The idea that the experience of an accelerated observer might be approximated by considering its worldline as comprising many small inertial pieces is a good one. And during each inertial step the speed of light seems to be constant everywhere. But at the velocity boosts or “frame jumps” between the steps, the apparent coordinates of all events (including those on the world line of a light signal) get shifted, so the light seems to jump ahead or back. Taking the limit of these approximations leads to the conclusion that the light signal does not seem to have constant velocity from the point of view of the accelerated observer. (Since the “frame jumps” lead to coordinate changes that are proportional to the distance of the event from the observer, this does not change the fact that every light signal seems to have the same speed when it reaches the observer, so there is no local change and it is just when the signal is far away from the observer that its velocity appears to vary.)
Source: (1001) Alan Cooper’s answer to A rotating frame can be divided into an infinite number of infinitesimal inertial frames. According to SR (special relativity) the light speed in each inertial frame is constant. Is light speed therefore constant in say the Sagnac experiment with SR? – Quora
A Quora question asks:
From your own perspective, frame of reference, if you are not accelerating, are you not moving at all?
Perhaps the reason people find this difficult to grasp is because of the ambiguous and unnecessary words “at all” at the end – which lend support to the idea that the word “moving” without mention of a context has any meaning at all. It does not.
And it never has. The claim that something is “moving” has never had any meaning without identification of relative to what, and it is perhaps unfortunate that by convention we often take the word without modification as meaning relative to the Earth without explaining that convention to small children (who then grow up thinking that there must be some kind of absolute property of “moving”).
From my own perspective, while sitting still in a bus I am not moving relative to the bus, but I know damn well that I am moving relative to the world outside. And it’s not just from my own perspective. Everyone else agrees with both of those relative motion statements.
So although it is just a tautology that from every perspective I am never moving relative to myself, it is false (or rather meaningless) that there exists any perspective from which I am ever not moving at all.
Source: (1000) Alan Cooper’s answer to From your own perspective, frame of reference, if you are not accelerating, are you not moving at all? – Quora