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July 30, 2010 / zitterbewegung

Zero-Point Fiction, A wake-up call to the free energy community?

Well for all the folks in the “energy for nothing” club, it turns out that there is a growing body of literature that dismisses zero-point electromagnetic energy as a physically observable phenomenon. Every since the dawn of quantum field theory, this item has been heavily debated.

The vacuum of space-time boils like a huge cauldron with virtual electromagnetic fluctuations. John Wheeler referred to this as a quantum foam (in analogy to the bubbles in a beer). The ‘free energy gang’ has been spouting grandiose claims about this bounty of power since the time of Nicola Tesla (who by the way I happen to have a ton of admiration and respect for and I personally believe that many of Tesla’s ideas are taken out of context).

Well, it might be all for naught! This whole issue is likely to be a misinterpretation of experimental data about the way molecular electric fields behave, known as the Van der Waals forces. These forces are very significant at the surface of very small objects (e.g., a few hundred atoms). This point was raised in a paper in Physical Review Letters in 2005. Here the author points out that,

Casimir effect gives no more (or less) support for the reality of the vacuum energy of fluctuating quantum fields than any other one-loop effect in quantum electrodynamics, like the vacuum polarization contribution to the Lamb shift, for example.

Jaffe goes on to say,

The Casimir force can be calculated without reference to vacuum fluctuations…There is a long history and large literature surrounding the question whether the zero-point fluctuations of quantized fields are ‘‘real’’

The whole point here is that this view says that the ZPE is “strictly” a property of the vacuum that is NOT accessible by any means. Let’s take a quick look at what quantum mechanics says about the world in which we live.

When objects in the everyday experience move we say that they obey Newton’s laws of motion, the basis of classical mechanics. Take for instance the motion of a bowling ball, we can toss it down the lane and know with “certainty” that it will hit those pins (unless you’re a career gutter bowler). With quantum motion things are not so simple. When we let go of the ball it is like it vanishes into la-la land (this is actually called Hilbert space in the books). Let’s look at this from an example, 1) is the classical (Newtonian) example (that’s a risky shot for a novice, but an old pro like me can use those to rack up a 190 on my slow nights!) 2) is the quantum example. Notice that the moment you let go of the ball it just spreads out like a cloud. By the time it gets down to the pins it a complete matter of probability as to which pin it strikes!  (in other words, quantum mechanics and bowling don’t mix!)

The ‘quantum nature’ of the ball is described by a so-called wavefunction. As the name implies, this means that the ball exhibits wave-like behavior when travelling and particle-like behavior when touching (i.e. interacting) with something. For those of you concerned about the ball merely hovering outside the lane, we’ll suppose that the lane acts as a boundary. Also the lane has magical properties (i.e. it can’t collapse the wavefuction and let us see the ball rolling on the classical path).

 So what is all this zero-point stuff about anyhow?

The ZPE is the term used to represent the lowest possible state of energy in the physical vacuum of space-time. Consider the diagram below, notice the term with the 1/2 in front (and the fact that it resides BELOW the zero energy line!) it’s the ZPE,

This diagram is an obvious ladder of rising energy states. Since the terms are quanta of radiation or photons, then the ladder can be thought of as small additions of thermal energy as you climb the rungs. This was actual how Planck made has break though discover that radiation was quantized into discrete packets, and this lead to the resolution of the infamous ultraviolet catastrophe. If we examine the 1/2 term there seems to be no energy present at all, so no heat, hence the moniker zero-point energy or “motion at absolute zero.”

Next we need to draw a distinction between just quantum mechanics and quantum field theory. In quantum mechanics we do what is called the first quantization. This is because the usual quantities we measure, the canonical quantities like position, momentum and energy are transformed into differential operators.

On the other hand in quantum field theory, it is the field itself that gets quantized this is referred to as second quantization. By the way, the two types of quantization are completely unrelated and very different. It is unfortunate that they got labeled 1st and 2nd as this suggests that the 2nd somehow is a subsequent procedure to the 1st. below a classical field is quantized,

Notice the field lines are transformed into a cloud of virtual quanta. This picture of second quantization gives us the intuitive notion of how the virtual quanta interact with the electromagnetic fluctuations of the vacuum.

Another note on the difference between 1st and 2nd quantization is in order. Recall in quantum mechanics we already postulated the dual wave-particle nature of matter, the wave function. But the goal of a quantization program is to create discrete representations of forces or quantities related to forces, but not masses. Notice in the diagram above the particle or mass remains unchanged by quantization, this is because the mass is treated as the origin of the charge or source. This invariance of mass under quantization is related to the fact that mass is an invariant scalar quantity. This is a subtlety that I shall not cover here as it is unnecessary to the present discussion. In field-theoretic terms this is referred to as a bare quantity. When calculating interactions of quantum fields it is typical to remove the bare quantities by a process called renormalization, which is also beyond the scope of this post so I will not venture into it.

What I’m driving at with all this is that you can’t make the quantum level of reality ‘stop moving.’ Remember that an everyday object has a well-defined position in space, but a thing as small as an atom doesn’t. This example gets even more extreme if we look at the physical vacuum of space-time. It is a random bath of virtual quanta also referred to as ‘off-shell’ photons. A virtual quanta is like a photon that you can’t observe directly, yes, it is only endowed with a quantum mechanical nature, recall the cloud around the source above.

We actually need to draw another distinction at the is point in the game, that is that fact that the field composed of virtual quanta exists INDEPENDENTLY of any source. We can think of the existence of the quantum field with a source at the origin as a means of ‘organizing’ the zero point electromagnetic vacuum fluctuations. This matter is studied in the subject of quantum electrodynamics or QED which is concerned with how electrons (or charged particles in general) and photons interact. One prominent example describing the exchange of virtual quanta is when two atoms or electrons get close to each other this is described by a process called Moller Scattering.

This is a t-channel Feynman graph that represents this process with two electrons interacting at the tree level. By tree level, it means the process is calculated to the lowest order that can be experimentally measured. Notice the blue wavy line, that’s the virtual photon. You can think of this as the electrons pushing on each other with their respective electric fields.

The conventional way to understand zero point energy in quantum field theory is by the crossing symmetry of the creation and destruction operators,

Where the first one is the destruction operator and the second is the creation operator. The q and p are coordinates and momenta of the fields respectively. If the destruction operator acts on the vacuum, it destroys as quanta so the result is zero. Conversely if the creation operator acts on the vacuum it creates a quanta of momentum k,

That’s not the end of the story though. The creation and destruction operators are built out of positive and negative frequency components. So the beauty of this approach is the elegant analogy with Young’s double slit experiment in optics and the notion of interference. The zero-point energy is a result of the superposition of these positive and negative frequency component of the creation and destruction operators,

It is a common procedure to ‘remove’ the ZPE from calculations by the process called Normal Ordering. This is accomplished by separating the positive and negative products in the fields and placing all the positive to the left, and negative to the right. This is envisioned as letting the operators take a direct path as opposed to an exchange path (which would create the interference and ZPE).


[2] Quantum Field Theory: A Modern Introduction, M. Kaku

[3] Modern Quantum Mechanics, J. Sakurai


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