From: goldenfieldquaternions@gmail.com
On Friday, August 24, 2018 at 7:03:00 PM UTC-5, Tom Roberts wrote:
> On 8/18/18 11:51 PM, Phillip Helbig (undress to reply) wrote:
> > In article <19886fb9-8614-4aee-acb1-2c1356393302@googlegroups.com>,
> > Lawrence Crowell writes:
> >> Two anti-masses will repel as can be seen with
> >> ma = -GMm/r^2,
> >> where for M and m negative this equation picks up an additional minus
> >> sign.
>
> That is a NEWTONIAN equation, and is irrelevant.
>
> > While (if I remember Steve Carlip's comments on this correctly) this is
> > correct, it is not obvious where the extra minus sign comes from. The
> > two on m and M cancel, so if you like the extra one is the one seen
> > explicitly in the equation above. But where---via a simple, heuristic
> > argument---does it come from? We can't just assume that that which we
> > wish to prove is true and insert it for that reason.
>
> In GR, negatively massive objects have an effect on geometry such that
> the timelike and null geodesics of small particles diverge from them (as
> opposed to positively massive objects for which such geodesics
> converge). Small particles with negative mass follow timelike geodesics,
> just like positive-mass particles.
>
> For two negative-mass objects that both have significant effects on the
> geometry, I don't know the answer except that this case must go smoothly
> into the above case as one object's mass is decreased.
>
> Tom Roberts
Newtonian gravity is the very weak field limit of general relativity.
Negative mass particles in general relativity have geodesics that
defocus from each other, which is by way of contrast different from
positive mass particles that do focus in spacetime. The nonrelativistic
weak field limit of that is Newtonian gravity.
LC
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