Hi all
First point: Ryans statement
a terminal velocity of c would be reached, AFTER AN INFINITE AMOUNT OF TIME.
is mathematically equivalent to my earlier statement(s)
you will approach the speed of light relative to your origin asymptotically from below... Your velocity will be bounded by, but never reach, the speed of light.
although (naturally) I prefer mine as being more physically meaningful.
Second point: MacM's argument is based entirely on the
assumption that Galilean relativity/Newtonian spacetime is the correct model. Of course if you make this assumption then relativity looks weird and magical.
But this assumption is incorrect.
The assumption is seen in statements such as
So where is its velocity limit created?
ie of
course there can be no limit to velocity unless something (like a brick wall) gets in the way. Of
course if we accelerate for twice as long we end up with a relative velocity twice as large.
In fact MacM earlier assumed even more explicitly that velocities can be added linearly. (Indeed he seems not to have acknowledged my correction and still assumes that velocities can always be added linearly.)
The point is that in our (relativistic) Universe two objects can continually accelerate away from each other and never reach a relative velocity of c. The mathematics for this is all clear and self-consistent. We can work out what the rocket sees, what the earth sees or what a third party sees and these viewpoints all make sense to one another.
However we can't do this in a way that preserves simple addition of velocities like MacM would like.
If you want to know
how do we know that we live in a relativistic Universe in which velocities don't add linearly then we can start a thread devoted to experimental tests of relativity S &/or G.
But if you want to know
why we live in a relativistic Universe rather than a sensible, comfortable, intuitive Newtonian one then you are unlikely to find an answer much more profound than "because we just do".