3 ms·
> But the difference is important: when you are falling down, you are in freefall, you don't experience any acceleration in spacetime. It is the surface of the
by tzs 2y ago
> But the difference is important: when you are falling down, you are in freefall, you don't experience any acceleration in spacetime. It is the surface of the earth that is experiencing acceleration towards you.
What if we replace the Earth in that scenario with another person? Alice and Bob are in empty space both in free fall. They each measure the relative velocity of the other and find that it is zero.
Sometime later they again measure relative velocity and now it is non-zero. Each sees that the other is now moving toward them.
Sometime later they measure again, and see that other is moving toward them even faster.
Since they are both in free fall, by your argument neither is experiencing any acceleration. But if no one is experiencing acceleration where do the velocity changes come from?
- dreamcompiler 2y agoThe velocity changes are an illusion because you're looking only at the spatial metric of distance. You have to look at temporal metrics too. The proper "a" here in F=ma is the time derivative of four-velocity or spacetime velocity, and that is constant. It's c (the speed of light). Its time derivative is zero; hence no force and no acceleration. Yes, this gets tricky because you have to care about "the speed of time through time." Welcome to general relativity. The answer here goes into more detail: https://physics.stackexchange.com/questions/102910/why-would-spacetime-curvature-cause-gravity https://physics.stackexchange.com/questions/102910/why-would...
- tsimionescu 2y agoMy original explanation was wrong. The correct explanation is related to the curvature of space-time: there is no acceleration, your speed and trajectory through space-time don't change. When the two people are far away from each other, they are both moving along through space time, having a speed that is, say, 1m/s through space, each towards the other, and (c-1) m/s in the time direction, both oriented towards the future. As they get close enough to each other, spacetime gets curved by their mass-energy, such that the direction of "the future" now points towards their shared center of mass. If we project this curvature back onto the flat plain in which they were originally moving, it will look as if their direction of movement has changed and their speed through space has increased, while their speed through time has decreased.