| The Geometry of Space-Time: A Teaching Package |
| >>The General Theory of Relativity (GR): The Key Ideas |
| >>The Bending of Light: Proof of GR? |
| >>Non-Euclidean Geometry: Space, but not as we know it |
| >>Exotic Geometry: A look at the Universe around us |
| Einstein was a believer in length and time contraction. He sought to make sense of all the hints that were shown by various experiments but was impended by a mental block. By disregarding absolute space, Einstein was able to explain the problem with the Michelson-Morley experiment. He asserted that you can never have an absolute velocity, that you can only have a velocity relative to something else. Like a car on the road can have a velocity of 30mph relative to an external, motionless observer but someone that is in the car will see the car as motionless and that it is the road that is moving at 30mph relative to them. This concludes that there is no ��being at rest in absolute space��. This further implies that you cannot measure the Earth��s motion through absolute space and that that is the reason the Michelson-Morley experiment turned out like it did. For neither Earth, nor car, nor anything else is there any standard of absolute motion; motion is purely ��relative��. By rejecting absolute space, Einstein also rejected the notion that everyone, regardless of his or her motion, must agree on the length, width and height of some car or a table or any other object. Einstein insisted that length, width and height also ��relative�� concepts. They depend on the relative motion of the object being measured and the person doing the measuring. By rejecting absolute time, Einstein also rejected the notion that everyone, regardless of his or her motion, must experience the flow of time in the same manner. Time is also ��relative��. Everyone traveling in their own way must experience a different time flow than others, traveling differently. These statements describe a new Universe, a Universe that goes against our own common sense and everyday notions of space and time. In this Universe, Newton��s laws of physics are cut at the foundations and we must now try to understand that it is possible for time to slow and for distances to become shorter depending on one��s motion relative to that being measured. This first principle asserts that the Michelson-Morley experiment was indeed correct and that no matter how accurate future experiments may become, the experiments will always show that there the universal speed of light,c: ?The principle of relativity: Whatever might be their nature, the laws of physics must treat all states of motion on an equal footing. The first postulate has some very strange consequences on the laws of physics. It states that the speed of light is constant, no matter how the observer is traveling. If you are traveling in a car and you shine a torch toward an observer who is standing on the road in front of you (i.e. at rest with respect to the floor and soon to be at rest for good if they do not get out the way of the car!), they will not measure the light from your torch as having c+v (where c is the speed of light and v is the speed of the car), they will measure it as . Moreover, if the car is reversing at the same speed, v the observer will not measure the light to be traveling at c-v; they will still measure a speed of c. Now think about it. If you throw a ball from a moving car it will have v+v' (where v' is the speed you throw the ball with) so why does it not work with light? A consequence of light having this constant value is that things around it have to change to help it maintain this value. The things that change are things we take for granted as being constant; space and time. Einstein��s theory demands that Newton��s idea of absolute space and time must be abandoned. Space can be warped and time can be distorted, length and time can be contracted. Another consequence is that nothing can travel faster than the speed of light; it is the upper-most limit for speed in the Universe. The second postulate is a basic assumption that is accepted in all sciences. It states that the effect of a force on an object is the same independent of what causes the force and also of where the object is or what its speed is. |
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| Relative Space and Time and Absolute Speed of Light |
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| Einstein��s new description consists of two fundamental principles: ?The principle of the absoluteness of the speed of light: Whatever might be their nature, space and time must be so constituted as to make the speed of light absolutely the same in all direction, and absolutely independent of the motion of the person who measures it. |