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- TL;DR Summary
- It is now generally believed that information is preserved in black-hole evaporation.

why need a correction to bekenstein bound if it s proven valid by casini and quantum theory..??

Hey to all,...

It is now generally believed that information is preserved in black-hole evaporation.

This means that the predictions of quantum mechanics are correct whereas Hawking's original argument that relied on general relativity must be corrected.

However, views differ as to how precisely Hawking's calculation should be corrected

why need a correction to bekenstein bound if it s proven by casini and quantum theory..??

casini proves the thermodynamics interpretation in the form of bekenstein bound as valid..

we know following the work of casini in 2008 about the von neumann entropy and the bekenstein bound ,

that the proof of the Bekenstein bound is no more matters of debat

here is how...

Casini defines the right-hand side of the Bekenstein bound as the difference between the expectation value of the modular Hamiltonian in the excited state and the vacuum state,

K V = t r ( K ρ V ) − t r ( K ρ V 0 ) .

With these definitions, the bound reads S V ≤ K V , which can be rearranged to give t r ( ρ V log ρ V ) − t r ( ρ V log ρ V 0 ) ≥ 0.

This is simply the statement of positivity of quantum relative entropy, which proves the Bekenstein bound.

[Casini, Horacio (2008). "Relative entropy and the Bekenstein bound". Classical and Quantum Gravity. 25 (20): 205021. arXiv:0804.2182] in 2008 using quantum field theory.

Quantum information is entangled, all the information accumulated inside the black hole is conserved after the evaporation of the black hole...

Bekenstein bound is entropy of a black hole

The Bekenstein–Hawking entropy is a statement about the gravitational entropy of a system

S = A/4ℓ_p^2 for ℓ = √{Għ/c^3} and A = 4πr_s^2 and r_s the Schwarzschild radius r_s = 2GM/c^2.

It is now generally believed that information is preserved in black-hole evaporation.

This means that the predictions of quantum mechanics are correct whereas Hawking's original argument that relied on general relativity must be corrected.

However, views differ as to how precisely Hawking's calculation should be corrected

why need a correction to bekenstein bound if it s proven by casini and quantum theory..??

casini proves the thermodynamics interpretation in the form of bekenstein bound as valid..

we know following the work of casini in 2008 about the von neumann entropy and the bekenstein bound ,

that the proof of the Bekenstein bound is no more matters of debat

here is how...

Casini defines the right-hand side of the Bekenstein bound as the difference between the expectation value of the modular Hamiltonian in the excited state and the vacuum state,

K V = t r ( K ρ V ) − t r ( K ρ V 0 ) .

With these definitions, the bound reads S V ≤ K V , which can be rearranged to give t r ( ρ V log ρ V ) − t r ( ρ V log ρ V 0 ) ≥ 0.

This is simply the statement of positivity of quantum relative entropy, which proves the Bekenstein bound.

[Casini, Horacio (2008). "Relative entropy and the Bekenstein bound". Classical and Quantum Gravity. 25 (20): 205021. arXiv:0804.2182] in 2008 using quantum field theory.

Quantum information is entangled, all the information accumulated inside the black hole is conserved after the evaporation of the black hole...

Bekenstein bound is entropy of a black hole

The Bekenstein–Hawking entropy is a statement about the gravitational entropy of a system

S = A/4ℓ_p^2 for ℓ = √{Għ/c^3} and A = 4πr_s^2 and r_s the Schwarzschild radius r_s = 2GM/c^2.