Is the mass defect still considered with invariant mass?

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SUMMARY

The discussion centers on the concept of invariant mass in the context of assembling a sphere of negative charges. It is established that the invariant mass of the sphere is greater than the sum of the invariant masses of the individual electrons due to the energy gained during assembly. The participants clarify that invariant mass is not additive and emphasize that mass defect exists independently of the concept of relativistic mass. The conversation highlights the importance of understanding mass-energy equivalence and the implications of energy conservation across different inertial frames.

PREREQUISITES
  • Understanding of invariant mass and rest mass concepts
  • Familiarity with Einstein's mass-energy equivalence principle
  • Knowledge of energy conservation in different inertial frames
  • Basic grasp of electrostatic fields and their effects on mass
NEXT STEPS
  • Study the implications of Einstein's mass-energy equivalence in composite systems
  • Explore the differences between invariant mass and relativistic mass in modern physics
  • Investigate the role of electrostatic fields in mass calculations
  • Learn about energy conservation laws in various inertial frames of reference
USEFUL FOR

Physicists, students of theoretical physics, and anyone interested in the nuances of mass and energy in relativistic contexts will benefit from this discussion.

  • #31
Mister T said:
You could also use solar energy to grow the food needed for a human to lift the book.

Yes, but that is just admitting that in fact the Earth (or the Earth plus the book plus the human) is not a closed system. There is energy flow across its boundary in both directions. What's more, if you are taking this energy flow into account, the system is not stationary either, so the notion of "potential energy" is not even well-defined. Obviously this is no longer "as simple as lifting a book", nor is it any good as an illustration of any point about potential energy or invariant mass.

So either you bring in complications that make the whole subject of this discussion pointless, or you accept a simple model in which the Earth-book system is closed, at least on the time scale required to lift the book (note that this time scale is much shorter than the time scale required to capture solar energy and grow the human's food), and in that model, the externally measured mass does not change when you lift the book.
 

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