Twin Paradox - Question on Space Time Diagram Analysis Resolution

[PAllen]

So what you're saying is without something to be compared side to side with said velocity, it might as well be zero because there is NOTHING to inform of otherwise. Acceleration and directional variance is all that matters?

Exactly ! ..

Doesn't that seem to be lacking somewhat?

only lacking a superfluous, obsolete, concept.

I mean, isn't there a reason things can't move faster than c?
If independent velocity didn't matter by itself, then why is light speed (non-varying) such an exception? Things going that fast aren't the same as zero, are they?

The invariance of light speed disproves any notion of absolute speed. You turn on a laser pulse moving away from you at c. I move in the same direction past you at .99999c. With a sense of absolute velocity, you might expect the light is moving only .00001 c relative to me. Instead, it is moving c relative to me, and you are moving at .99999c away from me. Each of thinks we are at rest. There is no way to choose. That is the essence of relativity. If there were any way to choose based on experiment 'who is really moving' all of relativity would be disproven.

 

[Ibix]

So what you're saying is without something to be compared side to side with said velocity, it might as well be zero because there is NOTHING to inform of otherwise. Acceleration and directional variance is all that matters?

Not quite. As long as I am not accelerating there is no way to say if I am moving or not. The presence or absence of other objects is not relevant to that. If there are other objects around it may sometimes be convenient to consider them to be moving, to consider myself to be moving, or both, but there's no obligation to use one of them.

Doesn't that seem to be lacking somewhat?

The Principle of Relativity, which is the formal name for the notion, underpins pretty much every physical theory we have. In other words, it underpins pretty much everything we do or have done, from pouring a drink on a train to traveling to the moon and everything in between. I'm not sure in what sense that is "lacking".

I mean, isn't there a reason things can't move faster than c?

There is - the principle of relativity. Google for "Nothing but Relativity" by Pal. It's only six pages long and requires only high school maths.

If independent velocity didn't matter by itself, then why is light speed (non-varying) such an exception? Things going that fast aren't the same as zero, are they?

The concept of an invariant speed, one that is the same in all frames of reference, follows from the principle of relativity. Things traveling at that speed cannot be considered to be at rest, true, so it is indeed an exception. This does not alter the fact that any other speed can always be treated as at rest - and you were talking about massive objects like space shuttles which cannot travel at light speed.