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Assuming we have 3 objects d,e,f moving on the same line while e is stationary, d is moving to the left at 'almost speed of light' and f is moving to the right at 'almost speed of light'. What is the speed at which f is moving from the perspective of d?

If its 0.9999999% speed of light, what does it say about their course? To my understanding, the perspectives of d,e and f are as followed:

  • from the perspective of d, e and f are both moving away at the sub speed of light
  • from the perspective of e, d and f are both moving away at the sub speed of light
  • from the perspective of f, e and d are both moving away at the sub speed of light

In order to keep all 3 statements true, all 3 objects (d, e and f) are supposed to be moving away from each other at a speed close to speed of light, so they should be virtually located on the vertices of an "invisible" equally-edged expanding triangle.

So my question is - what happened to the original straight line d,e and f were placed on during the acceleration of d and f to 'almost speed of light'?

Qmechanic
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Uri Abramson
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    There is no triangle. Nothing happened to the straight line. You simply don’t understand how relative velocities work relativistically. (See https://en.wikipedia.org/wiki/Velocity-addition_formula for the formula.) And none of them see either of the others moving “at the speed of light”. – G. Smith May 06 '19 at 01:55
  • If you like this question you may also enjoy reading this Phys.SE post. – Qmechanic May 07 '19 at 12:41

1 Answers1

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To avoid a proliferation of nines, let’s take the leftward velocity of D, and the rightward velocity of F, relative to E to be 0.9 $c$. Then, using relativitic addition of velocities as explained here, we find that D sees F move rightward at

$$\frac{0.9+0.9}{1+0.9\times 0.9}c = 0.9945 c.$$

Similarly F sees D move leftward at this same speed.

There is no triangle, just straight-line relative motion with various relative velocities which are all sub-luminal.

G. Smith
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  • Thank you. If they move on the same line which appears to be straight to all of them it would have to mean that one of the sentences I wrote would not be true or what am I missing? – Uri Abramson May 06 '19 at 06:29
  • Each of your three bullet points is wrong. None of the objects are moving away at the speed of light. From the perspective of D, objects E and F are not even moving at the same sub-light speed. – G. Smith May 06 '19 at 15:39
  • at near speed of light I mean. editing – Uri Abramson May 07 '19 at 12:34
  • That doesn’t change anything. Your conclusion that there must be triangle is still a non sequitur. There is no triangle. – G. Smith May 07 '19 at 15:33