That is exactly what happens only using time.
Light is measured as taking 8 minutes to get here. But in your limiting frame reference perspective it was instantly.
Light is measured as taking 4 years to get here. But in your limiting frame reference perspective it was instantly.
Light is measured as taking 10 million years to get here. Once again in your limiting frame reference perspective it was instantly.
And for any *real* reference frame, the times would be different. The 'limiting frame' is not a valid reference frame!
Go back to post #680. Did that make sense to you?
Now, what happens to the numbers as you let the velocity of the spaceship get closer and closer to the speed of light? That dilation factor gets larger and larger. Which means the measured distances and times get smaller and smaller.
In the limit of the speed of light, the dilation factor is infinite, so when you divide by it, ALL distances and times go to 0. No *actual* observer will ever be in this limiting frame since IT ISN'T A VALID FRAME. But the limit can still be done mathematically.