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The mass increases with the speed, as: m=gamma*m0.
It is unfortunate you picked electrons. Yes, from your frame of reference they will have such gravitational attraction but they will also have a much, much larger magnetic repulsion.
does that means they attract gravitationally stronger?
Let's consider we observe two electrons moving parallel and accelerated to such a speed that their relativistic mass is equal to that of planet (say) Jupiter. Will these electrons attract gravitationally each other as two objects of the size of Jupiter?
Quote from: graham.d on 13/02/2010 19:55:35It is unfortunate you picked electrons. Yes, from your frame of reference they will have such gravitational attraction but they will also have a much, much larger magnetic repulsion.  You mean "attraction"?Anyway the magnetic attraction can never be greater than the coulombian repulsion, so don't see your point.
in this exact moment, you and your friend close to you (immagine there is one) are both moving at ultra relativistic speed with respect to some ultra relativistic particle of cosmic rays. Are you attracting each other gravitationally as two (big) Jupiters?
The cosmic ray (if it could) would not see you attract each other (I mean gravitationally) more than you would normally, because of time dilation. When it comes to gravitational collapse, and even in the lesser case we are talking about, special relativity is insufficient to describe the events. It is fair to say that nothing should be observed by the cosmic ray than would be expected in the frame of you and your friend (however "attractive" she may be). In General Relativity the concept of mass is not so well defined. I think this is what lightarrow was alluding to.
....What you will notice though that will differ you from your stationary observer is that the universe will become more energetic the further your acceleration have taken you, and as I understand it, even at some 'time and place' observe what your stationary observer would call 'virtual photons' as being constantly existing, also I've seen references to what's called the 'heat bath' which is part of the hidden energy in a vacuum that now will appear for you.