Setting something up at the back of a science class today, ~11 year olds being introduced to the idea that light travels at a finite speed. Somebody asked "but why *that* speed?". The following happened telepathically in under a second after that:
Me: Glances up and smirks slightly
Teacher: Looks at me, "Don't you dare, I need to teach them about angles of reflection and we only have half an hour."
Me: "I know, but first principles..."
Teacher: "Maybe if you're good, at the end of term."
@_thegeoff Well, I'm intrigued. I had no idea there was an answer to that question.
I assume you mean you can explain it in terms of some other “fundamental” constants but my understanding is that we have no idea why those constants have their values beyond handwavey explanations like we exist therefore we must be in a universe with constants which allow life to exist.
@edavies Yeah, it's self referential to an extent. Ultimately the idea is that space and time are mathematically the same thing, 3 dimensions of space and one of time.
In 2D (X & Y) you can measure the distance between two points with Pythagoras: distance=sqrt(x^2+y^2). This is fairly easy to extend to 3D as well.
But add time, which it turns out needs to be done using imaginary numbers, and it gets more complex (sorry, yes, pun partially intended)....
@edavies ...but when we do the Pythagoras thing in 4D where one of the dimensions is imaginary, we're not strictly measuring a distance anymore, it's called a "spacetime interval". For example, the "interval" between you having dinner in Inverness in 2009 and watching a film in San Diego in 2025. It's not a distance, it's not a time, it's both.
But the weird thing is that for anything travelling at the speed of light, the interval between any two points in spacetime is always zero.
posted too soon... Clockwork Rocket takes place in a world where spacetime interval is x^2+y^2+z^2+t^2 and Dichronauts takes place in a world with spacetime interval of x^2+y^2-z^2-t^2
@robryk @edavies Whaaaa....? So effectively two spacelike dimensions and two timelike ones? I need to read this just to find an excuse not to try and work out whatever the hell that looks like.