I was thinking that if you are in empty space with another person (with no other objects around), and from a distance you see that the other person is approaching you a constant speed, you wouldn't actually know who is the one moving towards the other, you can assume that you're the one that's moving and he's at rest, or he is the one that is moving and you're at rest, making either assumption is correct, and the other person also has the freedom to make either assumption.
But I'm uncertain how it would be if we imagine the same situation with acceleration instead of a constant velocity, because one of you is experiencing time dilation.. Let's say you're the one accelerating towards the other person who is at rest, so after meeting him you're clocks wouldn't agree because of time dilation, right? So I have a question here:: Will you be able to tell that you were the one who was accelerating and he was the one at rest without having to check your clocks after meeting? (let's say the time dilation is not so huge that one would actually notice difference in age, and assume you can't sense inertia from acceleration, like you're just a camera)
Now I am not sure about that but I think the answer for that question would be: "No"
If the answer is indeed "No", then why does that happen? if you can't tell whether you're the one who is accelerating or the other person is, and either assumption can be correct, then why does only one of you experience time dilation?
Edit: @"because you imposed the artificial condition that you are unable to feel the effects of acceleration even though they would be there." What I meant is that can you tell you have accelerated (in empty space) depending only on observing another object? Or say, you have a camera in space that's filming an object which appears to be getting closer to your camera, can you tell whether your camera was actually pushed by something and the other object is at rest? or the other object is the one that's moving towards the camera?
I'm no expert, so I might not explained it properly, but , as far as I know, time dilation happens so that the speed of light remains constant, it seems to me that it's more valid to talk about observation rather than "sensing" acceleration physically, the light reflected from the object you see is affected by acceleration in some manner that it remains constant I believe, but even though you can't tell which object is accelerating and which is at rest, only one of them will experience time dilation.