Is there a power-energy relationship between matter and energy?

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Discussion Overview

The discussion revolves around the relationship between power and energy in the context of the mass-energy equivalence principle. Participants explore whether a power-energy relationship can be derived from the mass-energy equation, considering implications for constant velocity and the conversion of mass to energy.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant proposes that differentiating the mass-energy relationship equation could yield a power-energy relationship, suggesting that power is related to the acceleration of mass.
  • Another participant confirms that no power is required to maintain constant velocity in a lossless environment, implying that power is not relevant in that scenario.
  • A question is raised about how to calculate the power produced by the destruction of mass, indicating a need for clarity on the timing of energy release.
  • It is suggested that the conversion of mass to energy is not instantaneous, as instantaneous conversion would imply infinite power for an infinitely short duration.
  • One participant argues that the concept of power becomes meaningless in the context of instantaneous mass-energy conversion, while acknowledging that power can be calculated in certain rapid reactions.

Areas of Agreement / Disagreement

Participants express differing views on the nature of power in relation to mass-energy conversion, with some suggesting that power is not meaningful in this context, while others explore the implications of timing and reaction rates. No consensus is reached on the validity of a power-energy relationship derived from the mass-energy equation.

Contextual Notes

Participants note that the discussion involves assumptions about the definitions of power and energy, as well as the conditions under which mass is converted to energy. The implications of constant velocity and instantaneous conversion are also highlighted as areas of uncertainty.

danielu13
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I was looking at the mass-energy relationship equation, which by taking the derivative I would think that you you should get a power-energy relationship. What I get is:

[itex]P = \frac{mc^2}{2\sqrt{1-\frac{v^2}{c^2}}}*2a[/itex]

If this were to be true, a particle without acceleration would have no power, and thus release no energy. Or, it could be that all of the energy is instantaneously released and shows no power. Can someone help me where I went wrong in this?
 
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You figured correctly: no power is expended to keep an object moving at constant speed in a lossless environment.
 
But is there any way of figuring the power produced by the destruction of mass, as in the mass-energy relationship?
 
So the conversion between matter and energy is not instantaneous then?
 
If it was, there would be infinite power for an infinitely short time.

Conversion of mass to energy means the mass would no longer exist.

When a photon is emitted, it does not accelerate, it moves at c instantaneously.

My guess is that the consideration of power in this case is not meaningful.
 
danielu13 said:
I was looking at the mass-energy relationship equation, which by taking the derivative I would think that you you should get a power-energy relationship. What I get is:

[itex]P = \frac{mc^2}{2\sqrt{1-\frac{v^2}{c^2}}}*2a[/itex]

A power energy relationship is time.

The derivative would be a power vs mass relationship.

I do find it an interesting thought.
 
danielu13 said:
So the conversion between matter and energy is not instantaneous then?
On a molecular or atomic level I think it is -- therefore power is meaningless because as said it would be infinite or undefined.

I have, however seen people calculate power using a propagation rate or reaction rate of even a very fast reaction such as in a bomb. It provides interesting hyperbole but I don't think it is really all that useful.
 
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