Why does length contraction not cause Black holes?

[Justice Hunter]

So i was watching this video :



And it got me thinking... i began wondering why, when space contracts from someones frame of reference (In the video, this would be the frame of reference of the cat), why is it that the protons don't become black-holes when the space contracts?

If the density change has an effect on the electro-magnetic force, why would it not have any gravitational effects?

It seems to be contradictory, since from the reference frame of someone stationary, looking at the cat, there is no change in density of the protons in the wire, but instead, we see the cat contract. and we don't see things becoming black holes when moving at or near the speed of light, so i assume that the protons in the wire do not becomes black holes either.

So what is the reason length contraction doesn't create black holes in any reference frame?

 

[haushofer]

Length contraction arises because of the relativity of simultanity. So it's not because space itself contracts, but because every observer has it's own notion of 'simultanity', and because spatial length is defined via simultanious events one observes length contraction. The observed object itself doesn't care less about those observers.

 

[PeterDonis]

why is it that the protons don't become black-holes when the space contracts?

Because whether or not something is a black hole is not frame-dependent. The spacetime curvature an object produces is not due to its "density", which is frame-dependent; it is due to the object's stress-energy tensor, which is covariant. So an object's spacetime curvature doesn't change when you change frames.

If the density change has an effect on the electro-magnetic force, why would it not have any gravitational effects?

It's not the density change that affects the electromagnetic force; it's relative motion between the source and the object the source is acting on. Also, force is not the same as the source of the force. The EM force between a proton and an electron at rest relative to the proton will be different from the EM force between a proton and an electron moving past the proton at high speed. But the charge on the proton (the ultimate source of its EM force) does not change.

Similarly, the gravitational force between a massive body and an object at rest relative to it is different from the gravitational force between the same body and an object moving past it at high speed. But the body's mass, or more precisely its stress-energy tensor (the ultimate source of its gravitational force), does not change.

 

[Justice Hunter]

Thanks guys i understand now i think!