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Tuesday, 6 April 2010

Casimir effect, vacuum fluctuations and zero-point energy.

Or what I make of it.

'Any intelligent fool can make things bigger and more complex... It takes a touch of genius - and a lot of courage to move in the opposite direction.' Albert Einstein.

It turns out a great number of science lovers seek simple explanation of abstruse scientific topics rather than techno-babble and a pile of mind-bending equations. As one great physicist said, if you can’t break a complex scientific question down so that even your granddad understands it, you yourself don’t understand it. Whenever we come across such questions we relish the chance to stretch our thinking muscles and give our lay associative insights into the matter.

First, to put it simply, classical mechanics deals with macroscopic objects, that is, things visible to the naked eye, while quantum mechanics deals with the wave-particle duality of atoms and molecules. That said, according to quantum field theory (quantum description of a physical field), the Casimir effect is a physical force produced by quantised field.
A classical experiment to detect the Casimir effect consists in two uncharged metallic plates placed in a vacuum a few micrometers apart without any external electromagnetic field.

By the way, vacuum is a volume of space free of matter, although quantum theory holds that no volume of space is perfectly empty, that is, free of matter — even in interstellar space there are still a few hydrogen atoms per cubic centimetre.
 I wonder, as an aside, if the space between these hydrogen atoms could be considered a perfect (although minuscule) vacuum, since there would be literally nothing between them left!
Strictly speaking, vacuum is not in the least an empty space — on the contrary, is made up of quantised fields, vacuum being simply the lowest possible energy state of these fields. (According to Unruh ‘the notion of vacuum depends on the path of the observer through space-time. The accelerating observer will see the vacuum of the inertial observer like a state containing many particles in thermal equilibrium — a warm gas.’)

Classical physics maintains that the absence of an external field rules out the existence of a field between the plates and therefore of any force. However, if you study the case using quantum electrodynamics (quantum description of the creation and annihilation of quantum particles and how light and matter interact that also provides mathematical description of interactions between electrically charged particles through exchange of photons), you’ll supposedly see that virtual photons which make up a field are somehow affected by the plates, which results in the generation of a net force — either an attraction or repulsion depending on the way you arrange the plates.
At least scientists claim the force was measured and turned out to be within 5% of its predicted value, which, personally, makes me doubt whether they (the scientists) know exactly what was measured.

The strength of the force falls off rapidly with distance; it can only be measured when the distance between the objects is extremely small. On a submicrometre scale (separations of 10 nm—about 100 times the typical size of an atom—the Casimir effect produces the equivalent of 1 atmosphere of pressure), this force gets strong enough to become the dominant force between uncharged conductors. I guess such small distances only make sense in the field of micro technologies and nanotechnologies.

Casimir effect. Casimir plates
Casimir effect and vacuum fluctuations.
Casimir forces on parallel plates

'We are all agreed that your theory is crazy. The question that divides us is whether it is crazy enough to have a chance of being correct.'
Niels Borh. Speech on quantum theory at Celebrazione del Secondo Centenario della Nascita di Luigi Galvani, Bologna, Italy (October 1937)

What causes the Casimir effect? One interpretation is that the presence of conducting metals and dielectrics alters the vacuum expectation value of the energy or the vacuum energy (since its particle properties such as spin, polarization etc, cancel out) of the second quantized electromagnetic field (expected value in the vacuum). The lowest possible vacuum energy is zero-point energy. Probably a stupid question, but I wonder if no-energy state is possible, too.
Don’t worry about second quantization: when quantum mechanics studies a fixed number of particles through a wave function, it’s first quantization; when this wave function is used to deal with the theory of many particles, it’s second quantization.

The value of this energy depends on the shapes and positions of the conductors and dielectrics, so the Casimir effect makes its appearance as a force between such objects.

The field is considered a simple harmonic oscillator at each point in space, and the quantized field has a quantum harmonic oscillator at each point. To find the value of this force all possible oscillators at all points in space are added together, but the catch is that we get an infinite quantity. To my eye, in most cases infinity doesn’t make much sense (at least from a human’s point of view it’s equal to “never”), and it looks like neither does it to scientists, since they always try to remove it, for example by means of renormalization in all practical calculations. However, renormalization is unsatisfying and the removal of this infinity is still a pitfall on the thorny road to a Theory of Everything. In my humble opinion, many mathematical equations make no physical sense (like imaginary numbers and other artificial devices — a sort of Deus Ex Machina), but that’s probably due to my uneven relationship with maths.

Actually, the Casimir effect is commonly believed to be proof of the existence of zero-point energy in vacuum (the quantized electromagnetic field between a pair of grounded, neutral metal plates), but there isn’t a consensus among scientists on whether vacuum energy explains the Casimir effect as the force can be explained equally well by charge-current interactions (van der Waals force). Although the Casimir effect can be put down to virtual particles interacting with the objects, it is more easily calculated in terms of the zero-point energy of a quantized field in the intervening space between the objects.

Some brilliant calculation that underlies the Casimir experiment predicted the infinite vacuum energies, and I can picture many people jumping for joy and greed welling up within them, relishing the prospect of tapping into infinite amounts of zero point energy source for free. Luckily, there is no theoretical basis or practical evidence to support such possibility. Admittedly, the zero point energy might be infinite, which would allow to create Perpetuum mobile, but that sounds too good to be true — what about a violation of conservation of energy? There’s no such thing as free lunch. Anyway, if some day something like this proves to be true, it will mostly benefit the rich (their dream of zero investment and infinite profits would come true), the rest of us, as usual, will get the leftovers.
So far, humans have never managed to get round the fundamental laws of nature, probably because, in the first place, we don’t deserve it as a species. I mean, we still get ill, age and die, and to the best of my knowledge there’s no way to break this cycle as of yet.

Some scientists believe exotic matter (a hypothetical concept — material which violates one or more energy conditions or is not made of known baryonic particles) with negative energy density is required to stabilize a wormhole, which I’m at a loss to understand.
The closest known real representative of exotic matter is a region of pseudo-negative pressure density produced by the Casimir effect, or so they say. Therefore, if the Casimir effect could be used to produce a local region of negative mass, its effect would stabilize a wormhole and allow faster than light travel.
Roughly speaking (because there’re three concepts of mass: active gravitational, passive gravitational and inertial, and each can be negative or positive) negative inertial mass should allegedly accelerate in the opposite direction to that in which it’s pushed, to take the weirdness even further negative masses would supposedly be attracted to positive masses, yet positive masses would be repelled away from negative masses. As clear as mud.

Looks like one mass would be chasing another, I doubt anyone is really able to make any sense of it. The most tempting prospect of the combined system of positive and negative particles is that it would accelerate indefinitely without any additional input into the system. Again, an inexhaustible source of energy! However, for the time being this stuff seems to belong to the realm of science fiction rather than physics.

It turns out, the dynamic Casimir effect is theoretically possible as well — the production of particles and energy from an accelerated boundary, aka a 'moving mirror' or 'motion-induced radiation', but it hasn’t been verified experimentally yet. Basically, it’s used to explain acceleration radiation (Unruh effect — an accelerating observer would record black-body radiation, i.e. heat, where an inertial observer wouldn’t). What experiments do have demonstrated recently is the Casimir-based levitation due to repulsive forces between uncharged objects.

Well, to sum it all up, for now these theories seem to be plucked out of thin air to explain mysteries in ‘Lost’, rather than to be of some use in real life.
I hope so — to be honest, nanotechnology scares the living daylights out of me.

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  1. So, where's the explanation for grandfather? Maybe you don't wanna' bother him with "thin air"?

    What Einstein says in the beginning is right. In music I believe this absolutely: I never considered the fuga being too genius, but it takes lots of genius to create Antonin Dvoraks 8th Symphony. He had an idea, evaporated this and the result he evaporated again, again and again ... extract of an extracted extract of an extract.

    In history and sociology it's different: If you break it down to simple structures, you fail reality. Whenever you study original books from the past, which talk about everyday-live, you experience how poor and flat the thoughts in history-books are. But well, if I offer original thoughts of the 17th/18th century, Granddad won't eat it. I just tell him, I was in 1710 and had a very interesting conversation with a gallant cavalier in Amsterdam. We talked about Menuet and various masters of gallant dancing we had consulted. We sat in the cavalier's garden and the weather was fine. The particular items about gallant dancing and gallant philosophy won't interest him.

    No I won't evaporate an extract for grandfather, because this would give me a pain. ;)

  2. Well, I thought I explained the subject pretty simply.
    No doubt, history can best be learned from the contemporaneous works of literature, rather than history manuals.

  3. Bonjour,

    Vous êtes cordialement invité à visiter mon blog.

    Description : Mon Blog(, présente le développement mathématique de la conscience humaine.




    Clovis Simard

  4. Merci beaucoup pour l’invitation. Vous été très gentil. Je vais à visiter votre blog bientôt.


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