Relative Speed of Light Between Objects

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SUMMARY

The discussion centers on the relative speed of two objects approaching a third object at 75% of the speed of light (0.75c). Participants clarify that while each object perceives the other approaching, the speed cannot exceed the speed of light (c) due to relativistic effects. The relevant formulas for calculating relative velocity, particularly the velocity addition formula, are essential for understanding this phenomenon. The conversation also touches on the implications of length contraction and time dilation on the measurements of speed between the objects.

PREREQUISITES
  • Understanding of special relativity principles
  • Familiarity with the velocity addition formula
  • Knowledge of length contraction and time dilation effects
  • Basic grasp of inertial reference frames
NEXT STEPS
  • Study the velocity addition formula in detail
  • Explore the implications of time dilation and length contraction in special relativity
  • Analyze scenarios involving different speeds (0.8c and 0.9c) and angles of approach
  • Review sections 1.5 and 1.6 of the provided special relativity FAQ document
USEFUL FOR

Physicists, students of relativity, and anyone interested in understanding the nuances of relativistic speeds and their implications on measurements between moving objects.

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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