Can someone explain to me how those who believe relativity also believe that the Earth revovles around the sun. I thought that relativity claims that a moving body considers itself at rest. If so, we on Earth should consider ourselves at rest, such that the sun is revolving around us?
PF Mentor: I don't get your answer. Are we on the moving Earth considered still, such that the sun revolves around us?
If not, then we are moving, and we should be able to measure the so called ether wind.
PF Mentor: I don't get your answer. Are we on the moving Earth considered still, such that the sun revolves around us?
If not, then we are moving, and we should be able to measure the so called ether wind.
No, although the way it is usually presented that is probably an unfortunate impression that many students receive. General Relativity says that you can use any coordinate system you like and describes how to transform between them. Choosing a particular coordinate system is done in order to simplify the equations, but it is possible to use any coordinate system you wish. You can use a coordinate system where the Earth is at rest, but the equations will be messy.I thought that relativity claims that a moving body considers itself at rest.
Here you're talking about the http://www.aei.mpg.de/einsteinOnline/en/spotlights/equivalence_principle/index.html [Broken], but one thing to note is that in GR the equivalence principle only works in a local sense--it basically says that if a freefalling observer defines a coordinate system which only extends to a very small spacetime region around himself, then the laws of physics in this coordinate system will be arbitrarily close to the laws seen by an inertial observer in SR. For a large-scale coordinate system like one containing both the Earth and Sun, you wouldn't have this sort of equivalence between the measurements of an observer in curved spacetime and those of one in uncurved SR spacetime (although an orbiting observer is in freefall so their local observations in a small region of space and during a small interval of time would be like those of an SR observer).The answer, I thought, was that we don't consider ourselves moving. This is the whole spaceship thing with the beam going straight up and down for the guy on the ship.
A body moving in straight line, with constant speed, can consider itself at rest and derive the same laws of physics. The Earth moving around the sun does not move in a straight line nor does it have constant speed.Can someone explain to me how those who believe relativity also believe that the Earth revovles around the sun. I thought that relativity claims that a moving body considers itself at rest. If so, we on Earth should consider ourselves at rest, such that the sun is revolving around us?
Which particular measurements are you thinking of ?I still don't get one thing. If we consider ourselves as revolving around the sun, such that we are moving, why will our measurements of light be as if we are not moving.
nathan heiney said:I still don't get one thing. If we consider ourselves as revolving around the sun, such that we are moving, why will our measurements of light be as if we are not moving.
Perhaps because are measurements are "close enough" to satisfying the definition of locally inertial measurements? (you didn't respond to my post #9, can I take it you already understand that observers in freefall can be considered to be locally inertial in GR?) Of course if we're making measurements on the surface of the Earth we aren't in freefall so it's not a perfect case of the equivalence principle, but the G-forces are pretty small (I imagine an observer accelerating at 1G in flat spacetime would have a hard time noticing any deviations of the path of light beams), and the Earth itself is in freefall around the Sun. Certainly the equivalence principle would say that if someone on board the space station was doing experiments, their observed results should match those predicted by SR, since the space station is in freefall around the Earth.I still don't get one thing. If we consider ourselves as revolving around the sun, such that we are moving, why will our measurements of light be as if we are not moving.
Its speed never changes in inertial frames, but in non-inertial frames the speed can vary...I think nathan's question was about why our results seem to match those of inertial frames if we aren't actually moving at constant speed and direction in flat spacetime.Because light is constant, it's speed never changes... If you're measuring light it will always appear as if you are stationary, because there's no change in light's velocity to tell you otherwise...
This is potentially a little confusing, because the Earth moving around the Sun is moving in the closest possible approximation to a straight line in curved spacetime, no? The issue is that in curved spacetime there are no non-local frames that can be considered "inertial" ones, so no matter what possible path you take, if you make non-local measurements using a coordinate system where you're at rest, you'll find that the laws of physics do not match those of an inertial observer in SR.A body moving in straight line, with constant speed, can consider itself at rest and derive the same laws of physics. The Earth moving around the sun does not move in a straight line nor does it have constant speed.
Can you briefly define a non inertial frame please?Its speed never changes in inertial frames, but in non-inertial frames the speed can vary...I think nathan's question was about why our results seem to match those of inertial frames if we aren't actually moving at constant speed and direction in flat spacetime.
As dx said, one way of defining it would be a coordinate system where objects with no forces acting on them move at constant coordinate velocity. Another way might be to say that if you have an accelerometer moving at constant coordinate velocity, it will not measure any G-forces (in a non-inertial frame this would not be true for accelerometers at arbitrary positions--an object with nonzero proper acceleration as measured by accelerometers can have zero coordinate acceleration in non-inertial frames).Can you briefly define a non inertial frame please?