The solution to the Black Hole information paradox (2406.10644v1)

Abstract: The information paradox suggests that the black hole loses information when it emits radiation. In this way, the spectrum of radiation corresponds to a mixed (non-pure) quantum state even if the internal state generating the black-hole is expected to be pure in essence. In this paper we propose an argument solving this paradox by understanding the process of spontaneous symmetry breaking when the black-hole selects one among the many possible ground states, emitting then radiation as a consequence of it. Here the particle operator number is the order parameter. This mechanism explains the connection between the density matrix corresponding to the pure state describing the black-hole state and the density matrix describing the spectrum of radiation (mixed quantum state). From this perspective, we can recover the black-hole information from the superposition principle applied to the different possible order parameters (particle number operators).

• The paper proposes resolving the black hole information paradox by interpreting black hole evaporation as spontaneous symmetry breaking selecting a vacuum state.
• A key mechanism involves characterizing the particle number operator as an order parameter to understand the system's transition from symmetry to asymmetry.
• By analyzing density matrices and vacuum state degeneracy, the theory suggests information is conserved through superposition of entangled ground states.

An Analysis of Spontaneous Symmetry Breaking and the Black Hole Information Paradox

The paper presents a novel approach to addressing the longstanding black hole information paradox by employing the concept of spontaneous symmetry breaking. This paradox arises in the context of black hole evaporation, specifically when considering the emission of thermal Hawking radiation. The fundamental issue is that black holes, initially considered to completely absorb matter and information, appear to emit radiation that fails to preserve the quantum information associated with the consumed matter, leading to an apparent violation of unitarity.

Key Contributions

1. Spontaneous Symmetry Breaking Mechanism: The paper proposes that the spectrum of emitted radiation results from spontaneous symmetry breaking as the black hole selects a ground state from many possible configurations. This process can be compared to phenomena in condensed matter physics where a system settles into one of many degenerate states, leading to observable macroscopic consequences.
2. Order Parameter: Central to the proposal is the characterization of the particle number operator as the order parameter. In traditional quantum field theory contexts, the selection of an order parameter reflects the system's transition from a symmetrical configuration to an asymmetrical one.
3. Density Matrix Analysis: The paper explores the relationship between the density matrices of pure quantum states inherent to the black hole's internal configurations and the mixed state nature of the emitted radiation. By leveraging the superposition principle across various order parameters, the paper argues for the potential recovery of the initial information apparently lost during black hole evaporation.
4. Implication of Vacuum Degeneracy: It is posited that the degeneracy of potential vacuum states is analogous to the mixed state representation of the thermal radiation. The entanglement and superposition of these ground states provide a nuanced understanding of information conservation in line with quantum mechanics principles.

Implications and Speculative Directions

The implications of this research are multifaceted. Practically, it provides a framework that aligns the phenomena of black hole evaporation and the laws of quantum mechanics without forfeiting fundamental principles like unitarity. Theoretically, it opens avenues for reconsidering other quantum gravity phenomena through the lens of spontaneous symmetry breaking, potentially extending this paradigm to other instances where quantum and gravitational theories intersect.

Future directions might involve deeper exploration into the entanglement of ground states and the practical observation of the proposed particle-antiparticle emission dichotomy. Additionally, further development of this theory could benefit from more robust computational models or simulations that test the predictions of the spontaneous symmetry breaking processes in black holes.

In conclusion, the paper provides a compelling argument for resolving the black hole information paradox by interpreting black hole evaporation as a consequence of spontaneous symmetry breaking. This approach not only preserves quantum mechanical principles but also enriches the ongoing discussion in theoretical physics regarding the reconciliation of general relativity and quantum mechanics.