Half full or half empty?

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Pfhorrest
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Half full or half empty?

Postby Pfhorrest » Sat Sep 08, 2018 5:34 am UTC

Most of this is nothing new to most people here, but I found it an amusing line of thought to share:

TL;DR: A glass drinking vessel filled halfway to its brim with water in a room at standard temperature and pressure at sea level on Earth is mostly empty.

Is the glass half full or half empty?

The immediate snarky answer is that it's entirely full, but only half of it is full of water; the other half is full of air.

Further snarky thought will however lead one to remember that most of the volume of a given substance is empty space, sparsely dotted with atoms jostling about within it. Further thought along that line brings to mind the supposed fact that atoms themselves are mostly empty space, so the glass is definitely mostly empty.

Still further thought, however, reminds one that the fundamental subatomic particles are all infinitesimal points, interacting with each other through forces, which forces prevent other things from occupying some volume, but still in the end, the stuff "filling" the glass is a spattering of zero-volume points interacting with each other through empty space. So really, the glass isn't just mostly empty, it's entirely empty, and so is the whole universe.

But, still further thought will lead one to remember that those forces, and the point-particles themselves, are really all just excitations in energy fields, most of which usually have a nonzero value most places you might find glasses of water, and one of which, the Higgs field, definitely has a nonzero value everywhere. So, in a sense, the glass is again entirely full, and so is the whole universe.

At this point though, it's worth considering what exactly we mean by "full" to begin with. We say the glass is full of water when, upon trying to pour more water into it, that water just ends up on the table and not in the glass. In other words, the glass is full when you can't put anything more into it. But we can definitely put a lot more into that glass than is in there right now.

To start with, yeah, we could pour more water in, and then it will be more full.

But that water is still "mostly empty space". Under normal circumstances water, like any liquid, is mostly incompressible, but mostly dead is slightly alive mostly incompressible is slightly compressible. We could apply a force to the water to squeeze its atoms closer and closer together, and with the extra room we get out of that force in some wore water. We would also end up needing to squeeze the sides of the glass too or else they'll just shatter under the pressure eventually, but let's do that too.

Squeeze enough more water into there hard enough and the water will eventually become solid instead of liquid, but even solids can still be compressed, you just have to squeeze even harder. Thanks to adiabatic heating the glass itself might (temporarily?) become a liquid somewhere along the way here too, I'm not sure of all the specifics of the phase diagrams of glass and water.

In any case at some point you're going to end up with a hot dense plasma of hydrogen, oxygen, and silicon long since dissociated with each other. Keep squeezing more and more "water" (hydrogen-oxygen plasma) in there and some of those atoms will start to fuse together into denser and denser elements. Keep squeezing more into the glass and eventually even the electrons will start to fuse with the protons and you'll have a "glass"(-shaped magic force field) full of nothing but neutronium.

But it's still not full! Keep squeezing more and more into that "glass" until it contains enough mass that its self-gravitation makes it impossible for anything inside of it to escape from it... and congratulations, not only if your glass finally full, but you no longer need your magic force field to contain it! Because it's a black hole now. Anything more you want to add to it, you're going to need a larger volume, and you'll automatically get one real soon now, so yeah, now it's definitely full.
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Eebster the Great
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Re: Half full or half empty?

Postby Eebster the Great » Sat Sep 08, 2018 6:44 am UTC

The claim that atomic matter is "mostly empty space" always perplexed me. In what sense is it "mostly empty"? If we look at the 95% confidence for electron density, most of atomic matter actually is filled, at least in a majority of states, though clearly not all. In this electron density model, it seems relevant to distinguish between states of matter that are mostly empty and ones that are not. If we just take particles to have a "size" defined by their minimum observable size, then they are all points, and all space is almost entirely empty in the mathematical sense. But that can't be what they mean, right? Because that is just trivial.

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Soupspoon
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Re: Half full or half empty?

Postby Soupspoon » Sat Sep 08, 2018 10:45 am UTC

How about it being entirely full of punctuated foam? Or strings?

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Flumble
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Re: Half full or half empty?

Postby Flumble » Sat Sep 08, 2018 10:52 am UTC

It is necessarily both half full and half empty (even especially when observed!), because otherwise you'd have only half a glass.

I'd say this is more of a religious war than science, despite delving deep into physics.

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Re: Half full or half empty?

Postby Pfhorrest » Sat Sep 08, 2018 8:22 pm UTC

Eebster the Great wrote:The claim that atomic matter is "mostly empty space" always perplexed me. In what sense is it "mostly empty"? If we look at the 95% confidence for electron density, most of atomic matter actually is filled, at least in a majority of states, though clearly not all. In this electron density model, it seems relevant to distinguish between states of matter that are mostly empty and ones that are not. If we just take particles to have a "size" defined by their minimum observable size, then they are all points, and all space is almost entirely empty in the mathematical sense. But that can't be what they mean, right? Because that is just trivial.

FWIW I agree with these concerns and glossed quickly through them to arrive at the “everything is entirely full” (all volumes contain some nonzero energy content; there is no empty space anywhere) position halfway through.

It’s only in the following sense considering energy density, where only black holes have maximal energy density and so can be considered “full”, that I turn around and conclude almost everything is mostly empty again.
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Eebster the Great
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Re: Half full or half empty?

Postby Eebster the Great » Sun Sep 09, 2018 7:10 am UTC

Black holes contain the maximum mass per surface area, but that doesn't mean they are in any sense "full". They divide spacetime into two noninteracting parts, but they still have a density that varies with their radius; it's not like at some scale everything is just filled to the brim and there is no space for more stuff.

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Re: Half full or half empty?

Postby Sableagle » Sun Sep 09, 2018 6:19 pm UTC

Pfhorrest wrote:So really, the glass isn't just mostly empty, it's entirely empty, and so is the whole universe.
So, too, is my love life.

Don't think of it as emptiness. Think of it as freedom. If you're the only person in town, you don't need to wear clothes, just to give one example.
Oh, Willie McBride, it was all done in vain.

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Pfhorrest
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Re: Half full or half empty?

Postby Pfhorrest » Sun Sep 09, 2018 8:12 pm UTC

But for a given volume/radius of black hole, you cannot add anything more without it becoming greater in volume/radius, so in that sense any size black hole is “full”.
Forrest Cameranesi, Geek of All Trades
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PM 2Ring
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Re: Half full or half empty?

Postby PM 2Ring » Mon Sep 10, 2018 3:40 am UTC

Pfhorrest wrote:But for a given volume/radius of black hole, you cannot add anything more without it becoming greater in volume/radius, so in that sense any size black hole is “full”.

Sure, but that's just talking about the event horizon, which is a mathematical surface, it's not a physical object. Inside the EH, it's mostly empty, apart from the core of the black hole, and any stuff that's just fallen in & hasn't reached the core yet.

We need a theory of quantum gravity to say what the core is like. Plain GR says that it's a mathematical singularity, a zero-sized region that's been removed from the manifold, a bit like a pinhole in a sheet of graph paper. Quantum effects probably prevent the core from having zero size, but it will still be very small, smaller than an atom, because we don't expect those quantum gravity effects to become significant until you get down to the realm of the Planck length.

FWIW, although the Schwazschild radius is an important parameter of a black hole, and the area of the EH calculated from the Schwazschild radius in the usual way is also significant (in Planck units it's 4 times the entropy of the BH), there isn't a useful, unambiguous way to determine the volume inside the EH.

Eianz
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Re: Half full or half empty?

Postby Eianz » Mon Sep 10, 2018 11:54 am UTC

I'm a "pour way the water and leave the glass empty like my soul" kind of person

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Flumble
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Re: Half full or half empty?

Postby Flumble » Tue Sep 11, 2018 5:28 pm UTC

Sableagle wrote:
Pfhorrest wrote:So really, the glass isn't just mostly empty, it's entirely empty, and so is the whole universe.
So, too, is my love life.

Don't think of it as emptiness. Think of it as freedom.

So, really you're saying Scotland is like a glass filled halfway to the brim? Next time I order a double scotch, I'll expect to receive a glassful. :D

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Re: Half full or half empty?

Postby Sableagle » Tue Sep 11, 2018 6:27 pm UTC

Flumble wrote:
Sableagle wrote:
Pfhorrest wrote:So really, the glass isn't just mostly empty, it's entirely empty, and so is the whole universe.
So, too, is my love life.

Don't think of it as emptiness. Think of it as freedom.

So, really you're saying Scotland is like a glass filled halfway to the brim? Next time I order a double scotch, I'll expect to receive a glassful. :D


P8172251 Tiny sample glass.JPG
Oh, Willie McBride, it was all done in vain.

theoriok
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Re: Half full or half empty?

Postby theoriok » Wed Sep 12, 2018 7:09 am UTC

Half full or half empty?


Yes.

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Re: Half full or half empty?

Postby KittenKaboodle » Thu Sep 13, 2018 12:00 am UTC

theoriok wrote:
Half full or half empty?


Yes.


Cute, but I bet you are wrong. the OP wrote: "TL;DR: A glass drinking vessel filled halfway to its brim with water in a room at standard temperature and pressure at sea level on Earth "
Surely the condition will change by at least a molecule of water, nitrogen or oxygen in the time it takes to say, write, or transmit a representation of "yes" while if I write "No" I will be right most (virtually all) of the time


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