I will say one thing - Thanks for being polite as we have discussed this, I appreciate that.
Sometimes you think I don't understand what you are saying, most of the time I do, it just doesn't seem possible for some of it to be true.
It just seems impossible, for an essentially infinite number of different distances, and lengths of time in our reference frame, to always yield the same answer of time=0 and distance=0 when the Speed of light is a constant, even in your limiting frame.
Since Speed of Light is a constant even in your limiting frame, it defies logic that it can cover any distance instantly. The very definition of speed requires it to be a function of time.
If there is no time in your limiting frame, then how can there even be a concept of speed?
You said - It takes no time to travel no distance. That is exactly the same as in our reference frame, it takes no time for light to travel no distance.
It's just hard to discuss when some say I am switching reference frames, then you say it doesn't have a reference frame whenever I try to use what they are calling another frame.
OK, let's do it a different way. Take a star 4 light years away and a galaxy 10 million light years away. How long does it take light to go from the star/galaxy to us?
Let's answer this question in a number of different reference frames. In each case, I will give the time dilation factor.
1. The Earth: the star is 4 ly away, so light takes 4 years to travel. Time dilation factor is 1 (no shift). The galaxy is 10 million light years away, so it take light 10 million light years to travel.
2. A spacecraft going past Earth at 86% of the speed of light. Time dilation factor is 2 (all times and distances are divided by 2). In this frame, the star is 2 light years from Earth, so light takes 2 years to travel. The galaxy is 5 million light years from Earth, so light takes 5 million light years to travel.
3. A spacecraft going past Earth at 99.5% of the speed of light. Time dilation factor is 10 (all times and distances are divided by 10). In this frame, the star is .4=2/5 light years from Earth, so light takes .4 years to travel. The galaxy is 1 million light years from Earth, so light takes 1 million light years to travel.
4. A spacecraft going past Earth at 99.995% of the speed of light. Time dilation factor is 100 (all times and distances are divided by 100) In this frame, the star is .04 light years from Earth, and the light takes .04 years = 2 weeks to travel. The galaxy is 100,000 light years from Earth, so light takes 100,000 years to travel.
5. A spacecraft going past Earth at 99.99995% of the speed of light. Time dilation factor is 1000. In this frame, the star is now .004 light years from Earth and now takes .004 years = 1 1/2 days to travel. The galaxy is now 10,000 light years from Earth and the light from it takes 10,000 years to travel to Earth.
Now, I want to emphasize that all of these are describing the *exact* same situation: light traveling from either a star or a galaxy to the Earth. In each case, the speed of light is the same. That doesn't change when changing reference frames.
If we looked from a spacecraft going 99.99999999995% of the speed of light, that galaxy would only be 10 light years from Earth and the light would only take 10 years to travel. But that light would still be going at the same speed as in any other reference frame.
As we look from frames that are getting closer and closer to the speed of light, the dilation factor gets larger and larger, so the actual distances and times get smaller and smaller. In the *limit*, both the distances and times go to zero. But, since no spacecraft can go the speed of light, and no observer will be going the speed of light, that measurement of 0 is never going to happen.
Does this clear it up a bit?