Simple Nature - Light and Matter

are two possible explanations for this. One is that the aliens havetaken you to some other planet, maybe Mars, where the strength ofgravity is a third of what we have on earth. The other is that yourkeychain didn’t really accelerate at all: you’re still inside the flyingsaucer, which is accelerating at a third of a gee, so that it was reallythe deck that accelerated up and hit the keys.There is absolutely no way to tell which of these two scenarios isactually the case — unless you happen to have a chunk of FloatyStuffin your other pocket. If you release the FloatyStuff and it hoversabove the deck, then you’re on another planet and experiencinggenuine gravity; your keychain responded to the gravity, but theFloatyStuff didn’t. But if you release the FloatyStuff and see it hitthe deck, then the flying saucer is accelerating through outer space.The nonexistence of FloatyStuff in our universe is called theequivalence principle. If the equivalence principle holds, then an acceleration(such as the acceleration of the flying saucer) is alwaysequivalent to a gravitational field, and no observation can ever tellthe difference without reference to something external. (And supposeyou did have some external reference point — how would youknow whether it was accelerating?)The artificial horizon example 25The pilot of an airplane cannot always easily tell which way is up.The horizon may not be level simply because the ground has anactual slope, and in any case the horizon may not be visible if theweather is foggy. One might imagine that the problem could besolved simply by hanging a pendulum and observing which wayit pointed, but by the equivalence principle the pendulum cannottell the difference between a gravitational field and an accelerationof the aircraft relative to the ground — nor can any otheraccelerometer, such as the pilot’s inner ear. For example, whenthe plane is turning to the right, accelerometers will be tricked intobelieving that “down” is down and to the left. To get around thisproblem, airplanes use a device called an artificial horizon, whichis essentially a gyroscope. The gyroscope has to be initializedwhen the plane is known to be oriented in a horizontal plane. Nogyroscope is perfect, so over time it will drift. For this reason theinstrument also contains an accelerometer, and the gyroscope isalways forced into agreement with the accelerometer’s averageoutput over the preceding several minutes. If the plane is flown incircles for several minutes, the artificial horizon will be fooled intoindicating that the wrong direction is vertical.g / An artificial horizon.Gravitational Doppler shifts and time dilationAn interesting application of the equivalence principle is the explanationof gravitational time dilation. As described on p. 384,experiments show that a clock at the top of a mountain runs fasterSection 7.4 ⋆ General Relativity 427