Gravity, Inertia and Contraction

Boeley

Inertia has Lorentz-Fitzgerald contraction.

Is there a similar (parallel?) contraction equation for Gravitational forces?

Matterwave

What do you mean Inertia has Lorentz-Fitzgerald contraction? L-F contraction applies to length, how can it apply to a concept like inertia?

I've never heard of this...

Naty1

The short answer is, I believe, yes.

I took the question to be about momentum/inertia... mv. So with a velocity term, the poster implies gamma relationships of time expansion and length contraction.

I believe the question boils down to whether intertial and gravitational mass are equivalent...and so far as is known they are.

The "contraction equation for gravitational forces" is ,first, time dilation as a function of (increased) gravitational potential. So for example time passes more slowly at the bottom of a tower (at higher gravitational potential) on the earths surface than at the top of the tower...this has been experimentally verified at Harvard, I believe, to a very high degree of accuracy. and we have other supporting experimental evidence.

As for the corollary to length contraction, I'd take that to be curvature of spacetime, but that's probably not a technically equivalent comparison because in GR a free falling particle is in an inertial frame locally, that's equivalent to a steady velocity in SR and hence from that condition and perspective length contraction IS observed. That's why I made the simple answer a "yes"..

As I reread my answer after posting it I don't like it so much...maybe a more comprehnsive reply takes into account gravitational tensor relationships which are strictly a part of gravitational formulations. When an object of finite size is subjected to the gravitational influence of, say a black hole or a planet, the object is both stretched in the direction of the gravitational source and also compressed (thinner) by tidal forces as it is subjected to increasing gravitational potential...I don't know if either are velocity dependent.

I have not thought about how the contraction due to velocity and stretching due to gravitational forces in the direction of motion are accounted...hopefully somebody will enlighten us.