Violation of the weak equivalence principle due to gravity-matter - PowerPoint PPT Presentation

Violation of the weak equivalence principle due to gravity-matter entanglement c 1 , 2 , Francisco Pipa 3 and Marko Vojinovi´ c 4 Nikola Paunkovi´ 1 Department of Mathematics, IST, University of Lisbon 2 Security and Quantum Information Group (SQIG), Institute of Telecommunications, Lisbon 3 Department of Physics, IST, University of Lisbon 4 Group for Gravitation, Particles and Fields (GPF), Institute of Physics, University of Belgrade

Weak Equivalence Principle The local effects of particle motion in a gravitational field are indis- tinguishable from those of an accelerated observer in flat spacetime. Consequence: A particle in a gravitational field should follow the geodesic, since this is how the straight line in flat space looks like from the accelerated frame.

Deriving WEP (geodesic motion) in GR Single-pole approximation: dτ B µν ( τ ) δ (4) ( x − z ( τ )) � T µν ( x ) = √− g (1) . C Conservation of stress-energy tensor (assuming the local Poincar´ e in- variance for both S G [ g ] and S M [ g, φ ] ): ∇ ν T µν = 0 . (2) Replacing (2) into (1) , we obtain the geodesic equation, with u µ ≡ dz µ ( τ ) dτ and u µ u µ ≡ − 1 (Mathisson and Papapetrou [2, 3]; see also [4]): u λ ∇ λ u µ = 0 . Using Cristoffel symbols, d 2 z λ ( τ ) dz µ ( τ ) dz ν ( τ ) + Γ λ = 0 . µν dτ 2 dτ dτ

Quantising gravity Fundamental gravitational degrees of freedom ˆ g and ˆ π g : π g ≥ � π φ ≥ � ∆ˆ ∆ˆ g ∆ˆ φ ∆ˆ 2 , 2 . Separable state ( | g � and | φ � – coherent states of gravity and matter): | Ψ � = | g � ⊗ | φ � . Effective classical metric and stress-energy tensors: T µν ≡ � Ψ | ˆ g µν ≡ � Ψ | ˆ g µν | Ψ � , T µν | Ψ � .

Violation of WEP due to entanglement g � ⊗ | ˜ Entangled state (perturbation | ˜ Ψ � = | ˜ φ � , with coherent classical g � and | ˜ states | ˜ φ � ): Ψ � = α | Ψ � + β | ˜ Ψ | Ψ Ψ � . “Entangled” metric: Ψ � = g µν + β h µν + O ( β 2 ) . g g µν = � Ψ Ψ Ψ | ˆ g µν | Ψ Ψ g The perturbation is evaluated to be: g µν | ˜ Ψ � − � Ψ | ˜ � � h µν = 2 Re � Ψ | ˆ Ψ � g µν . “Entangled” geodesic equation with the manifestly covariant correc- tion: d 2 z µ ( τ ) dz ρ ( τ ) dz ν ( τ ) Γ µ + Γ Γ = 0 , ρν dτ 2 dτ dτ � � ν − 1 u λ ∇ λ u µ + β u ρ u ν + O ( β 2 ) = 0 . ∇ ρ h µ 2 ∇ µ h νρ

Bibliography [1] N. Paunkovi´ c and M. Vojinovi´ c, (2017), arXiv:1702.07744 [2] M. Mathisson, Acta Phys. Polon. 6, 163 (1937) [3] A. Papapetrou, Proc. R. Soc. A 209, 248 (1951) [4] M. Vasili´ c and M. Vojinovi´ c, JHEP , 0707, 028 (2007), arXiv:0707.3395 5

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