4 Points
" Here’s a question I’ve seen a lot in comments: OK, I’m accelerating up but then shouldn’t someone on the other side of the globe fall off? No, here’s why: Either watch again from 8:28 or read what I’ve written below… Spacetime is curved - it curves the opposite direction on the other side of the Earth. Neither us on this side of the Earth nor they on the other side are changing our spacial coordinates - we’re not moving up, they’re not moving down - Earth isn’t flying into one of us. BUT we both ARE accelerating. In curved spacetime you have to accelerate just to remain stationary. The traditional definition of acceleration is something changing its velocity. In general relativity you have to embrace a new definition of acceleration: it means deviating from a geodesic - not going on a straight line path through spacetime. Near the Earth a geodesic is a parabola so unless you’re moving in a parabolic arc (like on a zero-g plane) you are accelerating. This definition is the same as the old one so if you’re accelerating in deep space then your velocity is changing. BUT… if you are near a large mass you are in curved spacetime, now acceleration your velocity is changing. You can stay stationary relative to Earth’s surface and still be accelerating. This is because your acceleration should be measured not relative to the Earth’s surface but relative to free-falling objects - they are inertial observers. Imagine this - I’m in deep space and I make horizontal rows and rows of stationary golf balls. Then I hop in my rocket and accelerate up through them. Just think about what that looks like. Now my rocket is back on Earth just sitting there. I freeze time for a sec and make horizontal rows and rows of golf balls up into the atmosphere. Now unfreeze time. What do you see? If you just look at the golf balls and the rocket ship it looks the same as the situation in space where the golf balls were stationary and the rocket was accelerating. Einstein’s point was the golf balls have the better claim as the “stationary” thing since their experience is just like the golf balls in deep space - no forces experienced. The rocket on Earth is just like the rocket in space. It feels a force and hence an acceleration."
1 point