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Suppose there are two point particles A and B. They move away from each other due to their mutual interaction.

According to Einstein, there is no absolute space; so there is only relative motion between the two. In a way, I think we cannot even speak about which particle is moving away from the other. In this context, what does the Conservation of Momentum, or alternatively Newton's third law mean? How does it fit into all this?

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    $\begingroup$ I'm not sure I understand the question - what has the fact that the motion might look different in different frames to do with conservation of momentum? $\endgroup$ – ACuriousMind Apr 28 '17 at 11:06
  • $\begingroup$ Newton's III law has to do with accelerations of two point mass (there is interaction between them), and the accelerations are proportional to each other. Relative motion is quite different here -- in your context, you are referring to uniform motion (no acceleration) seemingly. $\endgroup$ – Shing Apr 28 '17 at 13:05
  • $\begingroup$ @ACuriousMind That's what am asking. $\endgroup$ – PhyEnthusiast Apr 29 '17 at 10:29
  • $\begingroup$ @PhyEnthusiast would you mind accepting the answer or else comment what is missing from the answer? $\endgroup$ – domj33 May 1 '17 at 11:49
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The interaction provides a force between them, so that the particles accelerate away from each other.

There is already the Galilean relativity or the equivalence of inertial frames, where you only have relative motion. In a frame co-moving with the centre of mass of the two particles the interaction looks pretty straightforward, but also in other frames it looks like if one particle is accelerated while the other is decelerated.

In Einstein's special relativity, what changes is the perception of simultaneity. While in one reference frame, it looks as if the particles where closest before passing a certain landmark, in another reference frame it looks as if the particles where closest just after the passing. But in any case the particles move away from each other.

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