What Is the Casimir Effect and Its Relation to Vacuum Energy?

[eimos]

Can anyone explain the casimir effect to me? I've only just got back to reading parallel worlds and it's mentioned quite alot, yet i have no idea what it is. Though i think it may have something to do with vacuum energy.

 

[DrChinese]

Can anyone explain the casimir effect to me? I've only just got back to reading parallel worlds and it's mentioned quite alot, yet i have no idea what it is. Though i think it may have something to do with vacuum energy.

Welcome to PhysicsForums, eimos!

Please check out this and other similar threads: Casimir Effect

It may also be helpful to look to Wikipedia and other similar spots. I would then suggest returning to this thread for specific followup questions.

 

[map19]

I have a different take on this: - the vacuum of space is full of radiation, practically the whole electromagnetic spectrum. When you put in your two plates, at a close spacing, the space between them can only contain wavelengths of a half-wave that is less than the spacing.
Thus the plates have lots of momentum transfer on the outside, from real and virtual EM and little on the inside. A net force pushing them together.
This explains why the plates have to be close together, and why the force reduces as you move them apart.
This says little about virtual particles.

 

[Vanadium 50]

Map19, I think I know what you are trying to say, but I think it got mangled. For example, the vacuum of space is most assuredly not "full of radiation".

 

[Bob S]

Here is an example of the Casmir effect causing an attractive force between two warships (not warpships) close broadside to broadside at sea.
Since we are now realizing that the Casimir effect can manifest itself under entirely classical circumstances, it is reasonable to wonder whether any observation of it has ever been reported on a macroscopic scale. The answer is not only affirmative but also fascinating. As reported in the professional physics literature in 1995, an entirely classical, that is, non-quantum, treatment of the Casimir force is all is needed to explain the mysterious attractive force between two parallel, rolling ships at sea with no wind and a building swell sailors were being warned about as far back as the early 19th century. By treating the two ships similarly to two atoms immersed in an ocean of random waves, one finds that, in analogy to the van der Waals force of chemical physics, such two vessels will also attract. (From http://www.interstellartechcorp.com/phyTheoretical.html

 

[map19]

the vacuum of space is most assuredly not "full of radiation"
I disagree. From the context you can see that I was talking EM. Maybe stronger in some places and weaker in others, but EM never dies.

 

[Vanadium 50]

Here is an example of the Casmir effect ...

From "Interstellar Technologies"? Are you sure that's a reputable site?

 

[Vanadium 50]

the vacuum of space is most assuredly not "full of radiation"
I disagree.

You don't get to disagree. This is not a matter of opinion.

EM radiation is a very specific thing: far-field solutions to Maxwell's equations. Space is most assuredly not filled with this, and if you shield against it, you still have Casimir forces.

 

[Born2bwire]

You don't get to disagree. This is not a matter of opinion.

EM radiation is a very specific thing: far-field solutions to Maxwell's equations. Space is most assuredly not filled with this, and if you shield against it, you still have Casimir forces.

Exactly, we could always enclose a volume of vacuum with reflectors on the exterior surface and absorbers on the interior, ensuring that radiation does not flow into the volume and any existing radiation inside will be dissipated. The Casimir effect can be explained by the change in the vacuum energy that results from the fluctuations of electromagnetic fields (without any real photons present) but it has also been shown to be the product of current and charge fluctuations on and within the scatterers themselves (Schwinger). Or, as originally formulated by Casimir and Polder, the effect is a result of relativistic effects. The vacuum energy and fluctuations do not need to be brought into the theory of the Casimir force at all. R. L. Jaffe has an interesting paper that discusses the ramifications (or more specifically the lack there of) of the Casimir effect in terms of what it can prove about its mechanisms. Jaffe is also part of the EGJK group that has developed some interesting methods of calculating the Casimir force.

 

[Bob S]

Posted by Bob S
Here is an example of the Casmir effect causing an attractive force between two warships (not warpships) close broadside to broadside at sea.

From "Interstellar Technologies"? Are you sure that's a reputable site?

One of my neighbors is a PhD physicist who was a naval commander before retirement. He says there definitely is an attractive "force" between two ships when they are very close, and it is attributed to the relatively calmer wave structure between them.

 

[fleem]

I cringe at classical "analogies" of quantum mechanical principles. They might be OK in popular literature but in the end they more often mislead than lead. Furthermore I think a majority of scientists fall prey to the same mistake. I believe it is grossly unscientific to assume the theories we've devised solely to predict the average behavior of many tiny machines (particle interactions) must unquestionably be assumed to be the founding axioms for theories designed to predict the behavior of a single one of those little machines. This includes the ideas of space-time, manifolds, continuums, dimensions, and yes, even the idea of non-integer values. All of those things we learned from observing classical phenomena (average behavior of many machines). It also includes pilot wave/Bohmian stuff. I'm not saying the universe is discrete in the sense that most think of "discrete", but it is discrete in that an interval doesn't exist unless there are events at each end (and saying it does exists is clearly unscientific because you can't measure or detect such an interval). You can't have the concept of dimension unless there are multiple intervals that happen to interact with, for example, Euclidean transforms, causing us to picture something we call "dimensions". "Dimensions" are an interpretation of the behavior of multiple intervals, and have nothing to do with the idea of a single interval. So any classical analogy misleads our understanding of a particle interactions. Now it may be that the Casimir effect might be somewhat classical (an effect related to many interactions), but from what I understand of it, it isn't.

 

[Vanadium 50]

One of my neighbors is a PhD physicist who was a naval commander before retirement. He says there definitely is an attractive "force" between two ships when they are very close, and it is attributed to the relatively calmer wave structure between them.

From "Interstellar Technologies"? Are you sure that's a reputable site?

And the fact your neighbor used to be in the Navy makes "Interstellar Technologies" reputable exactly why?

 

[conway]

Exactly, we could always enclose a volume of vacuum with reflectors on the exterior surface and absorbers on the interior, ensuring that radiation does not flow into the volume and any existing radiation inside will be dissipated...

It's not so easy. Any "aborber" must absorb a full quantum of energy; otherwise it will just re-radiate it. If the total amount of energy at a certain frequency is less than one quantum, how do you "absorb" it?

I'm not sure you can experimentally disprove the claim that the vacuum is full of classical e-m energy. Some people say it's a "fact", but I don't know how you would prove it either way.

 

[Born2bwire]

It's not so easy. Any "aborber" must absorb a full quantum of energy; otherwise it will just re-radiate it. If the total amount of energy at a certain frequency is less than one quantum, how do you "absorb" it?

Who cares? It's a thought experiment in regards to map19's statements. There is a background level radiation in the universe but it is not assumed to exist in the calculation of Casimir effects. The vacuum fluctuations that can be used as a means of calculating the Casimir effects are not directly observable. There are no photons and the expectation of the field values are zero. These are different from the background radiation.

 

[conway]

Who cares? It's a thought experiment in regards to map19's statements...

I don't know what you mean when you say "who cares?". You suggested a thought experiment and I offered the opinion that your thought experiment wouldn't work. Do you think I'm wrong or are you just saying you don't care if it works or not?

I would say that I care at least to the extent of being interested in whether or not I raised a valid rebuttal to your thought experiment.

 

[Vanadium 50]

the vacuum of space is full of radiation

I'm not sure you can experimentally disprove the claim that the vacuum is full of classical e-m energy.

Note that your statement is different than map19's.

Just out of curiosity, how many of the people here who are attempting to explain the Casimir effect have calculated it themselves, and how many have read about it in popularizations?

 

[conway]

Note that your statement is different than map19's.

I actually knew that.

But more to the point, in re-reading the thread, I see that I was responding equally well to your point about space being "most assuredly not" full of radiation; Bob S merely gave a better, more operational version of the same claim.

 

[Bob S]

From Bob S
One of my neighbors is a PhD physicist who was a naval commander before retirement. He says there definitely is an attractive "force" between two ships when they are very close, and it is attributed to the relatively calmer wave structure between them.
Originally Posted by Vanadium 50
From "Interstellar Technologies"? Are you sure that's a reputable site?

And the fact your neighbor used to be in the Navy makes "Interstellar Technologies" reputable exactly why?

(My neighbor is the only person I know who can write out the proof of the Brachistochrone problem w/o referring to his book collection. He is very sharp.) This effect, whether due to true Casmir forces or not, is taught to graduates of the U.S. Naval Academy in Annapolis. This has nothing to do with the trustworthyness of Interstallar Technologies.
Here is another version from Chemistry Daily
http://www.chemistrydaily.com/chemistry/Casimir_effect:
An effect analogous to the Casimir effect was observed by 18th century French sailors. Where two ships are rocking from side to side in conditions with a strong swell but light wind, and the ships come closer together than roughly 40 m, destructive interference eliminates the swell between the ships. The calm sea between the ships has a lower energy density than the swell to either side of the ships, creating a pressure that can push the ships closer together. If they get too close together, the ships' rigging can become entangled. As a countermeasure, a handbook from the early 1800s recommends that each ship should send out a boat rowed by 10 to 20 sailors to physically pull the ships apart.
Here is another from http://scienceweek.com/2004/sa041119-6.htm (see ref 5.)
3) Although the Casimir effect is deeply rooted in the quantum theory of electrodynamics, there are analogous effects in classical physics. A striking example was discussed in 1836, in P. C. Caussee's L'Album du Marin (The Album of the Mariner)(5). Caussee reported a mysteriously strong attractive force that can arise between two ships floating side by side -- a force that can lead to disastrous consequences. A physical explanation for this force was offered only recently by Boersma (1996), who suggested that it originates in the radiation pressure of water waves acting differently on the opposite sides of the ships. His argument goes as follows: the spectrum of possible wave modes around the two ships forms a continuum (any arbitrary wave-vector is allowed); but between the vessels their opposing sides impose boundary conditions on the wave modes, restricting the allowed values of the component of the wave-vector that is normal to the ships' surfaces. This discreteness created in the spectrum of wave modes results in a local redistribution of modes in the region between the ships, with the consequence that there is a smaller radiation pressure between the ships than outside them.

References (abridged):

1. Casimir, H. B. G. Proc. Kon. Ned. Akad. 51, 793-795 (1948).

2. Bordag, M., Mohideen, U. & Mostepanenko, V. M. Phys. Rep. 353, 1-205 (2001).

3. Kenneth, O., Klich, I., Mann, A. & Rezen, M. Phys. Rev. Lett. 89, 033001 (2002).

4. Boyer, T. H. Phys. Rev. A 9, 2078-2084 (1974).

5. Caussee, P. C. L'Album du Marin (Mantes, Charpentier, 1836).

 

[conway]

I actually knew that.

But more to the point, in re-reading the thread, I see that I was responding equally well to your point about space being "most assuredly not" full of radiation; Bob S merely gave a better, more operational version of the same claim.

Sorry, I meant Born2BWire, not Bob S.

 

[Born2bwire]

Note that your statement is different than map19's.

Just out of curiosity, how many of the people here who are attempting to explain the Casimir effect have calculated it themselves, and how many have read about it in popularizations?

/me raises hand for calculations.

I don't know what you mean when you say "who cares?". You suggested a thought experiment and I offered the opinion that your thought experiment wouldn't work. Do you think I'm wrong or are you just saying you don't care if it works or not?

I would say that I care at least to the extent of being interested in whether or not I raised a valid rebuttal to your thought experiment.

Any kind of radiation will require photons, there would not be any energy levels less than a quantum. map19's original contention was that actual radiation was a factor in the Casimir force. But this is not assumed in its derivations. The radiation pressure from EM radiation is a separate and known phenomenon. When we calculate the Casimir effects, we are assuming a quantum vacuum as our background medium. If we were to ensure this by having some mythical absorbing box encasing our vacuum, this could be modeled as a boundary condition. To any excited waves and fields inside the box, the medium would be like an infinite vacuum since there would be no reflections off of the absorbers. The Casimir force can be calculated as the result of current and charge fluctuations in and on the scatterers. These fluctuations are akin to the quantum vacuum fluctuations that were used to model the force in Casimir's paper, following the suggestion by Bohr. There are theoretically perfect absorbing boundaries that have been derived for EM waves, like the perfectly matched layer. Any one of these will not affect the waves and fields on the interior. To the interior, it is like being in an infinite medium. As such, such an absorbing box would not affect the current and charge fluctuations on the scatterers and thus would not affect the Casimir energy or force calculations. However, the absorbing box would at least ensure that the results are not from radiating waves.

 

[conway]

There are theoretically perfect absorbing boundaries that have been derived for EM waves, like the perfectly matched layer...

Yes, Z_0 =377. You can make one by rubbing a pencil on a piece of paper. But this is a classically valid theoretical model based on the unbroken continuity of matter. I don't believe you can construct such a perfect boundary using real atoms.

 

[Pythagorean]

From Bob S
One of my neighbors is a PhD physicist who was a naval commander before retirement. He says there definitely is an attractive "force" between two ships when they are very close...

I was a commercial fisherman in Alaska before I ever embarked on an academic journey.

I made the same observation as your naval commander PhD. The way I always thought of it when I was a laymen was that the waves outside the two vessels have higher amplitudes and more energy. The waves between the vessels are constrained by the vessels, they are obviously smaller and have less energy, so we tend to get pushed into each other and smack together.

Of course, wind rogue waves (waves that don't follow the directional trend of all the other waves) tend to mess it up. Sheer forces under the water (such as tide rips) will twist you away from each other, so you still have to tie up to the other boat of course.

It's really interesting to look back on my commercial fishing days with an academic education.

 

[map19]

Thank you for that. This is analogous to the cutoff frequency in a waveguide. As I said before, wavelengths have to be at least a half wave inside the boundaries to exist. Other wavelengths are quickly damped. For a waveguide the cutoff is transverse distance a, the cutoff wavelength is 2a.
So waves outside the two shiips hulls would have long wavelengths and waves inside would only be allowed to be short. The longer waves would dissipate their surface energy against the outer sides of the ships, pushing them together.
Large scale Casimir.
Calculating Casimir force is not hard, it's a mathematical exercise. Following it up with an experiment that gets the same result, that's what a physicist would do.
My belief that EM from the quantum vacuum drives Casimir is still with me. External EM would no doubt be a boost to the process.

 

[Born2bwire]

Yes, Z_0 =377. You can make one by rubbing a pencil on a piece of paper. But this is a classically valid theoretical model based on the unbroken continuity of matter. I don't believe you can construct such a perfect boundary using real atoms.

The impedance of free space is not an absorber. Defining a perfect absorbing boundary is more subtle than that, you have to have a lossy medium that is reflectionless at all angles of incidence but this has been defined. It doesn't matter whether or not we can actually make this, it's a thought experiment.

Thank you for that. This is analogous to the cutoff frequency in a waveguide. As I said before, wavelengths have to be at least a half wave inside the boundaries to exist. Other wavelengths are quickly damped. For a waveguide the cutoff is transverse distance a, the cutoff wavelength is 2a.
So waves outside the two shiips hulls would have long wavelengths and waves inside would only be allowed to be short. The longer waves would dissipate their surface energy against the outer sides of the ships, pushing them together.
Large scale Casimir.
Calculating Casimir force is not hard, it's a mathematical exercise. Following it up with an experiment that gets the same result, that's what a physicist would do.
My belief that EM from the quantum vacuum drives Casimir is still with me. External EM would no doubt be a boost to the process.

External EM would not affect the Casimir effect. There is no change in the energy of the external fields when you change the placement of the scatterers. That is the key point with the quantum vacuum analysis. The energy of the quantum vacuum is dependent upon the physical arrangement of the scatterers. This is not true for an electromagnetic wave. The amount of energy radiated is independent of other scatterers. You could get radiation pressure from the transfer of momentum from the photons but this is different from the Casimir effect.

 

[conway]

The impedance of free space is not an absorber. Defining a perfect absorbing boundary is more subtle than that, you have to have a lossy medium that is reflectionless at all angles of incidence but this has been defined. It doesn't matter whether or not we can actually make this, it's a thought experiment.

With thought experiments, sometimes it does matter whether or not you can actually make it.

 

[Vanadium 50]

It's still not clear to me that the fact that there is a force between two nearby ships means that its analogous to the Casimir effect.

The existence of a force is not sufficient to prove this. There's a force between a baseball and the ground, but it has nothing to do with Casimir. If the force is due, as Pythagorean suggests, to wave amplitude (and traveling wave amplitude) it's a different thing.

Also, from my own (albeit slight) experience on the water, I don't think this force has the right functional dependence to be a Casimir-analogue. If it were, the force would become unstoppable shortly after it became noticed. Remember, Casimir forces grow very quickly with decreasing separation.

 

[nrqed]

From Bob S
One of my neighbors is a PhD physicist who was a naval commander before retirement. He says there definitely is an attractive "force" between two ships when they are very close, and it is attributed to the relatively calmer wave structure between them.
Originally Posted by Vanadium 50
From "Interstellar Technologies"? Are you sure that's a reputable site?

(My neighbor is the only person I know who can write out the proof of the Brachistochrone problem w/o referring to his book collection. He is very sharp.) This effect, whether due to true Casmir forces or not, is taught to graduates of the U.S. Naval Academy in Annapolis. This has nothing to do with the trustworthyness of Interstallar Technologies.
Here is another version from Chemistry Daily
http://www.chemistrydaily.com/chemistry/Casimir_effect:
An effect analogous to the Casimir effect was observed by 18th century French sailors. Where two ships are rocking from side to side in conditions with a strong swell but light wind, and the ships come closer together than roughly 40 m, destructive interference eliminates the swell between the ships. The calm sea between the ships has a lower energy density than the swell to either side of the ships, creating a pressure that can push the ships closer together. If they get too close together, the ships' rigging can become entangled. As a countermeasure, a handbook from the early 1800s recommends that each ship should send out a boat rowed by 10 to 20 sailors to physically pull the ships apart.
Here is another from http://scienceweek.com/2004/sa041119-6.htm (see ref 5.)
3) Although the Casimir effect is deeply rooted in the quantum theory of electrodynamics, there are analogous effects in classical physics. A striking example was discussed in 1836, in P. C. Caussee's L'Album du Marin (The Album of the Mariner)(5). Caussee reported a mysteriously strong attractive force that can arise between two ships floating side by side -- a force that can lead to disastrous consequences. A physical explanation for this force was offered only recently by Boersma (1996), who suggested that it originates in the radiation pressure of water waves acting differently on the opposite sides of the ships. His argument goes as follows: the spectrum of possible wave modes around the two ships forms a continuum (any arbitrary wave-vector is allowed); but between the vessels their opposing sides impose boundary conditions on the wave modes, restricting the allowed values of the component of the wave-vector that is normal to the ships' surfaces. This discreteness created in the spectrum of wave modes results in a local redistribution of modes in the region between the ships, with the consequence that there is a smaller radiation pressure between the ships than outside them.

References (abridged):

1. Casimir, H. B. G. Proc. Kon. Ned. Akad. 51, 793-795 (1948).

2. Bordag, M., Mohideen, U. & Mostepanenko, V. M. Phys. Rep. 353, 1-205 (2001).

3. Kenneth, O., Klich, I., Mann, A. & Rezen, M. Phys. Rev. Lett. 89, 033001 (2002).

4. Boyer, T. H. Phys. Rev. A 9, 2078-2084 (1974).

5. Caussee, P. C. L'Album du Marin (Mantes, Charpentier, 1836).

Fascinating! Thanks for posting all this information

 

[conway]

I just did a seat-of-the-pants Casimir effect calculation which I will post if anyone's interested.

 

[map19]

perhaps you could email instead of posting. mphilo@xtra.co.nz
I would also be interested if anybody knows the correlation between calc numbers and experimental numbers. I expect only about an 80% correlation if em has not been accounted for.

nrqed. your post about the ships is what I said, in different words.
I see an analogy between the ships, frequencies in a waveguide, and the Casimir effect.
Of course the analogy is not exact, when are they ever ? we're talking water, rf, and quantum stuff. But it is similar.

Born2bwire. I think that external em would add to the Casimir force. Why would it not ?
If it's there and given the cutoff inside the plates, there is going to be an imbalance with many more frequencies external than internal, resulting in more momentum transfer outside than inside.

 

[Born2bwire]

perhaps you could email instead of posting. mphilo@xtra.co.nz
I would also be interested if anybody knows the correlation between calc numbers and experimental numbers. I expect only about an 80% correlation if em has not been accounted for.

nrqed. your post about the ships is what I said, in different words.
I see an analogy between the ships, frequencies in a waveguide, and the Casimir effect.
Of course the analogy is not exact, when are they ever ? we're talking water, rf, and quantum stuff. But it is similar.

Born2bwire. I think that external em would add to the Casimir force. Why would it not ?
If it's there and given the cutoff inside the plates, there is going to be an imbalance with many more frequencies external than internal, resulting in more momentum transfer outside than inside.

The first paper on accurate measurements of the Casimir force got results in agreement of 5%, S. K. Lamoreaux, Phys. Rev. Lett. Volume 78, page 5 which used corrections for the non-zero temperature and finite conductivity of the scatterers. Again, the reason why they will not have an effect is that the presence of a scatterer does not change the total energy of the EM radiation nor, more importantly, is the total energy dependent upon the position of the scatterers. The Casimir effect, relies on the fact that the presence of and position of scatterers affects the energy of the system, whether it is the vacuum state or say the quantum fluctuation currents and charges. The change in energy due to the change in position results in the force along the direction of spatial variation.

 

[Halcyon-on]

As reported in the professional physics literature in 1995, an entirely classical, that is, non-quantum, treatment of the Casimir force is all is needed to explain the mysterious attractive force

Bob S: can you give me the exact reference of the paper you pointed out.

I'm very sorry if what I'm going to say cannot be used in fiction movies or starships stories, but it turns out that that the Casimir effect is one of the biggest and most misleading myths of quantum mechanics. The fact is that the "Casimir’s original goal was to compute the van der Waal’s force between polarizable molecules at separations so large that relativistic (retardation) effects are essential. [...] These results were derived using the
standard apparatus of perturbation theory (to fourth or-
der in e) without any reference to the vacuum."

ref{ Title:"The Casimir Effect and the Quantum Vacuum"
arXiv:hep-th/0503158v1
Journal:Phys.Rev. D72 (2005) 021301
Abs: In discussions of the cosmological constant, the Casimir effect is often invoked as decisive evidence that the zero point energies of quantum fields are "real''. On the contrary, Casimir effects can be formulated and Casimir forces can be computed without reference to zero point energies. They are relativistic, quantum forces between charges and currents. The Casimir force (per unit area) between parallel plates vanishes as \alpha, the fine structure constant, goes to zero, and the standard result, which appears to be independent of \alpha, corresponds to the \alpha\to\infty limit.}

 

[Born2bwire]

Bob S: can you give me the exact reference of the paper you pointed out.

I'm very sorry if what I'm going to say cannot be used in fiction movies or starships stories, but it turns out that that the Casimir effect is one of the biggest and most misleading myths of quantum mechanics. The fact is that the "Casimir’s original goal was to compute the van der Waal’s force between polarizable molecules at separations so large that relativistic (retardation) effects are essential. [...] These results were derived using the
standard apparatus of perturbation theory (to fourth or-
der in e) without any reference to the vacuum."

ref{ Title:"The Casimir Effect and the Quantum Vacuum"
arXiv:hep-th/0503158v1
Journal:Phys.Rev. D72 (2005) 021301
Abs: In discussions of the cosmological constant, the Casimir effect is often invoked as decisive evidence that the zero point energies of quantum fields are "real''. On the contrary, Casimir effects can be formulated and Casimir forces can be computed without reference to zero point energies. They are relativistic, quantum forces between charges and currents. The Casimir force (per unit area) between parallel plates vanishes as \alpha, the fine structure constant, goes to zero, and the standard result, which appears to be independent of \alpha, corresponds to the \alpha\to\infty limit.}

That is Jaffe's paper is it not? It is a good read.

 

[Halcyon-on]

That is Jaffe's paper is it not? It is a good read.

Yes, it is the Jaffe's paper. Very enlightening indeed.