Relative velocity of third object

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Discussion Overview

The discussion revolves around the concept of relative velocity in the context of special relativity, specifically focusing on the relative velocities of three objects (A, B, and C) moving at significant fractions of the speed of light. Participants explore the implications of these velocities on measurements of distance and length contraction, as well as the application of the relativistic velocity addition formula.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents a scenario where A and B have a relative velocity of 0.9c, and B and C also have a relative velocity of 0.9c, questioning the relative velocity between A and C.
  • Several participants suggest using the relativistic formula for addition of velocities to find the relative velocity between A and C, with one participant calculating an approximate value of 0.9944c.
  • There is a discussion on how to justify the calculated relative velocity with respect to relative displacement after one second, leading to questions about the positions of B and C in A's frame after one second.
  • Participants discuss the implications of length contraction, questioning whether it should be considered in the context of the rods carried by B and C.
  • One participant explains that all segments of a rod will be uniformly shortened due to length contraction, while another participant raises a question about whether the shortening occurs symmetrically from the center of the rod.
  • A hypothetical scenario is introduced where B, C, and D travel together with a rod, prompting questions about whether the ends of the rod still touch B and D as observed by A after they return at a high velocity.
  • There is a discussion about the conditions under which the ends of the rod would still touch B and D, emphasizing the role of acceleration and proper length in determining the outcome.

Areas of Agreement / Disagreement

Participants express various viewpoints regarding the implications of relative velocity and length contraction, with no clear consensus reached on some of the more complex scenarios presented. The discussion remains unresolved on certain aspects, particularly regarding the effects of acceleration and the interpretation of measurements across different frames.

Contextual Notes

Participants acknowledge the need for careful consideration of the relativistic effects involved, including the assumptions about initial conditions and the nature of the measurements being discussed. The discussion highlights the complexities of applying relativistic principles in practical scenarios.

  • #31
DrGreg said:
Actually celerity (also known as proper velocity) is the other way round. In the example being discussed, the celerity of the "moving" object relative to the "stationary" frame is distance measured in the "stationary" frame divided by time measured in the "moving" frame.

Celerity is larger than velocity, because time measured in the "moving" frame is shorter than time measured in the "stationary" frame. And the celerity of light is infinite. At low speeds where relativistic effects are negligible, celerity is almost identical to velocity.

Celerity = \gamma x velocity​

Although some people have described celerity as rapidity, "rapidity" usually means something else ("hyperbolic angle").
Thanks for the clarification. Having never used it I was concerned that I may have been making exactly that mistake.
 
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  • #32
newTonn said:
So the actual velocity will be different from that observed from stationary frame and can attain a value higher than that of 'c'. You believe that this calculation is rapidity or celerity.
Could you please give me some links or references, so that i will be able to know more about this
As I mentioned before I have never used it myself because I find this kind of mixed-frame calculation very confusing. It seems that it is also confusing for you, so I would recommend against using it and I would instead recommend that you stick with single-frame and invariant measures.

My point was primarily that if you take distance in one frame and time in another frame you do not get velocity in any frame! So the fact that some number which is not velocity happens to be greater than c does not pose any problem.
 

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