Why isn't the statement ''there is no perfect vacuum in space'' logically/mathematically flawed?

[Lord Antares]

So, the definition of a vacuum is ''space devoid of matter'', which is straightforward.
However, to make a claim of a space without matter, you would have to say ''from point A to point B, there is no matter'' (or ''in between these end points there is no matter'' if you consider 3 dimensions).
Scientific papers say that there exists no vacuum in the universe because even in the most desolate parts of the universe there are about 3 atoms in a cubic meter. To me, this makes no sense and I drew this shitty illustration to help explain why:

EDIT: I am at work now and can't access the image. Imagine a cubic meter of space with 3 atoms in it. What I referred to below as the green area is the space of the whole cube and the blue area is a cubed space in between 2 of the atoms.

The green area (cubic meter) is clearly not vacuum. However, why isn't the blue area a perfect vacuum? Why isn't all the space in between these atoms considered vacuum?
Why would a cubic meter be used to show there is no vacuum since it is not a mathematically relevant unit? (As in, it is not a ''natural'' unit like the planck units)
Why couldn't I, following the same logic, say ''there are no atoms in this cubic centimeter of deep space; therefore, perfect vacuum exists.''?

Isn't then empty space/vacuum just equal to space? Isn't space/vacuum an entity through which particles and waves move and matter an entity off of which the same particles and waves bounce?
Doesn't any place in between matter/atoms possess the same properties as vacuum and why isn't it considered as such then?

I hope someone can clarify this; thanks for your answers in advance.
I am not a physicist or any kind of professional scientist but I wish to learn.

 

EDIT: I need to copy and paste this from another place where I wrote this for further clarification:

 

As I said, I'm not a physicist, but simply logically, the definition can't be exact.
Because the logic ''there is no perfect vacuum since there are ~3 atoms in a cubic meter even in the rarest parts of the universe'' is used to prove there is no vacuum, surely the statement ''there exists perfect vacuum since we know there are cubic centimeters in the universe which contain NO atoms'' must be just as valid because it uses the EXACT same logic, which absolutely nothing changed except for the unit of measurement.

You see what I mean? To state that there is or is no vacuum, you would have to state the end points between which are or aren't any particles. So why would you use a cubic meter to determine that? Why not the smallest possible unit you could use?

I guess the point of my statement is that I think it's ridiculous to state that there are no cubic meter-sized vacuums in the universe, because that has no relation to physics since it unnecessarily complicates the issue with scale.

I hope this makes sense now.

[ajb]

Space-time is 'populated' classically by field and quantum mechanically we have particles appearing and disappearing all the time. So yes, the simple idea of a 'true' vacuum is rather an approximation - but one that is good enough for lots of situations.

[Lord Antares]

Isn't a field just an area upon which a force acts? It doesn't necessarily have to contain matter. Or rather, it does contain matter but isn't filled with it completely.

 

True, we have particles randomly moving through space, but just dynamically moves this notion of vacuum.

 

No matter where particles are or how they move, there will always be the same amount of empty space between all of them, no?

If all particles in the universe were bunched around one area, the amount of empty space would be the same as if they were evenly spread out throughout the universe.

[Sensei]

In 1 Liter = 0.001 m^3,

at temperature 273.15 K and pressure 101325 Pa, there is 0.04464 mol.

(f.e. air at sea level and at 0 C temperature)

 

1L * 1000 = 1m^3

0.04464 mol/L * 1000 = 44.64 mol/m^3

 

1 mol = 6.022141*10^23 molecules.

 

44.64 mol = 44.64 * 6.022141*10^23 = 2.6882837424*10^25 molecules.

3 atoms versus 2.69*10^25.

Nearly 10^25 times as much.

 

These "3 average atoms per m^3" are accelerated, as they were ejected by stars in f.e. solar flare. Accelerated to significant fraction of speed of light.

Blink and these 3 atoms are gone, and new replacement particles are passing through the same region.

 

Not presence of protons or electrons, does not mean that there is no neutrinos (matter), anti-neutrinos (anti-matter), and photons.

If somebody is in cosmos between galaxies, still can see galaxies and stars, right?

So, photons have to arrive and pass through your reference m^3 of volume.

The same with neutrinos and antineutrinos emitted by the all stars, the all galaxies, around him/her.

There is ~65 billions of neutrinos passing through every 1cm^2 of area of your body per second just from the Sun.

Edited July 30, 2016 by Sensei

[Lord Antares]

I think I understand what you mean by motion of the particles. You mean that the fact they are moving THROUGH the green cube and not just standing in it means over a given period of time, all possible spaces or positions in the cube will be passed through by atoms? True, but this would mean that the vacuum area would also be constantly expanding, shrinking, curving and changing shape depending on the movement of particles. And there will be countless amounts of these spaces at any given time.

 

I am not familiar with quantum theory. I can follow what you said and your calculation, but I don't know the theory of neutrinos.

Are you saying that even though there may be only 3 atoms in the given area, there would be immense amounts of other particles which would fill this empty space? Would you say that, when you count in all the possible particles, all of the space would be filled at any given point in time?

[John Cuthber]

Imagine that - at some moment- I know the exact position of all the atoms in a volume of space. I can draw a box that doesn't include any of them and say that the box contains a vacuum.

Very shortly afterwards that box will have stuff in it,but that's beside the point; at that "instant" it was empty.

Unfortunately quantum mechanics tells us that's impossible.

It's not just that I can't know the exact locations of the particles.

The problem is that the exact position of the particles does not exist.

The particles have wave functions that extend throughout space. A box here on earth can not strictly rule out containing a particle that would conventionally be considered to be on Mars.

 

And then there's the problem of virtual particles popping in and out of existence everywhere.

[ajb]

Isn't a field just an area upon which a force acts?

Think about the electromagnetic field - it fills all of space.

 

 

 

True, we have particles randomly moving through space, but just dynamically moves this notion of vacuum.

To every field via the rules of quantum theory we can associate a 'species' of particle. Again by the rules of quantum theory we have particles appearing and disappearing all the time in any given region of space-time.

 

A true vacuum would have no fields nor any matter. Classically this notion is not great as we usually have the electromagnetic field - and when one looks at quantum theory we get all these particle pairs 'boiling' in and out of existence.

Edited July 31, 2016 by ajb

[Lord Antares]

I want to get back to my first post on this forum a bit.

 

Do fields populate all of space? Is it because the wave functions, as John said, extend thoughout all of space?

But does this really explain it? A field (or a wave) doesn't really occupy space in a way that matter does. Does it then make sense to say that no vacuum exists because fields populate everything to an extent?

[Argent]

True, but this would mean that the vacuum area would also be constantly expanding, shrinking, curving and changing shape depending on the movement of particles. And there will be countless amounts of these spaces at any given time.

None of which sounds close to perfection.

[swansont]

Restricting this to a classical vacuum, it's problematic to talk about a vacuum in a region between particles, because vacuum is a concept you tend to apply to quasi-static systems, rather than instantaneous conditions. So it's having no atoms in a volume over some appreciable length of time, and that won't happen. You could apply the same argument in the OP to a room at atmospheric pressure, but speak of a much smaller volume. It would be ridiculous to say that you have a perfect vacuum in the room (a multitude of them, really), it's just that they're really, really small.

[Lord Antares]

Restricting this to a classical vacuum, it's problematic to talk about a vacuum in a region between particles, because vacuum is a concept you tend to apply to quasi-static systems, rather than instantaneous conditions. So it's having no atoms in a volume over some appreciable length of time, and that won't happen.

 

Can you expand on that a bit? If I'm understanding you correctly, the vacuum would have to be there consistently, without moving around with the particles? But then you would have to quantify an ''appreciable length of time'', would you not? There would need to be some mathematics behind what would be considered a vacuum.

 

 

You could apply the same argument in the OP to a room at atmospheric pressure, but speak of a much smaller volume. It would be ridiculous to say that you have a perfect vacuum in the room (a multitude of them, really), it's just that they're really, really small.

 

And this was the issue that I had even when posting the OP. What ''size'' of vacuum qualifies as a proper one? How would you quantify it? Why can it not be considered for my very small spaces between particles, but it can be considered for, say, a meter cubed of space? The logic is the same, but the sizes are different, so how does this impact the definition? This is my primary question.

[Bender]

And this was the issue that I had even when posting the OP. What ''size'' of vacuum qualifies as a proper one? How would you quantify it? Why can it not be considered for my very small spaces between particles, but it can be considered for, say, a meter cubed of space? The logic is the same, but the sizes are different, so how does this impact the definition? This is my primary question.

Vacuum is zero pressure. Pressure is a statistical, macroscopic property. It is meaningless to talk about pressure (or the absence thereof) on the scale of particles.

[swansont]

Vacuum is zero pressure. Pressure is a statistical, macroscopic property. It is meaningless to talk about pressure (or the absence thereof) on the scale of particles.

 

 

 

Quite. Similar to temperature. There is no exact dividing line to say when you can apply it (do you need 10,000 atoms? 100 atoms not enough? What about 101?)

[Lord Antares]

Ah, I understand. That clears it up.

 

So, it doesn't make sense to talk about vacuum at a macroscopic scale. However, at a microscopic scale, there are lots of gaps between particles, especially in deep space where matter is, on average, really rare. There is more empty space everywhere than matter. But this is just space, not vacuum as it is usually defined, right?

[Bender]

Ah, I understand. That clears it up.

 

So, it doesn't make sense to talk about vacuum at a macroscopic scale. However, at a microscopic scale, there are lots of gaps between particles, especially in deep space where matter is, on average, really rare. There is more empty space everywhere than matter. But this is just space, not vacuum as it is usually defined, right?

Right. There is also (a lot) more empty space than matter in a solid piece of lead, to illustrate how pointless the concept of a microscopic vacuum is.

[Lord Antares]

Yes, but I didn't mention solids on purpose because some previous posters said that the exact size of particles doesn't exist (for example the wave functions of electrons etc), and therefore it cannot be stated that there are more gaps in solids than there is matter.

 

Alright, so, theoretically, what could be done with a real, macroscopic vacuum? In what way would it be interesting, primarily from the perspective of knowledge and science?

[swansont]

Ah, I understand. That clears it up.

 

So, it doesn't make sense to talk about vacuum at a macroscopic scale.

 

 

No, it only makes sense to talk about a vacuum at a macroscopic scale.

[Lord Antares]

Sorry, that was a typo. I meant to write ''microscopic scale''.