So it is both a single point and a wave that fills the universe…?
And what is the volume of a point? Have we figured out yet if space is quantized or continuous?
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Yes, it is both (get ready for this) UNTIL you measure it. Then it collapses into either a particle or a wave.
zero volume for electron, quark. zero size for electron, quark. Space has to be quantized to the Planck scale (10 -35 meters) in order for universes to come into existence via quantum fluctuations in empty space with enormous energy. If space was continuous, no Heisenberg Uncertainty principle, no quantum fluctuations, no quantum tunneling, in fact no universe if space is continuous as atoms couldn’t form.
What that really means is that all quantum things are some entity that is not a wave and not a particle, but some entirely strange concept absent from our possible experience, which we can approach mathematically but only analogize in words - let’s call them paves, or warticles.
The electron is a point of no dimensions AND a wave that fills the universe (which may, for all we know, be of infinite size). That does not mean that it is nothing, but that it is (in the old, theological sense) “immense” - in a similar manner to the way God is conceived as both fully contained in the body of Christ and not containable by the whole universe. “Immense” means “non-measurable” (because not having spatial dimensions). But at no time (given his existence, for Patrick’s benefit) is God “nothing” in the sense of “non-existence.”
So pointing out the non-occupation of space by an electron conceived as a particle tells us less about the particle than about the limits of human conception - since we exist neither as a point nor in infinity, but in measurable space. It shows us the limits of materialism, too, because what exists both as dimensionless and infinite isn’t matter in any normal sense.
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Agree.
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