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Mr.E is on a luxury spaceship travelling about 1/2 the speed of light and finds a cubic lump of unstable matter(attached to a bomb) in his cabin. He of course is an expert with bombs but this device is based on the unstable matter's critical mass. The lump of matter fluctuates a tiny amount constantly but if it is more than 2k.g, (say for the sake of argument) it will cause the bomb to explode. Right now it is at 1.9999k.g., if the ship accelerates making it over 2kg relative to the people anxiously monitering the ship from Earth they would think it should detonate yet relative to Mr.E and the fellow passengers its mass is still under 2kg?? Is this loose reasoning valid?

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  • $\begingroup$ No, with the critical mass, you are thinking about something like an atomic bomb. Now, the thing is that while the mass would increase, you'd still have as many atoms in the material. And therefore not enough to get a chain reaction and thus an explosion. $\endgroup$ – Raskolnikov Apr 15 '14 at 6:14
  • $\begingroup$ If an object is accelerating towards c would any inherent radioactivity of the object increase? $\endgroup$ – user128932 Apr 15 '14 at 6:22
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Critical mass is actually more about 'the right number of nuclei in a specified space'. As we are talking about solid matter this equivalently translates to a given number of atoms (or molecules depending on your matter). And this furthermore translates to our everyday mass. But it's 'not about mass', it is just a practical way to specify the quantity.

So in your example: It doesn't matter who sees how much mass. The question is whether is has the 'critical number of nuclei' in it and that doesn't change.

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  • $\begingroup$ critical number of nuclei within a critical volume, to be precise. So next we could calculate the relativistic dimensions of the bomb :-) (Yes, I know that only changes for the outside observer) $\endgroup$ – Carl Witthoft Apr 15 '14 at 11:56
  • $\begingroup$ This brings a new question but it's a nice game. For the outside observer, the size and shape of the lump of matter (let's assume a sphere for simplicity) will change. But so does the movement of inner particles (make them neutrons to follow the atomic bomb line). Consequently the size and shape for 'criticalness' changes as well. As a result it won't explode for the outside observer either. $\endgroup$ – Bgs Apr 15 '14 at 12:05
  • $\begingroup$ I'd just like to point out that in modern relativistic theory, mass is considered constant in all inertial frames. There is no relativistic increase of mass. Of course, the predictions of the theory are no different from before, it just comes down to the definition of mass. Issues like the one in the OP's question led to the idea that mass should really be defined as a Lorentz scalar. C.f.: en.wikipedia.org/wiki/Mass_in_special_relativity $\endgroup$ – Jonas Greitemann Jun 19 '14 at 12:56
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The bomb doesn't "care" what its mass might look like to an observer in another frame.

If you calculate critical mass you don't worry how big it might seem to observers located in billions of other possible frames of reference. Local frame of reference is the only one valid for making calculations concerning the occurence of local phenomena.

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