Split Thread Michael Mozina's thread on Dark Matter, Inflation and Cosmology

[Michael Mozina]

You think the Casimir setup actually has blue arrows in it?

No, I believe there is a positive energy density and positive kinetic force pushing into every surface of the everything in the chamber.

So if you push the plates together what happens?

At that point the plates are now pushed together and the have nowhere else to go.

 

[Tubbythin]

Not really because these oscillations occur both outside and between the plates. There are simply more of these oscillations going on outside the plates than between them.

I love it how you pretend this isn't in complete contradiction to everything you've been saying up to now.

 

[Michael Mozina]

You are mixing up force, pressure, and energy density. The "force from an energy density" is nonsense.

Ok. "Pressure from an energy density". Are you happier?

 

[Michael Mozina]

I love it how you pretend this isn't in complete contradiction to everything you've been saying up to now.

Huh?

 

[Tubbythin]

No, I believe there is a positive energy density and positive kinetic force pushing into every surface of the everything in the chamber.

Yet another abuse of a scientific word to mean something other than it means in irs usually definition. As someone has already asked, why do you keep putting kinetic infront of everything?

At that point the plates are now pushed together and the have nowhere else to go.

I'll rephrase that. What happens when you push the plates closer together?

 

[Michael Mozina]

Yet another abuse of a scientific word to mean something other than it means in irs usually definition. As someone has already asked, why do you keep putting kinetic infront of everything?

Because ultimately the kinetic energy of the standing waves in the chamber are providing the kinetic energy that pushes the plates together. It is a kinetic energy transfer in the final analysis.

I'll rephrase that. What happens when you push the plates closer together?

The energy density between the plates decreases.

 

[Tubbythin]

Huh?

One minute you say: "I was simply pointing out that the term "zero point energy" relates to the kinetic energy of everything we can't remove from our experiments". This is in complete contradiction to what schroedingersdawg just posted and you don't even acknowledge it.

 

[Tubbythin]

Because ultimately the kinetic energy of the standing waves in the chamber are providing the kinetic energy that pushes the plates together. It is a kinetic energy transfer in the final analysis.

That's nonsensical

The energy density between the plates decreases.

And the volume?

 

[ben m]

No, I believe there is a positive energy density and positive kinetic force pushing into every surface of the everything in the chamber.

You believe that in spite of the facts. These experiments are conducted in a residual gas of 10^-7 torr (10^-5 N/m^2), which is the same on both sides (in gap/out of gap) of a Casimir experiment yielding zero NET force. Meanwhile, Casimir experiments observe a NET force as high as 10^-2 N/m^2. What in the hell would ever make you think that the 10^-2 N/m^2 force was "just" a product of the gas molecules? Did you spend more than ten microseconds thinking about it? How do you get a 10^-2 Pa net force by imagining an imbalance in two 10^-5 Pa pressures?

Photon pressure? You want photon pressure? Good, Casimir and Polder thought of that and it's in their original equation. The full force between a sphere and a plate, including the vacuum term and the thermal term, is: (http://prl.aps.org/forward/PRL/v78/i1/p5_1)

[latex]F = 2\pi R \frac{\hbar c \pi^2}{720a^3}(1 + \frac{720}{\pi^2}f(\xi))[/latex] where [latex]\xi = kTa/\hbar c[/latex] and [latex]f(\xi) = 1.202(\xi^3/2\pi) - (\xi^4\pi^2/45)[/latex]. (The form of the f(\xi) equation changes at large \xi which are irrelevant for these experiments.)

There, Michael: the effect of "EM forces" in the vacuum chamber isn't something you have to guess at with a brain full of Wikipedia images. It's something you calculate, like a physicist does. I invite you to calculate the actual EM force on the Casimir effect experiment. You will find the same thing that everyone else does: THE CONTRIBUTION FROM BLACKBODY PHOTONS IS TINY.

http://prl.aps.org/forward/PRL/v78/i1/p5_1
In conclusion, we have given an unambiguous demon-
stration of the Casimir force with accuracy of order 5%.
Our data is not of sufficient accuracy to demonstrate the
finite temperature correction, as shown in Fig. 4(b).

The residual-gas effect, that you imagine to be large, is in fact tiny. The blackbody photon effect, which you imagine to be large, is in fact tiny.

Why don't you take some time to sweep these mistakes out of your mind, then re-read Edd's explanation very, very carefully.

 

[Michael Mozina]

And the volume?

The total volume in the chamber stays exactly the same regardless of the distance between the plates. All you're doing is creating a lower energy density between the plates than the ambient energy density. The energy density between the plates is still a "relative" number and not "negative" in any way. It's simply less than the energy density outside the plates, thus the plates are pushed together.

 

[Michael Mozina]

You believe that in spite of the facts.

No. Factually speaking there is an energy density everywhere in the chamber that has nothing to do with the gas pressure inside the chamber. When talking about this energy density, I'll simply stick with edd's label. It works.

That energy density is greater than zero everywhere in the chamber. It is simply greater on the outside of the plates, and lower between them. There's nothing magical going on here that cannot be described as a simple kinetic energy transfer between the standing EM waves in the chamber and the plates. There is no area anywhere in the chamber that has a "negative energy density".

 

[ben m]

Ok. "Pressure from an energy density". Are you happier?

Nope! I am standing on a concrete floor whose energy density is 10^14 J/cm^3. Its pressure is zero and (unless I go out of my way to compress it) it does not exert any noteworthy forces. Meanwhile there is a stockpile of argon gas in my lab, with a comparatively tiny energy density, but which is exerting rather hazardous forces on its walls and fittings.

Force comes from dU/dx, not from U. Pressure comes from dU/dV, not from U.

 

[Michael Mozina]

One minute you say: "I was simply pointing out that the term "zero point energy" relates to the kinetic energy of everything we can't remove from our experiments". This is in complete contradiction to what schroedingersdawg just posted and you don't even acknowledge it.

It in no way contradicts his post that I can tell. Those oscillating waves are everywhere in the chamber, not just between the plates! The kinetic energy of those standing QM waves in the chamber act to "push" the plates together.

 

[Tubbythin]

The total volume in the chamber stays exactly the same regardless of the distance between the plates. All you're doing is creating a lower energy density between the plates than the ambient energy density. The energy density between the plates is still a "relative" number and not "negative" in any way. It's simply less than the energy density outside the plates, thus the plates are pushed together.

The volume between the plates?

 

[ben m]

No. Factually speaking there is an energy density everywhere in the chamber that has nothing to do with the gas pressure inside the chamber. When talking about this energy density, I'll simply stick with edd's label. It works.

Good! So stop calling it kinetic energy, get it? Stop hinting that it has something to do with the vacuum chamber or its imperfections, as you did by saying "We can't even remove every atom from a "vacuum", let alone every EM carrier particle and every neutrino, etc. ".

That energy density is greater than zero everywhere in the chamber. It is simply greater on the outside of the plates, and lower between them.

Yes! Good! Almost there!

There is no area anywhere in the chamber that has a "negative energy density".

Wonderful! You have learned so much.

The situation you have just described is one of negative pressure. Positive energy density (U) with a positive dU/dV has negative pressure.

 

[Tubbythin]

It in no way contradicts his post that I can tell. Those oscillating waves are everywhere in the chamber, not just between the plates! The kinetic energy of those standing QM waves in the chamber act to "push" the plates together.

Again with the random use of kinetic. And ahem:

No, that's absolutely not what I'm saying. I'm saying that inside the chamber are "real particles" that carry the EM field and those particles "push" against all sides of all the plates.

 

[Reality Check]

Not really because these oscillations occur both outside and between the plates. There are simply more of these oscillations going on outside the plates than between them.

That is the problem with relying on pretty pictures for your understanding of physics. The oscillations do not physically exist!

The waves in the diagram are an (incorrect) representation of the QM mathematics. The mathematics shows that the force on the outside of the plates is greater than the force on the inside.

This means that the plates move together.

Positive pressure would move the plates further apart.

Scientists call a pressure from a force that results in attraction rather than repulsion, negative pressure. It turns out if you do the math that the values of negative pressure are actually negative.

 

[ben m]

One thing that (perhaps) MM is missing, which is important:

Let's imagine the non-Casimir experiment. We set up a vacuum chamber and inject a cloud of gas into it, establishing a total pressure---let's call it a 1 liter chamber and 0.0044 moles of gas so the pressure is 1 bar. Now we put a pair of plates into the cell , fix their separation, and seal their edges, so there's a little 0.1 liter sub-volume defined by the plates. We evacuate the space between the plates----now there's 0.004 moles of gas in the open 0.9 liter volume, and this is exerting a force on the plates, pushing them together. Let's un-fix the plate separation and let the gas do its work. Bang! The plates fly together. Let's look at what remains.

The gas expanded from 0.9 l back to 1.0 liters. Its pressure dropped from 1 bar to 0.9 bar. By exerting a force on the plate while it was moving, the gas did approximately 1 J of work; from conservation of energy, the total energy in the gas is now 1J lower than it was before. (The energy density is even lower, since the original energy stockpile has dropped by 1 J and also spread out from 0.9l to 1.0l.

That change in energy, believe it or not, determines the pressure---not vice-versa. Whether or not you agree, you must agree with all of the signs of the quantities above: +work on the plate, -dU energy change with +dV volume change.

Is that what happens in the Casimir effect equivalent? Something did work on the plates to move them together---there was a force exerted over a distance. But did the energy density of the 0.9l chamber change? No, it's still a vacuum chamber just like any other. Did its total energy change? Well, yes---the total energy increased since this part of the chamber expanded from 0.9l to 1.0l while the energy density remained constant.

The change in energy has the opposite sign of the change we encountered in the real-gas case.

ETA: I want to emphasize (a) this is the same thing Edd (and everyone else) have said, and (b) we are not making this up for your benefit, this exact keep-track-of-signs question is standard issue Freshman physics problem set material.

 

[schrodingasdawg]

Not really because these oscillations occur both outside and between the plates. There are simply more of these oscillations going on outside the plates than between them.

The modes outside the plate don't contribute to the attraction between the plates. They either have no effect at all, or actually inhibit the attraction.

Imagine the Casimir plates being contained within a perfectly conducting box. What's of concern are the forces acting along the axis perpendicular to the plates, so imagine this axis going from left to right. To the far left is the left box wall; to the far right is the right box wall; and in the middle are the two perfectly conducting plates. The distance between the plates is assumed to be much smaller than the distance from either plate to the walls.

The scenario is divided into three relevant regions. (The walls are assumed to be immovable, so the regions outside the box are irrelevant.) There is the left region, between the left wall and the left plate; there is the right region, between the right wall and the right plate; and there is the central region, between the two plates.

The allowed EM modes along the left-right axis are considered independently for each region. The boundary to each region is perfectly conducting, so the EM field must be zero at these points. This limits the allowed modes to sinusoidal waves with nodes at the boundaries.

In the left region, fewer modes are available the closer the left plate is to the left wall. Thus the EM field in the left region will have less energy if the left plate is further left. The force exerted is proportional to the distance between the plate and the wall to the negative fourth power. Call the distance L; the force is proportional to L^-4.

Replace "left" in the paragraph above with "right", and we've covered another region. Call the relevant distance here R; the force is proportional to R^-4.

In the central region, fewer modes are available the closer the plates are together. The EM field in the central region will have less energy if the plates are closer together--that is, if the left plate is further right and the right plate is further left. Call the distance D. The force on each plate is proportional to D^-4.

There is a force acting on the left plate proportional to D^-4 - L^-4. (Positive sign for right-ward force.) As L is much larger than D, the D-term dominates and the net force is to the right. The force acting on the right plate is proportional to R^-4 - D^-4. (Positive sign for right-ward force.) As R is much larger than D, the D-term dominates and the net force is to the left. In the limit that L and R are infinitely large (i.e. in the limit that there is no box containing the experiment), the only force between the plates is that due to the EM modes between the plates---the D-term. The influence of the EM fields outside the plates vanishes.

Another way of looking at it, perhaps, is that (assuming the experiment is not contained within a box) the allowed modes outside the plates are the same regardless of the plates' position, so the positions of the plates has no bearing on the energy of the EM field outside them.

 

[edd]

The energy density and force from that energy density is simply 'greater' on the outside of the plates, and 'less' between them. There is still some small force pushing into the insides of the plates. That force is simply "less than" the energy density that is pushing the plates together.

If all we did is look at "pressure" from a single surface (like my wing analogy), you might be "tricked" into believing that the pressure on the top of the wing is "negative". It's not. The pressure under the wing is "greater" that the pressure on top of the wing, and the "pressure difference" causes upward lift. The same analogy is true here. The *whole* chamber has an energy density, not just the region between the plates. The "ambient energy density" is simply greater than the energy density between the plates and the plates are 'pushed together' from the outside force of that ambient energy density.

So the energy between the plates is dropping as you agreed to earlier, and on the outside of the plates whatever positive pressure material is in a growing volume and is therefore cooling, like everyday gases.

Give me a shout when you're ready to start conserving energy and we can pick this discussion up again.