Relative Speed of Light Between Objects

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Discussion Overview

The discussion revolves around the relative speed of light between two objects moving towards a third object at significant fractions of the speed of light. Participants explore the implications of relativistic velocity addition and the perceptions of speed from different reference frames, including the application of relevant formulas at various speeds and angles.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the assumption that two objects moving towards each other at 75% of the speed of light would appear to approach each other at 150% of the speed of light, suggesting that the observed speed must be less than the speed of light.
  • The same participant requests formulas applicable to different speeds (0.8c and 0.9c) and various approach angles (e.g., 120 degrees or 91 degrees).
  • Another participant distinguishes between the separation rate of two objects and the relative velocity each ascribes to the other, noting that while the distance may increase at up to 2c, each object measures the other's speed as less than c due to relativistic effects like length contraction and time dilation.
  • A third participant emphasizes the definition of relative velocity, stating it is the velocity of one object in the rest frame of the other, and references specific sections of a document for further clarification.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of relative speeds and the implications of relativistic effects. There is no consensus on the specific outcomes or interpretations of the formulas discussed.

Contextual Notes

Participants reference the need for specific formulas and the complexities introduced by relativistic effects, indicating that assumptions about measurements and perceptions of speed may vary significantly between different observers.

Skaperen
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TL;DR
Given that motion in space is relative to the observer and that motion is limited to the speed of light, I am wondering how that relationship determines relative speed of objects that would seem to exceed the speed of light between them.
This is one of my thought experiments where I am drawing a big blank, If you have 2 objects approaching a 3rd object from opposite directions (just enough off to avoid collision) at 75% of the speed of light, the first assumption is that each observing the other would see the other object approaching at 150% of the speed of light. That can't be. What speed would each appear to be approaching as viewed by the other? I'm certain this must be less than 100% since true speed of anything is relative to the observer.

Just because an observer has accelerated to a speed that would pass the 3rd object at 0.75c does not mean their speed relation to any other object (doing the same at 180 degrees) can exceed 100% the speed of light. I would like to know what formulas apply to a case like this including at different speeds (0.8c and 0.9c) and different approach angles, (such as 120 degrees or 91 degrees).
 
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There is a distinction between the separation rate that I measure between two objects that I see as in motion and the relative velocity either of those objects ascribes to the other. According to me the distance between two objects may increase at up to 2c, but each one will measure the other doing less than c. From my perspective this is because their rulers are length contracted and their clocks are time dilated and incorrectly synchronised, so I can understand their measures even if I don't agree. From their perspective it's my rulers and clocks that are acting oddly.

Motore has already linked to the relevant formulae.
 
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One should not confuse this issue. By definition the relative velocity between too (pointlike) objects is the velocity of one object in the rest frame of the other (at least the latter must have positive invariant mass of course). See Sect. 1.5 and 1.6 in

https://itp.uni-frankfurt.de/~hees/pf-faq/srt.pdf
 

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