Is E=mc² Truly Equivalent to kE=(π)r² in Energy-Mass-Volume Relationships?

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Discussion Overview

The discussion centers on the relationship between energy, mass, and volume, specifically examining whether E=mc² is equivalent to kE=(π)r², where r represents the radius of a nucleus and k is a constant. The scope includes theoretical considerations and conceptual clarifications regarding nuclear physics and energy-mass relationships.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants propose that energy is proportional to mass and that mass is proportional to volume, suggesting a potential equivalence between E=mc² and kE=(π)r².
  • One participant questions the validity of the claim that mass is proportional to volume, using the example of deuterium to argue that adding a neutron may not increase nuclear volume.
  • Another participant asserts that the relationship between volume and mass in a nucleus is complex and not merely proportional, referencing the semi-empirical mass formula.
  • One participant argues that even if the proportionality were true, the relationship should involve an r³ term rather than r², as volume is related to the cube of the radius.
  • A participant discusses the formula for mass in relation to volume and density, questioning the method of measuring volume through cross-sectional area.
  • Another participant clarifies that the cross-section referred to is two-dimensional and can be used in particle physics to estimate nuclear volume.
  • One participant expresses skepticism about the proportionality of mass and volume, suggesting that if it were true, the mechanics of atomic bombs would be fundamentally different.

Areas of Agreement / Disagreement

Participants do not reach consensus on the validity of the claims regarding the relationship between mass, volume, and energy. Multiple competing views remain, particularly concerning the proportionality of mass to volume and the implications for nuclear energy.

Contextual Notes

Limitations include unresolved assumptions about the nature of nuclear volume and mass relationships, as well as the complexity of nuclear structure that may affect the proposed equivalences.

Andy Lee
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1. Energy is proportional to mass.
2. Mass (of nucleus) is proportional to volume.
3. Volume can be determined from cross-sectional area.

If this is the case, then is E=mc^2 equivalent to kE=(pi)r^2 where r is the radius of the nucleus and k is some constant?
 
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Is number 2 even correct? If I add one neutron to hydrogen to make deuterium, is the nuclear now bigger in volume?
 
Thanks, that helps.
 
Even if (2) were true (and DaleSpam has pointed out it isn't), you would expect an r3 term, not an r2 term. (Volume of a sphere isn't proportional to area).
 
2. Mass = Volume x Density

What's the idea to measure volume of as a cross section anyway?
Volume of n-sphere can be easily calculated without any cross sectional area using formulas.
Cross section of 4D objects is 3D object.

I have no idea how to calculate mass-radius relationship for nucleus, it's difficult because it's a compound, but for example mass of electron = coupling * Planck's mass * Planck's length / classical electron radius
 
I think Andy Lee meant the two-dimensional cross-section which can be observed in particle physics - this can be used to estimate the volume of the nucleus.
 
If 2. were correct I don't think atomic bombs would exist (at least not in the way they do in this universe!) since the energy as I understand it comes from the difference in mass of the nucleus and the constituents of the nucleus, so if they were proportional there wouldn't be any release of excess energy.
 

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