I am a bit confused about the implications of length contractions;
For example, in the muon decay problem, we assume that the distance between the muon and the earth is contracted only in the frame of reference of the muon (I've heard justification saying this is because it is Earth's atmosphere) but suppose there were no atmosphere then in the reference frame of Earth shouldn't the length between them also be contracted?
What I don't get is if one object is moving at a speed relative to another object, shouldn't this movement affect the distance between them in the reference frames of both of them, since their movement is merely relative?
Answer
Don't confuse time dilation and length contraction,(even if length contraction is a consequence of time dilation) because there is no length contraction for the distance between two reference frames. The length (or distance) must be found in one reference frame, and the observer must be in another reference frame, he may not be part of the reference frame of the distance.
By consequence, it is not the distance between muon and Earth which is contracted. It is the distance between the starting point A of the muon and Earth (if we suppose that the muon is traveling from A to Earth).
From the Earth frame the distance A-Earth is at its largest. For the muon frame, the distance A-Earth is contracting according to its relative velocity.
The example of David Z is the opposite example: There is a distance in the muons' frame (between two muons which are belonging to the same frame) which is observed from the Earth frame.
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