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I was wondering if, in special relativity there is a connection to mass in lorrenz contraciton. As if I understand it correctly, things approaching the speed of light will appear shorter to stationary observers. For any non zero mass to approach the speed of light, a force is required, and energy must be put into the system, and as energy and mass are one in the same and it approaches infinity reaching light speed. My point is this, if this truly is the case then would the huge mass create its own bending of space similar to that of a black hole and thus be the reason for the dialation effect? I am of course wrong as my lecturer in Uni has told me so and is an active member of cern, but he didn't really have the time to explain to me why? Or where my reasoning has gone wrong. So if someone can enlighten me further and see where im tripping up then I would be grateful.
There's a fairly simple argument that makes this seem plausible. First you have to make the assumption that a black hole, being a singularity, will have to appear to be a black hole to all inertial reference frames, i.e. you'll see a black hole regardless of whether you're moving or not. Then, just imagine that in any case of a moving mass, you can fly alongside it in a spaceship. It will appear to be stationary to you, and therefore not a black hole. Since it isn't a black hole to you, it won't be a black hole to anyone else.
I'm just talking about singularities in the mathematical sense, and that they're a signature in this case of a black hole. When you create a black hole, you end up with a singularity in the space-time of general relativity that exists in all coordinate systems, which means that the black hole exists in all coordinate systems. There's usually a proof done when discussing Schwarzschild (non-rotating, static) black holes, that while there appear to be two singularities, one at the center and one at the event horizon, only the one at the center appears to exist in all coordinate frames:http://en.wikipedia.org/wiki/Schwarzschild_metricEven if the singularities at the centers of black holes aren't infinitely small, the fact that they appear in general relativity is still a signature that a black hole exists, and the fact that according to GR, black holes are black holes in all reference frames should still hold.
Well kind of guys, thanks for the input. Although I see that it may not be possible for a black hole to form as it doesn't take into account momentum and angular momentum, I am still left wondering if the dilation effect from a black hole and the relativistic effects of near light speed non zero masses are connected? I mean a black hole isn't the only thing that can bend space. I mean the one thing they both have in common is huge mass is required for both. Is it just a coincidence that both phenomena act in a similar way or is there a deeper connection?
Had to look that one up some more.Reading the wiki didn't bring me any intuitive understanding but How Do You Add Velocities in Special Relativity did In a limited sense, that is As I understands it you use 'rapidity' as a way of 'transforming' the relativistic math treating different frames motion, relative any frame defined, be it yours or not. It's not a new theory of motion, more an alternative way of describing it, simplifying the mathematics involved, well, as I understands it?
the idea of relativistic mass seems to be losing popularity. For one thing transverse mass is different from longitudinal mass.Instead of speaking or 'relativistic mass' it might be better to speak of 'relativistic velocity'. http://en.wikipedia.org/wiki/Rapidity