If You Took Out All The Empty Space Between The Atoms That Make Up A Person

According to the intrawebs,

“If You Took Out All The Empty Space Between The Atoms That Make Up A Person, The Entire Human Race Would Fit Into A Container The Size Of A Sugar Cube”

Googling sort of confirmed it, and I don’t have any reason to doubt it nessasarily but, wow, that’s kind of mind-blowing if true!

Daddy, what’s a sugar cube?

“Well, son, it’s a … Whooaaah! Look at all those colors…!”

This is clearly not true, because everyone except that person would still be the same size.

It’s not true, anyway. All that “empty space” isn’t empty. It’s full of fields. That might seem like nitpicking, but the particles that the “empty” space is in between are also just fields, and there’s no reason to say one sort of field counts and the other doesn’t.

Why can’t my hand go through my desk? (physics question)

Stranger

I guess a reasonable way to interpret this is to imagine the entire human race compressed to the density of a neutron star, which is more meaningful than “removing the space between the atoms”. The weight of the total human population is, apparently, 316 million tons (at least it was in 2013). Compressed to neutron star density (1017 kg/m3), that would be about 3 cubic centimeters, so yeah, about the size of a sugar cube.

I guess a meaningful thing you could say is to ask about actual states of matter, like what would volume would the mass of the human race take up if we were squished to the density of a neutron star.

With these numbers:
8 x 109 people
70kg per person
5 x 1017 kg/m3 density

I get 1cm3, exactly 1 sugar cube

[ ETA: ninjaed, but my estimate came out to exactly one sugar cube! ]

Eh, I think your value for neutron star density is a bit better than mine, so I’ll take your 1 cc sugar cube over my jumbo size 3 cc sugar cube.

BTW, I just want to go on the record to say that I do not approve of doing this experiment in real life.

If you removed the blood vessels from every living human- there would no longer be any living humans.

On another note, I remember once reading “If compressed to the density of a neutron star, the Great Lakes would fit in your bathroom sink- which would immediately rip itself off the wall and fall unimpeded to the earth’s core.”

How about doing it to a mole of moles?

Like this?

Slight nitpick, if the neutron-Great-Lakes are going to fall unimpeded to the earth’s core, wouldn’t they also fall unimpeded through the bathroom sink, rather than taking it along for the ride?

In the absence of some kind of magic holding the material at that density, I think rather than falling, it would explode out to the density of normal matter. I’m having a hard time visualizing what it would be like for the Great Lakes to suddenly appear inside my house, but I don’t think it would be good for property values in the whole neighborhood.

That doesn’t seem right, but I guess it depends on what one means by “taking out all the empty space between atoms”. The nominal size of the electron shells forming a typical atom is about 100,000 times bigger than its nucleus. In a neutron star, there are no atoms – the electrons shells have disappeared, electrons and protons have combined to form neutrons, and the neutron star is essentially comprised entirely of packed neutrons, or IOW essentially the nuclei of the original atoms. So wouldn’t it be about 100,000 times smaller and denser than the theoretical scenario of the original atoms packed close together, if such a thing were possible?

Cube that number, because atoms are three-dimensional.

Never mind. The OP’s headline – “If You Took Out All The Empty Space Between The Atoms …” misstated the article’s premise, which was actually “…atoms have a lot of vacant space inside them. If we remove all the empty space from all the atoms…”. So the neutron star calculation was correct.

Ah, now that does make sense. Because I’d imagine removing just the space between the atoms but retaining their integrity would take you to some condition akin to white dwarf density.

I read several articles that stated essentially the same thing. I just copy and pasted that sentence from one of the article’s lede.

No worries, I was just initially mystified by the neutron star calculations, so just clarifying what the premise was.