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### Half full or half empty?

Posted: 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.

### Re: Half full or half empty?

Posted: 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.

### Re: Half full or half empty?

Posted: Sat Sep 08, 2018 10:45 am UTC
How about it being entirely full of punctuated foam? Or strings?

### Re: Half full or half empty?

Posted: 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.

### Re: Half full or half empty?

Posted: 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.

### Re: Half full or half empty?

Posted: 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.

### Re: Half full or half empty?

Posted: 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.

### Re: Half full or half empty?

Posted: 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”.

### Re: Half full or half empty?

Posted: 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 Schwarzschild radius is an important parameter of a black hole, and the area of the EH calculated from the Schwarzschild 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.

### Re: Half full or half empty?

Posted: 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

### Re: Half full or half empty?

Posted: 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.

### Re: Half full or half empty?

Posted: 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.

### Re: Half full or half empty?

Posted: Wed Sep 12, 2018 7:09 am UTC
Half full or half empty?

Yes.

### Re: Half full or half empty?

Posted: 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

### Re: Half full or half empty?

Posted: Thu Sep 20, 2018 10:56 am UTC
If the definition of "full" is "solid with atomic matter"

Then good luck finding any volume within the universe that is "full".

I mean seriously, can we even say that about a lone proton?

### Re: Half full or half empty?

Posted: Fri Sep 21, 2018 12:30 am UTC
Ice is a solid and is atomic matter. Not sure exactly what you mean.

### Re: Half full or half empty?

Posted: Fri Sep 21, 2018 9:30 am UTC
I like the mostly empty interpretation. I ain't paying the price of a pint for this, I mean look at the neutrino flux!

### Re: Half full or half empty?

Posted: Fri Sep 21, 2018 3:45 pm UTC
Eebster the Great wrote:Ice is a solid and is atomic matter. Not sure exactly what you mean.

Well as the discussion goes, "matter" consist of mostly empty space. Now lets zoom in on an atom, still mostly empty space. Now lets zoom in on a proton, lo and behold, several sub-particles and a bunch of empty space.

So if the definition of "full" is "no empty space" - where in the universe can you find any volume that is "full"?

If you are going to, for whatever reason, take the position that a glass of water is still mostly empty, can you really call anything "full"?

### Re: Half full or half empty?

Posted: Fri Sep 21, 2018 7:41 pm UTC
p1t1o wrote:
Eebster the Great wrote:Ice is a solid and is atomic matter. Not sure exactly what you mean.

Well as the discussion goes, "matter" consist of mostly empty space. Now lets zoom in on an atom, still mostly empty space. Now lets zoom in on a proton, lo and behold, several sub-particles and a bunch of empty space.

So if the definition of "full" is "no empty space" - where in the universe can you find any volume that is "full"?

If you are going to, for whatever reason, take the position that a glass of water is still mostly empty, can you really call anything "full"?

You have to read my first post, which specifically addressed the idea that matter is "mostly empty" at the microscopic scale.

### Re: Half full or half empty?

Posted: Fri Sep 21, 2018 8:36 pm UTC
You both seem to be getting hung up at stages of consideration I already moved past in the first post.

All of space can be considered "empty" inasmuch as it's all point particles with zero extension.

But all of space can also be considered "full" inasmuch as it all has something in it, even if it's not something with a finite classical extension. Quantum fields permeate everything, everywhere.

But almost none of it has as much in a given place as could possibly be at that place, and most of it has far, far closer to nothing there than it has to as much as possible there.

So in that last sense, most of everything is mostly empty. None of it is completely empty, and there are a few places here and there that are as full as they can get (black holes), and some examples of any in-between energy density state you might care to find exist somewhere or another, but most of it is mostly empty.

### Re: Half full or half empty?

Posted: Sat Sep 22, 2018 5:28 am UTC
Perhaps a different definition of "full" and "empty" would be helpful. Consider that we normally use the words in a qualified manner to refer to something of interest that a container could hold. Beer in a mug is interesting, air in a mug is not.

Full: the condition where one cannot put any more {thing of interest} in {container}. A parking lot is full if all of the parking spaces are occupied, even if they are occupied by motorcycles.

Empty: the condition where {container} has no {things of interest} in them. A parking lot is empty if there are no cars in it, even if it is full of water. (Of course, calling it a parking lot at that point might be inappropriate, or the lot could be considered full and empty at the same time.)

Jose

### Re: Half full or half empty?

Posted: Sat Sep 22, 2018 7:34 am UTC
You'll note I did settle on a definition rather like that, and then removed the qualifiers to get a concept of absolute fullness. A volume is full if nothing more can be put into it; and, of course, empty if there is nothing in it. Nothing is ever really empty in an absolute sense (though, of course, it may be empty of a particular thing, like your parking lot may be empty of cars, or a glass may be empty of water), but most volumes can have a lot more put into them than they already have.

In the first post, I even continued just putting more and more water into the glass. Of course the glass at some point needed reinforcement to contain the water in its volume, and at some point the water once in the glass seamlessly transitioned into other substances (other phases of water including water plasma, a plasma of dissociated hydrogen and oxygen ions, a quark-gluon plasma), but I just kept pumping more and more water into the glass until it couldn't take any more. So even a glass filled to the brim with water, at standard temperature and pressure on Earth, still isn't actually full of water, because you can still put more water into it if you try hard enough.

### Re: Half full or half empty?

Posted: Sat Sep 22, 2018 10:46 am UTC
Don't forget the old phrase used to demonstrate pitfalls for natural-language processing:
The room was empty and full of flies.

### Re: Half full or half empty?

Posted: Sun Sep 23, 2018 5:34 am UTC
Pfhorrest wrote:You both seem to be getting hung up at stages of consideration I already moved past in the first post.

All of space can be considered "empty" inasmuch as it's all point particles with zero extension.

But all of space can also be considered "full" inasmuch as it all has something in it, even if it's not something with a finite classical extension. Quantum fields permeate everything, everywhere.

But almost none of it has as much in a given place as could possibly be at that place, and most of it has far, far closer to nothing there than it has to as much as possible there.

So in that last sense, most of everything is mostly empty. None of it is completely empty, and there are a few places here and there that are as full as they can get (black holes), and some examples of any in-between energy density state you might care to find exist somewhere or another, but most of it is mostly empty.

To me, "empty" or even "mostly empty" does not mean "having somewhat less than is the maximum amount physically possible to cram in there," it means, "containing nothing or almost nothing." Thus, interstellar space is mostly empty, because it contains almost nothing (in any definition; even the quantum fields are all very close to zero nearly everywhere). But my refrigerator is mostly full because there are very few places in there that contain almost nothing.

Like, it just isn't the case that anybody uses or has ever used these words in this way in any context except to smugly assert that the universe is mostly empty. If you are using a word in a way it has never been used before just to prove your point, your point is probably wrong.

The idea of a black hole being "full" also seems like nonsense. The interior of a black hole is actually mostly empty using any of your definitions or my definitions. Most of the inside is a high vacuum, with only a very small core actually containing matter. It is the kind of "mostly empty" that people believe atoms are, but which they actually aren't.

### Re: Half full or half empty?

Posted: Sun Sep 23, 2018 11:19 am UTC
If the physical size of a black hole is taken to mean the space contained within its event horizon, then it is indeed “completely filled” in the sense that no more mass/energy can be crammed into that volume of space, since any such addition MUST cause the event horizon to expand further and encompass more space.

If, however, we only mean the volume of the singularity itself, then we are in a place where our current knowledge breaks down. Classical Relativity would describe it as a space of zero volume and infinite density, while quantum descriptions would place it at the Planck density or some other finite limit.

### Re: Half full or half empty?

Posted: Sun Sep 23, 2018 7:06 pm UTC
Technically it is the surface area that matters, not the volume. You could cram more stuff in the same volume by rotating the black hole, causing the event horizon to attain an oblate shape, which has a greater surface area per volume.

### Re: Half full or half empty?

Posted: Sun Sep 23, 2018 10:59 pm UTC
I’m not calling anything with just “somewhat less” than maximal capacity “mostly empty”, but things with MUCH less than maximal capacity, which is mostly everything, as even solid rock is much less dense than the densest that anything could possibly be.

### Re: Half full or half empty?

Posted: Sun Sep 23, 2018 11:40 pm UTC
But why is density relevant? I've never heard anyone suggest that a bucket with one liter of mercury in it is "more full" than a bucket with two liters of water.

### Re: Half full or half empty?

Posted: Mon Sep 24, 2018 1:17 am UTC
Density becomes relevant if you consider something full when you can no longer put more into it. You can always put more in if you pack it in more densely.

### Re: Half full or half empty?

Posted: Mon Sep 24, 2018 2:10 am UTC
So, which is more full—a bucket with twenty kilograms of mercury taking up two liters, or an otherwise-identical bucket with forty kilograms of mercury taking up one liter?

### Re: Half full or half empty?

Posted: Mon Sep 24, 2018 3:51 am UTC
The second bucket will have to be filled with a bunch of something in the other liter to make that happen, so the second is more full.

### Re: Half full or half empty?

Posted: Mon Sep 24, 2018 1:15 pm UTC
But what if it's just that the second bucket is being spun at such speed that the centrifugal force is compressing twice the amount of mercury into half the volume..?

Basically we're just continuing your original post though - proving its correctness Namely that there are multiple definitions of 'full' each of which is reasonable but which are none-the-less mutually contradictory...

### Re: Half full or half empty?

Posted: Mon Sep 24, 2018 7:00 pm UTC
Pfhorrest wrote:Density becomes relevant if you consider something full when you can no longer put more into it. You can always put more in if you pack it in more densely.

But that's still not what full means. You are not addressing the example. A bucket that is FULL of water is definitely more full than one that is HALF FULL of mercury, even though it weighs less, because that's what full actually means in the context of the real world outside this thread.

### Re: Half full or half empty?

Posted: Mon Sep 24, 2018 7:39 pm UTC
I'm not saying that just being more dense is enough to be "more full", but that density becomes relevant, in a given context, to a more general sense of fullness. In the example in the first post, I never added anything but more water to the glass, until it reached a point that no more water could possibly be added to it, and only then called it really full of water. After adding as much water as would fit at standard temperature and pressure, "filling" the glass in one, common, sense, I started pumping more and more water in at higher and higher pressure (increasing the density of the water in the process), demonstrating that the glass was actually still not "full" in another, more general, sense. If the glass was half full (in the common sense) of mercury instead, then the context under discussion would be mercury and not water, and more mercury could be added at standard temperature and pressure, but then even once it was "full" of mercury that way, we could pump more and more mercury into it at higher and higher pressures (increasing the density of the mercury to fit the additional stuff in).

I'm not contesting that the common sense of "full" is the one you're suggesting, just saying that that sense has a lot of specific context baked into it, which context I tried to spell out in the first post to be clear about that. A glass "full" of water, in the context of a standard temperature and pressure environment, on Earth, and so on... is still not as "full" as it could possibly be in any possible context. And it's much closer to "empty" (but not actually empty, of course) than it is to "full" in that broadest most context-free sense, since many, many, many times more than what is currently "filling" it, in the common context, could be added to it in other contexts, before it got as full as it could ever possibly be in any context.

### Re: Half full or half empty?

Posted: Tue Sep 25, 2018 12:12 am UTC
Pfhorrest wrote:A glass "full" of water, in the context of a standard temperature and pressure environment, on Earth, and so on... is still not as "full" as it could possibly be in any possible context.

I mean, there is less mass in it, but it is just as full. What you are saying is that in the common sense of the word, this would be full, but in another sense, it would not be full. Of course, that's true. In yet another sense, it would be fuller than full. And in another sense still, fullness doesn't apply. I can make as many senses up as I like. But in the sense people actually use, it is full, and in the sense you are proposing, "fullness" is trivially impossible. So I am proposing one sense is better than the other.

### Re: Half full or half empty?

Posted: Tue Sep 25, 2018 12:50 am UTC
I'm not just making up arbitrary willy nilly word-senses though, but considering the implications of generalizing the common word-sense and removing the baked-in context that's assumed (rightly, as obvious) in casual conversation, in the vein of the original snarky answer that "it's entirely full, but only half of it is water, hurr hurr".

By that kind of thinking, everything everywhere is entirely full, because every volume is entirely filled with some medium or another, however diffuse it may be.

...unless you pick a small enough volume that there are no particles in it at all, because your whole volume fits between particles, by which thinking the entire universe is empty, because you can consider the particles to be pointlike in extension and add up tiny volumes between them equivalent to the volume of the universe.

...unless you don't think of particles as having classical boundaries at all, but rather as smeared-out excitations of all-permeating fields, in which case you can say the whole universe is full again, in that every volume is entirely filled with a bunch of fields, regardless of however low their energy density in a given volume may be.

And then if we want to come back around from that line of overthinking to a way of reckoning some volumes to be more or less full than others, instead of just everything everywhere equally full, we can simply not-disregard energy density, and think of something as full not just if it has something in it, but if it has as much as it can possibly have in it.

Which brings us back around to something like the common sense of "full", that being a state where you can't add any more; just now, with the contextual assumptions stripped away. You can pour more water from a faucet into a glass half-filled with water, until it fully displaces the air that was already filling the other half, and under normal assumptions of normal circumstances that's the most water you can add to the glass, so it's full, but what if we disregarded those assumptions? What if we tried cramming water in between all the gaps in between the bits of water in the glass? And then kept doing that? How much could we do that? There is a limit, and at that point the glass is full in this broader more abstract sense.

You realize of course that this whole thing is a kind of conceptual game, right? Playing around with ideas? You seem to just be objecting to the playing of that game. Nobody is honestly proposing that we stop talking about glasses half-full of water as being half-full and pedantically whine to the mundanes that actually it's mostly empty because science. This is just playing around with the line of thought that jokes "actually it's entirely full, just half of it is air" and seeing where that goes. If you don't like that game, don't play.

### Re: Half full or half empty?

Posted: Tue Sep 25, 2018 3:41 am UTC
I mean, there is a practical sense in which the volume of a substance can be measured. As long as you are comfortable with that, then it makes sense to divide the volume of the container by the volume of the substance and determine that way how full it is. When you want to generalize this concept of "fullness," clearly you want to generalize volume, not mass. You are describing black holes, and those are not "full" in the volumetric sense that naturally generalizes from the fullness of a bucket. And things that actually are full in the conventional sense are ranked as empty in your sense. So it isn't a generalization at all. It is a completely different notion. A generalization would consider all the things already describable as "full" or "empty" the same way they already are, but additionally assign terms to things that couldn't be described properly by the conventional term in a way that is still in a certain sense consistent with expectations.

An actual generalization of volume that can be used on the microscopic scale is the "space-filling model" of atoms, and in that sense, there are some substances that are largely empty and others that are largely full, and the distinction between the two matches expectation. This is a proper generalization, not a non sequitur like density.

### Re: Half full or half empty?

Posted: Tue Sep 25, 2018 5:16 am UTC
Consider the experiment in which gasses are collected for later analysis. A jar is filled with water, and inverted on a stand partly submerged in a deep pan of water. A tube which will be expelling the desired gas is introduced into the jar from underneath, and the reaction is begun.

The gas we are collecting travels through the tube and bubbles into the jar, displacing the pre-existing water.

Are we emptying the jar or filling it?

Jose

### Re: Half full or half empty?

Posted: Tue Sep 25, 2018 10:25 am UTC
...unless you pick a small enough volume that there are no particles in it at all, because your whole volume fits between particles, by which thinking the entire universe is empty, because you can consider the particles to be pointlike in extension and add up tiny volumes between them equivalent to the volume of the universe.

...unless you don't think of particles as having classical boundaries at all, but rather as smeared-out excitations of all-permeating fields, in which case you can say the whole universe is full again, in that every volume is entirely filled with a bunch of fields, regardless of however low their energy density in a given volume may be.

You're skipping a relevant step there. The electron cloud of an atom is not a set of points, but it is not space-filling "all-permeating" either. The density is high in a small volume of space, and essentially zero further away. That gives atoms and molecules a fairly well-defined volume.

A Eebster says, that gives us a straightforward generalization of "empty" and "full". By that concept, air is 99.9% empty. And water has about 40% empty space - a tad less than random packed spheres. In other words, water is "full" in the sense that you cannot put more molecules in the empty space between the water molecules - not even small molecules, because water is already rather small.

### Re: Half full or half empty?

Posted: Tue Sep 25, 2018 3:59 pm UTC
Zamfir wrote:In other words, water is "full" in the sense that you cannot put more molecules in the empty space between the water molecules - not even small molecules, because water is already rather small.

Tell that to Ice XII