You might find it strange
Reference to Strange quark, or possibly the seemingly strange behavior of matter at the quantum scale.
To speak to an ancient Siberian brassiere.
Reference to bra-ket notation used in Quantum Mechanics. Ket is an ancient Siberian language which is dying out. "Bra" is short for brassiere.
I could fix your car,
A mechanic fixes your car.
But I'll surely break the laws there.
Physics at the quantum scale seems to break the macro-scale laws of physics
News of me has recently been big,
Interest in QM continues to rise...
Though that doesn't make sense at all.
QM has to do with things that are small not big
You couldn't see me wave,
QM has a lot to do with understanding wave functions in objects too small to see.
Because I'm actually very small.
Again, QM deals with the very small