Gravitational mass vs inertial mass

[Neitrino]

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 ?

 

[cesiumfrog]

"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?

 

[Entropia]

The concept of gravitational mass and inertial mass can be confusing, but they refer to two different aspects of an object's mass. Gravitational mass is a measure of how much an object is affected by the force of gravity, while inertial mass is a measure of an object's resistance to changes in its motion. In other words, gravitational mass is related to the strength of an object's gravitational pull, while inertial mass is related to its momentum and how difficult it is to change that momentum.

In the quote from Sean Carroll's lecture book, he is discussing the hypothetical scenario of a "gravitation atom," which is a system of two particles bound together by their mutual gravitational attraction. In this scenario, the two particles would have a negative binding energy, meaning that they are held together by the attractive force of gravity rather than a traditional binding force like electromagnetism.

Carroll is pointing out that in this scenario, the two particles would have different values for their gravitational and inertial masses. This is because the force of gravity, which is responsible for binding the particles together, is also a source of acceleration. In other words, gravity is not just a force that pulls objects towards each other, but it also causes them to accelerate towards each other. This acceleration contributes to an object's inertial mass, meaning that the two particles in the "gravitation atom" would have a larger inertial mass due to their mutual gravitational attraction.

In terms of which mass would be bigger, it is difficult to say without more information about the specific scenario. However, in general, the inertial mass of the particles in the "gravitation atom" would be larger than their gravitational mass due to the contribution of the gravitational force to their acceleration. This is a unique aspect of gravity, as other forces do not contribute to an object's inertial mass in the same way.