KinderCalculus/mathematics of time travel
Algebra can be hard for young children. To entice them to persevere, we use an application from high science -- time travel. This example uses only basic algebra and the Pythagorean Theorem, yet has such mind-blowing consequences.
The following vocabulary change will also help:
- grid = coordinate system
- drifting = steady velocity, no speed and direction changes
- drifting grid = inertial reference frame
- squishy = dilation & contraction of time & space
Our approach uses the light time clock example. First one must establish what time travel is intuitively and formally. Intuitively, it is best explained in the aging twin context: one twin travels near light speed and returns to find that his twin aged much more than he did. Formally, if T is the travelling twin's clock reading and t is the stationary twin's reading, then T!=t. With some loss of generality, we can rewrite this inequality as,
(1) T = t *( some non 1 number).
Deriving this equation will establish time travel.
The proof of time travel will rely on the following following assumptions:
- Pythagorean's theorem
- the equivalence of drifting grids for c and physical principles.
Stated traditionally, this means that the "laws of physics and the speed of light are the same in all inertial reference frames". In the context of the light clock, if the light clock is at "rest", the light path would be vertical. But since the rocket is in an equivalent inertial frame (ie. drifting grid), the rocket observer would see a vertical light path too.
Source - The Manga Guide to Relativity