I had to make it unnecessarily wordy to get to the character limit. Simple question: How small can you crush a car? Any shape, doesn't have to be a cube, could be a sphere, maybe even a tetrahedron.
Say I have a Toyota Camry. What is the minimum volume I can crush this into?
Drop it on a neutron star.
Density of a neutron star is roughly the same as an atomic nucleus, $3 *10^{17} kg/m^3$. Assuming the car weights around 1.5Ton that's $5 *10^{-15} m^{3}$ so a sphere of radius $10^{-5} m$ or $10 um$
If you could heat the car and melt all its parts, then mold that into a sphere, that's the minimum volume.
In crashes, that may not happen. But, a lot of mechanical energy is converted into heat, which basically melts the parts and moulds them somehow.
If we have to go to the minimum, I think that sphere made earlier is the lowest we can go.
At what point do you stop calling it a crushed car, and start calling it something else? (For example - a bunch of neutrons). If you do want to stop referring it to a car a some point during its destruction, and if you are adamant about crushing it, then the answers by Nawaj and Martin Beckett should help you out.
If you don't want to ever stop calling it a car, then read on! Collide the Camry with a requisite amount of antimatter. The car will survive as a burst of gamma radiation. The total energy thus released would be roughly $10^{20}$ joules. $10^{34}$ photons is what would be left of the car.
But a photon is not something you could really prescribe a volume to. They don't "Occupy space" in the same manner normal matter (fermions) do. This answer tells you why. So we could just be done with it and say that your car now has $0$ volume.
