have you ever thought about how weird it is that light can go though solid objects?

@tyr solidity is an illusion! Atoms are 99% empty space by volume

@tyr just remember that the nucleus is very, very small

@banjo only if you localize their wave functions!

@aphyr yeah it depends on epistemology. From a de Broglie-Bohm pilot wave view they are 99% empty space. I guess even for probability you could find like to volume off the 99% confidence interval of the probability density function… that would be interesting

@banjo IIRC pilot-wave doesn't generalize past 2D, right? I recall an extensive conversation to this effect when I was working in QSD, but the details are beyond me now :(

@aphyr it should be fine for 3D but it breaks for relativistic QM… but so does a lot of stuff 😁

It’s what we learned in chemistry, I can’t claim to have looked at QCD or anything sub atomic

@aphyr btw in case you’re curious I did a deep dive into this.

Hyperphysics has a numeric integrator for the radial density function of the hydrogen 1s orbital. Over 99.9% of the probability density for the electron is contained within a range of 0.001*a0 to 6*a0 (the function is highly right skew). a0 is the classical Bohr radius of hydrogen, which is 5.292*10^-11 m. So our “lower bound” of the electron cloud at 99.9% confidence becomes 5.292*10^-14

(More in next toot)


The nucleus of hydrogen is just a proton, so the nuclear (RMS) radius is 0.87*10^-15 m.

The relative amount of free space in the sphere between the lower bound of the electron orbital and the outer edge of the nucleus is (Ve-Vn)/Ve with Ve as the electron volume and Vn of the nuclear volume.

This works out to (re^3-rn^3)/re^3 (r being the radii) or approximately 0.9999955562% empty space. I tried to compare with the classical value but I got 100% for that 😅


Sorry but I can’t help myself.

I think I did this wrong - I should be comparing the amount of empty space to the outer edge of the orbital. Bad diagram:

Outer. Inner. Nucleus

This would give (Vinner-Vnuclear)/Vouter as the total amount of free space, the remainder being occupied either by electron or proton, and the amount of this free space is only 4.4*10^-10%, or essentially nothing!!

@aphyr is right!

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