E=mc^2 and gravitational potential energy

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Discussion Overview

The discussion revolves around the implications of Einstein's equation E=mc² in the context of gravitational potential energy, specifically regarding whether lifting an object increases its mass and how this relates to gravitational potential energy. Participants explore the conceptual and theoretical aspects of mass, energy, and gravitational interactions.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants propose that lifting a boulder increases its mass slightly due to E=mc², raising questions about the implications for gravitational potential energy.
  • Others argue that the increase in potential energy does not belong solely to the boulder, suggesting a need for clarification on the system's energy dynamics.
  • One participant discusses the work done to separate two attracted objects, indicating that this work increases the energy level of the system and thus its mass, distinguishing between the mass of individual particles and the mass of the system as a whole.
  • Another participant mentions bonding energy and suggests that the proper mass of a combined system is greater than the sum of its parts, hinting at the complexities of mass in gravitational contexts.
  • There is a question about the location of the "extra mass" resulting from energy increases, with one participant acknowledging a misunderstanding regarding the role of Earth in the scenario.
  • A later reply suggests that the inertia is contained within the energy itself, implying a non-traditional view of mass and energy relationships.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the relationship between mass, energy, and gravitational potential energy. The discussion remains unresolved, with no consensus on the implications of lifting an object in relation to its mass and energy.

Contextual Notes

There are limitations in the assumptions made about mass and energy interactions, particularly regarding the definitions of mass in different contexts and the implications of gravitational binding energy. The discussion does not resolve these complexities.

Archosaur
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So, I've heard that if you lift a boulder into the air, it's mass increases slightly as per e=mc^2.
Well, my question is, does gravity act on this new mass? If so then shouldn't it have slightly more gravitational potential energy, and thus slightly more mass etc. ad nauseum?

Would the infinite series I've suggested converge?
 
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Archosaur said:
So, I've heard that if you lift a boulder into the air, it's mass increases slightly as per e=mc^2.
Where did you hear that? The increase in potential energy, which is what I assume you are talking about, doesn't belong to the boulder by itself.
 
When two objects are attracted to one another, one must do work to separate them. That work increases the energy level of the system and via E = mc2 the mass of the system. The mass of the particles is one thing and the mass of the system is another. The fact is that the mass of the system is a combination of the mass of the parts and the interaction between them.

Also, the infinite regress does converge because it only take a finite amount of energy to separate the bound particles from one another (this is the binding energy of the system).
 
The question is slightly messed up, but yes, the proper mass of the sum of two separate mass is greater than the total mass of both put together. This is usually described as bonding energy.

I can't make out exactly how you are conceptualizing this, and the fact that you ask if it converges tells me your not that clear about it either. But yes, gravity is self gravitating (nonlinear) in some sense, and it does converge.
 
Doc Al said:
Where did you hear that? The increase in potential energy, which is what I assume you are talking about, doesn't belong to the boulder by itself.

Gah... of course :/
Forgetting that the Earth is a thing is an embarrassing mistake.

But then... where is this extra mass? Doesn't mass have to "be" somewhere?
 
That's the magic of E=mc2. The inertia is in the energy itself.
 

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