The Einstein Lift Experiments in .NET

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The Einstein Lift Experiments
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The Einstein lift experiments are a simple set of thought experiments that can be used to describe the equivalence principle. In Einstein s day, he used lifts or elevators to illustrate his points. We will do so in a more modern sense using spaceships. In all of these experiments, we consider scenarios with no rotation. We begin by considering a spaceship that is deep in interstellar space far from any source of gravitational elds. Furthermore, the spaceship is designed such that the astronaut inside has no way of communication with the outside universe;
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in particular, there are no windows in the spacecraft so he cannot look outside to determine anything about his state of motion or location in the universe. When reading through these experiments, remember Newton s rst law: A particle at rest or in uniform motion remains at rest or in uniform motion unless acted upon by an external force. Case 1. In the rst experiment, consider a spaceship that is not accelerating but is instead moving uniformly through space with respect to an inertial observer. The astronaut is holding a small ball, which he subsequently releases. What he will nd is that, in accordance with Newton s rst law, the ball simply remains at rest with respect to the astronaut where he released it. (see Fig. 6-1) Case 2. We now consider an accelerating ship. The spaceship is still located deep in space far from any planets, stars, or other source of gravitational eld.
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Fig. 6-1. Art the astronaut in an unaccelerated spaceship in deep space, far from any gravitational elds. He releases a ball in front of him, and it remains there at rest with respect to the astronaut.
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Fig. 6-2. An accelerating spaceship. This time when the astronaut releases the ball, it
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falls straight to the oor as he sees it.
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But this time, the spaceship is accelerating with a constant acceleration a. For de niteness, we take the acceleration to be identical to the acceleration due to gravity at the surface of the earth; i.e., a = g = 9.81 m/s2 . If the astronaut releases the ball in this situation, he will nd that from his perspective, it falls straight to the oor. (see Fig. 6-2) Case 3. Turning to a third scenario, we now imagine a spaceship on earth that sits comfortably on the launchpad. The dimensions of the spacecraft are such that the tidal effects of gravity cannot be observed and that the rotational motion of the earth has no effect. We all know what happens when the astronaut releases the ball in this situation; it falls straight to the oor, just like it did in the previous situation. (see Fig. 6-3) The situation inside the spacecraft on the launchpad is the same as the spacecraft with acceleration g in deep space.
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Fig. 6-3. Spaceship on the launchpad, resting on the surface of the earth. Drop a ball,
and it falls straight to the oor.
Case 4. Finally, we consider one more situation: a spacecraft in free fall on earth. Let s say that the spaceship is in a mineshaft falling straight down. In this case, when the astronaut releases the ball, he will nd a situation to that he encountered deep in space when not accelerating. When he releases the ball, it remains stationary where he released it. (see Fig. 6-4) The point of these experiments is the following: In a region of spacetime that is small enough so that the tidal effects of a gravitational eld cannot be observed, there are no experiments that can distinguish between a frame of reference that is in free fall in a gravitational eld and one that is moving uniformly through space when no gravitational eld is present. More speci cally, Cases 2 and 3 are indistinguishable to the astronaut. Assuming he cannot look outside, he can in no way differentiate whether or not he is accelerating deep in space with acceleration g or if he is stationary on the surface of the earth. This implies that any frame that is accelerated in special relativity is indistinguishable from one in a gravitational eld, provided that the region of spacetime used to make measurements is small enough; that is, tidal forces cannot be observed. Cases 1 and 4 illustrate that there is no experiment that can distinguish uniform motion through space in the absence of a gravitational eld from free fall within a gravitational eld. Again, to the astronaut provided that his environment is completely sealed these situations seem identical. Cases 1 and 4 are illustrations of the weak equivalence principle.
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