Creation of a localised source in quantum field theory Jorma Louko - PowerPoint PPT Presentation

Creation of a localised source in quantum field theory Jorma Louko School of Mathematical Sciences, University of Nottingham RQIN 2017, YITP, Kyoto University, Japan, 4–7 July 2017 E. G. Brown and JL JHEP 1508 , 061 (2015) L. J. Zhou, M. E. Carrington, G. Kunstatter, JL PRD 95 , 085007 (2017) W. M. H. Wan Mokhtar and JL in preparation t r

Plan 1. Motivation: Firewalls − → Correlation breakdown in quantum field theory 2. Wall for scalar field in 1 + 1 3. Wall for spinor field in 1 + 1 4. Pointlike source for scalar field in 3 + 1 5. Summary

1. Motivation: Firewall proposal Almheiri et al 2013 Suppose BH evaporates fully and the process preserves unitarity + I ◮ Pure state on Σ 2 ⇒ S 2 B ′ and C ′ strongly correlated B’ C’ singularity S 1 _ I S 0

1. Motivation: Firewall proposal Almheiri et al 2013 Suppose BH evaporates fully and the process preserves unitarity + I ◮ Pure state on Σ 2 ⇒ S 2 B ′ and C ′ strongly correlated B’ ◮ Evolution ⇒ C’ B and C strongly correlated singularity S 1 B C _ I S 0

1. Motivation: Firewall proposal Almheiri et al 2013 Suppose BH evaporates fully and the process preserves unitarity + I ◮ Pure state on Σ 2 ⇒ S 2 B ′ and C ′ strongly correlated B’ ◮ Evolution ⇒ C’ B and C strongly correlated singularity ◮ Hawking ⇒ B and A strongly correlated A S 1 B C _ I S 0

1. Motivation: Firewall proposal Almheiri et al 2013 Suppose BH evaporates fully and the process preserves unitarity + I ◮ Pure state on Σ 2 ⇒ S 2 B ′ and C ′ strongly correlated B’ ◮ Evolution ⇒ C’ B and C strongly correlated singularity ◮ Hawking ⇒ B and A strongly correlated A Contradicts entanglement S 1 B C monogamy theorem ?!? _ I S 0

1. Motivation: Firewall proposal Almheiri et al 2013 Suppose BH evaporates fully and the process preserves unitarity + I ◮ Pure state on Σ 2 ⇒ S 2 B ′ and C ′ strongly correlated B’ ◮ Evolution ⇒ C’ B and C strongly correlated singularity ◮ Hawking ⇒ B and A strongly correlated A Contradicts entanglement S 1 B C monogamy theorem ?!? Almheiri at al (AMPS) 2013 _ I resolution proposal: S 0 A – B correlations broken by “drama” at the shrinking horizon even for macroscopic BH Cf Fuzzball Mathur 2002 Energetic Curtain “Firewall” Braunstein 2009 et al 2013

2. Wall for scalar field in 1 + 1 Brown and JL 2015 t 1+1 Minkowski φ ( t , x ) massless ∂ 2 t φ − ∂ 2 x φ = 0 Dirichlet wall x

2. Wall for scalar field in 1 + 1 Brown and JL 2015 t 1+1 Minkowski φ ( t , x ) massless ∂ 2 t φ − ∂ 2 x φ = 0 Dirichlet wall → ∂ 2 t φ − ∆ θ ( t ) φ = 0 forming wall, duration 1/λ x

2. Wall for scalar field in 1 + 1 Brown and JL 2015 t 1+1 Minkowski φ ( t , x ) massless ∂ 2 t φ − ∂ 2 x φ = 0 Dirichlet wall → ∂ 2 t φ − ∆ θ ( t ) φ = 0 forming wall, duration 1/λ x

2. Wall for scalar field in 1 + 1 Brown and JL 2015 t 1+1 Minkowski φ ( t , x ) massless ∂ 2 t φ − ∂ 2 x φ = 0 Dirichlet wall t 0 → ∂ 2 t φ − ∆ θ ( t ) φ = 0 µ infrared cutoff (required) forming wall, duration 1/λ x ◮ Total energy radiated: � E tot � = + ∞ , from | x | → ( t 0 − λ − 1 ) +

2. Wall for scalar field in 1 + 1 Brown and JL 2015 t 1+1 Minkowski φ ( t , x ) massless ∂ 2 t φ − ∂ 2 x φ = 0 near− Dirichlet wall t 0 → ∂ 2 t φ − ∆ θ ( t ) φ = 0 µ infrared cutoff (required) forming wall, duration 1/λ x ◮ Total energy radiated: � E tot � = + ∞ , from | x | → ( t 0 − λ − 1 ) + ◮ Softer: to λ − 1 from Dirichlet ⇒ � E tot � ∝ λ ln( λ/µ )

2. Wall for scalar field in 1 + 1 Brown and JL 2015 t 1+1 Minkowski φ ( t , x ) massless ∂ 2 t φ − ∂ 2 x φ = 0 near− Dirichlet wall t 0 → ∂ 2 t φ − ∆ θ ( t ) φ = 0 µ infrared cutoff (required) forming wall, duration 1/λ x ◮ Total energy radiated: � E tot � = + ∞ , from | x | → ( t 0 − λ − 1 ) + ◮ Softer: to λ − 1 from Dirichlet ⇒ � E tot � ∝ λ ln( λ/µ ) − λ →∞ ∞ − − → Divergent for sharp wall formation Cf Anderson and DeWitt 1986

2. Wall for scalar field in 1 + 1 Brown and JL 2015 t 1+1 Minkowski φ ( t , x ) massless ∂ 2 t φ − ∂ 2 x φ = 0 near− Dirichlet wall t 0 → ∂ 2 t φ − ∆ θ ( t ) φ = 0 detector µ infrared cutoff (required) forming wall, duration 1/λ x ◮ Total energy radiated: � E tot � = + ∞ , from | x | → ( t 0 − λ − 1 ) + ◮ Softer: to λ − 1 from Dirichlet ⇒ � E tot � ∝ λ ln( λ/µ ) − λ →∞ ∞ − − → Divergent for sharp wall formation Cf Anderson and DeWitt 1986 ◮ Atom coupled to φ : use Unruh-DeWitt detector

2. Wall for scalar field in 1 + 1 Brown and JL 2015 t 1+1 Minkowski φ ( t , x ) massless ∂ 2 t φ − ∂ 2 x φ = 0 near− Dirichlet wall t 0 → ∂ 2 t φ − ∆ θ ( t ) φ = 0 detector µ infrared cutoff (required) forming wall, duration 1/λ x ◮ Total energy radiated: � E tot � = + ∞ , from | x | → ( t 0 − λ − 1 ) + ◮ Softer: to λ − 1 from Dirichlet ⇒ � E tot � ∝ λ ln( λ/µ ) − λ →∞ ∞ − − → Divergent for sharp wall formation Cf Anderson and DeWitt 1986 ◮ Atom coupled to φ : use Unruh-DeWitt detector Transition probability finite for sharp wall formation

2. Wall for scalar field in 1 + 1 Brown and JL 2015 t 1+1 Minkowski φ ( t , x ) massless ∂ 2 t φ − ∂ 2 x φ = 0 near− Dirichlet wall t 0 → ∂ 2 t φ − ∆ θ ( t ) φ = 0 detector µ infrared cutoff (required) forming wall, duration 1/λ x ◮ Total energy radiated: � E tot � = + ∞ , from | x | → ( t 0 − λ − 1 ) + ◮ Softer: to λ − 1 from Dirichlet ⇒ � E tot � ∝ λ ln( λ/µ ) − λ →∞ ∞ − − → Divergent for sharp wall formation Cf Anderson and DeWitt 1986 ◮ Atom coupled to φ : use Unruh-DeWitt detector Transition probability finite for sharp wall formation Moral: sharp wall formation singular gravitationally but nonsingular for a matter coupling

3. Wall for spinor field in 1 + 1 Wan Mokhtar and JL in preparation t 1+1 Minkowski ψ ( t , x ) massless MIT bag wall / D ψ = 0 x

3. Wall for spinor field in 1 + 1 Wan Mokhtar and JL in preparation t 1+1 Minkowski ψ ( t , x ) massless MIT bag wall / D ψ = 0 / → D � θ ( t ) , n ψ = 0 forming wall, duration 1/λ x

3. Wall for spinor field in 1 + 1 Wan Mokhtar and JL in preparation t 1+1 Minkowski ψ ( t , x ) massless MIT bag wall / D ψ = 0 / → D � θ ( t ) , n ψ = 0 forming wall, duration 1/λ x

3. Wall for spinor field in 1 + 1 Wan Mokhtar and JL in preparation t 1+1 Minkowski ψ ( t , x ) massless MIT bag wall / D ψ = 0 / → D � θ ( t ) , n ψ = 0 (no infrared cutoff) forming wall, duration 1/λ x ◮ Total energy radiated: � E tot � − λ →∞ ∞ − − → Divergent for sharp wall formation

3. Wall for spinor field in 1 + 1 Wan Mokhtar and JL in preparation t 1+1 Minkowski ψ ( t , x ) massless MIT bag wall / D ψ = 0 / → D � θ ( t ) , n ψ = 0 detector (no infrared cutoff) forming wall, duration 1/λ x ◮ Total energy radiated: � E tot � − λ →∞ ∞ − − → Divergent for sharp wall formation ◮ Atom coupled to ψ : Unruh-DeWitt detector Transition probability diverges for sharp wall formation

3. Wall for spinor field in 1 + 1 Wan Mokhtar and JL in preparation t 1+1 Minkowski ψ ( t , x ) massless MIT bag wall / D ψ = 0 / → D � θ ( t ) , n ψ = 0 detector (no infrared cutoff) forming wall, duration 1/λ x ◮ Total energy radiated: � E tot � − λ →∞ ∞ − − → Divergent for sharp wall formation ◮ Atom coupled to ψ : Unruh-DeWitt detector Transition probability diverges for sharp wall formation sharp wall formation singular both gravitationally Moral: and for a matter coupling

4. Pointlike source for scalar field in 3 + 1 Zhou et al 2016 t 3+1 Minkowski φ ( t , x ) massless ∂ 2 t φ − ∇ 2 φ = 0 Formed source r

4. Pointlike source for scalar field in 3 + 1 Zhou et al 2016 t 3+1 Minkowski φ ( t , x ) massless ∂ 2 t φ − ∇ 2 φ = 0 Formed source → ∂ 2 t φ − ∆ θ ( t ) φ = 0 θ ( t ): origin boundary condition forming (spherically symmetric sector) source, duration 1/λ r

4. Pointlike source for scalar field in 3 + 1 Zhou et al 2016 t 3+1 Minkowski φ ( t , x ) massless ∂ 2 t φ − ∇ 2 φ = 0 Formed source → ∂ 2 t φ − ∆ θ ( t ) φ = 0 θ ( t ): origin boundary condition forming (spherically symmetric sector) source, duration 1/λ r ◮ � T 00 � well defined; time-dependent even for t > r + λ − 1

4. Pointlike source for scalar field in 3 + 1 Zhou et al 2016 t 3+1 Minkowski φ ( t , x ) massless ∂ 2 t φ − ∇ 2 φ = 0 Formed source → ∂ 2 t φ − ∆ θ ( t ) φ = 0 t 0 θ ( t ): origin boundary condition forming (spherically symmetric sector) source, duration r 1/λ ◮ � T 00 � well defined; time-dependent even for t > r + λ − 1 � ∞ , � E tot � = “ ∞ − ∞ ” r → 0 + ◮ t = t 0 > λ − 1 : � T 00 � → ⇒ −∞ , r → t 0 − not defined