Atom Interferometric Tests of Gravity Claus L ammerzahl Centre for - PowerPoint PPT Presentation

Atom Interferometric Tests of Gravity Claus L¨ ammerzahl Centre for Applied Space Technology and Microgravity (ZARM), University of Bremen, 20359 Bremen, Germany Gravitational wave Detection with Atom Interferometry Firenze 24. – 25.2.2009 C. L¨ ammerzahl (ZARM, Bremen) Atom Interferometric Tests of Gravity Firenze, 24.1.2009 1 / 54

Main theme Gravity can only be explored through the motion of test particles Test particles Orbits and clocks Massive particles and light What is gravity depends on the structure of the equation of motion Existence of inertial systems Order of differential equation Dependence on particle parameters Applies to test particles exploring gravitational waves Gravitational waves may influence physics of test particles C. L¨ ammerzahl (ZARM, Bremen) Atom Interferometric Tests of Gravity Firenze, 24.1.2009 2 / 54

Outline Questioning Newton’s laws 1 Newton’s first law: Inertial systems Newton’s second law: The law of inertia Newton’s third law: Law of reciprocal action C. L¨ ammerzahl (ZARM, Bremen) Atom Interferometric Tests of Gravity Firenze, 24.1.2009 3 / 54

Outline Questioning Newton’s laws 1 Newton’s first law: Inertial systems Newton’s second law: The law of inertia Newton’s third law: Law of reciprocal action The Universality of Free Fall with quantum matter 2 Violation of UFF from space–time fluctuations Universality of Free Fall for charged particles Universality of Free Fall for spinning particles C. L¨ ammerzahl (ZARM, Bremen) Atom Interferometric Tests of Gravity Firenze, 24.1.2009 3 / 54

Outline Questioning Newton’s laws 1 Newton’s first law: Inertial systems Newton’s second law: The law of inertia Newton’s third law: Law of reciprocal action The Universality of Free Fall with quantum matter 2 Violation of UFF from space–time fluctuations Universality of Free Fall for charged particles Universality of Free Fall for spinning particles (Fundamental) Decoherence 3 C. L¨ ammerzahl (ZARM, Bremen) Atom Interferometric Tests of Gravity Firenze, 24.1.2009 3 / 54

Outline Questioning Newton’s laws 1 Newton’s first law: Inertial systems Newton’s second law: The law of inertia Newton’s third law: Law of reciprocal action The Universality of Free Fall with quantum matter 2 Violation of UFF from space–time fluctuations Universality of Free Fall for charged particles Universality of Free Fall for spinning particles (Fundamental) Decoherence 3 Anomalous spin couplings 4 C. L¨ ammerzahl (ZARM, Bremen) Atom Interferometric Tests of Gravity Firenze, 24.1.2009 3 / 54

Outline Questioning Newton’s laws 1 Newton’s first law: Inertial systems Newton’s second law: The law of inertia Newton’s third law: Law of reciprocal action The Universality of Free Fall with quantum matter 2 Violation of UFF from space–time fluctuations Universality of Free Fall for charged particles Universality of Free Fall for spinning particles (Fundamental) Decoherence 3 Anomalous spin couplings 4 Spin and space–time fluctuations 5 C. L¨ ammerzahl (ZARM, Bremen) Atom Interferometric Tests of Gravity Firenze, 24.1.2009 3 / 54

Outline Questioning Newton’s laws 1 Newton’s first law: Inertial systems Newton’s second law: The law of inertia Newton’s third law: Law of reciprocal action The Universality of Free Fall with quantum matter 2 Violation of UFF from space–time fluctuations Universality of Free Fall for charged particles Universality of Free Fall for spinning particles (Fundamental) Decoherence 3 Anomalous spin couplings 4 Spin and space–time fluctuations 5 Nonlinearity 6 C. L¨ ammerzahl (ZARM, Bremen) Atom Interferometric Tests of Gravity Firenze, 24.1.2009 3 / 54

Outline Questioning Newton’s laws 1 Newton’s first law: Inertial systems Newton’s second law: The law of inertia Newton’s third law: Law of reciprocal action The Universality of Free Fall with quantum matter 2 Violation of UFF from space–time fluctuations Universality of Free Fall for charged particles Universality of Free Fall for spinning particles (Fundamental) Decoherence 3 Anomalous spin couplings 4 Spin and space–time fluctuations 5 Nonlinearity 6 Anomalous dispersion – higher order equations 7 C. L¨ ammerzahl (ZARM, Bremen) Atom Interferometric Tests of Gravity Firenze, 24.1.2009 3 / 54

Outline Questioning Newton’s laws 1 Newton’s first law: Inertial systems Newton’s second law: The law of inertia Newton’s third law: Law of reciprocal action The Universality of Free Fall with quantum matter 2 Violation of UFF from space–time fluctuations Universality of Free Fall for charged particles Universality of Free Fall for spinning particles (Fundamental) Decoherence 3 Anomalous spin couplings 4 Spin and space–time fluctuations 5 Nonlinearity 6 Anomalous dispersion – higher order equations 7 Summary 8 C. L¨ ammerzahl (ZARM, Bremen) Atom Interferometric Tests of Gravity Firenze, 24.1.2009 3 / 54

Questioning Newton’s laws Outline Questioning Newton’s laws 1 Newton’s first law: Inertial systems Newton’s second law: The law of inertia Newton’s third law: Law of reciprocal action The Universality of Free Fall with quantum matter 2 Violation of UFF from space–time fluctuations Universality of Free Fall for charged particles Universality of Free Fall for spinning particles (Fundamental) Decoherence 3 Anomalous spin couplings 4 Spin and space–time fluctuations 5 Nonlinearity 6 Anomalous dispersion – higher order equations 7 Summary 8 C. L¨ ammerzahl (ZARM, Bremen) Atom Interferometric Tests of Gravity Firenze, 24.1.2009 4 / 54

Questioning Newton’s laws Newton’s first law: Inertial systems Outline Questioning Newton’s laws 1 Newton’s first law: Inertial systems Newton’s second law: The law of inertia Newton’s third law: Law of reciprocal action The Universality of Free Fall with quantum matter 2 Violation of UFF from space–time fluctuations Universality of Free Fall for charged particles Universality of Free Fall for spinning particles (Fundamental) Decoherence 3 Anomalous spin couplings 4 Spin and space–time fluctuations 5 Nonlinearity 6 Anomalous dispersion – higher order equations 7 Summary 8 C. L¨ ammerzahl (ZARM, Bremen) Atom Interferometric Tests of Gravity Firenze, 24.1.2009 5 / 54

Questioning Newton’s laws Newton’s first law: Inertial systems Finsler geometry Motivation generic generalization of GR leads to deformed light cones and mass shells has been discussed within Quantum Gravity (Jacobson, Liberati & Mattingly) Very Special Relativity (Cohen & Glashow) Finsler space Finsler length function ds 2 = F ( x, dx ) , F ( x, λdx ) = λ 2 F ( x, dx ) Finsler metric tensor f µν ( x, dx ) is defined as ∂ 2 F 2 ( x k , y m ) g µν ( x, y ) = 1 ds 2 = g µν ( x, dx ) dx µ dx ν , where 2 ∂y µ ∂y ν C. L¨ ammerzahl (ZARM, Bremen) Atom Interferometric Tests of Gravity Firenze, 24.1.2009 6 / 54

Questioning Newton’s laws Newton’s first law: Inertial systems Finsler geometry Geodesics � 0 = d 2 x µ x ) dx ρ dx σ ds 2 + { µ δ ds = 0 ⇒ ρσ } ( x, ˙ ds ds { µ x ) = g µν ( x, ˙ with ρσ } ( x, ˙ x ) ( ∂ ρ g σν ( x, ˙ x ) + ∂ σ g ρν ( x, ˙ x ) − ∂ ν g ρσ ( x, ˙ x )) Main characteristics of geodesic motion Geodesic equation fulfills Universality of Free Fall { µ ρσ } ( x, ˙ x ) cannot be transformed to zero ∀ ˙ x ⇒ gravity cannot be trans- formed away locally ⇔ Einstein’s elevator does not hold ⇔ no inertial system Condition to be able to transform away v gravity is stronger then pure UFF. Acceleration toward the Earth depends on a 2 horizontal velocity. a 1 Speculation: violation of UGR, G = G ( T ) C. L¨ ammerzahl (ZARM, Bremen) Atom Interferometric Tests of Gravity Firenze, 24.1.2009 7 / 54

Questioning Newton’s laws Newton’s first law: Inertial systems Parametrizing deviations from Riemann/Minkowski Special case: “power law” metrics ds 2 = ( g µ 1 µ 2 ...µ 2 n ( x ) dx µ 1 dx µ 2 · · · dx µ 2 n ) 1 r Deviation from Riemann/Minkowksi � � ds 2 r = dx µ 1 · · · dx µ 2 r g µ 1 µ 2 · · · g µ 2 r − 1 µ 2 r + φ µ 1 ...µ 2 r This gives dx µ ds 2 = ( g µν + φ µνρ 3 ...ρ 2 r n ρ 3 · · · n ρ 2 r ) dx µ dx ν , n µ = � g ρσ dx ρ dx σ Additional assumption: φ µ 1 ...µ 2 r possesses spatial indices only (from light propagation) C. L¨ ammerzahl (ZARM, Bremen) Atom Interferometric Tests of Gravity Firenze, 24.1.2009 8 / 54

Questioning Newton’s laws Newton’s first law: Inertial systems Quantum mechanics in Finsler space Finslerian Hamilton operator H ( λp ) = λ 2 H ( p ) H = H ( p ) with “Power–law” ansatz (non–local operator) � � 1 1 g i 1 ...i 2 r ∂ i 1 · · · ∂ i 2 r H = r 2 m Simplest case: quartic metric � � 1 1 g ijkl ∂ i ∂ j ∂ k ∂ l H = 2 2 m Deviation from standard case � � 1 − 1 ∆ 2 + φ ijkl ∂ i ∂ j ∂ k ∂ l H = 2 2 m � − 1 1 + φ ijkl ∂ i ∂ j ∂ k ∂ l = 2 m ∆ ∆ 2 C. L¨ ammerzahl (ZARM, Bremen) Atom Interferometric Tests of Gravity Firenze, 24.1.2009 9 / 54