.6 10 -35 m  Generalized Heisenberg uncertainty relations (GUP)  Generalized commutators between p e q  Modified quantum physics Phenomenological quantum gravity  General ‘remark’: one cannot determine a position with an accuracy better than the Planck length L P =  hG/c 3 = 1.6 10 -35 m  Generalized Heisenberg uncertainty relations (GUP)  Generalized commutators between p e q  Modified quantum physics Detecting signatures of Planck scale-physics in highly-sensitive metrological systems

5. Solution: Basic assumptions: Heisenberg dynamics 3° harmonicFreq. shift Deformed commutation relations from

6.  Test on a wide mass range  High mechanical quality factor  ‘isolated’ oscillators  Exploit the slow decay to obtain frequency/3° harmonic vs amplitude curves

7. 1° oscillator: m  1 g SiN membrane 0.5 x 0.5 mm 2 x 50nm mass = 135 ng Q = 8.6x10 5 3° oscillator: m  100 ng m = 20 μg f m = 141 KHz Q = 1.2 x10 6 T = 4.3 K 2° oscillator: m  100  g

10. Evidence of deformed commutator? Structural non-linearity

11. ‘Model-independent’ limits

13. MPMP H atom

14. MPMP AURIGA

15. MPMP H atom Equivalence principle

16. AURIGA MPMP H atom Equivalence principle  vs q 3° harmonic M. Bavaj. et al., arXiv: 1411.6410

17. We have a Planck energy concentrated on a Planck length? What’s the meaning of our measurements? (my poor man view) NO … but we are are searching tiny ‘residual’ effects Which models are we limiting/questioning? Strictly speaking, NO ONE : no model predicts a deformed commutator for macroscopic variables … but is there any satisfactory model?

18. If a deformed commutator applies to the coordinates of a fundamental constituent, then its effect on a macroscopic object (composed of N such constituents) should decrease as 1/N what is a fundamental constituent? geometrical properties of space-time  property of each particle

19. … A different point of view: a foamy space-time

20. If a deformed commutator applies to the coordinates of a fundamental constituent, then its effect on a macroscopic object (composed of N such constituents) should decrease as 1/N what is a fundamental constituent? geometrical properties of space-time  property of each particle not in the spirit of quantum mechanics: the position and momentum of an oscillator c.m. should be THE meaningful (i.e., measurable) quantities. Uncertainty relation between p and q is tightly related to the general problem of quantum measurements (see Braginsky, Caves, etc.) Focus on peculiar quantum properties

21. Tracks in the quantum+GR field are diversified …

22. … we are just setting some experimental poles