22.1 Length Contraction
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Jordan Tucker
@Sander Bouwhuis. No, length contraction is not a side effect of time asynchrony. Consider we know the length of a train when at rest, and we know its velocity when in motion, so we can calculate its contracted length. We place two clocks along the track so that the distance between them is equal to the contracted length of the train, and we synchronize those clocks. As the train passes, the clock furthest in the direction of the train records the time when the front of the train reaches it, while the other clock records the time when the back of the train reaches it. Both clocks will record the same time. Since those clocks are synchronized, the length of the train must be contracted when in motion relative to the clocks.
Of course, those at rest relative to the train will say that the clocks are in motion and out of sync. So it's all relative.
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Roelof Vuurboom
From George's perspective Gracie seconds are longer so Gracies meters are longer and if Gracie's meters are longer fewer meters will fit in a particular physical distance (in this case the train) so Gracie will measure the train to be shorter.
Roelof Vuurboom
From George's perspective Gracie seconds are longer so Gracies meters are longer and if Gracie's meters are longer fewer meters will fit in a particular physical distance (in this case the train) so Gracie will measure the train to be shorter. Again the metric is changing (how much physical distance is actually in a metre) due to the definition a meter: light covers a constant amount of distance in a given time. If the time unit changes (in this case a second becomes longer) light will cover more physical distance in that time unit and so the metre becomes longer. With a longer metre you will measure less metres for any given physical distance. The physical length hasn't change just the metric for measuring the length has.
Amos Ferrero
// Roelof said: "From George’s perspective Gracie seconds are longer so Gracies meters are longer" //
From George’s perspective Gracie seconds are longer than George's clock seconds, that's true, but that not make Gracie meters longer. Gracies meters are shorter from George perpective. Both measure the same time dilation and length contraction in the other frame of reference.
// Roelof said:"f the time unit changes (in this case a second becomes longer) light will cover more physical distance in that time unit and so the metre becomes longer" //
You are giving a strange definition of a meter, the distance traveled by light in Geroge reference frame each second of Gracies reference frame, that has no sense.
Luke Gurbin
Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame.
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