- #1

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What is the total energy of a particle in a potential? Is it

$$E=\gamma m_0 c^2+E_pot$$

or is it still

$$E=\gamma m_0 c^2$$

where ##m_0## is a bigger mass than the particle would have in absence of the potential?

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- Thread starter greypilgrim
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In summary, the total energy of a particle in a potential is given by the formula E = \gamma mc^2 + q \Phi for the electromagnetic field. However, for gravity, there is no satisfactory answer for where the equivalent of potential energy resides. Electric potential energy is not part of the energy of the particle but rather the energy of the system, and it is proportional to the square of the field. On the other hand, gravitational potential energy is negative relative to the local rest mass and contributes to the inertia of the particle.

- #1

- 492

- 33

What is the total energy of a particle in a potential? Is it

$$E=\gamma m_0 c^2+E_pot$$

or is it still

$$E=\gamma m_0 c^2$$

where ##m_0## is a bigger mass than the particle would have in absence of the potential?

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- #2

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[itex]E = \gamma mc^2 + q \Phi[/itex]

where [itex]\Phi[/itex] is the electric potential.

- #3

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(For gravity, where energy acts as a source so everything is non-linear, this gets much more complicated and as far as I know there isn't any satisfactory answer to where the equivalent of potential energy resides, not even in GR).

- #4

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stevendaryl said:

[itex]E = \gamma mc^2 + q \Phi[/itex]

where [itex]\Phi[/itex] is the electric potential.

But how does this work with

$$E^2=c^2\cdot \mathbf{p}^2+m^2\cdot c^4 \enspace ?$$

If we look at two identical particles with the same velocity where one is in an electric potential and the other is not, the right sides of this equation are the same, but not the energy squared on the left?

- #5

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In contrast, gravitational potential energy (which is negative relative to the local rest mass) is part of the energy of the particle and is assumed to contribute its inertia, but to get the usual conservation laws to work (at least for a weak field approximation) there also has to be positive energy in the field which compensates for the double effect of each particle having the whole potential energy.

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