General Relativity in Software

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General Relativity
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There is no absolute standard for position in the Universe, nor is there an absolute standard for velocity Another way of saying this is that any reference frame is just as valid as any other as long as acceleration does not take place The notions of the center of the Universe and at rest are relative If we measure position or velocity, we must do so with respect to something, such as Earth or the Sun or a space ship coasting through the void
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ACCELERATION IS DIFFERENT!
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Einstein noticed something special about accelerating reference frames compared with those that are not accelerating This difference is apparent if we consider the situation of an observer who is enclosed in a chamber that is completely sealed and opaque Imagine that you are in a space ship in which the windows are covered up and the radar and navigational equipment have been placed on standby There is no way for you to examine the surrounding environment and determine where you are, how fast you are moving, or what direction you are moving However, you can tell whether or not the ship is accelerating This is so because acceleration always produces a force on objects inside the ship When the ship s engines are fired and the vessel gains speed in the forward direction, all the objects in the ship (including your body) are subjected to a force directed backward If the ship s retro rockets are fired so that the ship slows down (decelerates), everything in the ship is subjected to a force directed forward If rockets on the side of the ship are fired so that the ship changes direction without changing its speed, this too is a form of acceleration and will cause sideways forces on everything inside the ship Some examples are illustrated in Fig 16-5 The greater the acceleration, or change in velocity, to which the space ship is subjected, the greater is the force on every object inside it If m is
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No force No acceleration
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Force Acceleration
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Force Acceleration Figure 16-5 When a vessel in deep space is not accelerating, there is no force on the objects inside When the ship accelerates, there is always a force on the objects inside
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the mass of an object in the ship (in kilograms) and a is the acceleration of the ship (in meters per second per second), then the force F (in newtons) is their product: F ma
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This is one of the most well-known formulas in physics This acceleration force occurs even when the ship s windows are covered up, the radar is switched off, and the navigational equipment is placed on standby There is no way the force can be blocked out In this way, Einstein reasoned, it is possible for interstellar travelers to determine whether or not their ship is accelerating Not only this, but they can calculate the magnitude of the acceleration as well as its direction When it comes to acceleration, there are absolute reference frames
THE EQUIVALENCE PRINCIPLE
Imagine that our space ship, instead of accelerating in deep space, is set down on the surface of a planet It might be tail-downward, in which case the force of gravity pulls on the objects inside as if the ship is accelerating in a forward direction It might be nose-downward so that gravity pulls on
Special and General Relativity
the objects inside as if the ship is decelerating It could be oriented some other way so that the force of gravity pulls on the objects inside as if the ship is changing course in a lateral direction Acceleration can consist of a change in speed, a change in direction, or both If the windows are kept covered, the radar is shut off, and the navigational aids are placed on standby, how can passengers in such a vessel tell whether the force is caused by gravitation or by acceleration Einstein s answer: They can t tell In every respect, acceleration force manifests itself in precisely the same way as gravitational force From this notion came the equivalence principle, also known as Einstein s principle of equivalence The so-called acceleration force is exactly the same as gravitation Einstein reasoned that the two forces act in an identical way on everything, from human bodies to subatomic particles and from light rays to the very fabric of space-time This is the cornerstone of the theory of general relativity
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