I want to show time as the 4th dimension using the Pythagorean Thingie. I'm pretty sure it's doable, cavediver, Son Goku and others have gone at it partway more than once. But I need more detail.
Here's the dealie. If I have two roads square to one another, such that I can travel 3 miles to the intersection, turn right, and travel 4 miles to the destination
then if I go "as the crow flies" instead, it will only be 5 miles. This is because
a² + b² = c²
that is, 3 x 3 = 9, 4 x 4 = 16, 9 + 16 = 25, 25 = 5 x 5. Yeah?
So, if time is in fact a 4th dimension at right angles to space, then if I travel 3 light years in 4 years (averaging 75% of C) then my total experience should be 5 years-and-light years altogether. If I were to treat space as the constant, 3 light years, then my experienced time would be only 2 years, a 50% time dilation. But I know that's wrong, space gets compressed too. Just for a lark, treat time as a constant, 4 years, then I would only experience 1 light year of travel, 33% space dilation. Also wrong, of course.
I'm guessing, sort of feeling my way along, and I come up with the notion that the proportions of the squares can guide me. Perhaps my perceived distance can be 9 / 25 of 5 = 1.8 light years; and my perceived time can be 16 / 25 of 5 = 3.2 years.
This seems reasonable enough, but I'm sure I'm still missing something. I can't see any reasons why I couldn't switch space and time around, and get 3.2 light years in 1.8 years. Symmetrical?
I expect this problem somewhere to make me subtract the square of distance directly from the square of time. With my reversed figure, 4 light years in 3 years, this would be 9 - 16 = -7
Then when it makes me get the square root of -7 my calculator could explode and so forth. Yeah?
But I don't see anything in this figure that really makes me do that. And I need it. I neeed my audience to be able to see, very clearly and simply why ftl travel is impossible / absurd. What am I missing? Please someone make me smarter than I am.
Evolution of the physics model, Pythagoras to La Maitre. Cosmology, please.
Edited by Iblis, : god does NOT play horseshoes with the wtfverse
Edited by Iblis, : does he?
Edited by Iblis, : praps it's more like mumblety peg