1. Antigravity and Equivalence principle Savely G Karshenboim Pulkovo observatory (ГАО) (St. Petersburg) and Max-Planck-Institut für Quantenoptik (Garching)

2. Outline EP Deflection of light Dirac equation Problem of binding energy Consistent picture Curved space Inertial systems Red shift for photons vs. blue shift for clocks Two-body systems with antiparticles

3. Matter, antimatter and light We do have an efficient access to matter to study its gravity, but we do not have an efficient access to antimatter to study gravity. However, the world does not consist of matter and antimatter. There are purely neutral objects, such as photons.

4. Matter, antimatter and light However, the world does not consist of matter and antimatter. There are purely neutral objects, such as photons. Comparison of light and matter in gravitation field gives a hint, what could we expect from comparison of matter and antimatter.

5. EP: for light and matter Red shift Deflection of light

6. Curved space and deflection of light

7. Curved space is a good concept if it universally affects everything, i.e. in case of EP.

8. Curved space and deflection of light Curved space is a good concept if it universally affects everything, i.e. in case of EP. We may also speak about a flat space with the gravitational interaction presented, but nothing remains unaffected.

9. Curved space and deflection of light Curved space is a good concept if it universally affects everything, i.e. in case of EP. We may also speak about a flat space with the gravitational interaction presented, but nothing remains unaffected. There is no material substance to realize the flat space.

10. Free falling elevator and deflection of light Light propagation from inside of an elevator Light propagation from outside of an elevator Falling elevator versus time

11. Free falling M-elevator and deflection of light Light propagation from inside of an M elevator Light propagation from outside of an M elevator Falling M elevator versus time

12. Free falling M and Mbar elevators and deflection of light Light propagation from inside of M and anti-M elevators, in case of EP Light propagation from outside Falling elevator versus time

13. Deflection of light (suggesting antigravity) matter: hydrogen antimatter: antihydrogen

14. Deflection of light (suggesting antigravity) matter: hydrogen antimatter: antihydrogen neutral: positronium, photons and photons Does not look really great!

15. Deflection of light (suggesting antigravity) matter: hydrogen antimatter: antihydrogen neutral: positronium, photons and photons Does not look really great! Real light behaves in as an ultrarelativistic particle of matter!

16. Deflection of light and EP There is no way to simultaneously (but separately) keep exact EP for matter and light, antimatter and light in case of antigravity. The only possibility is to allow m g /m i to vary for matter and antimatter at the same level as we are able to verify deflection of light as it follows from GR (~1%).

17. EP: the Dirac equation Dirac equation describes an electron. Dirac equation has been checked with a high accuracy. It predicts a positron with the same mass (rest energy) and opposite charge. If gravitation for electron and positron is not the same we would arrive at a problem.

18. Problem of binding energy In case of inertial mass and in case of EP, binding energy is sufficient to describe a bound state. In case of non-universal m g /m i for different components, we should rather speak about `bound masses´. I.e. We have to split the binding energy between the components. E.g. comparing g-2 of e + and e –, we observe certain energy levels.

19. Antigravity and inertial systems Inertial system: a free particle has no acceleration. Energy may conserve. Non-inertial system: a free particle may be acceletared. It has no potential energy, but may change its kinetic energy. Energy cannot be conserved.

20. Antigravity and inertial systems Non-inertial system: a free particle may be acceletared. It has no potential energy, but may change its kinetic energy. Energy cannot be conserved. Introduce forces of inertia: they immitate potential energy and immitate conservation of energy.

21. EP and non-inertial systems The force of inertia is proportional to the inertial mass of a particle. The force of gravity is proportional to the gravitational mass of the particle. As far as these two masses are the same, we cannot locally distinguish a non-inertial frame and an inertial frame with a [different] gravity.

22. EP and non-inertial systems As far as these two masses are the same, we cannot locally distinguish a non-inertial frame and an inertial frame with a [different] gravity. The free falling system looks like an inertial system.

23. EP and non-inertial systems As far as these two masses are the same, we cannot locally distinguish a non-inertial frame and an inertial frame with a [different] gravity. The free falling system looks like an inertial system (for an insider!). The oudsider may see the source of gravity and thus distinguish (in part) between the gravity and non-inertiality.

24. EP and non-inertial systems As far as these two masses are the same, we cannot locally distinguish a non-inertial frame and an inertial frame with a [different] gravity. The free falling system looks like an inertial system (for an insider!). The oudsider may see the source of gravity and thus distinguish (in part) between the gravity and non-inertiality.

25. EP and non-inertial systems The oudsider may see the source of gravity and thus distinguish in part between the gravity and non-inertiality. The outsider understands that the free falling system is a non-inertial system with gravity, where forces of inertia and gravity exactly compensate each the other

26. EP and non-inertial systems The oudsider may see the source of gravity and thus distinguish in part between the gravity and non-inertiality. The outsider understands that the free falling system is a non-inertial system with gravity, where forces of inertia and gravity exactly compensate each the other as far as m i =m g.

27. EP and non-inertial systems The outsider understands that the free falling system is a non-inertial system with gravity, where forces of inertia and gravity exactly compensate each the other as far as m i =m g. If m i  m g then some `free´ particles will have got accelerated. The energy is not conserved

28. EP and non-inertial systems The outsider understands that the free falling system is a non-inertial system with gravity, where forces of inertia and gravity exactly compensate each the other as far as m i =m g. If m i  m g then some `free´ particles will have got accelerated. The energy is not conserved unless we explicitly introduce the forces of inertia and gravity which do not compensate each the other anymore.

29. Conservation of energy and `true´ inertial frames All variety of coordinates in GR and the very possibility to introduce the `curved´ space come from universality of gravity

30. Conservation of energy and `true´ inertial frames All variety of coordinates in GR and the very possibility to introduce the `curved´ space come from universality of gravity and from universal cancelation between forces of inertia and forces of gravity. Not anymore.

31. Conservation of energy and `true´ inertial frames All variety of coordinates in GR and the very possibility to introduce the `curved´ space come from universality of gravity and from universal cancelation between forces of inertia and forces of gravity. Not anymore. Now we have to introduce the `absolute´ inertial frame with gravity.

32. Conservation of energy and `true´ inertial frames A good choice is an inertial system in which we explicitely describe gravity, e.g., the Earth gravity. We are still free falling in respect to all other gravitation sources, which are not taken into account explicitly, which is not good.

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

34. 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 ).

35. 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.

36. 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!

37. 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.

38. 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

39. 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 (∞).

40. 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.

41. 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 

42. 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

43. 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

44. 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

45. 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.

46. 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.

47. 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

48. 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.

49. 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

50. Effects, uncertainties, sensitivities: now including particle physics 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) kaons  m/m B mesons m/m D mesons m/m Anti-p helium g-2 (Dirac eq) 10 -18 Solar gravity (day-night) Earth gravity (1 m) best clocks

51. Testing the equivalence principle Laboratory (UW): Earth gravity Laser Lunar Ranging: Solar gravity where and

52. Testing the equivalence principle Laboratory (UW): Earth gravity Laser Lunar Ranging: Solar gravity Kaons: galactic field where and Other mesons: D B

53. 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 oscillations. Data on oscillations of K, B & D mesons leave no chance for antigravity.

54. References Atoms with antiparticles: Kaons:

55. To conclude: matter is a `magic´ word Nucleon structure: three consituent quarks contains a combination of sea quarks and antiquarks with admixture of gluons + a `label´ which is of matter.