1. Experimental Tests of Continuous Symmetries Gerco Onderwater KVI/Rijksuniversiteit Groningen, The Netherlands

2. Continuous Symmetries Are related to space and time. Translations and rotations in space, and time can take any value, hence they are continuous. A physics law is said to be symmetric under such transformations if it does not change, i.e. the law is invariant.

3. Noether's Theorem Continuous symmetry ↔ conservation law Invariant underConservation of (1) time translationenergy (2) space translationmomentum (3) rotationangular momentum (?) boostLorentz generators

4. How to Test? Two possibilities: (1)Test that a process is the same when occuring here and there, now and then, etc. (2)Test the associated conservation law explicitly Important constraint: the trial system is isolated from external influences!

5. (1) Time Invariance & Energy Conservation

6. What is Energy? Energy can be defined as the capacity for doing work. It may exist in a variety of forms and may be transformed from one type of energy to another. Transformations constrained by conservation principle One way to state this principle is "Energy can neither be created nor destroyed". Another approach is to say that the total energy of an isolated system remains constant. E 1 =-E 2 or E 1 +E 2 =C: this we can test!

7. Types of Energy A complete test of energy conservation would require the demonstration that each of the kinds of energy below are equivalent nuclearelectric potentialkineticthermal masschemical In the end, all energy is kinetic or potential Note that potential energy can be sub-divided according to each of the four known forces

8. Joule's Paddlewheel Exp't [Philos. trans. Royal Soc. London, 140, pp. 61-82 (1840)] Classical experiment to show equivalence of 3 types of energy gravity – kinetic - thermal

9. Photoelectric Effect Emission of electrons under illumination. The electron kinetic energy increases with decreasing photon wavelength, the rate with intensity. Demonstrates equivalence of quantum and kinetic energy

10. Classic Laws Other observation-based laws, effects and relations that support continuous symmetries BernouilliVoltOhmKirchhoff AmpereBiot-SavartCoulombBragg CharlesCurie-WeissDopplerFaraday GaussJouleKepplerLe Chatelier LenzMachMaxwell Meissner NewtonWien Planck Kelvin Rayleigh-JeansSnellStefan-Boltzmann and probably some...

11. Watt Balance Electrical standard of kg Change SI to QM standard HW

12. When a DC voltage is applied to a Josephson junction, an oscillation of frequency occurs at the junction. Josephson junction standards can yield voltages with accuracies of one part in 10 10. NIST has produced a chip with 19000 series junctions to measure voltages on the order of 10 volts with this accuracy. Josephson Voltage Standard

13. Quantum Hall resistance standard

14. Quantum Hall Array Standard (QHARS) 1cm  1cm 100  standard

15. Metrological triangle new standard ?

16. Beta Decay Mystery Beta energy expected to be mono-energetic A continuous spectrum was observed Two explanations (1) energy non-conservation (2) new invisible particle Did not fulfill closed system requirement

17. Time Invariance Search for time variation of reaction rate Weak Interaction Oklo natural reactor: |Ġ F /G F |<1x10 -11 /year EM Interaction Quasar H spectra:  = -(0.7±0.2)×10 -5 for 0.5<z<3.5 Proton/electron mass:  = (2.0±0.6)x10 -5 / 12 Gyr Strong Interaction  Rb / Cs = -(0.9±2.9)x10 -15 /year This will be discussed in more detail later in the course Eur. Phys. J. A 8, 137–140 (2000)Phys. Rev. Lett. 96, 151101 (2006)Phys. Rev. Lett. 87, 091301 (2001)Phys. Rev. Lett. 92, 230802 (2004)

18. Energy in Quantum Mechanics The uncertainty principle states that Et≥ħ Does this mean energy conservation may be violated (briefly)? HW: wrong question

19. (2) Spatial Invariance & Momentum Conservation

20. What is Momentum? Momentum can be though of as the tendency of an object to continue in its direction of travel Classically:p = mv Relativistic:p = mv Massless:p = E/c = h/ Quantum:p = -iħ Change requires an external force

21. Every Day Life

22. Compton Effect The increase in wavelength of a photon scattering of an electron Demonstrates that photons carry energy and momentum  = h/m e c ( 1-cos) + 1

23. e + e - → 2  Ps → 1 : E  =2m e p  =E  /c ≠ p Ps =0FORBIDDEN Ps → 2 : E  =m e p  +p  =0ALLOWED Collinearity = (relativistic four) momentum conservation Phys. Rev. 77, 205–212 (1950)

24. (3) Rotation Invariance & Angular Momentum Conservation

25. What is Angular Momentum? Angular momentum is the measure of rotation around some fixed point in space (also includes spin) Classically:L = rxp Relativistic:L = rxp Massless:L = S Quantum:L = -iħrxp Change requires an external torque

26. Kepler's Second Law A line joining a planet and its star sweeps out equal areas during equal intervals of time Tested in solar system observations

27. Michelson-Morley Classic experiment to test isotropy of c Modern version: compare f laser,xy vs time of day (2 rotation)   c/c = (2.6±1.7)x10 -15 Phys. Rev. Lett. 21, 020401 (2003) Phys. Rev. D 67, 056006 (2003)

28. Isotropy of  -Decay Measure differential decay rate and see if it varies with orientation w.r.t. some fixed frame (stars) () =    [ 1 +  1 cos() + 2 cos(2) ]   < 1.6x10 -7   < 2x10 -6 Phys. Rev. D 14, 1 (1976)

29. Isotropy of Mass Measure Zeeman splitting for 3 He(J=½) and 21 Ne(J= 3 / 2 ) (Hughes-Drever experiments) Search for orientation-dependent binding energy = inertial mass Lowest order: quadrupole splitting (so 3 He is not sensitive) |E/E| < 1.6x10 -26 Phys. Rev. Lett. 14, 1541 (1989) Phys. Rev. Lett. 64, 2261 (1990)

30. Pion Decay Best limit of angular momentum conservation in weak interaction comes from ( → e)/( → ) ~ 10 -4 The small factor is “unexpected” in view of (giant) phase for electron decay, but… Axial vector delivers wrong helicity (need l =1 for angular momentum conservation) More: absence of pseudo scalar (P) coupling in WI ++ ++