So I've recently been studying relativity a lot trying to understand it and I feel like I grasp most things conceptually but I have one issue I've been trying to understand for the last couple days and I just can't seem to find an answer anywhere.
Let's say you're traveling very fast, somewhere close to the speed of light. At this point you're in an inertial reference frame. From this frame you shouldn't be aware that you are anywhere near the speed of light. Now you want to accelerate by 5 m/s to a new reference frame that is even closer to the speed of light. Is there any difference in the amount of energy required to accelerate to the new reference frame in this scenario from the amount required to accelerate by 5 m/s from a slower reference frame like here on Earth?
I sort of understand the concept of relativistic energy but if that somehow applies here I don't get how. If you are in an inertial reference frame, then it seems that the amount of energy required to accelerate to a new reference frame should be the same no matter what your frame is. However, from various things I've read I get the impression that the energy required to accelerate at a constant rate is not constant, which seems to make sense from a static reference from but not from an accelerating one.
I'm sure I'm missing something or there's a flaw in my thinking somewhere. I hope this all makes sense since I'm still very new to this. Also, if there's a way to explain the concept with little to no math that would be very helpful since I still don't grasp a lot of the math involved in relativity. I'll take what I can get though. This has been eating at me too much.
Update: For anyone wondering about this same thing I finally found the answer explained in a way I grasped it here.