A Simple Relativity Question

  • Thread starter garys_2k
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A "Simple" Relativity Question...

I was asked this question on another forum, and it seems easy at first glance but may be more subtle: What would an observer on a very massive star (yeah, a well insulated observer) see about a small body falling in toward the star, from very far away?

Would the apparant mass of the body change? If so, how would you calculate its mass at any point during the fall? Ditto the incoming body's speed -- what would it be as if fell? All the questions from the reference of the observer on the star.

Obviously SR will influence the apparant mass and speed, but what about GR? Does a freefalling body undergo GR changes? Also, does the fact that the observer is sitting in a pretty deep gravity well influence what he measures about that falling body?

I thought I knew how to handle these cases, but when put all together I'm not sure what the net effects are.

Thanks in advance for any help!

Answers and Replies

  • #2

In modern language, "mass" is taken to automatically mean the "rest mass" of the object. Therefore, there are no changes to the mass of the object, not in SR, not in GR. The energy an object has can change from one observer to another (but it does so in classical mechanics with kinetic energy as well). Mass is a *part* of the energy the object has.

The spacetime geometry telling the object how to move in this case is not as novel as the geometry as you approach the horizon of a black hole. The trajectory will qualitatively look the same as an object falling toward Earth (of course, we know that as it speeds up, it never reaches light speed...this is a constraint from the spacetime geometry).
What else does relativity say? It says that an observer on the surface of the massive planet will see the passage of time as being slower for the falling object as it speeds up toward the planet. This is the same effect as in the instructive example of infalling muons from "cosmic radiation". They live longer than we'd expect them to due to their relative motion. There are two effects, though: one due to the fact that observers in relative motion have different notions of space and time, the second due to the curvature of spacetime, such that observers at different locations in that curved geometry have different notions about space and time.