Gravitational mass vs inertial mass

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SUMMARY

The discussion centers on the distinction between gravitational mass and inertial mass as presented in Sean Carroll's lecture book. It highlights that if gravitation did not couple to itself, a "gravitation atom" would exhibit differing inertial and gravitational masses due to negative binding energy. Specifically, the gravitational mass of the entire system would equal the sum of its components' gravitational masses, while the inertial mass would reflect the energy required to overcome gravitational binding. This leads to the conclusion that inertial mass is fundamentally linked to energy, raising questions about the nature of mass in gravitational contexts.

PREREQUISITES
  • Understanding of gravitational mass and inertial mass concepts
  • Familiarity with binding energy in physics
  • Knowledge of self-coupling in gravitational theories
  • Basic principles of energy conservation in physical systems
NEXT STEPS
  • Explore the implications of negative binding energy in gravitational systems
  • Research the concept of self-coupling in general relativity
  • Study the relationship between mass and energy in the context of Einstein's theory
  • Investigate how gravitational and inertial mass are measured in experimental physics
USEFUL FOR

Physicists, students of theoretical physics, and anyone interested in the foundational concepts of mass and energy in gravitational contexts.

Neitrino
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In Sean Carroll's lecture book is written:

"... if gravitation did not couple to itself, a "gravitation atom" (two particles bounded by their mutual gravitational attraction) would have a different intertial mass (due to negative binding energy) than gravitational mass..."

Would you please clarify why? or which mass would be bigger ?
 
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"Without self-coupling", the gravitational mass of the whole would be only the sum of the gravitational masses of the components (which is exactly how charge works in electrodynamics). However, it is obvious (since it would take work to overcome the gravitational binding) that the energy of the whole is not just the sum of the quantities of energy that the components possesses separately. Could it be that you're asking why inertial mass is identified with energy?
 

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