general_relativity

# general_relativity - previous home next Remarks on General...

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previous home next Remarks on General Relativity Michael Fowler University of Virginia Einstein’s Parable In Einstein’s little book Relativity: the Special and the General Theory , he introduces general relativity with a parable. He imagines going into deep space, far away from gravitational fields, where any body moving at steady speed in a straight line will continue in that state for a very long time. He imagines building a space station out there—in his words, “a spacious chest resembling a room with an observer inside who is equipped with apparatus.” Einstein points out that there will be no gravity, the observer will tend to float around inside the room. But now a rope is attached to a hook in the middle of the lid of this “chest” and an unspecified “being” pulls on the rope with a constant force. The chest and its contents, including the observer, accelerate “upwards” at a constant rate. How does all this look to the man in the room? He finds himself moving towards what is now the “floor” and needs to use his leg muscles to stand. If he releases anything, it accelerates towards the floor, and in fact all bodies accelerate at the same rate. If he were a normal human being, he would assume the room to be in a gravitational field, and might wonder why the room itself didn’t fall. Just then he would discover the hook and rope, and conclude that the room was suspended by the rope. Einstein asks: should we just smile at this misguided soul? His answer is no—the observer in the chest’s point of view is just as valid as an outsider’s. In other words, being inside the (from an outside perspective) uniformly accelerating room is physically equivalent to being in a uniform gravitational field . This is the basic postulate of general relativity. Special relativity said that all inertial frames were equivalent. General relativity extends this to accelerating frames, and states their equivalence to frames in which there is a gravitational field. This is called the Equivalence Principle . The acceleration could also be used to cancel an existing gravitational field—for example, inside a freely falling elevator passengers are weightless, conditions are equivalent to those in the unaccelerated space station in outer space. It is important to realize that this equivalence between a gravitational field and acceleration is only possible because the gravitational mass is exactly equal to the inertial mass. There is no way to cancel out electric fields, for example, by going to an accelerated frame, since many different charge to mass ratios are possible. As physics has developed, the concept of fields has been very valuable in understanding how bodies

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