Can not be done (?)
Date: Friday, September 16, 2005 @ 23:06:07 GMT
Topic: Science

From an older SciAm article; Matt Visser of Washington University in St. Louis adds some technical details on why the science is sure we should not bother with trying to find a way to harness ZPE for useful, inexhaustible, clean power (if it were that clear & simple!):

"The Zero Point Energy (ZPE) is an intrinsic and unavoidable part of quantum physics. The ZPE has been studied, both theoretically and experimentally, since the discovery of quantum mechanics in the 1920s and there can be no doubt that the ZPE is a real physical effect.

The "vacuum energy" is a specific example of ZPE which has generated considerable doubt and confusion. In a completely empty flat universe, calculations of the vacuum energy yield infinite values of both positive and negative sign--something that obviously does not correspond to the nature of the real world.

Observation indicates that in our universe the grand total vacuum energy is extremely small and quite possibly exactly zero. Many theorists suspect that the total vacuum energy is exactly zero.

It definitely is possible to manipulate the vacuum energy. Any objects that change the vacuum energy (electrical conductors, dielectrics and gravitational fields, for instance) distort the quantum mechanical vacuum state. These changes in the vacuum energy are often easier to calculate than the total vacuum energy itself. Sometimes we can even measure these changes in the vacuum energy in laboratory experiments.

In classical physics, if you have a particle that is acted on by some conservative force, the total energy is E = (1/2) mv2 + V(x). To find the classical ground state, set the velocity to zero to minimize the kinetic energy, (1/2)m v2, and put the particle at the point where it has the lowest potential energy V(x). But this result is only a classical approximation to the real world. Because the classical ground state completely specifies both the particle's speed (zero) and position (at the minimum), it violates the famous Heisenberg Uncertainty Principle (m dv dx > hbar). Quantum physics, via the Uncertainty Principle, forces the particle to spread out both in position and velocity and so causes it to have an energy somewhat higher than the classical minimum. The ZPE is defined as this shift:

E(ZPE) = E(quantum minimum) - E(classical minimum) > 0

Classically, we can calculate the natural oscillation frequency that the particle would have if we were to give it a small push. Quantum mechanically, it is now an undergraduate exercise to use the Heisenberg uncertainty relation (more precisely, Schroedinger's differential equation) to show that

E(ZPE) approx. = (1/2) hbar omega0

where hbar is Planck's constant times and omega0 is the natural oscillation frequency. The ZPE in this sense shows up almost everywhere: it affects molecular bonds, condensed matter physics, small oscillations of any system.

The next step is to realize that the electromagnetic field can be thought of as an infinite collection of coupled oscillators--one at each point in space. Again, the classical ground state is the case in which the electric and magnetic fields both must be zero. Quantum effects mean that this case does not hold true; there is also a Heisenberg uncertainty principle for electric and magnetic fields (it's a little more complex). The good news is that the potential for electromagnetism is exactly quadratic and so can be solved exactly. The bad news is that there is an infinite number of modes. Formally we can write

(Electromagnetic vacuum energy) = sum over all modes (1/2) hbar omega(mode)

The infinity in this equation is what excites the free lunch crowd (the modern descendants of the perpetual motion crowd), who envision an endless ZPE for humanity to tap into. Not quite, unfortunately..

The first and most obvious problem is that there are other quantum fields in the universe apart from electromagnetism. Electrons, for starters, plus neutrinos, quarks, gluons, W, Z, Higgs and so on. In particular, if you do the calculation for electrons you will find that what are known as Fermi statistics give rise to an extra minus sign in the calculation.

Adding minus infinity to plus infinity gives mathematicians nightmares and even makes theoretical physicists worry a little. Fortunately, nature does not worry about what the mathematicians or physicists think and does the job for us automatically. Consider the grand total vacuum energy (once we have added in all quantum fields, all particle interactions, kept everything finite by hook or by crook, and taken all the proper limits at the end of the day). This grand total vacuum energy has another name: it is called the "cosmological constant," and it is something that we can measure observationally.

In its original incarnation, the cosmological constant was something that Einstein put into General Relativity (his theory of gravity) by hand. Particle physicists have since taken over this idea and appropriated it for their own by giving it this more physical description in terms of the ZPE and the vacuum energy. Astrophysicists are now busy putting observational limits on the cosmological constant. From the cosmological point of view these limits are still pretty broad: the cosmological constant could potentially provide up to 60 percent to 80 percent of the total mass of the universe.

From a particle physics point of view, however, these limits are extremely stringent: the cosmological constant is more than 10(-123) times smaller than one would naively estimate from particle physics equations. The cosmological constant could quite plausibly be exactly zero. (Physicists are still arguing on this point.) Even if the cosmological constant is not zero it is certainly small on a particle-physics scale, small on a human-engineering scale, and too tiny to be any plausible source of energy for human needs--not that we have any good ideas on how to accomplish large-scale manipulations of the cosmological constant anyway.

Putting the more exotic fantasies of the free lunch crowd aside, is there anything more plausible that we could use the ZPE for? It turns out that small-scale manipulations of the ZPE are indeed possible. By introducing a conductor or a dielectric, one can affect the electromagnetic field and thus induce changes in the quantum mechanical vacuum, leading to changes in the ZPE. This is what underlies a peculiar physical phenomenon called the Casimir effect. In a classical world, perfectly neutral conductors do not attract one another. In a quantum world, however, the neutral conductors disturb the quantum electromagnetic vacuum and produce finite measurable changes in the energy as the conductors move around. Sometimes we can even calculate the change in energy and compare it with experiment. These effects are all undoubtedly real and uncontroversial but tiny.

More controversial is the suggestion, made by the physicist Julian Schwinger, that the ZPE in dielectrics has something to do with sonoluminescence. The jury is still out on this one and there is a lot of polite discussion going on (both among experimentalists, who are unsure of which of the competing mechanisms is the correct one, and among theorists, who still disagree on the precise size and nature of the Casimir effect in dielectrics.) Even more speculative is the suggestion that relates the Casimir effect to "starquakes" on neutron stars and to gamma ray bursts.

In summary, there is no doubt that the ZPE, vacuum energy and Casimir effect are physically real. Our ability to manipulate these quantities is limited but in some cases technologically interesting. But the free-lunch crowd has greatly exaggerated the importance of the ZPE. Notions of mining the ZPE should therefore be treated with extreme skepticism."

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