Can pressure be negative?

[Ziggurat]

But is this really "negative pressure" like what would happen if you could get a negative reading on a barometer?

Yes. Sol's answer is correct, but I'll give you an alternative reasoning, because if you don't believe the theory behind it, then his answer might not convince you.

In the Casimir effect, the pressure diverges towards infinity as the plate separation approaches zero. If the pressure is negative inside, that's not a problem: all it means is that the slope of the energy vs. volume diverges, the energy inside the plates can still be finite.

But if the pressure is really a positive pressure outside, then we DO have a problem. And the reason it's a problem is that this result doesn't depend on the geometric details outside the plates. Which means that the outside pressure is always infinite. But the only way to get an external pressure that's always infinite is for the external energy density to be infinite as well (actually, you need a negative infinity energy density to get a positive infinity pressure).

So either we've got negative pressure inside the plates which only diverge at one point and our vacuum energy always remains finite, or we've got positive infinite pressure outside, along with infinite negative energy densities. The former solution is acceptable. The latter... is not.

You say it "pulls them together" -- but that isn't what I expect from negative pressure

It should be. A positive pressure between the plates would push the plates outwards. A negative pressure between the plates will therefore pull them inwards. The vacuum pressure outside the plates is negligible.

I'd think the term would mean in outward, apart effect, not an inward together effect

A negative pressure outside the plates would indeed pull the plates outward. But the vacuum pressure outside the plates is negligible. It's the pressure between the plates which is significant enough to measure.

 

[I Ratant]

Nitpick: "suction" is a misnomer. Suction doesn't exist, because if it did we wouldn't have an upper limit on the height to which mercury could rise in a barometer. If suction were a real effect, then an ever larger evacuated chamber at the top of the barometer tube would "suck" the mercury ever higher, but this never happens because the upper limit isn't the result of "suction", it is the result of an excess pressure from outside of the barometer pushing the mercury up the tube. No matter how much "suction" one provides by a larger vacuum tube, the mercury will only rise up as high as the atmospheric pressure can push it.

In the context in which you put it, "negative pressure" is more appropriately labeled as a pressure differential, where the pressure inside the soda straw is less than that of the atmosphere shoving the liquid up the tube. So while the relative pressure is negative inside the straw, the absolute values of both the pressure inside and outside the soda straw are still positive (it's just a question of which is bigger).

So, in this context, terms like "negative" pressure and "suction" are misnomers. However, when discussing pressure in the limited context of fluids & hydrostatic (and hydrodynamic) scenarios, it is only a subset of ideas of pressure, as was outlined nicely within the OP.

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Yeah, but sometimes we sciencey guys use jargon.
Watching things collapse with the delta pressures we can induce between atmospheric and the inside of a sealed container, say, and those collapses occur with pressure existing inside the container, getting to a point where there's that "negative pressure" kinda boggles the old head-bone, as to what could occur.
I'll just accept zero as the lower limit.
Outside of social pressures, of course, which do have negative values.

 

[rwguinn]

Yes. Sol's answer is correct, but I'll give you an alternative reasoning, because if you don't believe the theory behind it, then his answer might not convince you.

In the Casimir effect, the pressure diverges towards infinity as the plate separation approaches zero. If the pressure is negative inside, that's not a problem: all it means is that the slope of the energy vs. volume diverges, the energy inside the plates can still be finite.

But if the pressure is really a positive pressure outside, then we DO have a problem. And the reason it's a problem is that this result doesn't depend on the geometric details outside the plates. Which means that the outside pressure is always infinite. But the only way to get an external pressure that's always infinite is for the external energy density to be infinite as well (actually, you need a negative infinity energy density to get a positive infinity pressure).

So either we've got negative pressure inside the plates which only diverge at one point and our vacuum energy always remains finite, or we've got positive infinite pressure outside, along with infinite negative energy densities. The former solution is acceptable. The latter... is not.



It should be. A positive pressure between the plates would push the plates outwards. A negative pressure between the plates will therefore pull them inwards. The vacuum pressure outside the plates is negligible.



A negative pressure outside the plates would indeed pull the plates outward. But the vacuum pressure outside the plates is negligible. It's the pressure between the plates which is significant enough to measure.

I agree with the effects you detail 9as much as I understand them)-a negative pressure would indeed pull the plates--which don't exist, according to one post previously--together.
But how the hell, other than that force, would you measure negative pressure when every measurement device I know of is based on a complete vacuum. And when you do, is it really pressure, or something else we didn't find till now?
This reeks of "In the beginning, there was nothing. Then it blew up"I don't understand it, but I can accept that the math--so far--supports it...

 

[rwguinn]

.
Yeah, but sometimes we sciencey guys use jargon.
Watching things collapse with the delta pressures we can induce between atmospheric ambient and the inside of a sealed container, say, and those collapses occur with pressure existing inside the container, getting to a point where there's that "negative pressure" kinda boggles the old head-bone, as to what could occur.
I'll just accept zero as the lower limit.
Outside of social pressures, of course, which do have negative values.

FTFY--and I agree fully...

 

[Ziggurat]

But how the hell, other than that force, would you measure negative pressure

Pretty much all measurements of pressure are really measurements of force converted to pressure.

when every measurement device I know of is based on a complete vacuum.

Not a problem. The Casimir effect is pretty small, and only measurable for very small gaps. So it's quite easy to build a vacuum gauge which doesn't have any parts subject to measurable Casimir effect forces.

 

[Michael Mozina]

I'll just accept zero as the lower limit.
Outside of social pressures, of course, which do have negative values.

Those same social pressures seem to suck half my comments into a black hole. I guess there really is "negative pressure" after all.

 

[rwguinn]

Pretty much all measurements of pressure are really measurements of force converted to pressure.

which was my second point--how do you know it's "negative pressure" and not something else, other than mathematically?

Not a problem. The Casimir effect is pretty small, and only measurable for very small gaps. So it's quite easy to build a vacuum gauge which doesn't have any parts subject to measurable Casimir effect forces.

very small? Nano-meters and less is, technically, "damn tiny".
If you say so--a force gage measures force, and not causality...

 

[Ziggurat]

which was my second point--how do you know it's "negative pressure" and not something else, other than mathematically?

If you don't believe in any math, then there's no point in even doing physics. Physics is predicated on the idea that math actually has relevance to reality. You've got to believe in some math, or you can't do physics at all. So the question is whether the math involved here is too complex or speculative to draw a conclusion. And I'd say no, I think the explanation I gave is sufficiently simple and robust that we can draw a conclusion about negative pressure existing with considerable certainty.

very small? Nano-meters and less is, technically, "damn tiny".
If you say so--a force gage measures force, and not causality...

I'm not sure what your point is. Are you asking how we can determine that the pressure we measure in Casimir effects is actually a pressure and not some non-pressure force? Well, that's easy: measure its area dependence. If it scales with area, then obviously it's a pressure, pretty much by definition. And it does. Or did you mean something else?

 

[Michael Mozina]

The Casimir effect is quantum, yes. It's proportional to Planck's constant, which makes it quantum by definition.

The very small distance requirement sort of shoots your whole wrapped universe concept in the foot however since gravity would rip it apart long before the the Casimir effect took place. Assuming it's a "round" (and wrapped) object, such an effect might end up being a repulsive influence at a very small distance.

There's no need for curvature of space. You could do the experiment I outlined simply by constraining some field to be non-zero only inside a hoop, and then measure the tension in the hoop. You could (at least in principle) swing the pressure from positive to negative by changing the spin of the field that's non-zero inside the hoop (by changing the material it's made out of, for example).

And what would it interact with outside of the hoop?

In any case, my point was that at least if you buy the math behind it, that example (realistic or not) proves that Casimir pressures can be negative, and that the negative pressure cannot be due to a force from outside.

That doesn't "prove" anything of the sort. They can *CERTAINLY* be caused by an EM attraction between the two plates, but Guth didn't have two separate things to work with so the analogy isn't even applicable. Whatever the 'cause' it's not caused by a "negative pressure" in the chamber because the chamber always contains 'positive pressure" since we are physically incapable of building any other kind of vacuum.

I'd post the WIKI image that shows that even the QM effect can be expressed as "high and low" pressures, not necessary "absolute negative" pressure, but I see that PS actually did something useful in this thread after all.

 

[Michael Mozina]

If you don't believe in any math, then there's no point in even doing physics. Physics is predicated on the idea that math actually has relevance to reality. You've got to believe in some math, or you can't do physics at all.

The problem is that a "simplified (perhaps oversimplified) math formula can end up giving you the wrong impression about the physical processes in play and they can easily obscure the difference between "absolute" and "relative" concepts.

Even from a QM perspective, the process can be seen as "greater pressure" on one side of the plate and "less pressure' on the other, resulting in a "relatively lower" pressure region between the plates that isn't actually a "negative' pressure. For the "sake of simplicity" it might be handy to compute the pressure on the top of a wing to calculate lift and describe the pressure on the top as a "negative' value. That doesn't mean that the ABSOLUTE pressure on the top of the wing is actually "negative', it's just "less than' the pressure below.

That same analogy applies to the plates at the level of QM. Those blue arrows point into the plates *EVERYWHERE*, not just in the middle. The QM pressures are 'smaller' in the middle than on the outside because there is MORE pressure on one side and 'less pressure" on another. Math can *easily* obscure the difference between relative and absolute pressure, and IMO you're being fooled by your love of formulas and dread of empirical physics. At the level of empirical physics, it's impossible for that vacuum to hold "negative pressure" because no container on Earth is capable of reaching even a ZERO pressure.

 

[edd]

I think we need an emergency response team to Perpetual Student's place to make sure he's not drinking any coffee, or he'll be needing a new keyboard.

 

[rwguinn]

If you don't believe in any math, then there's no point in even doing physics. Physics is predicated on the idea that math actually has relevance to reality. You've got to believe in some math, or you can't do physics at all. So the question is whether the math involved here is too complex or speculative to draw a conclusion. And I'd say no, I think the explanation I gave is sufficiently simple and robust that we can draw a conclusion about negative pressure existing with considerable certainty.



I'm not sure what your point is. Are you asking how we can determine that the pressure we measure in Casimir effects is actually a pressure and not some non-pressure force? Well, that's easy: measure its area dependence. If it scales with area, then obviously it's a pressure, pretty much by definition. And it does. Or did you mean something else?

I don't know if you're deliberately misunderstanding me, or simply haven't read all my comments.
The mathematics, as we know it supports the hypothesis. Yes, F/A=P, by definition.
Look at a column of water (on earth), 32 feet high. The Pressure at the bottom is 1 atm-approximately.
The Cause of that pressure is gravity--and I am confusing myself with that example.
It looks to me like a chicken and egg matter-which came first, the force or the pressure? At the macro level, the equation works all ways--F=P*A, P=F/A, A=F/P.
At my comfort-level of understanding, It's a wonderful trick, but per Clarke's law, looks like magic...
You guys carry on. Wonderful stuff, but I don't understand it..

 

[Ziggurat]

Even from a QM perspective, the process can be seen as "greater pressure" on one side of the plate and "less pressure' on the other, resulting in a "relatively lower" pressure region between the plates that isn't actually a "negative' pressure.

I already explained about why such an interpretation is not valid. It would require infinite pressures and infinite negative energy densities outside the plates. Why is such an answer preferable to you?

 

[edd]

which was my second point--how do you know it's "negative pressure" and not something else, other than mathematically?

You have P=F/A. Now, E=Fx (work done is force x distance), so P=-E/Ax - the minus sign here I put in because the energy comes out of the system to do the work. But Ax = V (area x depth is volume) so P=-E/V - more strictly P=-dE/dV. Looked at this way it's not a mathematical convention over which way the vectors P and F point, but it's a physical question over where the energy from the force goes. In a negative pressure piston for example, the energy in the chamber rises as the volume increases, whereas in a positive pressure one the energy rises as the volume decreases. You have to do a bit of maths to get there, but you end up with an unambiguous physical definition of when the pressure is positive or negative - which way does the energy flow from the material that does the work? And the maths you use isn't really that difficult and certainly not that abstract.

 

[Michael Mozina]

I already explained about why such an interpretation is not valid. It would require infinite pressures and infinite negative energy densities outside the plates. Why is such an answer preferable to you?

Well, for starters, I don't personally believe that the effect is *INFINITE* like you do. That's another of your mathematical primrose paths IMO. Atoms have finite physical shapes, so there is bound to be an actual "limit" on the effect that is far less than infinity IMO. That infinity claim is another of those things that you can't demonstrate in a lab.

 

[Michael Mozina]

I think we need an emergency response team to Perpetual Student's place to make sure he's not drinking any coffee, or he'll be needing a new keyboard.

Now that would be entertaining.

 

[Ziggurat]

Well, for starters, I don't personally believe that the effect is *INFINITE* like you do.

Even if you constrain yourself to the pressures that have been directly measured and assume that we cannot extrapolate that pressure any further, then it's still going to be a big positive pressure. Which means that the vacuum must still have a large negative energy density.

So why is a huge negative vacuum energy density better than a small positive vacuum energy density? Hell, why is a negative vacuum energy of any size better than a negative pressure?

 

[Michael Mozina]

Even if you constrain yourself to the pressures that have been directly measured and assume that we cannot extrapolate that pressure any further, then it's still going to be a big positive pressure. Which means that the vacuum must still have a large negative energy density.

Er, no. It has a some positive pressure and a LOT of KINETIC ENERGY. There is no such thing as "negative energy" other than the "vibe" I get from astronomers.

So why is a huge negative vacuum energy density better than a small positive vacuum energy density?

It's not. I'm simply proposing a "small positive KINETIC energy *EVERYWHERE* inside the chamber. The is more kinetic energy imparted to the outside surface sand less kinetic energy imparted to the inside surfaces and a "lower overall pressure" between the plates.

Hell, why is a negative vacuum energy

What the hell is negative vacuum energy? I'm talking about particle kinetic energy, specifically photons. I have no idea what 'negative vacuum energy" might even be.

 

[rwguinn]

You have P=F/A. Now, E=Fx (work done is force x distance), so P=-E/Ax - the minus sign here I put in because the energy comes out of the system to do the work. But Ax = V (area x depth is volume) so P=-E/V - more strictly P=-dE/dV. Looked at this way it's not a mathematical convention over which way the vectors P and F point, but it's a physical question over where the energy from the force goes. In a negative pressure piston for example, the energy in the chamber rises as the volume increases, whereas in a positive pressure one the energy rises as the volume decreases. You have to do a bit of maths to get there, but you end up with an unambiguous physical definition of when the pressure is positive or negative - which way does the energy flow from the material that does the work? And the maths you use isn't really that difficult and certainly not that abstract.

That I can understand, but

Even if you constrain yourself to the pressures that have been directly measured and assume that we cannot extrapolate that pressure any further, then it's still going to be a big positive pressure. Which means that the vacuum must still have a large negative energy density.

So why is a huge negative vacuum energy density better than a small positive vacuum energy density? Hell, why is a negative vacuum energy of any size better than a negative pressure?

Wouldn't that require a negative volume?
I always though that the definition of energy was that it is always positive?
E=|F*x|, KE=1/2 MV², PE=1/2kx², E=mC²...
You guys are turning my world downside-up!

 

[Ziggurat]

Er, no. It has a some positive pressure and a LOT of KINETIC ENERGY.

Give me E(V) then. Find a positive E(V) which will satisfy our observations.

Oh, but that's "barking math on command". Except it isn't: it's just getting you to support your claims.

The truth is, there is no positive E(V) which will give us a positive, volume-independent pressure. It's not possible. So either we have a negative energy density and a positive pressure outside the plates, or a positive energy and a negative pressure inside the plates. One or the other. You cannot reconcile these results with a simultaneously positive pressure and a positive energy.

What he hell is negative vacuum energy? I'm talking about particle kinetic energy, specifically photons.

This isn't radiation pressure, Michael. Radiation pressure cannot explain the Casimir effect.