Time Dilation: Can You Chase Something Too Fast?

[i.h87]

Forgive me if this has already been asked as I'm trying to understand this, but I can't seem to find the right info..

Basically, what I want to know is if it is possible to chase something so fast that you won't catch it due to time dilation. If an object is traveling at a low sublight speed and another object is following the same path at a near light speed can time dilation make it so that the faster object never catches up to the slower object, or is this nullified because traveling on the same path gives them the same frame of reference?

 

[PeterDonis]

Basically, what I want to know is if it is possible to chase something so fast that you won't catch it due to time dilation. If an object is traveling at a low sublight speed and another object is following the same path at a near light speed can time dilation make it so that the faster object never catches up to the slower object

No. As long as both objects are traveling at less than the speed of light, the faster object will always catch up to the slower one eventually.

or is this nullified because traveling on the same path gives them the same frame of reference?

I'm not sure what you mean by this, but the reason the faster object will catch up is that, if you look at things in the frame in which that object is at rest, the slower object is moving *towards* the faster object in that frame.