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Course Queries Syllabus Queries 2 years ago
Posted on 16 Aug 2022, this text provides information on Syllabus Queries related to Course Queries. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.
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With the rapidity ϕϕ defined so that vc=tanhϕvc=tanhϕ, say you have 3 parallel moving reference frames SS, S′S′ and S′′S″ with a constant but different velocity/rapidity.
If the rapidity of S′S′ in relation to SS is ϕ1ϕ1,and the rapidity of S′′S″ in relation to S′S′ is ϕ2ϕ2,then the rapidity of S′′S″ in relation to SS is ϕ1+ϕ2ϕ1+ϕ2
Alright here's a very crude heuristic(definitely not a f="https://forum.tuteehub.com/tag/proof">proof) on why(without using velocity composition) rapidity is additive.
Impose these two constraints:
1) the constancy of speed of light in all frames. This means that the rapidity of light tanhϕc=1tanhϕc=1 is the same in all frames of reference.
Consider this case:
You observe a frame of reference S′S′ moving with tanhϕ1=vtanhϕ1=v with respect to SS followed by a light beam with tanhϕc=1tanhϕc=1. we know the rapidity of light in the S′S′ frame is the same as in SS. Given this fact we'd like to find out what is the relation f(ϕ1,ϕc)f(ϕ1,ϕc) between the old and new rapidities in the new frame S′S′ such that:
2) The second constraint is that the rapidity of an object at rest is zero. So if there's an object moving with velocity vv in REPLY 0 views 0 likes 0 shares Facebook Twitter Linked In WhatsApp
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