Does E=mc^2 apply to gravitational potential energy?

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Discussion Overview

The discussion centers on the application of the equation E=mc² to gravitational potential energy within the context of general relativity. Participants explore the implications of energy transformations during an object's fall and the relationship between mass and energy in both classical and relativistic frameworks.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant references an idealized experiment from Schutz's text, questioning whether the mass of an object remains constant as it falls, given that energy is conserved in classical mechanics.
  • Another participant argues that relativistic mass is largely discarded in modern physics, emphasizing that "mass" typically refers to invariant mass.
  • A different viewpoint suggests that gravitational potential energy is more a property of the gravitational field than of the object itself, complicating the association of energy with mass.
  • Some participants express that the original question mixes concepts from Newtonian mechanics, special relativity (SR), and general relativity (GR), suggesting it may be unanswerable in its current form.
  • There is a discussion about how energy changes when an object falls, with one participant asserting that the total energy of a system remains constant, while another emphasizes the importance of defining the system being analyzed.
  • Several participants engage in a dialogue about measuring mass and energy, questioning the feasibility of measuring an object's mass as it falls and the implications of frame of reference on energy measurements.
  • A participant draws an analogy with a mousetrap on a scale, discussing how energy input from outside affects weight measurements, while another contrasts this with an internal energy source.

Areas of Agreement / Disagreement

Participants express a range of views, with no consensus reached on the application of E=mc² to gravitational potential energy. There are competing interpretations of mass, energy, and how they relate in different frames of reference.

Contextual Notes

The discussion highlights limitations in defining gravitational potential energy in relativity and the challenges of measuring mass in motion. There is also ambiguity regarding the definitions of mass and energy in different contexts.

  • #61
PeterDonis said:
Note that these energy levels are energy levels of bound states in a "potential well" created with a mirror. So measurements of these energy levels are not measurements of "gravitational time dilation" for neutrons. They are measurements of whether the gravitational potential works like any other potential in the Schrödinger equation to determine bound state energy levels.
Exactly, but wasn't this the point of the debate? Perhaps I don't understand, what the issue is here... Of course, I've not claimed that this has anything to do with time dilation. It's just a non-relativistic model after all.
 
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  • #62
vanhees71 said:
wasn't this the point of the debate?

No. The poster I was responding to was claiming that that experiment was a measurement of gravitational time dilation for neutrons. As you agree, it isn't.
 
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  • #63
Of course not...
 

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