The gravitational mass carried by sound waves

Abstract: We show that the commonly accepted statement that sound waves do not transport mass is only true at linear order. Using effective field theory techniques, we confirm the result found in [1] for zero-temperature superfluids, and extend it to the case of solids and ordinary fluids. We show that, in fact, sound waves do carry mass---in particular, gravitational mass. This implies that a sound wave not only is affected by gravity but also generates a tiny gravitational field, an aspect not appreciated thus far. Our findings are valid for non-relativistic media as well, and could have intriguing experimental implications.

• The paper demonstrates that sound waves, contrary to prior beliefs, carry non-zero net gravitational mass in superfluids, solids, and fluids due to non-linear interactions.
• Using effective field theory and examining phonon coupling with gravity, the research derives an equation showing the carried mass is proportional to energy, scaled by medium properties.
• This finding has implications for condensed matter physics and astrophysics, potentially detectable in ultra-cold atomic gases or natural events like earthquakes using quantum gravimeters.

Gravitational Mass in Sound Waves: An Examination of Non-linear Contributions

This paper presents a rigorous study on the gravitational mass associated with sound waves, challenging the established assumption that sound waves transport no net mass. The research employs effective field theory (EFT) to demonstrate that sound waves, contrary to conventional understanding, do indeed carry gravitational mass in a variety of media, including zero-temperature superfluids, ordinary fluids, and solids. This mass can be positive or negative, depending on the specific medium.

Key Findings

The authors validate and extend the findings of previous work by Nicolis, whereby phonons in zero-temperature superfluids demonstrate an effective gravitational interaction, manifesting as a negative effective gravitational mass. The investigation considers several key points:

• Non-zero Mass Carriage: In contrast to earlier beliefs, sound waves in superfluids, solids, and fluids are shown to have non-zero net mass due to non-linear interactions. This result substantially revises the prior assumption that sound waves merely transport energy and momentum.
• Sound Waves in Various Media: The paper extends the analysis to classical sound waves in solids and fluids, showing that in the non-relativistic limit, the mass they carry is proportional to their energy, modulated by a factor dependent on the medium's equation of state.
• Equation of Mass: For a sound wave, the mass $M$ carried is expressed as:

$$M = - \frac{d \log c_s}{d \log \rho_m} \frac{E}{c_s^2}$$

where $\rho_m$ is the medium's mass density, $c_s$ is the sound speed, and $E$ is the wave's energy.

The research reconciles the mathematical outcomes with physical interpretations. The method involves examining the phonons' coupling with gravity through the phonon effective Lagrangian, thereby modifying the gravitational field equations. Importantly, the phenomena remain significant even in the non-relativistic domain and pertain to classical as well as quantum scenarios.

Implications and Experimental Prospects

Theoretically, the discovery advances the understanding of wave dynamics in media where mass transport had been overlooked. Practically, the phenomenon could affect phonon-mediated transport properties, including potential relevance to astrophysical contexts such as neutron star dynamics where high-density media play a crucial role.

From an experimental standpoint, the paper foresees potential detection through controlled environments such as ultra-cold atomic gases, where sound speeds are minimal, thereby amplifying the effect. Moreover, natural events like earthquakes might demonstrate detectable gravitational mass effects, providing avenues for empirical investigation using sophisticated measurement technologies like quantum gravimeters.

Conclusion

The research meticulously addresses the overlooked aspect of mass transport by sound waves, offering a thorough theoretical foundation and suggesting realistic experimental validations. These findings pave the way for further exploration into the interaction between acoustics and gravity, suggesting new applications and theoretical inquiries in both condensed matter physics and astrophysics. The paper invites reconsideration of fundamental assumptions about wave dynamics and encourages future studies to explore novel interactions between sound and gravitational fields.