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Could someone explain a bit length contraction. According to the special theory of relativity objects that travel at relativistic speeds will decrease in length.

  1. Do the atoms of the object come closer to each other or it is an illusion or something else?

  2. Looking for examples i came across with that of muons. But this actually says that one perspective is time dilation and one other is distance contraction which is not the contraction of the object.

rob
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Special and general relativity postulate that all of us are embedded in a geometric/mathematical structure called spacetime.

Length contraction is not caused by the fact that the atoms are "shortened". It is space itself - containing the atoms - that is being contracted. In the end of the day, atoms of a moving object will appear closer to each other than if the object is not moving. But that is because they are inside space which itself is contracted.

From the perspective of someone located on the earth, the clock of a travelling muon is running slower than clocks on earth. So you would come to the conclusion that it reaches the ground at say 4 microseconds.

From the perspective the muon they are not moving, hence they will say that your clock is running slower. Still, they would agree that they reach the ground after 4 microseconds because the ground is being contracted towards them due to length contraction.

  • Minor comment: the muon lifetime is about two microseconds, so the probability that a muon has not decayed after four seconds is approximately $10^{10^{-6}}$. For comparison the total number of protons in the universe is much smaller than $10^{10^{2}}$. Perhaps change your sample time to "four microseconds," or use an example particle with a longer half-life? – rob Jun 12 '20 at 15:10
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    I did not intend to have any realistic value there, only mentioned a specific number for the sake of comparison. But thank you for the comment, I changed it! – MegAmaNeo1 Jun 12 '20 at 15:11