lifegazer said:
Answer this please: you treat time as space. So, in the twin-paradox, the spacetwin flies all around the galaxy and comes back to earth, only to find his brother - who hasn't moved much at all - claiming to have experienced, say for convenience, twice as much time as his space-brother, comparatively.
My question is this - given that the earth-twin hasn't moved much, why is his time-path twice as long as the spacetwin who has been moving to Andromeda and back, so to speak? If time is space, how can the body moving the least travel the furthest?
It's not twice as long on all axis, only on one.
There are three dimensions in space, but for the sake of argument, let's simplify and imagine a 2-D grid.
You and I both start at 0,0.
You move 6 to the right. Putting you at 6,0.
I move 36 up, 4 to the right, 24 down, 2 to the right, and then 12 down. Now I am still at 6,0 just like you. Only It took me 78 steps to get there, and it only took you six.
In the meantime, assuming the grid is uniform, each of my movements was exactly the same as each of yours. We started and ended at the same place, I just took a different path to get there.
My experience of one grid space is exactly the same as your experience of one grid space. (Or one second, or one foot)
What Einstein demonstrated was that by changing how oyu move through one dimension you can make the relative quantities appear to different for a journey that starts and ends at the same place. Because essentially there are actually shorter distances between two points than a straight line as a straight line appears to be from one set of dimensions.
Because I traveled through one dimension (Y) on a different route than you did.
But the quantities available, 3 spatial dimensions and one time dimensions can be interchangeable.
We can demonstrate a body that changes speed, and then if distance stays the same time must change.
If Time changes and speed stays the same distance must change.
If distance changes time stays the same, speed must change.
These things are all equivalent mathematically. And when I use the word "chgange" up there I don't mean the individual unist up there. A second is still a second, a foot is still a foot. I mean the total amount within a given equation in order to make 'c' = 'c'.
And it's not like Einstein started out to make an equation in which Light speed always equalled C. He found out that in fact, in reality no matter what the frame of reference, light always does equal c all the time under all circumstance. Once he found that out, he tried to find an expression that matched that mathematcially.
It was a case of finding a hypothesis that matched the results, not finding results that matched his hypothesis like you're attempting to do.