Relativistic Mass and Volume Change in a Rapidly Expanding Sphere

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Discussion Overview

The discussion revolves around the concept of relativistic mass in the context of a rapidly expanding sphere. Participants explore the implications of this expansion on the mass and energy of the system, considering both theoretical and practical aspects of relativity.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant questions whether the "relativistic mass" of a 10 kg sphere would increase as its radius expands rapidly at a speed of 1/2c, suggesting that some particles are moving at high velocity while others remain stationary.
  • Another participant argues that the sphere as a whole is not moving and therefore does not have any relativistic mass, proposing to use "momentum" instead of "relativistic mass" and stating that the total energy/mass of the system would not increase if the energy source is internal.
  • A different viewpoint suggests that while the outer layer of the sphere gains momentum due to relativistic effects, the mass becomes distributed as the volume expands, implying that the sphere is "becoming heavier" and proposing a potential "lorentz-volume factor" to quantify this change.
  • Another participant counters the previous claim by stating that if the energy source is internal, the mass remains unchanged, while external energy would increase the mass according to the energy-mass equivalence principle.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between the sphere's expansion, its mass, and the source of energy. There is no consensus on whether the sphere's mass increases or remains unchanged, leading to an unresolved discussion.

Contextual Notes

The discussion includes assumptions about the source of energy and its impact on mass, as well as the definitions of relativistic mass and momentum. The implications of the Lorentz factor in relation to volume change are also explored but not definitively resolved.

Frogeyedpeas
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suppose I have a 10 kg sphere with homogenous distribution of mass (aka density is same everywhere) that is 10 m^3. Now suppose I rapidly increased its radius at a speed of 1/2c m^3 (and because its homogenous the volume increased correspondingly). Now my question is whether that would cause the "relativistic mass" of the box to increase. Clearly some particles are moving at high velocity while one in the middle is stationary. Would it be possible to treat this entire system as opposed to each individual particle of mass?
 
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The sphere as a whole system is not moving and would not have any relativistic mass. However, let's do away with the term "relativistic mass", as it is confusing and doesn't need to be used any more. Instead we can use the term "momentum", as Einsteins equation e=mc^2 is actually an incomplete portion of the larger equation which uses momentum as well.

In a real world scenario this expansion would require a source of energy, and assuming this source of energy already existed inside the sphere then the total energy/mass of the system would not increase nor would it's momentum.
 
See, if one just considers the outer layer of the sphere; then, yes it is gaining momentum (ie becoming heavier) due to the lorentz factor, but at the same time as the volume expands this mass gets distributed around so the sphere is definitely becoming "heavier". Relativity says it has to. I was wondering if this could be measured by some lorentz-volume factor that measures the increase or decrease in the quantity (m/(1-v^2/c^2)^(1/2). But instead of using v one uses d(volume)/dt
 
Frogeyedpeas said:
so the sphere is definitely becoming "heavier". Relativity says it has to.
This is not correct if, as Drakkith mentioned, the source of energy was inside the sphere.

If the energy comes from outside the sphere then the mass of the sphere increases by the additional energy divided by c^2. If the energy comes from inside then the mass is unchanged.
 

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