Speed of light relative to observers?

[albert36]

I don't see any pedagogical value in the concept of inertia.

My post #13 [Penrose, Road to Reality] provides some. If I am interpreting them correctly they comply with the comments I also already posted from Wikipedia, but of course the words are different. I'd provide them here, but I don't know how to without the possibility of taking something out of the context which Penrose provides. His discussion seems overly lengthy...maybe eight or ten pages.

The law is about frames of reference, The difference between a state of rest and a state of uniform motion is the frame of reference of the observer.

moving "inertially" (i.e., without having any force applied to change their motion) follow the trajectories they do because of the geometry of spacetime, not because of any property of the objects.

After reading Penrose several times a more precise description I think he provides is that inertial movement is that which follow geodesics. And I think a geodesic the result of local spacetime geometry AND that induced by the object. In other words, don't two objects with different properties in general move along different 'geodesics' because different objects have different gravitational fields of their own?

 

[albert36]

Sounds like I was thinking 'wrong" ...

Crowell says:
"...In GR, the "lines" are geodesics, which are interpreted as the world-lines of particles that aren't subjected to any nongravitational forces. Since a geodesic is uniquely determined by any initial segment, you can't have different geodesics for red and blue light.,,"

Post # 4: https://www.physicsforums.com/threads/are-photons-affected-differently-by-gravity.391798/

 

[dayalanand roy]

Momentum is a well-defined concept. Inertia is not. It turns out the concept of inertia is meaningful only in the low speed limit of Newtonian physics. And even then it is not a particularly useful concept.

Thanks.

 

[dayalanand roy]

Dear all the participants
Thanks for your educating discussion. I am also trying to get something out of it.

 

[PeterDonis]

I think a geodesic the result of local spacetime geometry AND that induced by the object.

In general, this is what GR would predict; but we do not have any way of solving the equations for this in the general case. What we do, instead, is to approximate most objects as "test objects", which are assumed to have negligible effect on the spacetime geometry. Test objects then follow geodesics of the background geometry that is generated by the bodies that are massive enough not to be test objects. This is how, for example, we would model the motion of spacecraft in orbit around the Earth.

What is less obvious, but turns out to be true, is that we can do this same trick even for objects that are clearly not "test objects" in themselves, but which are sufficiently isolated. For example, in modeling the orbit of the Earth and the other planets around the Sun, we can treat the planets as following geodesics of the background spacetime geometry generated by the Sun, while ignoring the effects of the planets themselves. This works because the Sun is much more massive than any of the planets (the most massive planet, Jupiter, is less than 1/1000 the mass of the Sun), and because all of the planets are well isolated, which means that the distance between them is much, much larger than any of their masses (where "mass" here means the "geometric mass" $GM / c^2$, where $M$ is the mass in conventional units). I believe there is a theorem to the effect that, under these conditions, the "self-gravity" of the planets cancels out, and does not affect the geodesics that the planets travel on, as long as we are not concerned with the internal structure of the planets themselves, but only the orbits of their centers of mass.

Sounds like I was thinking 'wrong" ...

Not necessarily. What you quoted assumes that the light itself has no effect on the spacetime geometry, i.e., that the rays of red and blue light are "test objects" in the above sense. More precisely, it assumes that, whatever effect the light has on the geometry, it is the same for red and blue light (which just means the two colors of light must have the same energy density).