1. Equivalence principle, antigravity of antimatter and all that Savely G Karshenboim D.I. Mendeleev Institute for Metrology (St. Petersburg) and Max-Planck-Institut für Quantenoptik (Garching)

2. Antigravity and equivalence principle for antimatter (i) Antigravity of antimatter: Precision spectroscopy of fundamental atoms, containing antiparticles, in the presence of galactic and Solar gravity Precision spectroscopy of fundamental atoms, containing antiparticles, in the presence of galactic and Solar gravity

3. Equivalence principle and antigravity  Equivalence principle:  Equivalence principle: in free fall we could not recognize gravitation (if neglecting the gradients)  Antigravity: no equivalence principle  while the matter is falling free  the antimatter is rising free

4. Red shift = {(E=mc 2 ) + (m i =m g ) + Newtonian gravity} All clocks upstairs are blue shifted, photon frequencies are not shifted. When photon is going up it disagrees with the clock by / = (gh/c 2 ). E = m 0 c 2 + m 0 gh E = m 0 c 2 h E = (m 0 +  m) (c 2 + gh) E = (m 0 +  m)c 2 h 0 =  mc 2 h h =  m(c 2 +gh) ground state excited statetransition frequency

5. Gravitational and motional effects  I will discuss gravitational effects and ignore motional effects.  That is possible because I am interested in differential effects.  Motional effects are closely related to gravitational and often cancel them.  However, differential motional effects such as Doppler effect are equal to zero.

6. Red shift = {(E=mc 2 ) + (m i =m g ) + Newtonian gravity} E = m 0 c 2 + m 0 gh E = m 0 c 2 h E = (m 0 +  m) (c 2 + gh) E = (m 0 +  m)c 2 h 0 =  mc 2 h h =  m(c 2 +gh) ground state excited statetransition frequency All clocks upstairs are blue shifted, photon frequencies are not shifted. When photon is going up it disagrees with the clock by / = (gh/c 2 ).

7. Red shift = {(E=mc 2 ) + (m i =m g ) + Newtonian gravity} E = m 0 c 2 + m 0 gh E = m 0 c 2 h E = (m 0 +  m) (c 2 + gh) E = (m 0 +  m)c 2 h 0 =  mc 2 h h =  m(c 2 +gh) ground state excited statetransition frequency All clocks upstairs are blue shifted, photon frequencies are not shifted. When photon is going up it disagrees with the clock by / = (gh/c 2 ). The shift is universal for all clocks once the gravity is proportional to their inertial mass and thus the shift by itself cannot be detected.

8. Red shift = {(E=mc 2 ) + (m i =m g ) + Newtonian gravity} E = m 0 c 2 + m 0 gh E = m 0 c 2 h E = (m 0 +  m) (c 2 + gh) E = (m 0 +  m)c 2 h 0 =  mc 2 h h =  m(c 2 +gh) ground state excited statetransition frequency All clocks upstairs are blue shifted, photon frequencies are not shifted. When photon is going up it disagrees with the clock by / = (gh/c 2 ). The shift is universal for all clocks once the gravity is proportional to their inertial mass and thus the shift by itself cannot be detected. That is correct for all clocks of matter. Once we suggest antigravity for antimatter – that is not correct for antimatter anymore!

9. Red shift = {(E=mc 2 ) + (m i =m g ) + Newtonian gravity} E = m 0 c 2 + m 0 gh E = m 0 c 2 h E = (m 0 +  m) (c 2 + gh) E = (m 0 +  m)c 2 h 0 =  mc 2 h h =  m(c 2 +gh) ground state excited statetransition frequency All clocks upstairs are blue shifted, photon frequencies are not shifted. When photon is going up it disagrees with the clock by / = (gh/c 2 ). The shift is universal for all clocks once the gravity is proportional to their inertial mass and thus cannot be detected. That is correct for all clocks of matter. Once we suggest antigravity for antimatter – that is not correct for antimatter anymore! Gravitational red shift is a generic property of any relativistic theory of gravitation.

10. Can we measure the absolute red shift (in respect to zero gravity r=∞) ? Hydrogen:  Gravity m g = m i m g = m i  Spectroscopy 1s-2s Other transitions  Theory calculable frequency in terms of m e and  Ry Antihydrogen:  [Anti]gravity m g = – m i m g = – m i  Spectroscopy 1s-2s ? HFS ?  Theory needs m e+ & m p- otherwise: all is the same as for H

11. Can we measure the absolute red shift (in respect to zero gravity r=∞) ? Hydrogen:  Gravity m g = m i m g = m i  Spectroscopy 1s-2s Other transitions  Theory calculable frequency in terms of m e and  Ry Antihydrogen:  [Anti]gravity m g = – m i m g = – m i  Spectroscopy 1s-2s ? HFS ?  Theory needs m e+ & m p- otherwise: all is the same as for H To be blue shifted (∞).To be red shifted (∞).

12. Can we measure the absolute red shift (in respect to zero gravity r=∞) ? Hydrogen:  Gravity m g = m i m g = m i  Spectroscopy 1s-2s Other transitions  Theory calculable frequency in terms of m e and  Ry Positronium:  [Anti]gravity m g = 0 m g = 0  Spectroscopy 1s-2s HFS  Theory needs m e+ & m e- calculable frequency in terms of m e and  Antihydrogen:  [Anti]gravity m g = – m i m g = – m i  Spectroscopy 1s-2s ? HFS ?  Theory needs m e+ & m p- otherwise: all is the same as for H To be blue shifted (∞).To be red shifted (∞).To be not shifted.

13. Can we measure the absolute red shift (in respect to zero gravity r=∞) ?  Hydrogen 1s-2s  Equivalence for H m g = m i  Frequency is calculable in terms of m e and   Positronium 1s-2s  Antigravity: m g = 0  Frequency is calculable in terms of m e and 

14. Can we measure the absolute red shift (in respect to zero gravity r=∞) ?  Hydrogen 1s-2s  Equivalence for H m g = m i  Frequency is calculable in terms of m e and   Positronium 1s-2s  Antigravity: m g = 0  Frequency is calculable in terms of m e and  while neglecting gravity

15. Can we measure the absolute red shift (in respect to zero gravity r=∞) ?  Hydrogen 1s-2s  Equivalence for H m g = m i  Frequency is calculable in terms of m e and   Positronium 1s-2s  Antigravity: m g = 0  Frequency is calculable in terms of m e and  Comparison of theory against experiment for Ps is the same as comparison of H and Ps, because theory of Ps speaks in terms of Ry from H

16. Can we measure the absolute red shift (in respect to zero gravity r=∞) ?  Hydrogen 1s-2s  Equivalence for H m g = m i  Frequency is calculable in terms of m e and   Positronium 1s-2s  Antigravity: m g = 0  Frequency is calculable in terms of m e and  Comparison of theory against experiment for Ps is the same as comparison of H and Ps, because theory of Ps speaks in terms of Ry from H

17. Can we measure the absolute red shift (in respect to zero gravity r=∞) ?  Hydrogen 1s-2s  Equivalence for H m g = m i  Frequency is calculable in terms of m e and   Positronium 1s-2s  Antigravity: m g = 0  Frequency is calculable in terms of m e and  Comparison of theory against experiment for Ps is the same as comparison of H and Ps, because theory of Ps speaks in terms of Ry from H The results are consistent at level of about few parts in 10 9.

18. Can we measure the absolute red shift (in respect to zero gravity r=∞) ?  Hydrogen 1s-2s  Equivalence for H m g = m i  Frequency is calculable in terms of m e and   Positronium 1s-2s  Antigravity: m g = 0  Frequency is calculable in terms of m e and  Comparison of theory against experiment for Ps is the same as comparison of H and Ps, because theory of Ps speaks in terms of Ry from H The results are consistent at level of about few parts in 10 9 suggesting no gravitational effects.

19. How large is absolute red shift?  Motion around center of galaxy:  v = 10 -3 c  / = 10 -6  Motion around Sun  v =10 -4 c  /=10 -8 Basic equations: a = v 2 /R a = U/R  U = a · R  / =  U/c  = v 2 /c 2 It is huge! v a R

20. Can we measure the absolute red shift?  Hydrogen 1s-2s  Equivalence for H m g = m i  Frequency is calculable in terms of m e and   Positronium 1s-2s  Antigravity: m g = 0  Frequency is calculable in terms of m e and  10 9 The results are consistent at level of about few parts in 10 9. Should be red shifted (∞). Should be immune.

21. Theory again?  Universality of the red shift for matter sources:  Universality of free fall for matter:  Applicability of the Dirac equation for an electron and CPT (m e+ = m e- ): Proved experimentally! Proved experimentally! Proved experimentally in g-2 experiment! Proved experimentally in g-2 experiment!

22. Theory again?  Applicability of bound state QED:  We do not know the field of our galaxy:  We do not know about the Sun: Proved experimentally in H etc. spectroscopy! Proved experimentally in H etc. spectroscopy! The Sun gravitation is enough! The Sun gravitation is enough! Not less than about the Earth! Not less than about the Earth! Besides: antiprotonic helium and muonium point in the same direction!

23. Theory again? OK: no galaxy, no CPT, no QED aphelion: 152.1 Gm perihelion: 147.1 Gm U/c 2 = 3 × 10 -10 – quite a large `small’ effect for spectroscopy

24. Theory again? OK: no galaxy, no CPT, no QED aphelion: 152.1 Gm perihelion: 147.1 Gm U/c 2 = 3 × 10 -10 – quite a large `small’ effect for spectroscopy We consider differential effects and do not care about Doppler effect etc.

25. Theory again? OK: no galaxy, no CPT, no QED aphelion: 152.1 Gm perihelion: 147.1 Gm U/c 2 = 3 × 10 -10 – quite a large `small’ effect for spectroscopy might be done for positronium, antiprotonic helium muonium, antiprotonic helium and antihydrogen

26. Atoms with antiparticles: just to remind positronium: muonium: antimuon + electron antiprotonic helium:  -particle + antiproton antihydrogen:  truly neutral in any sense  mass of the antiparticle >> mass of the particle (m  =207m e )  mass of the antiparticle = ¼ of mass of the particle  there is a small disturbing electron…  I hope you already know what it is: a truly antiatom  not yet cold enough, but hopefully will be (winter is coming)

27. Atoms with antiparticles: just to remind positronium: muonium: antimuon + electron antiprotonic helium:  -particle + antiproton antihydrogen:  truly neutral in any sense  mass of the antiparticle >> mass of the particle (m  =207m e )  mass of the antiparticle = ¼ of mass of the particle  there is a small perturbing electron (let be neglected)  I hope you already know what it is: a truly antiatom  not yet cold enough, but hopefully will be (winter is coming)

28. Effects, uncertainties, sensitivities Gravitation effect  U/c 2 Uncertainty/Sensitivity 10 -6 10 -9 10 -12 10 -15 Solar gravity (∞) Galactic gravity (∞) Solar gravity (perihelion-aphelion) Moon gravity (day-night) Earth gravity (100 m) Ps 1s-2s (th+exp) Mu 1s-2s (th+exp) H 1s-2s (exp) H HFS 1s (th + exp) Anti-p helium g-2 (Dirac eq) 10 -18 Solar gravity (day-night) Earth gravity (1 m) best clocks

29. small No room for antigravity, but a small room for `non-universality’  antigravity: inertial mass of particles and antiparticles is [about] the same gravitational mass = + inertial mass (matter) = – inertial mass (antimatter) = [almost] 0 (truly neutrals)  no chance ! Still possible: small  a small violation of equivalence principle small  a small difference in gravitation for a particle and antiparticle of a certain kind