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The point is exactly that agreeing on a particular value for one measured quantity causes other quantities to have different measured values, for the values in question of distance, time and velocity (any one of which can be calculated from the other two). The limitation we're stuck with is, at its root, that we have no way to measure time passively. While ...

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I think the purpose of that example is to show how observers from different frames of reference can disagree on what they actually observe, or measure. The example you provided can be solved with a simple galilean transformation. This example is crucial because it shows you how different observers can disagree on the same event, which seems pretty intuitive ...

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Since the train has no relativistic velocity, you will not see any effect such as time dilation, length contraction, lack simultaneity and so on. The importance of this example as a prelude of Special Relativity is that it shows that even Galilean Relativity has some physical quantities which are not absolute. Namely (in this example) the length of the path ...

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From those we can get $f(x(t),t) = x + Ct + D\,$ after integration. How can I interpret this $f(x(t),t)$? The constants of integration $D$ and $C$ are, respectively, the displacement between the origins of the two frames at time $t=0$ and the constant velocity with which the origin of the primed frame moves with respect to the origin of the unprimed ...

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It is possible as soon as one is sure to be very distant from every body (gravitational source) in the universe. This is because all inertial forces behave as gravitational forces. If one is confined to stay in a closed room and observes the motion of bodies therein, he/she cannot decide whether the observed accelerated motion is due to a gravitational field ...

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In a non-inertial frame, since the frame is accelerating the person feels a force. A simple example is this. You just stand on a bathroom scale. While the frame moves, if the scale reading is not changing, then the frame is inertial. Otherwise it's non-inertial. This is how gravity is explained in general relativity. So if the person is aware of the ...

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In a non-inertial frame, observers will see fictitious forces with no reaction pair. For example, in a frame accelerating linearly forward, there appears to be a force acting backwards, and one cannot find the reaction (or source) of this force.

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