# Relative velocity between colinear free falling objects

Can anyone answer this question: In the context of GR, If two objects are in collinear free fall, far enough apart so that the field intensity differs for each object, and one measures the relative velocity between the objects in the coordinate system of the objects using (say) a radar system falling with one of the objects, will it be found that there is a time invariant velocity between them as measured by the radar, or will the velocity difference measured this way be time variant?

Related Special and General Relativity News on Phys.org
berkeman
Mentor
Can anyone answer this question: In the context of GR, If two objects are in collinear free fall, far enough apart so that the field intensity differs for each object, and one measures the relative velocity between the objects in the coordinate system of the objects using (say) a radar system falling with one of the objects, will it be found that there is a time invariant velocity between them as measured by the radar, or will the velocity difference measured this way be time variant?
Welcome to the PF.

What is the context of this question? Is it for schoolwork?

Welcome to the PF.

What is the context of this question? Is it for schoolwork?
No, it is related to a somewhat different take on GR. It is not an alternate theory, but more related to what Feynman called the machinery of gravity. I believe the correct answer is such a measurement would show the velocity measured as described to be time invariant, but what I don't know for sure is if GR implies this or not. I have been unable to find a clear answer to this in any text or online. Do you know the answer? To the best of my knowledge no such experiment ever has been done. In any event, thanks for asking. DavidF

berkeman
DrGreg
Gold Member
You might first like to consider whether this is true in Newtonian theory. At low relative speeds in low gravitational fields, Newtonian theory gives almost exactly the same results as GR.

A.T.
...a somewhat different take on GR. It is not an alternate theory...I don't know for sure is if GR implies this or not....
If you don't know what GR predicts here, how do you know you aren't proposing an alternate theory?

pervect
Staff Emeritus

n general relativity, geodesic deviation describes the tendency of objects to approach or recede from one another while moving under the influence of a spatially varying gravitational field. Put another way, if two objects are set in motion along two initially parallel trajectories, the presence of a tidal gravitational force will cause the trajectories to bend towards or away from each other, producing a relative acceleration between the objects.
As another poster has mentioned, you might also want to consider if tidal forces exist in Newtonian gravity or not. (This shouldn't be a terribly hard question, there isn't any trick to it.)

Note that there's some fine technical points about how relative velocities work in GR that I'm skipping over, which could potentially become important, but at this point feel it would be more confusing than helpful to go into the specifics.

A.T.
Newtonian Physics, the answer is time variable difference
Just like in GR.

You might first like to consider whether this is true in Newtonian theory. At low relative speeds in low gravitational fields, Newtonian theory gives almost exactly the same results as GR.
You might first like to consider whether this is true in Newtonian theory. At low relative speeds in low gravitational fields, Newtonian theory gives almost exactly the same results as GR.
I know the answer in Newtonian physics is the difference velocity is time variant because the "non homogeneous field" exists for both objects. I think this would also be true in GR if the only difference between GR and Newton's view was that the "field" is replaced by "space-time curvature". However that is too simplistic: There is a lot more to consider in GR than in Newtonian physics Re; gravity. Consider Einstein's "Happiest thought" that he exemplified with an observer in an accelerated chest in empty space being unable to distinguish between his being "at rest on the earth" or in his actual state. If I had two such chests co-linear, with the upper one accelerated less than the lower one, and two observers (one in each chest) and they both released balls from their roofs, certainly the relative velocities between the balls would be time invariant while they were falling. Also note that the "illusion" (if you can call it that) is obtained by having the chests accelerated upward while the observers are in the chests forced downward. This suggests (among other things) that objects in free-fall are no longer in curved space-time. Thanks for your interest David F

Last edited:
If you don't know what GR predicts here, how do you know you aren't proposing an alternate theory?
I buy GR hook line and sinker as an "almost" perfect description of the way gravity works. Neither Einstein nor Newton addressed the causes for their descriptions that more or less agree for low velocities and not great distances. What I am addressing is the "cause" for gravity and somethings I have uncovered may result in a small change in GR metrics. If you want to call that an "alternate theory", so be it. In thew larger sense I don't myself think it is. Best, DavidF

[

As another poster has mentioned, you might also want to consider if tidal forces exist in Newtonian gravity or not. (This shouldn't be a terribly hard question, there isn't any trick to it.)

Note that there's some fine technical points about how relative velocities work in GR that I'm skipping over, which could potentially become important, but at this point feel it would be more confusing than helpful to go into the specifics.
Note that I have as a model co-linear objects in free-fall, not parallel ones, so there are no geodesic deviations as you quote them. Of course tidal forces exist in both Newtonian physics and GR. Read my answer to Dr Greg. In any event, thanks for commenting. Davidf

berkeman
Mentor