If I want to solve a Millenium Problem, I’m (likely) going to need to think like Einstein. Maybe I already do. They say there is a fine line between madness and genius.
But let’s learn what we can from Einstein himself. Einstein developed special relativity during his so-called Wunderjahr (“wonder year”). He settled 4 major questions in math/physics all while he was 26. (See, I’m already late.) Special relativity is perhaps the most famous (with general relativity not coming until later).* It also makes a very nice example of the power of thought experiments. So let’s start here.
Suppose you are on a very fast subway/train/bus (like, presumably, the one pictured). But let’s imagine that there are no windows. How can you tell whether the bus is really moving?
There’s actually two of us on the bus, say the two protagonists of a Disney movie/musical: Beauty tosses the Beast a palantir. The Beast catches it. The Beast tosses it back to Beauty. What happens?
As frequently done in physics, we make some simplifying assumptions. The palantir is a point mass (i.e. it has mass, but takes up no space, existing only at a specific point, and we forget about such pesky details as rotational inertia, or its quantum analog, “spin”). Indeed, Beauty and the Beast are also point masses (this is why we have been referring to them using the pronoun it). We also assume that Beauty and the Beast each tosses the ball with the same force (gender equality, or is it something more?). Beauty stands toward the head of the bus, and the Beast towards its foot. So, what happens?
Well, relative to the inertial reference frame of the bus, the ball moves at the same speed in both legs of its journey, just with exactly opposite direction. The amount of time taken is exactly the same. (Gosh, physics is so weird. O:)
I’m getting tired. Let’s leave the next step for Part II.
* Yes, the explanation of blackbody radiation was also extremely important, and effectively launched the field of quantum mechanics (of which Einstein was no fan, look up “Einstein,” “dice”). More on this in the distant, distant future (as in, after the supercomputer figures out the question of life, the universe, and everything, for which we–in this universe–already know the answer… or so they say).
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