1. Lecture 2 Searching for variation of fundamental constants Les Houches, 25 Sept. 2014 E.A. Hinds Centre for Cold Matter Imperial College London

2. The “cosmological principle” Natural laws and fundamental constants do not depend on position or time This idea dates back to Isaac Newton’s concept of universal gravitation The qualities…which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever. Rule 3 of Reasoning in Philosophy (Principia Mathematica 3 rd Ed.) Averaging over small scale local variations, the observable universe is homogeneous and isotropic The idea is now under intense scrutiny because we can because theory encourages it

3. temperature fluctuations are only 10 -5 The cosmic microwave background light emitted when the universe was only 380,000 years old ESA/Planck Collaboration the seeds of today’s stars and galaxies It’s amazingly homogeneous and isotropic

4. Possible variation of constants Ratio of electric/gravitational force between electron and proton also 10 39 P. A. M. Dirac. “The cosmological constants”. Nature 139, 323 (1937). In 1937 (on his honeymoon) Dirac noticed an interesting coincidence: Age of universe expressed in units of is  = 10 39 a time built from fundamental constants Was gravity initially as strong as electricity, but evolved over time? Perhaps G varies as 1/  ! Bohr to Gamov on reading Dirac’s paper: “Look what happens to people when they get married!”

5. Edward Teller raised the possibility of experimental tests inconsistent with fossil record. E. Teller “On the change of physical constants”, Phys Rev. 73, 801 (1948). Teller: “Further evidence on the change of constants may be obtained from the appearance of distant spiral nebulae. Light emitted from the farthest observed galaxies has originated about 500 million years before the present time”. sun hotter earth at 90C …. if, it would be 10% larger 200M years ago. Started the search for temporal variation of constants

6. Method of quasar spectroscopy hot distant quasar emits light continuum Cold gas cloud absorbs on many lines. Observation made on earth Redshift gives age and distance of gas cloud.

7. Line frequencies shift variously if  changes Calculate sensitivies - a few % or less Anchor lines (cm -1 ) +ve shifters (cm -1 ) -ve shifters (cm -1 ) Dzuba, Flambaum ….

8. 0 -2 Murphy et al., MNRAS 327, 1208 (2003) and refs therein 2001-3 Results from Keck telescope in Hawaii Spectra from 128 clouds at redshifts from 0.2 up to 3.7. Binned result Slope Average

9. T. Rosenband et al. Science 319, 1808 (2008) But there is no such  in the present Al + / Hg + = 1.052871833148990438(55) 5 parts in 10 17 Heavy atom Light atom

10. 2011 result including VLT telescope in Chile New quasar absorption data: Some absorbers indicate a positive  ! What’s going on? Webb et al., PRL 107, 191101 (2011) The “Australian” dipole It appears that  varies in space along a specific direction! Emphasises that constants may vary in space as well as time

11. A search for  variation with position or local density  -doublets of CH by comparing on earth and in space

12. Molecular energy intervals depend on:  (fine structure constant)  spin-orbit  (electron/proton mass)  rotation energy ,  vary with time or position ff f   = K  + K    CH has large sensitivities KK and KK Kozlov PRA 80 022118 (2009) We want to test whether

13. J=1/2 J=3/2 537 GHz Lowest two levels of CH X 2  (v=0) + 3.3 GHz  -doubling + 0.7 GHz  -doubling 1 0 1 0 F hyperfine 1 2 2 1 F K  = -8 K  = +6 K  =0.6 K  = 1.7

14. Ar CHBr 3 CH 193 nm excimer PMT X 2  A 2  3.3 GHz Molecular beam Ramsey spectroscopy of CH J=1/2 Truppe et al., Nat. Comms 4, 2600 (2013)

15. Ramsey spectra rf on rf off T 0-2-3123 Frequency – 3 335 479 (kHz) Signal 1/T Frequency

16. what’s happening on the Bloch sphere First  /2 pulse Initial state superposition state frequency of microwaves  resonance frequency  0 Free precession for time T 2 nd  /2 pulse  = (  -  0 )T sin 2  cos 2  Final state

17. a systematic effect In an ideal standing wave: A cos(kz) cos(  t) Phase of field has nothing to do with position A real standing wave always has a little travelling component: A cos(kz) cos(  t) +  cos(kz-  t) Now the phase depends a bit on position and hence on velocity … and indeed we see a small velocity-dependence of the resonance frequency

18. A small systematic frequency shift speed (m/s) frequency shift (Hz) starts at 3 rd antinode starts at 4 th antinode This shift depends on (i) position at first pulse (ii) velocity Kr Ar He

19. Results 1 0 1 0 + J=1/2 3 335 479 356 (3) Hz 3 263 793 447 (3) Hz 3 349 192 556 (3) Hz 703 978 340 (21) Hz 701 677 682 (6) Hz 722 487 624 (16) Hz 724 788 315 (16) Hz 1 2 2 1 + J=3/2 std. deviation 1000 x improvement in precision No previous lab measurements Truppe et al., Nat. Comms 4, 2600 (2013)

20. 1 0 1 0 + J=1/2 1 2 2 1 + J=3/2 Truppe et al., Ap. J., 780, 71 (2014) Measurement of the 530 GHz interval to almost 1 ppb

21. velocity km/s CH (3335 MHz) OH (1667 MHz) Constraining  and  in the milky way Example: CH and OH observed towards Cassiopeia A Single hyperfine line Double-peaked line shape due to velocity distribution v from Doppler shift relative to lab frequency Fit to two Gaussians K  = 0.6 K  = 1.7 If  or  different on earth and in Cas A “velocity” shift between CH and OH K  = -1.1 K  = 2.6 OH lab frequency Hudson, Lewandowski, Sawyer, Ye, PRL. 96, 143004 (2006)

22. Results 26 lines in 5 Milky Way sources: CasA, RCW36, Heiles2, L134N, W51  = (0.3 ± 1.1) × 10 -7   = (-0.7 ± 2.2) × 10 -7 Best constraint on variation of  with density Bagdonaite et al. PRL 111, 231101 (2013) Ammonia gives stronger limit & looks back over 7.5 Gyr   = (1.5 ± 1.5) × 10 -7

23. Outlook In future, Square Kilometre Array could see both CH lines Could reach below 10 -8 for both  /  and  CH  -doublets very sensitive to varying constants - no sign of variation with density Could probe both density and redshift variation

24. Summary  may change over time, if so, by < 10 -15 per year over cosmological times and by < 10 -16 per year now  may change with position, Australian dipole 2×10 -5 across the universe but Whitmore & Murphy arXiv:1409.4467 (15 Sep 2014) weakens the evidence  and  may change with local density But if so,  not more than a few × 10 -7 (from CH) and  not more than a few × 10 -7 (from ammonia) So far, fundamental constants are pretty constant