How come electrons still have energy left? They should've expelled all their energy to the surroundings as 0K is a temperature that's obviously the lowest possible. From thermodynamics, if the surrounding temperature is maintained at 0K, all energy from the system should be expelled to the surroundings.
And, about the big bang, since the density shall become infinite; with electrons still vibrating, when the volume becomes 0, they should start colliding such that mass is thrown outwards. Sort of a bang.
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Since 0K has never been achieved, it can't be said that electrons can still remain in their ground states.