- #1

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## Main Question or Discussion Point

I am looking for an expression for the total energy of a particle of rest mass [tex]m_0[/tex] that includes kinetic and gravitational potential, if there is such a thing. If I take the product of the time-components of the four-velocity and four-momentum vectors, I get

[tex]

m_0 c^2 \gamma^2

[/tex]

where

[tex]

\gamma^2 = (dt/d\tau)^2 = \frac{dt^2 c^2}{g_a_b dx^a dx^b}

[/tex]

whereas if I take the dot product of the two vectors I simply get [tex]m_0 c^2[/tex].

Are either of these expressions correct?

[tex]

m_0 c^2 \gamma^2

[/tex]

where

[tex]

\gamma^2 = (dt/d\tau)^2 = \frac{dt^2 c^2}{g_a_b dx^a dx^b}

[/tex]

whereas if I take the dot product of the two vectors I simply get [tex]m_0 c^2[/tex].

Are either of these expressions correct?