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Let's consider a simple experiment in which a stone tied to a string is moving in a uniform circular motion in a horizontal plane. We can analyze this experiment from inertial and non-inertial frames. An observer in an inertial frame sees the stone having a radial acceleration and concludes that there must be a radial force causing it. He observes the taut ...

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In an inertial frame the only force that causes a particle to move in a circular motion is the centripetal force. The reason that a particle does not "fall" into the center is because it has some tangential velocity, so it moves away from the center tangentially as it is falling towards it. The relationship between the centripetal acceleration and tangential ...

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Law of Special Relativity: The speed of light remains constant for all observers no matter their state of motions. $L$ and therefore $t$ would therefore remain constant irrelevant to your state of motion.

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First off, you state If the time it took light is, $t=\frac{L}{c}$ then I know that the train was stationary. I must ask, stationary with respect to what? It may not seem so to you but answering this question with most likely highlight the error in your reasoning/understanding of the principles involved. Equivalently, a correct answer to this ...

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An intuitive way to see why this method would not work (or any other method inside a truly sealed train) is that the speed of the train is always relative to something else. There is nothing stopping me from describing the situation as rails moving under a stationary train at a certain speed. Now, you propose to measure the speed at which the rails move ...

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Update and note: In the answer below, I do assume the OP and reader are aware of the Galilean relativity of motion but wonder why the invariance of the speed of light cannot be used to find an absolute rest frame. If this isn't he case, then Rod Vance's excellent answer is more appropriate. I switch on the torch and measure the amount of time it takes ...

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By your assumptions, the train will always be stationary. Light will always take time $\frac{L}{c}$ to traverse the distance simply because $c$ is a constant. Additionally, even if your train was moving at $c$, it would still not matter because you are still at zero velocity with respect to the coach. Relativistic measurements would come into picture if you ...

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The fundamental postulate of special relativity, indeed of Galilean relativity, is that there is no experiment that determine the state of motion of any inertial frame relative to the outside world unless the measurement uses data gleaned from outside the frame. Read Galileo's wonderful and very famous allegory of Salviati's Ship for a poetic and rock ...

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That's because the equation of motion is a 2nd order differential equation. F=ma. If you integrate it to get r(t), you get two arbitrary integration constants. So you have two degrees of freedom, making the absolute r(t) and the absolute v(t) invariant when adding a constant. This holds with relativistic equations of motion, and even relativistic QM. As ...

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