The wavefunction argument is incorrect. At the level of quantum mechanics, particles’ wave-functions can easily be zero, trivially at points, with a little more effort over ranges. At the level of QFTs, yes vacuum fluctuations kick in, and do prevent space from being “empty”.
Because a particle’s wave function never hits zero or some other reason?
I was thinking of vacuum energy, actually—the wavefunction argument just makes it worse.
The wavefunction argument is incorrect. At the level of quantum mechanics, particles’ wave-functions can easily be zero, trivially at points, with a little more effort over ranges. At the level of QFTs, yes vacuum fluctuations kick in, and do prevent space from being “empty”.