The tension between classical and relativistic mechanics

Posted on Thu 09 January 2020 in Ramblings

When I was considering writing my post on time dilation, I expected precisely zero feedback... just on the basis that nobody would read it. I'm really pleased with the feedback I actually got, and you've all spurred me to write another post on the topic. So today, I'm going to give you a brief glimpse into what caused all this ruckus: Einstein's general theory of relativity.

If you remember, Einstein first came up with the special theory of relativity in 1905, and it took another ten years to get to the general theory of relativity. This alone should show you that the jump from the special theory to the general theory was a major leap - but let's step back and see what this is all about.

Our very good childhood friend, Isaac Newton, published his Prinicpia in SIXTEEN EIGHTY SEVEN, which is... like... aaaaages ago. With this, he laid the foundation of "classical mechanics", which are the physical concepts and mathematical methods that describe the motion of objects under a variety of forces.

Classical mechanics worked well - really well. There were tweaks here and there there over the ~centuries~, but overall, classical (or "Newtonian") physics had things pretty much nailed... That is, until we started thinking about things that were really heavy, really small, or really fast... at that point, classical mechanics started to fray at the edges.

One of the earliest recognised failures of classical mechanics was the "precession of the perihelion of Mercury". Don't worry what those words mean; basically, Mercury's orbit didn't behave quite the way that classical mechanics said it should. The effect is suuuuper tiny: classical mechanics says that Mercury's orbit should change by 5557 arcseconds per century, but in reality it changes by 5600 arcseconds per century... a difference of 43 arcseconds.

How big is 43 arcseconds? It's about two-thirds of one degree. If you stand on a flat field and imagine a soccer ball on the ground, a kilometer away, the angle drawn from the ground under your feet to the top of that soccer ball is bigger than the 43 arcsecond discrepancy.

... I'm gonna say that again in case you missed it: that was per century. Less than a kilometre-away-soccer-ball every hundred years. Yikes.

Where did this discrepancy come from? It all started from a very fair assumpiton of Isaac Newton's: he perched his calculations on the basis that things were consistent. Well, the universe Does Not Roll That Way™. Space warps; time stretches; light falls into gravity wells. But because these effects aren't really visible in our day-to-day life, it took almost two hundred years - and the genius of Einstein - before classical mechanics was overturned by the general theory of relativity in 1915.

Okay this has become a little long and rambling now, so I'm going to take a break and come back to the topic next week! :)