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muppet

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**"scalar gravity" -Feynman lectures on gravitation**

Hi all,

I'm trying to understand the following claim from Feynman's lectures on gravitation, section 3.1 (p.30 in my edition). He's considering how heating or cooling two clouds of gas would change their mutual gravitational attraction.

Feynman said:Electric forces are unchanged by random motions of the particles. Now the interaction energy is proportional to the expectation value of [itex]\gamma=1/\sqrt{1-v^2/c^2}[/itex]. Since the resulting potential is not velocity dependent the proportionality factor must go as [itex]\sqrt{1-v^2/c^2}[/itex]. This means that the interaction energy resulting from the operator 1, corresponding to a scalar field, must go as [itex]\sqrt{1-v^2/c^2}[/itex]. This means that the spin-zero theory predicts that the attraction between masses of hot gas would be less than that for cool gas.

I don't understand this statement. The electric scalar potential is the time component of a four vector which gets dotted into another four vector, so that the resulting physics is invariant. I don't see anything in the expression for a Yukawa potential that I can identify with the velocity dependence he's talking about. Can someone please explain?

Thanks in advance.