This is because, in GR, what changes is the way we measure the lengths of things, both in space and in time. If you want the observer to be stationary with respect to the coordinates, you need to change coordinates. This observer is moving with respect to the coordinate r as well as through time. The thing is, in GR this is not the case: you can actually calculate that such an observer has a positive acceleration, going upward.Īn observer which feels stationary is one which does not perceive any acceleration: a free-falling observer. One would think, a stationary observer is one whose spatial (r, θ, φ) coordinates are fixed while the temporal coordinate t evolves.
NON CURVED SPACE PLUS
The coordinates we usually have for it are the spherical ones: radius with respect to the centre (r), latitude (θ), longitude(φ), plus time (t). Maybe this will help: consider a region on the surface of the earth. What happens when there’s no path to curve and no force to start the motion?īonus question: And what‘s up with gravitons? What are force-carrying particles doing in a discussion about a phenomenon that’s not a force? Why was Einstein trying to combine the “force” of gravity with the EM and nuclear forces when he had already established that gravity was geometry, not a force? Suppose it’s just you and the Earth one meter apart in an otherwise empty Universe, completely motionless relative to each other. EVERYTHING is moving and so you follow a straight line that passes through curved space. both you and the Earth are orbiting the Sun, and all that’s orbiting Sagittarius A-star, and so on. You know that when the trap door opens, you’ll just hang there in midair.Įxcept of course you are moving.
You’re not following a straight for the Earth to curve. But you’re not afraid because you’re stationary relative to the Earth. You stand on the trap door with a noose around your neck and the hangman’s hand on the lever. You’re a convicted murderer, sentenced to hang by the neck until dead. But if you’re stationary relative to the Earth, why would you begin to fall in the first place if there’s no actual force to create an attraction and no path to take you thru curved space? The deflection of an asteroid as it passes near Earth gives the illusion of a force it’s traveling in a straight line, it’s just that the straight line itself passes thru curved space. Gravity isn’t a force, it’s the result of the curved geometry of space-time. That’s the best I can do to put the question into a title.