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Mass by definition is the amount of matter contained in a body. But for a relativistic object its relativistic mass is greater than the actual rest mass. If accelerating a body increases its mass then by definition it is increasing the amount of matter in a body.

So my question is where does this extra matter come from?

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  • $\begingroup$ No, that is not the way to look at it any more.....profmattstrassler.com/articles-and-posts/… is a very good article. Well worth a read. $\endgroup$
    – user108787
    Commented Sep 17, 2016 at 12:02
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    $\begingroup$ Closely related: physics.stackexchange.com/q/133376/50583 $\endgroup$
    – ACuriousMind ♦
    Commented Sep 17, 2016 at 12:10
  • $\begingroup$ The amount of matter does not increase. The resistance to having it's state of motion change increases. One way of looking at it is to say that the particle's mass increases, but that point of view leads to problems in interpretation, as you have discovered. Physicists abandoned that point of view at least half a century ago. Einstein warned against it. For unknown reasons, the idea that mass increases persists. In the current interpretation, mass is constant. $\endgroup$
    – garyp
    Commented Sep 17, 2016 at 12:22
  • $\begingroup$ @garyp. Because they still teach it that way, in my neck of the woods anyway. Also, TV documentaries love the drama aspect of it. $\endgroup$
    – user108787
    Commented Sep 17, 2016 at 13:32

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'Perceived mass' is just another name for energy, and the contribution to that from kinetic energy specifically depends on relative motion of body and observer.

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