|MadSci Network: Physics|
Dear Ray, It seems that this question is a follow-up to a previous question and response. Unfortunately, I didn’t write that response, and I’m afraid I couldn’t find it in the MadSci Archives, so I’ll just have to do my best to answer what I think you’re asking. I apologize if I repeat some of the things stated in your first response, but I think for completeness sake, I’ll start from the beginning. In formulating his Theory of Special Relativity, Einstein developed two postulates… 1. The Relativity Postulate – The laws of physics are the same in every inertial reference frame. 2. The Speed of Light Postulate – The speed of light in a vacuum, measured in any inertial reference frame, always has the same value of c (3.00E8m/s), no matter how fast the source of light and the observer are moving relative to each other.* You can think of a reference frame as what is moving along with you, that is, what is at rest in your perspective. So if you are in a rocket ship, what is at rest with respect to that rocket is part of your reference frame. Anything moving with respect to you is in another reference frame. In Special Relativity, an inertial reference frame is one that is not accelerating, that is one that is moving at a constant velocity. The first postulate states that all the laws of physics are the same in all inertial reference frames. What is implied is that it doesn’t matter how the frames are moving relative to each other, no matter how fast, as long as they are not accelerating. This means that there is no way to determine how fast you are moving without looking outside your frame. Nothing you can do inside your frame is affected by your motion. Or, another way of putting it is that there is nothing wrong with thinking that you are at rest and the rest of the universe is moving. (Nothing wrong in the physics, that is, psychologically is another matter.) One issue that these postulates do not address is acceleration. This is dealt with in Einstein’s Equivalency Principle. Einstein made the assumption that gravity and acceleration were equivalent because of gravitational experiments that had been done, and his thoughts about what would happen in an accelerating frame away from gravity. First, Einstein knew that according to all experiments, in a uniform gravitational field, all objects seem to fall with the same acceleration, regardless of their mass or chemical composition. (This was noticed by Galileo Galilei and demonstrated in his experiment, which might be apocryphal, of dropping two different masses off the Leaning Tower of Pisa.) This is different from the affects of every other force that we know of. Gravity seems to affect every object of matter in exactly the same way. Near the Earth’s surface, this acceleration is 9.8m/s/s. Second, Einstein wondered what would happen to objects in an accelerating reference frame if that frame was not within a gravitational field. Imagine that you are in a rocket and the rocket is accelerating upwards with an acceleration of 9.8m/s/s. In order for you to accelerate along with the rocket, the floor would have to push on you upwards with a force equal to your weight. You would stand on the floor and feel like you were pushing back on the floor with a force equal to your weight. If you were holding an apple, you would have to push upwards on it with a force equal to its weight to keep it accelerating along with you and the rocket. The instant you let it go, it would stop accelerating along with you and it would start drifting to the bottom of the rocket. The rocket would keep accelerating upwards at 9.8m/s/s and so you would think that the apple was falling downward at 9.8m/s/s, and this is totally independent of the mass of the apple, since it is really the acceleration of the rocket which is producing the apparent acceleration of the apple. Any object released within the rocket would appear to accelerate downward with the same acceleration of 9.8m/s/s. It is the similarity of these two situations, a frame in a uniform gravitational field and an accelerating frame outside of any gravitational field, that lead Einstein to the Equivalence Principle, that is, to consider them equivalent. So what would be an inertial reference frame in a gravitational field? If a stationary frame in a gravitational field is like an accelerating one outside of a gravitational field, then perhaps one in freefall in gravity would be like a non-accelerating field away from gravity. A frame in freefall is accelerating “downward” completely under the influence of the gravitational field. Near the Earth’s surface, that would be a frame that was accelerating downward at 9.8m/s/s. In such a frame, since all objects are accelerating downward with the same acceleration, there would be no relative acceleration between objects within the frame, and so it would appear exactly like an inertial frame in special relativity, non-accelerating and away from any gravitational field. Einstein then extended his first Special Relativity postulate to include inertial reference frames within gravitational fields, and that what happens in a frame which is stationary within a gravitational field would be the same as what happens in an accelerating frame without any gravity. Now I think I’m in a position to respond to your question. (Phew!) Light in a uniformly moving rocket is not bent. An observer within the rocket will say that the light moves along a straight line, that’s simple enough. An observer will say that the light also follows a straight line, although that line will include the motion of the rocket. (Please take a look at this website http://www.gpc.edu/~jguinn/MadSci/EquivPrinc.pdf where I have made a diagram to help with this explanation.) Imagine that the rocket moves from Point 1 to Point 2, an observer within the rocket would say that the light went straight across the rocket. An observer outside the rocket would also say that the light moved in a straight line, but that it moved a longer distance since it moved not only “vertically” but “horizontally” in our diagram. (This is a diagram that is commonly used to explain the time dilation within moving frames. If the rocket was accelerating, the light would still appear to move in a straight line for the external observer, but the internal observer would see the path deviate from a straight line. This is completely consistent with what we have stated above about inertial frames. An accelerating rocket is not an inertial frame in special relativity, and so the laws of physics, as stated for inertial frames, do not hold. According to the Equivalence Principle, this must be the same thing that happens when light moves in a gravitational field. This was experimentally verified first by observing how star light was bent as it passed near the surface of the sun during a solar eclipse. The eclipse was not necessary for the bending, just for it to be observed. Since the sun is so bright, stars are usually not visible when apparently near the sun’s surface. Well, Ray, I hope somewhere in there I answered the question you wanted answered. If not, please ask again and perhaps I’ll get a chance to try again. Thank you for your interest. Sincerely, Jim Guinn Georgia Perimeter College * J. D. Cutnell and K. W. Johnson, “Physics,” 6th Ed., John Wiley & Sons, Inc., 2004.
Try the links in the MadSci Library for more information on Physics.