Astrophysical constraints on Planck scale dissipative phenomena

Abstract: The emergence of a classical spacetime from any quantum gravity model is still a subtle and only partially understood issue. If indeed spacetime is arising as some sort of large scale condensate of more fundamental objects then it is natural to expect that matter, being a collective excitations of the spacetime constituents, will present modified kinematics at sufficiently high energies. We consider here the phenomenology of the dissipative effects necessarily arising in such a picture. Adopting dissipative hydrodynamics as a general framework for the description of the energy exchange between collective excitations and the spacetime fundamental degrees of freedom, we discuss how rates of energy loss for elementary particles can be derived from dispersion relations and used to provide strong constraints on the base of current astrophysical observations of high energy particles.

Analysis of Astrophysical Constraints on Planck Scale Dissipative Phenomena

The paper "Astrophysical constraints on Planck scale dissipative phenomena" by Stefano Liberati and Luca Maccione explores the intersection of quantum gravity models and astrophysical observations, specifically focusing on dissipative effects at the Planck scale. The authors utilize the framework of dissipative hydrodynamics to speculate on energy exchange mechanisms between matter and spacetime fundamental constituents. Their approach seeks to constrain these processes using high-energy particle observations from astrophysical sources.

Dissipative Phenomena in Quantum Gravity

Quantum Gravity (QG) has traditionally struggled with experimental validation due to its focus on Planck scale phenomena, which are challenging to access. The emergence of classical spacetime from discrete quantum models remains a complex issue. It has been postulated that Lorentz symmetry may be violated at this scale, leading to modified kinematics, including dispersion and dissipation. Previous research has predominantly examined dispersive effects related to Lorentz invariance violation (LIV), but dissipative aspects have been less explored.

In their analysis, Liberati and Maccione highlight the Kramers-Kronig relations, which connect dispersion and dissipation in the propagation of perturbations within a medium under causality-preserving conditions. They argue that assuming modified dispersion relations in QG models without considering dissipation could negate previous LIV constraints.

The Analogue Gravity Framework

The authors adopt an analogue gravity framework, wherein spacetime is conceptualized as a fluid. They consider matter propagation as collective excitations analogous to perturbations in fluid hydrodynamics. This perspective leads to modified dispersion relations, wherein dissipative terms arise naturally. By invoking the generalized Navier-Stokes equation, they derive constraints from astrophysical observations.

Astrophysical Constraints

Liberati and Maccione derive stringent constraints on the dissipative terms by analyzing high-energy electromagnetic and neutrino spectra from astrophysical sources such as the Crab Nebula and Mkn 501. Notably, constraints derived from observations of photons with energies up to 80 TeV from the Crab Nebula provide an upper limit on the "spacetime viscosity" to be less than $1.3 \times 10^{-26}$. Similarly, bounds from neutrino data suggest constraints of the order of $2 \times 10^{-27}$.

These constraints suggest that any viable emergent spacetime model must exhibit properties akin to those of a superfluid at high energies, preventing low-scale dissipative effects detectable via current astrophysical observations.

Theoretical Implications and Future Developments

The paper influences the theoretical landscape by proposing strong bounds on the allowed dissipation in QG models, based on astrophysical evidence. These bounds exceed the Planck scale, suggesting a need for theories with minimal dissipation or for those with protective symmetries that prevent dissipation at detectable levels. The findings imply that future QG models should incorporate dissipative hydrodynamic frameworks while ensuring consistency with observational data.

For future theoretical exploration, higher-order terms in the hydrodynamic expansion could be considered to assess their phenomenological impact, retaining relevance in lower-energy regimes. Additionally, the possibility of observational verification could help refine theoretical models concerning spacetime emergence and its implications at different energy scales.

Conclusion

Liberati and Maccione's work enriches the discourse on Planck scale phenomena by offering astrophysical constraints on dissipative processes. Their approach fosters a better understanding of emergent classical spacetime and offers valuable insights for future quantum gravity models. The constraints derived herein act as guiding principles for further theoretical developments, concurrently linking quantum gravity phenomenology and astrophysical observation.