The Search for Quantum Gravity Effects

Transcription

1 The Search for Quantum Gravity Effects Claus Lämmerzahl Center for Applied Space Technology and Microravity (ZARM) University of Bremen Noncommutative Geometry and Physics: Fundamental Structure of Space and Time Cambridge, C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

2 Space-time structure There are many aspects of space time structure C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

3 Space-time structure There are many aspects of space time structure manifold differentiable, granular, discrete, non commutative,... C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

4 Space-time structure There are many aspects of space time structure manifold differentiable, granular, discrete, non commutative,... metric background, fluctuating,... C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

5 Space-time structure There are many aspects of space time structure manifold differentiable, granular, discrete, non commutative,... metric background, fluctuating,... connection metric, torsion, non metricity, background or fluctuating C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

6 Space-time structure There are many aspects of space time structure manifold differentiable, granular, discrete, non commutative,... metric background, fluctuating,... connection metric, torsion, non metricity, background or fluctuating more general structures,... C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

7 Space-time structure There are many aspects of space time structure manifold differentiable, granular, discrete, non commutative,... metric background, fluctuating,... connection metric, torsion, non metricity, background or fluctuating more general structures,... Whatever space-time is: We can explore space-time only through the observation of light rays, particles, fields,... Structure of space time is encoded in the dynamics of physical objects C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

8 The need for experiments Today s standard theories and standard space time notion as explored by point particles, light rays, and fields Frame theories Quantum theory Special Relativity General Relativity Statistical mechanics Problems Incompatibility of quantum theory and General Relativity Problem of time Occurrence of singularities Interactions Electrodynamics Gravity Weak interaction Strong interaction Wish Unification of all interactions Need of modifications of standard theories, but standard theories derived from observations need for larger domain of experience, other observations, more precise measurements C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

9 Outline 1 The situation of standard physics C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

10 Outline 1 The situation of standard physics 2 The search for Quantum Gravity effects: General remarks C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

11 Outline 1 The situation of standard physics 2 The search for Quantum Gravity effects: General remarks 3 Tests of Lorentz invariance C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

12 Outline 1 The situation of standard physics 2 The search for Quantum Gravity effects: General remarks 3 Tests of Lorentz invariance 4 Tests of General Relativity C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

13 Outline 1 The situation of standard physics 2 The search for Quantum Gravity effects: General remarks 3 Tests of Lorentz invariance 4 Tests of General Relativity 5 Tests of Quantum Theory C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

14 Outline 1 The situation of standard physics 2 The search for Quantum Gravity effects: General remarks 3 Tests of Lorentz invariance 4 Tests of General Relativity 5 Tests of Quantum Theory 6 Unexplained observations C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

15 Outline 1 The situation of standard physics 2 The search for Quantum Gravity effects: General remarks 3 Tests of Lorentz invariance 4 Tests of General Relativity 5 Tests of Quantum Theory 6 Unexplained observations 7 Conclusion and outlook C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

16 Outline The situation of standard physics 1 The situation of standard physics 2 The search for Quantum Gravity effects: General remarks 3 Tests of Lorentz invariance 4 Tests of General Relativity 5 Tests of Quantum Theory 6 Unexplained observations 7 Conclusion and outlook C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

17 The situation of standard physics Structure of standard physics Einstein Equivalence Principle Universality of Free Fall Universality of Gravitat. Redshift Lorentz Invariance Equations of motion for matter Maxwell equation Dirac equation Matter determines gravity Gravity determines dynamics General Relativity Gravity = Metric Einstein equations C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

18 The situation of standard physics The present situation All aspects of Lorentz invariance are experimentally well tested and confirmed Foundations Postulates c = const Principle of Relativity C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

19 The situation of standard physics The present situation All aspects of Lorentz invariance are experimentally well tested and confirmed Foundations Postulates c = const Principle of Relativity Tests Independence of c from velocity of the source Universality of c Isotropy of c Independence of c from velocity of the laboratory Time dilation Isotropy of physics (Hughes Drever experiments) Independence of physics from the velocity of the laboratory C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

20 The situation of standard physics The present situation Many aspects of the Universality of Free Fall are experimentally well tested and confirmed Postulate In a gravitational field all structureless test particles fall in the same way C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

21 The situation of standard physics The present situation Many aspects of the Universality of Free Fall are experimentally well tested and confirmed Postulate In a gravitational field all structureless test particles fall in the same way Tests UFF for Neutral bulk matter Charged particles Particles with spin No test so far for Anti particles C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

22 The situation of standard physics The present situation Many aspects of the Universality of the Gravitational Redshift are experimentally well tested and confirmed Postulate In a gravitational field all clocks behave in the same way g C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

23 The situation of standard physics The present situation Many aspects of the Universality of the Gravitational Redshift are experimentally well tested and confirmed Postulate In a gravitational field all clocks behave in the same way g Tests UGR for Atomic clocks: electronic Atomic clocks: hyperfine Molecular clocks: vibrational Molecular clocks: rotational Resonators Nuclear transitions No test so far for Anti clocks C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

24 The situation of standard physics The Einstein Equivalence Principle Point particle C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

25 The situation of standard physics The Einstein Equivalence Principle Point particle EEP Geodesic equation in Riemann space 1 C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

26 The situation of standard physics The Einstein Equivalence Principle Point particle EEP Geodesic equation in Riemann space 1 Spin 1/2 particle C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

27 The situation of standard physics The Einstein Equivalence Principle Point particle EEP Geodesic equation in Riemann space 1 Spin 1/2 particle EEP Dirac equation in Riemann space 2 C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

28 The situation of standard physics The Einstein Equivalence Principle Point particle EEP Geodesic equation in Riemann space 1 Spin 1/2 particle EEP Dirac equation in Riemann space 2 Electromagn. field C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

29 The situation of standard physics The Einstein Equivalence Principle Point particle EEP Geodesic equation in Riemann space 1 Spin 1/2 particle EEP Dirac equation in Riemann space 2 Electromagn. field EEP Maxwell equation in Riemann space 3 C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

30 The situation of standard physics The Einstein Equivalence Principle Point particle EEP Geodesic equation in Riemann space 1 EEP Spin 1/2 particle EEP Dirac equation in Riemann space 2 EEP Point particle, Dirac and Maxwell eqn in same Riemann space Electromagn. field EEP Maxwell equation in Riemann space 3 EEP C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

31 The situation of standard physics The present situation All predictions of Einstein s General Relativity are experimentally well tested and confirmed Foundations The Einstein Equivalence Principle Universality of Free Fall Universality of Gravitational Redshift Local Lorentz Invariance C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

32 The situation of standard physics The present situation All predictions of Einstein s General Relativity are experimentally well tested and confirmed Foundations The Einstein Equivalence Principle Universality of Free Fall Universality of Gravitational Redshift Local Lorentz Invariance Predictions from GR Solar system effects Perihelion shift Gravitational redshift Deflection of light Gravitational time delay Lense Thirring effect Schiff effect Strong gravitational fields Binary systems Black holes Gravitational waves Cosmology C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

33 The situation of standard physics Application: Metrology A m SR ensures uniqueness of timekeeping in moving frames SR: Constancy of speed of light mol s GR ensures uniqueness of timekeeping in gravitational fields cd 10 4 GR ensures uniqueness of definition of mass kg unknown ageing of prototype K SR & GR = Physics of space and time fundamental metrology C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

34 The search for Quantum Gravity effects: General remarks Outline 1 The situation of standard physics 2 The search for Quantum Gravity effects: General remarks 3 Tests of Lorentz invariance 4 Tests of General Relativity 5 Tests of Quantum Theory 6 Unexplained observations 7 Conclusion and outlook C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

35 The search for Quantum Gravity effects: General remarks Implications of a new theory Unresolved fundamental inconsistency Standard physics cannot be completely correct There have to be modifications to standard physics Ordinary modifications Modifications in Maxwell, Dirac, Einstein equations Violation of Einstein Equivalence Principle Search for violations of the Einstein Equivalence Principle C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

36 The search for Quantum Gravity effects: General remarks Implications of a new theory Unresolved fundamental inconsistency Standard physics cannot be completely correct There have to be modifications to standard physics Ordinary modifications Modifications in Maxwell, Dirac, Einstein equations Violation of Einstein Equivalence Principle Search for violations of the Einstein Equivalence Principle Other modifications Modified notion of space time (e.g. space time fluctuations) But: space-time is explored by particles, photons,... Modified space time properties result in modified equations of motion Search for fundamental noise, decoherence, non conserved probablility,... (only later it might be useful to assign certain effects to space-time properties) C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

37 The search for Quantum Gravity effects: General remarks Hierarchy of theories Full theory Quantum Gravity Experiment Observation Clock readout Interference fringes acceleration counting events... C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

38 The search for Quantum Gravity effects: General remarks Hierarchy of theories Full theory Quantum Gravity derived Effective theory Dilaton scenarios Axion fields Torsion... Experiment Observation Clock readout Interference fringes acceleration counting events... C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

39 The search for Quantum Gravity effects: General remarks Hierarchy of theories Full theory Quantum Gravity derived Effective theory Phenomenology Test theory Experiment Observation Dilaton scenarios Axion fields Torsion... Standard Model Extension PPN formalism c 2 formalism Robertson Mansouri Sexl THɛμ formalism χ g formalism... Clock readout Interference fringes acceleration counting events... C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

40 The search for Quantum Gravity effects: General remarks Hierarchy of theories Full theory Quantum Gravity derived Effective theory Phenomenology Test theory Experiment Observation Dilaton scenarios Axion fields Torsion... Standard Model Extension PPN formalism c 2 formalism Robertson Mansouri Sexl THɛμ formalism χ g formalism... Clock readout Interference fringes acceleration counting events... C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

41 The search for Quantum Gravity effects: General remarks Hierarchy of theories Full theory Quantum Gravity derived Test theories mediate between experiment and full theory Effective theory Phenomenology Test theory Experiment Observation Dilaton scenarios Axion fields Torsion... Standard Model Extension PPN formalism c 2 formalism Robertson Mansouri Sexl THɛμ formalism χ g formalism... Clock readout Interference fringes acceleration counting events... C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

42 The search for Quantum Gravity effects: General remarks The role of test theories Test theories generalize specific predictions Noncommutative theory Noncommutativity non locality higher derivatives in field equations anomalous dispersion all implications of anomalous dispersion [x μ,x ν ]=iθ μν preferred directions violation of Lorentz invariance all sorts of violations of LI and all implications String theory Low energy limit scalar tensor theory additional scalar field couples differently to various matter fields violation of UUF, UGR general scalar tensor theories Scheme with symmetry breaking breaking of Lorentz invariance all sorts of violations of LI and all implications C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

43 The search for Quantum Gravity effects: General remarks The role of test theories Canonical/loop quantum gravity Fluctuating metric non unitary terms in effective Schrödinger equation general non unitarity In quasiclassical limit higher order and non linear terms appear general higher order theories anomalous dispersion general non linearities Since there is no complete theory available (no mapping between theoretical notions and observed quantities), predictions can serve just as hints to the possible structure of effects Examples... C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

44 The search for Quantum Gravity effects: General remarks Predictions from loop quantum gravity Modified Maxwell equations Gambini & Pullin 1999 t E = B +2χl P 2 B t B = E 2χl P 2 E. Alfaro, Morales Tecotl & Urrutia = B t E + ϑ 1 B + ϑ 2 Δ( B)+ϑ 3 ΔB + ϑ 4 (B 2 B)+... 0= E + t B + ϑ 1 E + ϑ 2 Δ( E)+ϑ 3 ΔE +..., Modified Dirac equation Alfaro, Morales Tecotl & Urrutia 2002 i γ a a ψ mψ γ ab a b ψ =0, C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

45 The search for Quantum Gravity effects: General remarks Predictions from string theory Modified Maxwell equations Ellis, Mavromatos & Nanopoulos 1999 E + ū t E =0 B =0 B (1 ū 2 ) t E + ū t B +(ū )E =0 E = t B, Modified Dirac equation Ellis et al 2000 iγ a a ψ ū a γ 0 i a ψ mψ =0 C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

46 The search for Quantum Gravity effects: General remarks Scalar tensor theories Effective Lagrangian From string theory: effective Lagrangian for gravity with long ranged dilaton like scalar field (Damour et al 1993, 1994, 2002) L eff = 1 16πG R(g) 1 8πG gμν D μ ϕd ν ϕ 1 4e 2 (ϕ) F μνf μν ( ψa γ μ (D μ ia μ )ψ A + m A (ϕ) ψ ) A ψ A A ϕ = dilaton field ϕ 0 = vacuum expectation value given by cosmological evolution Parameters depending on dilaton field: mass of fermion coupling to electromagnetic field energy levels of atoms C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

47 The search for Quantum Gravity effects: General remarks Scalar tensor theories Strengths of couplings Strength of coupling of dilaton to mass m A : α A = ln m A(ϕ) ϕ ϕ=ϕ0 Strength of coupling of dilaton to electromagnetism: α em = e2 (ϕ) ϕ Energy differences: α AA = E AA (ϕ) ϕ ϕ=ϕ0 ϕ=ϕ0 Gravitational constant One obtains a composition dependent gravitational constant: Acceleration of test body 1 by body 2: a 1 = (m g) 1 G(m g ) 2 (m g ) 2 (m i ) 1 r12 2 = G 12 r12 2 Then G 12 = G (m g) 1 (m i ) 1 (m g ) 2 (m i ) 2 G (1 + α 1 α 2 ) C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

48 The search for Quantum Gravity effects: General remarks Scalar tensor theories Consequences UFF: η = a A a B 1 2 (a A + a B ) = G 13 G (G 13 + G 23 ) (α A α B ) α E α 2 had PPN: γ parameter: γ 1= 2 α2 had 1+α 2 had Redshift: ν AA (r 1 ) ν AA (r 2 ) 1+(1+α AA α E) U E(r 2 ) U E (r 1 ) c 2 UGR: Comparison of two different clocks at same position: Time dependence ν AA (r) ν BB (r) = F (Z Ae 2 (ϕ)) F (Z B e 2 (ϕ)) δ ln e 2 = α 2 had δu(t) α 2 had H 0δt C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

49 The search for Quantum Gravity effects: General remarks Predictions Effect dilaton cosmon varying e UFF η < UGR PPN γ PPN β α/α y 1 Damour and Polyakov 1994, Damour, Piazza, and Veneziano 2002 Wetterich 2002, 2003 Ellis et al 1999, 2000 Sandvick et al 2000 On the present status of predictions Specific predictions are not important Predictions open the door to a whole range of effects Then test theories take over the description of experiments C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

50 The search for Quantum Gravity effects: General remarks Test theories Further reasons for using test theories Parametrization and identification of possible violation Quantification of degree of validity Different (!) experiments can be compared C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

51 The search for Quantum Gravity effects: General remarks Test theories Further reasons for using test theories Parametrization and identification of possible violation Quantification of degree of validity Different (!) experiments can be compared Kinematical test theories Robertson Mansouri Sexl C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

52 The search for Quantum Gravity effects: General remarks Test theories Further reasons for using test theories Parametrization and identification of possible violation Quantification of degree of validity Different (!) experiments can be compared Kinematical test theories Robertson Mansouri Sexl Dynamical test theories c 2 formalism 1 parameter χ g formalism 19 parameter Extended Standard Model 19 + n48 parameter PPN formalism 10 parameter Oneneedsasmanytestsasthereareparameters C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

53 The search for Quantum Gravity effects: General remarks Test theories Further reasons for using test theories Parametrization and identification of possible violation Quantification of degree of validity Different (!) experiments can be compared Kinematical test theories Robertson Mansouri Sexl Dynamical test theories c 2 formalism 1 parameter χ g formalism 19 parameter Extended Standard Model 19 + n48 parameter PPN formalism 10 parameter Oneneedsasmanytestsasthereareparameters Dynamical test theories are superior C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

54 The search for Quantum Gravity effects: General remarks Test theories, Phenomenology Phenomenology = Generalizations of Maxwell and Dirac equations 4πj μ = η μρ η νσ ν F ρσ 0 = iγ a D a ψ + mψ with γ a γ b + γ b γ a =2η ab Standard equations C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

55 The search for Quantum Gravity effects: General remarks Test theories, Phenomenology Phenomenology = Generalizations of Maxwell and Dirac equations 4πj μ = η μρ η νσ ν F ρσ + χ μρνσ ν F ρσ 0 = iγ a D a ψ + mψ + Mψ with γ a γ b + γ b γ a =2η ab + X ab Standard equations Particular case: Standard Model Extension C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

56 The search for Quantum Gravity effects: General remarks Test theories, Phenomenology Phenomenology = Generalizations of Maxwell and Dirac equations 4πj μ = η μρ η νσ ν F ρσ + χ μρνσ ν F ρσ + χ μρσ F ρσ 0 = iγ a D a ψ + mψ + Mψ with γ a γ b + γ b γ a =2η ab + X ab Standard equations Particular case: Standard Model Extension More general cases with charge non conservation Q 0 α 0 C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

57 The search for Quantum Gravity effects: General remarks Test theories, Phenomenology Phenomenology = Generalizations of Maxwell and Dirac equations 4πj μ = η μρ η νσ ν F ρσ + χ μρνσ ν F ρσ + χ μρσ F ρσ + χ μρνστ ν τ F ρσ = iγ a D a ψ + mψ + Mψ + γ ab D a D b ψ +... with γ a γ b + γ b γ a =2η ab + X ab Standard equations Particular case: Standard Model Extension More general cases with charge non conservation Q 0 α 0 Higher derivative models C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

58 The search for Quantum Gravity effects: General remarks Test theories, Phenomenology Phenomenology = Generalizations of Maxwell and Dirac equations 4πj μ = η μρ η νσ ν F ρσ + χ μρνσ ν F ρσ + χ μρσ F ρσ + χ μρνστ ν τ F ρσ ζ μρστ ν F ρσ F τν 0 = iγ a D a ψ + mψ + Mψ + γ ab D a D b ψ N(ψ)ψ with γ a γ b + γ b γ a =2η ab + X ab Standard equations Particular case: Standard Model Extension More general cases with charge non conservation Q 0 α 0 Higher derivative models Non linear terms C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

59 The search for Quantum Gravity effects: General remarks Possible effects Possible geometry relevant effects Anisotropic speed of light Anisotropy in quantum fields Violation of UFF, UGR Birefringence Anomalous spin coupling Anomalous coupling of charge Anomalous dispersion Newton / Coulomb potential Nonlinearities Charge non conservation Active passive mass and charge Other possible effects Decoherence Modified interference Non localities Non unitarity C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

60 The search for Quantum Gravity effects: General remarks Possible effects Possible geometry relevant effects Anisotropic speed of light Anisotropy in quantum fields Violation of UFF, UGR Birefringence Anomalous spin coupling Anomalous coupling of charge Anomalous dispersion Newton / Coulomb potential Nonlinearities Charge non conservation Active passive mass and charge Other possible effects Decoherence Modified interference Non localities Non unitarity Structure of parameters Usually: parameters are assumed to be constant In unification scenarios: parameters depend on time and position, through one or more fields (dilaton, cosmon) scalar tensor theories C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

61 The search for Quantum Gravity effects: General remarks The magnitude of Quantum Gravity effects Typical laboratory energies 1eV QG energy scale E Planck ev } Expectation: QG effects in laboratory C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

62 The search for Quantum Gravity effects: General remarks The magnitude of Quantum Gravity effects Typical laboratory energies 1eV QG energy scale E Planck ev } Expectation: QG effects in laboratory E QG E Planck is just a hypothesis until now, E QG might be smaller QG effects in large extra dimensions : deviations from Newton s law String-theory-motivated dilaton scenarios (DPV 2002): UFF may be violated at level, and γ Low-energy data suggest that electroweak and strong interactions unify at GUT energy scale of GeV, perhaps also gravity would be of the same strength as the other interactions at that scale C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

63 The search for Quantum Gravity effects: General remarks The magnitude of Quantum Gravity effects Typical laboratory energies 1eV QG energy scale E Planck ev } Expectation: QG effects in laboratory E QG E Planck is just a hypothesis until now, E QG might be smaller QG effects in large extra dimensions : deviations from Newton s law String-theory-motivated dilaton scenarios (DPV 2002): UFF may be violated at level, and γ Low-energy data suggest that electroweak and strong interactions unify at GUT energy scale of GeV, perhaps also gravity would be of the same strength as the other interactions at that scale Amplification by large factor given by experimental setup QG effects on neutral kaon system: amplified by M L,S/ M L M S QG induced interferometric noise: 1/f noise (e.g. search for fundamental noise in high precision long term stable optical resonators, Schiller et al 2004) Sensitivity of some clock comparison experiments is amplified by m pc 2 /(hν) (ν = clock frequency, m p = the proton mass) C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

64 The search for Quantum Gravity effects: General remarks The magnitude of Quantum Gravity effects Typical laboratory energies 1eV QG energy scale E Planck ev } Expectation: QG effects in laboratory E QG E Planck is just a hypothesis until now, E QG might be smaller QG effects in large extra dimensions : deviations from Newton s law String-theory-motivated dilaton scenarios (DPV 2002): UFF may be violated at level, and γ Low-energy data suggest that electroweak and strong interactions unify at GUT energy scale of GeV, perhaps also gravity would be of the same strength as the other interactions at that scale Amplification by large factor given by experimental setup QG effects on neutral kaon system: amplified by M L,S/ M L M S QG induced interferometric noise: 1/f noise (e.g. search for fundamental noise in high precision long term stable optical resonators, Schiller et al 2004) Sensitivity of some clock comparison experiments is amplified by m pc 2 /(hν) (ν = clock frequency, m p = the proton mass) Some laboratory experiments (grav. wave interferometers) may reach C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

65 The search for Quantum Gravity effects: General remarks The magnitude of Quantum Gravity effects Typical laboratory energies 1eV QG energy scale E Planck ev } Expectation: QG effects in laboratory E QG E Planck is just a hypothesis until now, E QG might be smaller QG effects in large extra dimensions : deviations from Newton s law String-theory-motivated dilaton scenarios (DPV 2002): UFF may be violated at level, and γ Low-energy data suggest that electroweak and strong interactions unify at GUT energy scale of GeV, perhaps also gravity would be of the same strength as the other interactions at that scale Amplification by large factor given by experimental setup QG effects on neutral kaon system: amplified by M L,S/ M L M S QG induced interferometric noise: 1/f noise (e.g. search for fundamental noise in high precision long term stable optical resonators, Schiller et al 2004) Sensitivity of some clock comparison experiments is amplified by m pc 2 /(hν) (ν = clock frequency, m p = the proton mass) Some laboratory experiments (grav. wave interferometers) may reach Laboratory/controlled experiments may well search for possible QG effects C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

66 The search for Quantum Gravity effects: General remarks Observations vs. Experiment Comparison: high nergy cosmic ray observation low energy laboratory exp. C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

67 The search for Quantum Gravity effects: General remarks Observations vs. Experiment Comparison: high nergy cosmic ray observation low energy laboratory exp. Astrophysical observations + Availability of ultra high energies of more than ev No systematic repeatability No unique interpretation C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

68 The search for Quantum Gravity effects: General remarks Observations vs. Experiment Comparison: high nergy cosmic ray observation low energy laboratory exp. Astrophysical observations + Availability of ultra high energies of more than ev No systematic repeatability No unique interpretation Laboratory search + Repeatability of the experiment, systematic variation of initial and boundary conditions, used for: Identification of cause Improvement of precision of result Only small energies are available + Ultra low temperatures, ultrastable devices like optical resonators can be obtained in the laboratory only C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

69 The search for Quantum Gravity effects: General remarks Observations vs. Experiment Comparison: high nergy cosmic ray observation low energy laboratory exp. Astrophysical observations + Availability of ultra high energies of more than ev No systematic repeatability No unique interpretation Laboratory search + Repeatability of the experiment, systematic variation of initial and boundary conditions, used for: Identification of cause Improvement of precision of result Only small energies are available + Ultra low temperatures, ultrastable devices like optical resonators can be obtained in the laboratory only Due to stability and repeatability of experiments, laboratory searches for quantum gravity effects may be as promising as astrophysical observation C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

70 The search for Quantum Gravity effects: General remarks Strategy: Exploration of new regimes Standard physics experimentally well proven for standard energy, velocity, distance,... Search for new effects need to go to non standard situations: C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

71 The search for Quantum Gravity effects: General remarks Strategy: Exploration of new regimes Standard physics experimentally well proven for standard energy, velocity, distance,... Search for new effects need to go to non standard situations: Non standard situations Extreme high energies. Deviations from the standard dispersion relation Extreme low energies. Space time fluctuations, decoherence may affect quantum systems at temperatures lower than 500 fk achieved in BECs C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

72 The search for Quantum Gravity effects: General remarks Strategy: Exploration of new regimes Standard physics experimentally well proven for standard energy, velocity, distance,... Search for new effects need to go to non standard situations: Non standard situations Extreme high energies. Deviations from the standard dispersion relation Extreme low energies. Space time fluctuations, decoherence may affect quantum systems at temperatures lower than 500 fk achieved in BECs Extreme large distances. Dark energy, dark matter, Pioneer anomaly related to large distances Ultra low frequency gravitational waves (early universe) Extreme small distances. higher dimensional theories: violation of Newton s law at small (sub mm) distances C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

73 The search for Quantum Gravity effects: General remarks Strategy: Exploration of new regimes Standard physics experimentally well proven for standard energy, velocity, distance,... Search for new effects need to go to non standard situations: Non standard situations Extreme high energies. Deviations from the standard dispersion relation Extreme low energies. Space time fluctuations, decoherence may affect quantum systems at temperatures lower than 500 fk achieved in BECs Extreme large distances. Dark energy, dark matter, Pioneer anomaly related to large distances Ultra low frequency gravitational waves (early universe) Extreme small distances. higher dimensional theories: violation of Newton s law at small (sub mm) distances Extreme long timescales. Search for space time fluctuations in terms of 1/f noise Time dependence of constants Extreme short timescales. Short time scales large energies C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

74 Outline Tests of Lorentz invariance 1 The situation of standard physics 2 The search for Quantum Gravity effects: General remarks 3 Tests of Lorentz invariance 4 Tests of General Relativity 5 Tests of Quantum Theory 6 Unexplained observations 7 Conclusion and outlook C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

75 Postulates Tests of Lorentz invariance Postulates of SR Postulate 1: The velocity of light is constant. Postulate 2: The relativity principle. The meaning of the postulates c does not depend on the velocity of the source uniqueness of c the velocity of the observer the direction of propagation its frequency and polarization The meaning of c For all particles the velocity of light is the limiting velocity c = c + = c = c ν = vp max = ve max = v grav c is universal and can, thus, be interpreted as geometry All physics is the same in all inertial systems Experimental results do not depend on the orientation of the laboratory Experimental results do not depend on the velocity of the laboratory C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

76 Tests of Lorentz invariance Independence of c from the velocity of the source normal v orbital plane ψ R r Earth Description and result (Brecher 1977) Model c = c + κv Time of flight consideration: May happen Reversal of chronological order (one light ray may overtake the other) Multiple images... Result κ C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

77 Tests of Lorentz invariance Independence of c from the velocity of the source γ π 0 γ v =0 C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

78 Tests of Lorentz invariance Independence of c from the velocity of the source γ π 0 γ v =0 detector detector proton source p π 0 γ L v Be target clock C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

79 Tests of Lorentz invariance Independence of c from the velocity of the source γ π 0 γ v =0 detector detector proton source p π 0 γ L v Be target clock Description and result (Alväger et al 1964) Model c = c + κv Result κ 10 6 at v = c C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

80 Tests of Lorentz invariance Tests of the universality of c t δt c δc c Polarization / dispersion of light Method: Comparison of arrival times of light with different polarization / different frequency from distant galaxies l x Result Carrol, Field and Jackiw 1992, Kauffmann and Haugan 1995, Kostelecky and Mathews 2002 c + c Schafer 1999, Biller 1999 c + c ν c ν c ν C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

81 Tests of Lorentz invariance Tests of the universality of c Velocity of neutrinos Method: Comparison of arrival times of photons and neutrinos from supernova SN1987a Result Longo 1987, Stodolsky 1988 Limiting velocity of protons c v ν c 10 8 Result Coleman and Glashow 1998 v max p c c C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

82 Tests of Lorentz invariance Tests of the universality of c Limiting velocity of electrons deflector e source e accelerator γ e target L γ e p detector e detector Result Giurogossian et al 1965 v max e c c 10 6 Other tests by Brown et al 1963, Alspector et al 1976, Kalbfleisch et al 1976 with result of same order of accuracy C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

83 Tests of Lorentz invariance Test of isotropy of c Interference experiment Michelson Morley... Measuring frequency of light in rotating resonator Model independent description Light wave ϕ = Ae i(k+ x ωt) +Be i(k x ωt) Dispersion relation ω = k ± c ± Boundary conditions Effective: 2 way velocity of light 2 c = c + c ϑ Observable frequency ν = m 2L c C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

84 Tests of Lorentz invariance Test of isotropy of c Interference experiment Michelson Morley... Measuring frequency of light in rotating resonator Model independent description Light wave ϕ = Ae i(k+ x ωt) +Be i(k x ωt) Dispersion relation ω = k ± c ± Boundary conditions Effective: 2 way velocity of light 2 c = c + c ϑ Observable frequency ν(ϑ) = m 2L c(ϑ) C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

85 Tests of Lorentz invariance Test of isotropy of c Interference experiment Michelson Morley... Measuring frequency of light in rotating resonator Result Herrmann, Peters et al 2005 Cryogenic resonators, one rotating, one fixed Result Δ ϑ c c (2.5 ± 4) ϑ Interpretation (Müller et al 2004) Velocity of light Electron properties (in L) C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

86 Tests of Lorentz invariance Summary: Test of isotropy of c δ θ c c 10 8 Ether theory prediction Michelson & Morley 1887 Morley & Miller 1904 {z } Interferometer Tomaschek 1924 Illingworth 1927 Joos 1930 Kennedy 1926 Cavities z } { Essen 1955 Trimmer et al 1964 Cedarholm et al 1958 Jaseja et al 1964 Brillet & Hall 1979 Wolf et al 2002 Müller et al 2002 Schiller et al 2005 Peters et al C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

87 Tests of Lorentz invariance Test of independence of c from laboratory velocity Interference experiment Kennedy Thorndike... Measuring frequency of light in moving resonator Model independent description Same description as above Observable frequency ν = m 2L c v C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

88 Tests of Lorentz invariance Test of independence of c from laboratory velocity Interference experiment Kennedy Thorndike... Measuring frequency of light in moving resonator Model independent description Same description as above Observable frequency ν(v) = m 2L c(v) v C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

89 Tests of Lorentz invariance Test of independence of c from laboratory velocity Cavity clock comparison Method and result Wolf et al 2004 Whispering gallery modes Comparison with H maser Result Δ v c c (4.5 ± 4.5) δv rotation of Earth p=5 p=5 p=5 m=3 m=30 m=100 Whispering gallery modes C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

90 Tests of Lorentz invariance Hughes Drever experiments The model Modified Schrödinger equation i t ψ = 2 ( δ ij + α ij) i j ψ 2m Leads to a splitting of the Zeeman singlett C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

91 Tests of Lorentz invariance Hughes Drever experiments The model Modified Schrödinger equation i t ψ = 2 ( δ ij + α ij) i j ψ 2m Leads to a splitting of the Zeeman singlett Experiments experiment method estimate Hughes et al 1960 NMR with 7 Li α ij Drever 1961 NMR with 7 Li α ij Prestage et al NMR with 9 Be + α ij Lamoreaux et al. 1986, 1989, 1990 NMR with 201 Hg α ij Chupp et al 1989 NMR with 21 Ne α ij C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

92 Tests of Lorentz invariance Methods for testing time dilation General: Comparison of identical cloks in different motion Transport of macrocopic clocks Photon absorption / emission Two photon absorption Rotor experiments Saturation spectroscopy Particle decay C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

93 Tests of Lorentz invariance Test of time dilation: Transport of clocks The Experiment by Hafele and Keating 1968 C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

94 Tests of Lorentz invariance Test of time dilation: Photon emission / absorption ν 0 Description Simple consequence ν Description v Doppler effect ν ± = ν v 2 (1 ± v) ν 0 ν 2 0 = ν +ν independent of synchronization Experiments Ives & Stilwell 1938 Otting 1939 Pound & Rebka 1960 Mandelberg & Witten 1962 Olin 1973 Junckar 1985 MacArthur 1986 C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

95 Tests of Lorentz invariance Test of time dilation: 2 Photon absorption Description Resonance condition for v =0 2v v=0 laser = ν 1 + ν 2 ν 2 Resonance condition for v 0 ν v laser ν v laser ν 1 = ν + = ν v laser (1 + v) 1 v 2 ν 1 ν 2 = ν = ν v laser (1 v) 1 v 2 Consequence v mirror with νlaser v=0 = νlaser v 1 v 2 v = ν + ν ν + + ν No need of synchronization C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

96 Further tests Tests of Lorentz invariance Time dilation with saturation spectroscopy Rotor time dilation experiments Sagnac effect Experiments testing E = mc 2... C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

97 Tests of Lorentz invariance Proposal for test of anomalous dispersion Model anomalous dispersion relation m 2 = E 2 p 2 + η E3 E ( Pl wave vector k(ω) =ω 1+ 1 ) ω 2 ω QG no longer homogeneous relation First estimate present day sensitivity of LIGO: h = ΔL L 10 21,forL 4km sensitivity of advanced LIGO: h = ΔL L at 10 Hz. measuring periodic signal each 0.1 s over one year: h ΔL L E lab E Planck C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

98 Tests of Lorentz invariance Proposal for test of anomalous dispersion mirror interference experiment with two different frequencies I(ω) = 1 (1 + cos φ(ω)) 2 L with φ(ω) =k(ω)δl + φ 0 light source frequency doubler ω ω ω beam splitter L mirror unequal arm interferometer frequency filter for ω intensity measurement frequency filter for ω intensity measurement C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

99 Tests of Lorentz invariance Proposal for test of anomalous dispersion Intensity (ordinary dispersion) comparison of intensity for two waves with ω and ω =2ω For anomalous dispersion, the variation of the intensity for ω =2ω is slightly different from being twice the variation for ω Interference effect related to phase difference 1 δl Intensity (anomalous dispersion) 1 ω 2 φ(2ω) φ(ω) = 3 δl 2 ω QG δl C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

100 Tests of Lorentz invariance Proposal for test of anomalous dispersion Alternative set up: Interference in frequency space frequency SHG SHG e 3iωt (forbidden) e 2iωt u (2ω) 2 (x, t) e 2iωt u 0 (x, t) e iωt e iωt e iωt x =0 x = L position Phase shift: φ(2ω) =φ 0 +(k(2ω) 2k(ω)) δl δl: switching between 3 SHGs The sensitivity is available, at least in principle C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

101 Tests of Lorentz invariance Identification of effects Anomalous dispersion relation Prediction of anomalous dispersion from non commutative geometry k 2 = ω 2 + ω3 ω QG Effective Maxwell equation Maxwell equations on classical curved space time (Drummond & Hathrell 1982) D ν F μν + ξ 2 R μν ρσ ν F ρσ =0, ξ 2 = α/(90πm 2 e ) Dispersion relation: ω = ω( k) k depends on direction of propagation Group velocity group velocity homogenous in k isotropic Effective Maxwell v group = v group ( k) yes no Anomalous dispersion v group =1+ ω ω QG no yes From dependence of v on k, for example, various models can be distinguished. C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

102 Outline Tests of General Relativity 1 The situation of standard physics 2 The search for Quantum Gravity effects: General remarks 3 Tests of Lorentz invariance 4 Tests of General Relativity 5 Tests of Quantum Theory 6 Unexplained observations 7 Conclusion and outlook C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

103 Tests of General Relativity The structure of GR Einstein s theory of gravity metric theory of gravity Perihelion shift gravitational redshift light deflection grav. time delay Lense Thirring effect Schiff effect Einstein Equivalence Principle Universality of Free Fall Universality of Gravitational Redshift Special Relativity {z } Clock tests C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

104 Tests of General Relativity Description of tests of the Universality of Free Fall Haugan formalism Ansatz: Hamiltonian E = mc m ( δ ij + δm iij m Canonical equations ) ( v i v j + m δ ij + δm ) gij U ij ( x) m a i = δ ij j U + δmij i m ju + δ ij δm gkl m ju kl ( x), For diagonal mass tensors δm iij = m i δ ij, δm gij = m g δ ij : a i = δ ij m g m i j U Comparison of acceleration of two different particles: Eötvös coefficient η = a 2 a (a 2 + a 1 ) = (m g/m i ) 2 (m g /m i ) ( 1 ) 1 2 (mg /m i ) 2 +(m g /m i ) 1 C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

105 Tests of General Relativity Description of tests of the Universality of Free Fall Particles with spin Ansatz: Hamiltonian ( ) i t ϕ = 1 δ ij δmij i 2m m δ ( mij ik σk i j ϕ + c D A i j m + 1 ) m ai j σ j i i ϕ [ + mu(x)+c σ mu(x)+δm gij U ij (x) ] +c D T σ + mc 2 DB σ ϕ Canonical equations [ ( ) ] a i = δ ij δm ij i j U + m +2 δ m ij ik m + δij C k S k j U + δ ij δm gkl m ju kl ( x) Spin dependent forces C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

106 Tests of UFF Tests of General Relativity Tests with classical bulk matter Method Grav field Accuracy Experiment Pendula Earth η 10 3 Newton 1686 Pendula Earth η Bessel 1832 Torsion balance Sun η Eötvös, Pekar, Fekete 1922 Pendula Earth η 10 5 Potter 1932, 1927 Torsion balance Sun η Roll, Krotkov, Dicke 1964 Torsion balance Sun η Braginski, Panov 1972 Free Fall Earth η Niebauer, Hughes, Faller 1987 Free Fall Earth η Kuroda & Mio 1989, 1990 Torsion balance Sun η Adelberger et al Torsion balance Sun η Adelberger et al 2002 Earth-Moon motion Sun η Williams et al future Free fall in orbit Earth η MICROSCOPE 2009 Free fall in orbit Earth η GG Free fall in orbit Earth η STEP C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

107 Tests of UFF Tests of General Relativity Tests with quantum matter Method Grav field Accuracy Experiment Free fall neutron Earth η Koester Atom interferometery Earth η 10 9 Chu, Peters 1999 Gravitational self energy Method Grav field Accuracy Experiment Torsion pendulum and LLR Sun η Baessler et al 1999 Charged particles Method Grav field Accuracy Experiment Free fall of electron Earth η 10 1 Witteborn & Fairbank 1967 Particles with spin Method Grav field Accuracy Experiment Weighting polarized bodies Earth η 10 8 Hsie et al C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

108 UFF and charge Tests of General Relativity Standard theory In standard theory from ordinary coupling: a μ = αλ C cr μ νv ν Anomalous coupling Anomalous coupling H = p2 p2 + mu(x)+κeu(x) = (1+κ 2m 2m + m e ) U(x). m Charge dependent anomalous gravitational mass tensor Can be generalized to charge dependent anomalous inertial mass tensor (e.g. Rohrlich 2000) Charge dependent Eötvös factor It is possible to choose κ s such that for neutral composite matter UFF is fulfilled while for isolated charges UFF is violated C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

109 UFF and spin Tests of General Relativity Standard theory In standard theory from ordinary coupling: a μ = λ C R μ νρσv ν S ρσ of UFF at the order m/s 2, beyond experiment violation Anomalous coupling Speculations: violation P, C, andt symmetry in gravitational fields (Leitner & Okubo 1964, Moody & Wilczek 1974) suggest V (r) =U(r)[1+A 1 (σ 1 ± σ 2 ) r + A 2 (σ 1 σ 2 ) r], One body (e.g., the Earth) is unpolarized V (r) =U(r)(1+Aσ r). Hyperfine splittings of H ground state: A p 10 11, A e 10 7 Hari Dass 1976, 1977, includes velocity of the particles [ V (r) =U 0 (r) 1+A 1 σ r + A 2 σ v ( c + A 3 r σ v )] c C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

110 Tests of General Relativity Spin spin interactions The model direct spin spin interaction between electrons V = α s μ e σ μ e σ r The experiments Method Accuracy Experiment Molecular spectra α Ramsey 1979 NMR α Aleksandrov et al. (1983) NMR α Anselm & Neronov 1985 torsion pendulum α s Graham & Newman 1985 induced ferromagnetism α s Vorobyov & Gitarts 1988 induced ferromagnetism α s Bobrakov et al 1991 Hawkins 1989 torsion balance α s Ritter et al torsion balance α s Pan, Ni & Chen 1992 induced paramagnetism α s Chui & Ni 1993 induced paramagnetism α s Ni et al C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

111 Tests of General Relativity Spin mass interactions The model The experiments V = σ r Wineland & Ramsey 19 Method Accuracy Experiment weight of pol. bulk matter η 10 8 Hsieh et al 1989 g torsion balance sg p 4π c Ritter et al 1993 NMR experiments 31 Hz Velyukhov 1968 proton magnetometer 0.3 Hz Young 1969 ground state hyperfine separationindeuteron δν < 10 4 Hz D kg 1 NMR D( 9 Be) kg 1 Wineland et al D(e) kg 1 D(n) kg 1 nuclear spin precession D(n) kg 1 Venema et al g comparison of frequencies sg p c (e) , Youdin et al g of Hg and Cs magnetom. sg p c (n) torsion C. Lämmerzahl pendulum (ZARM, Bremen) Search for QG Effects Hou Cambridge & Ni / 99

112 Tests of General Relativity Spin velocity interactions The model The experiments V = σ v Method Accuracy Experiment torsion pendulum δe ev Phillips & Woolum 1969 torsion pendulum δe ev Phillips 1987 relative frequency of Hg κ(e) Hz, Berglund et al and Cs magnetometers κ(n) Hz torsion pendilum Ni et al 1999 C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

113 Tests of General Relativity Tests of the Universality of Gravitational Redshift Description Gravitational redshift ν(x 1 )= maydependonusedclock Comparison of two colocated clocks Null test ν 1 (x 1 ) ν 2 (x 1 ) ( 1 (1 + α clock ) U(x ) 1) U(x 0 ) c 2 ν(x 0 ) ( 1 (α clock2 α clock1 ) U(x 1) U(x 0 ) c 2 Tested quantity: α clock2 α clock1 Need of large differences in the gravitational potential ) ν1 (x 0 ) ν 2 (x 0 ). C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

114 Tests of General Relativity Tests of the Universality of Gravitational Redshift Tests Comparison Accuracy Experiment Cs Resonator Turneaure & Stein 1987 Mg Cs (fine structure) Godone et al 1995 Resonator I 2 (electronic) Braxmaier et al 2002 Cs H-Maser (hf) Bauch et al 2002 Each time a better clock was available, immediately a redshift experiment has been carried through C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

115 Clocks Tests of General Relativity Atomic clocks based on principal transitions based on fine structure based on hyperfine transitions Molecular clocks based on rotational transitions based in vibrational transitions Light clocks Gravitational clocks planetary motion binary systems Rotation Earth pulsars Decay of particles All based on different physical principles, laws. C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

116 Clocks Tests of General Relativity Clocks of different nature exhibit a different dependence on fundamental constants Scaling of transition energies (in units of Rydberg energy) Hyperfine energies g(m e /m p )α 2 f(α) Vibrational energies in molecules m e /m p Rotational energies in molecules m e /m p Fine-structure energies α 2 Electronic energies (incl. relativistic effects) f(α) Cavity frequency 1/α Weak interaction splitting/zeeman frequency G F Energy levels are influenced by structure of Maxwell equations structure of Dirac equation time dependence of α, m e,orm p position dependence of α, m e,orm p C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

117 Universal tool Tests of General Relativity Clocks are a universal tool for testing space time properties GR: Physics of position and time (trajectories of particles and light rays) SR: Based solely on clock comparison experiments UGR: clock comparison experiment Clock with hypothetic anomal dependence on position, orientation, and velocity Clock 1 ν 1 Clock with different hypothetic anomal dependence on position, orientation, and velocity Clock 2 ν 2 comparison ν 2 ν 1 C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

118 Tests of General Relativity Tests of predictions measurement of PPN parameters Metric g 00 = 1+2α U c 2 2β U 2 g i := g 0i = 4μ (J r) i c 3 r 3 g ij = (1+2γ) U c 2 c 4 Standard tests Test Experiment Parameter Gravitational redshift GP-A α H maser Perihelion shift Astrophys. observation 2(α+γ) β Light deflection VLBI γ Gravitational time delay Cassini γ Lense Thirring LAGEOS 10% Schiff GP-B 0.5% (expected) C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

119 Tests of General Relativity Modified Newton potential Prediction Higher dimensional theories Moduli Axion Effective potential in Loop QG (e.g. Bjerrum-Bohr, Donoghue, Holstein 2003) C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

120 Tests of General Relativity Test of Newton potential U = GM r (1+αe r/λ) long range limits short range limits C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

121 Outline Tests of Quantum Theory 1 The situation of standard physics 2 The search for Quantum Gravity effects: General remarks 3 Tests of Lorentz invariance 4 Tests of General Relativity 5 Tests of Quantum Theory 6 Unexplained observations 7 Conclusion and outlook C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

122 Linearity Tests of Quantum Theory Superposition principle: Bialynicki Birula & Mycielski 1976, Weinberg 89, Shomony 1997 The model Non linear Schrödinger equation i t ψ = 2 2m Δψ + α ln(a3 ψ 2 )ψ dim(a) =m attenuator (1st position) attenuator (2nd position) Experiment Shull et al 1980 phase shift l = vτ δφ = 2 τα ln b Comparison with experimental data α ev C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

123 Linearity Tests of Quantum Theory Model Nonlinearity in Maxwell 0= ν F μν + α μνρστ F νρ F στ Standard nonlinearities: Heisenberg Euler and Born Infeld Consequences Frequency doubling astrophysical test ( duplication of atomic lines) Birefringence of electromagnetic waves in external strong magnetic fields (experiments are under development) C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

124 Decoherence Tests of Quantum Theory Model for influence of space time fluctuations Hawking 1982, Ellis et al 1984: Markovian master equation for two level system i d ( E + dt ρ =[H, ρ]+hρ, H = 1 2 ΔE 0 ) 0 E 1 2 ΔE Requirements (i) hρ hermitian if ρ is, (ii) trρ =1, (iii) trρ 2 1, (iv) conservation of energy Solution ρ(t) = 1 ( ) 1 e 1 2 (α+γ)t iδet 2 e 1 2 (α+γ)t+iδet α, γ > 0, α,γ h 1 Experiment Neutron interferometry: α + γ GeV C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

125 Tests of Quantum Theory Space time fluctuations Ansatz for the strain noise spectrum (Amelino Camelia 2000) ( ) 2 ΔL = S sf (ν)dν with S sf (ν) =ζ Λ ( ) α ( ) LPl ν γ, L c Λ c/λ Λ=length characteristic of experimental setup Specification for two random walk hypotheses: ( S α=1,γ= 2 m ) ( ) 2 2 Hz sf = ζ RW1 Hz 1 Λ ν Devices S α=2,γ= 2 sf = ζ RW2 ( m Λ ) 3 ( Hz ν low frequencies and small devices are preferred setups Optical resonators: access to μhz range. ) 2 Hz 1, data of a frequency comparison between two optical resonators has been analyzed. C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

126 Tests of Quantum Theory Space time fluctuations measured quantity = ν 2 ν 1 ( ) ( ν2 ν 1 δl sf 2 δ = ν 1 L 2 + ( δl lock 2 + ( δl phys 2 L 2 L 2 δllock 1 L 1 ) δlsf 1 L 1 ) δlphys 1 L 1 ) +... = S sf + S phys + S lock + half of total noise represents upper bound to S sf. setup A: resonators parallel in different cryostats setup B: two cavities orthogonally in same cryostat Comparison with RW ansätze ζ RW ζ RW Parameters are of order 1: rules out RW hypothesis 1 (Schiller et al 2004). C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

127 Tests of Quantum Theory Space time fluctuations Remark: For Ansatz g μν = g (b) μν + h μν, h μν 1, g (b) μν = <g μν > also inertial (= inertial mass and maximum velocity) and gravitational properties of particles and fields will be modified. Possible further approach to space-time fluctuations: tests of LLI and UFF work in progress C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

128 Summary Tests of Quantum Theory No deviation from standard physics has been seen No signal of Quantum Gravity has been detected but... C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

129 Outline Unexplained observations 1 The situation of standard physics 2 The search for Quantum Gravity effects: General remarks 3 Tests of Lorentz invariance 4 Tests of General Relativity 5 Tests of Quantum Theory 6 Unexplained observations 7 Conclusion and outlook C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

130 Unexplained observations Problems with General Relativity? Unexplained observations C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

131 Unexplained observations Problems with General Relativity? Unexplained observations Dark Matter (Zwicky 1933) Needed to describe galactic rotation curves, lensing, structure formation C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

132 Unexplained observations Problems with General Relativity? Unexplained observations Dark Matter (Zwicky 1933) Needed to describe galactic rotation curves, lensing, structure formation Dark Energy (Turner 1999) Needed to describe the accelerated expansion of our universe C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

133 Unexplained observations Problems with General Relativity? Unexplained observations Dark Matter (Zwicky 1933) Needed to describe galactic rotation curves, lensing, structure formation Dark Energy (Turner 1999) Needed to describe the accelerated expansion of our universe Pioneer Anomaly (Anderson et al 1998, 2002) Non Newtonian acceleration of Pioneer spacecraft toward the Sun C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

134 Unexplained observations Problems with General Relativity? Unexplained observations Dark Matter (Zwicky 1933) Needed to describe galactic rotation curves, lensing, structure formation Dark Energy (Turner 1999) Needed to describe the accelerated expansion of our universe Pioneer Anomaly (Anderson et al 1998, 2002) Non Newtonian acceleration of Pioneer spacecraft toward the Sun Flyby anomaly (ESA and NASA communications) Satellite velocities are too large by a few mm/s after fly bys C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

135 Unexplained observations Problems with General Relativity? Unexplained observations Dark Matter (Zwicky 1933) Needed to describe galactic rotation curves, lensing, structure formation Dark Energy (Turner 1999) Needed to describe the accelerated expansion of our universe Pioneer Anomaly (Anderson et al 1998, 2002) Non Newtonian acceleration of Pioneer spacecraft toward the Sun Flyby anomaly (ESA and NASA communications) Satellite velocities are too large by a few mm/s after fly bys Increase of Astronomical Unit (Krasinski & Brumberg 2005, Pitjeva in Standish 2005) Distance Earth Sun increases by 10 m/cy C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

136 Unexplained observations Problems with General Relativity? Unexplained observations Dark Matter (Zwicky 1933) Needed to describe galactic rotation curves, lensing, structure formation Dark Energy (Turner 1999) Needed to describe the accelerated expansion of our universe Pioneer Anomaly (Anderson et al 1998, 2002) Non Newtonian acceleration of Pioneer spacecraft toward the Sun Flyby anomaly (ESA and NASA communications) Satellite velocities are too large by a few mm/s after fly bys Increase of Astronomical Unit (Krasinski & Brumberg 2005, Pitjeva in Standish 2005) Distance Earth Sun increases by 10 m/cy Quadrupole and octupole anomaly (Tegmark et al 2004, Schwarz et al 2005) Quadrupole and octupole of CMB are correlated with Solar system ecliptic C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

137 Unexplained observations Problems with General Relativity? Unexplained observations Dark Matter (Zwicky 1933) Needed to describe galactic rotation curves, lensing, structure formation Dark Energy (Turner 1999) Needed to describe the accelerated expansion of our universe Pioneer Anomaly (Anderson et al 1998, 2002) Non Newtonian acceleration of Pioneer spacecraft toward the Sun Flyby anomaly (ESA and NASA communications) Satellite velocities are too large by a few mm/s after fly bys Increase of Astronomical Unit (Krasinski & Brumberg 2005, Pitjeva in Standish 2005) Distance Earth Sun increases by 10 m/cy Quadrupole and octupole anomaly (Tegmark et al 2004, Schwarz et al 2005) Quadrupole and octupole of CMB are correlated with Solar system ecliptic Gravity at large distances? Weak gravity? Small accelerations? C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

138 Unexplained observations The Pioneer anomaly The orbits C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

139 Unexplained observations The Pioneer anomaly The anomalous acceleration The acceleration seems to appear just with the last flyby, that is, after entering an escape orbit. C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

140 Unexplained observations The Pioneer anomaly Observation Anomalous acceleration of Pioneer 10 and 11 spacecraft of a Pioneer =(8.74 ± 1.33) m/s 2 toward the Sun (Anderson et al 1998, 2002) Acceleration is constant starting with last flyby Remark / Question a Pioneer a Newton 10 5 Systematic effect? Maybe. Influence from cosmic expansion? Very probably not. Drift of clocks t t + αt 2 with α s 1? New physics?... C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

141 Unexplained observations The flyby anomaly Observation After satellite flybys at Earth the velocity is too large by a few mm/s (Antreasian & Guinn 1998, Anderson & Williams 2001, Morley 2005, Campbell 2006) GEGA1: Two way S band Doppler residuals & range residuals NEGA: Two way X band Doppler residuals & range residuals C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

142 Unexplained observations The flyby anomaly Observations Earth flybys Mission agency year pericentre v [km/s] e Δv [mm/s] Galileo NASA Dec km ± 0.08 Galileo NASA Dec km a NEAR NASA Jan km ± 0.13 Cassini NASA Aug km Stardust NASA Jan km???? b Rosetta ESA Mar km ± 0.05 Hayabusa Japan May km???? c MESSENGER d private Aug km a no reliable data: too low orbit with too large atmospheric drag b no reliable data: thruster activities c no data available d US spacecraft operated by a private company KinetX Anomaly seems to exist also for flybys at other planets. C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

143 Unexplained observations The flyby anomaly Thanks to J. Campbell. Kinetic and potential energy of Rosetta (Anderson, Campbell & Nieto 2006) C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

144 Unexplained observations The flyby anomaly 8 7 Δv NEAR [mm/s] Galileo 1 2 Rosetta Cassini 0 Messenger 0-1 e Δv as function of e (should be function of e and r perigee ). C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

145 Unexplained observations The flyby anomaly 8 7 Δv NEAR [mm/s] Galileo 1 2 Rosetta Cassini 0 Messenger 0-1 e Δv as function of e (should be function of e and r perigee ). Remarks / Questions More systematic study needed: Dependence on height, velocity, inclination, excentricity,...? Effect on escape orbits only C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

146 Unexplained observations The flyby anomaly First analysis Velocity increase is related to an anomalous acceleration of a flyby m/s 2, a flyby a Newton 10 5 First error analysis Atmospheric drag Errors in Earth gravity model Ocean tides Earth solid tides Charging of spacecraft Magnetic moment of spacecraft Further non gravitational forces (trapped air, ion plasma drag,...) Nothing could explain the flyby anomaly C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

147 Unexplained observations The flyby anomaly Attempts at explanation within standard theory Spin rotation coupling Attempts at explanation by new physics (not published) Non conservative potential energy Non Newtonian gravity (e.g. Moffat, PPN, Yukawa,...) Modifications of relativity Torsion (eps2 model); fit the data, but not compatible with stability of planetary orbits Nothing could explain the flyby anomaly C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

148 Unexplained observations The flyby anomaly Next flybys Tasks Rosetta Earth flyby on 13 November 2007 (pericentre altitude 4942 km) Rosetta Earth flyby on 13 November 2009 (pericentre altitude 2483 km) Rosetta Mars flyby in February 2007 Continuous observation of Rosetta Earth flybys (velocity, ranging, position, spacecraft conditions,...) Measurement of deflection angle Precise tracking of Rosetta Mars flyby Today s Mars gravity models good enough; can be analyzed better using Mars gravity models obtained by Mars Reconnaicance Mission. Other conditions than on Earth, other systematics (weaker atmospheric drag, smaller albedo, smaller Solar wind,...). Will make the effect universal if observed. Dedicated flyby explorer mission? With precise clocks onboard. C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

149 Unexplained observations The flyby anomaly Next flybys Tasks Rosetta Earth flyby on 13 November 2007 (pericentre altitude 4942 km) Rosetta Earth flyby on 13 November 2009 (pericentre altitude 2483 km) Rosetta Mars flyby in February 2007 Continuous observation of Rosetta Earth flybys (velocity, ranging, position, spacecraft conditions,...) Measurement of deflection angle Precise tracking of Rosetta Mars flyby Today s Mars gravity models good enough; can be analyzed better using Mars gravity models obtained by Mars Reconnaicance Mission. Other conditions than on Earth, other systematics (weaker atmospheric drag, smaller albedo, smaller Solar wind,...). Will make the effect universal if observed. Dedicated flyby explorer mission? With precise clocks onboard. C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

150 Unexplained observations Increase of the Astronomical Unit Observation Various groups reported Krasinsky & Brumberg 2005: 15 ± 4 m/cy Pitjeva 2005: 7 ± 1 m/cy (in Standish 2005) Remarks / Question Ġ excluded by LLR Mass loss of Sun leads only to 1 m/cy Influence of cosmic expansion by many orders of magnitude too small Increase of Solar wind plasma on long timescales? Drift of clocks t t + αt 2 with α s 1?... C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99

151 Unexplained observations Quadrupole / Octopole anomaly Observation Oliveira-Costa et al (2004), Schwarz et al (2005) Anomalous behavior of low l contributions of CMB: Quadrupole and octopole are aligned to > 99.87% C.L. Quadrupole and octopole aligned to ecliptic to > 99% C.L. No correlation with the galactic plane Remarks / Question Influence of Solar system on CMB observations? Systematics? C. Lämmerzahl (ZARM, Bremen) Search for QG Effects Cambridge / 99