The discussion of inertial frames applies to Lorentz transformations as well, which, like Galilean transformations, are linear. The transformations for rotational frames are not, which is why a rotating frame is not inertial.
The initial statement that I made was that an objects apparent position is not identical to its actual position at any given instant in time, primarily due to the speed of light. In other words when we see the Sun we see where it was apx 8 and a half minutes ago.
Do you agree or disagree with that statement?
If I answer this then will you do me the courtesy of answering the quesions that I posed in my previous post? If you demand that I answer your questions but you refuse to answer mine then I don't see any use in continuing this discussion, nor will I respond to you again unless and until you show the courtesy to reciprocate. If you choose not to then my post stands, and I have no reason not to be content with that.
Now, I answer that there are two statements there.
1) "The initial statement that I made was that an objects apparent position is not identical to its actual position at any given instant in time, primarily due to the speed of light."I agree if you insert the word "necessarily" before the word "identical". However, there are certainly cases where an object's apparent position can coincide with its actual position, the case of a stationary object WRT an observer in an inertial frame being the trivial example. Here is another example:
2) "In other words when we see the Sun we see where it was apx 8 and a half minutes ago."This is true, of course. But the crux of the matter here is: Where was the sun 8.5 minutes ago? Was it where we see it now or was it where we saw it 8.5 minutes ago, 2 degrees behind where we see it now? The former is the correct answer because the apparent motion is due not to the Sun revolving around us, but due to our rotation, and as I've tried to make clear already, these are not relative. If you would argue that they are, then kindly address the questions from my previous post.
MrJesse is quit adamant that the actual position is the same as the apparent position, except for a little parallax that I taught him about.
And he is correct (although we should take into accout refraction due to the atmosphere as well, but that's a different story). In your Earth/Pluto thought experiment you will not get 102 degrees difference from parallax, not even close. The correction for parallax will be miniscule. Nor will you get even close to 2 degrees due to parallax in 8.5 minutes considering the position of the Sun as seen from the surface of the Earth.
But since we are discussing rotating frames (which for some reason you seem to think are inertial) let's keep our thought experiments focused on that. Or better yet, do a real experiment and see for yourself the difference between spinning and orbiting. And keep those questions from my previous post in mind when you do. :)
This is true, of course. But the crux of the matter here is: Where was the sun 8.5 minutes ago? Was it where we see it now or was it where we saw it 8.5 minutes ago, 2 degrees behind where we see it now? The former is the correct answer because the apparent motion is due not to the Sun revolving around us, but due to our rotation, and as I've tried to make clear already, these are not relative.
And of course I left out the most important part (although I had alluded to it above) that the Sun is in the same place now that it was 8.5 minutes ago, which is where we see it now.