Zero-Point Energy Demystified (Script) (Patreon)

The mysterious zero-point energy - the quantum vacuum - has been a misrepresented subject of science fiction and science baloney for too long. Let’s talk about what vacuum energy really can, and really can’t do.

It seems pretty crazy that space itself might contain a higher density of energy than the nucleus of the atom. This is the prediction of quantum field theory; there exists an energy of the vacuum resulting from the non-zero zero-point energies of the quantum fields that fill our universe. For the electromagnetic field alone, this energy density has been estimated to be up to a crazily high 10^112 ergs/cm^3. On the other hand, our observations of the accelerating expansion of the universe suggest a vacuum energy density of 10^-8 ergs/cm^3. As we discussed in our episode on the vacuum catastrophe, this mismatch between the measured and theoretical values of vacuum energy is one of the greatest unsolved problems in physics.

Despite this minor glitch, quantum field theory is arguably the most successful theory in all of physics in terms of sheer predictive power. This means we should take the idea of zero-point energy seriously, and are justifiably perplexed at the mismatch between theory and measurement. But the scientific validity of zero-point energy has also encouraged some pretty terrible pseudoscience and outright quackery on the subject. From accessing this energy as a free power source, manipulating it to generate warp fields, or pushing against the vacuum energy in a propulsionless spaceship engine. Today I want to debunk some of the nonsense surrounding the quantum vacuum.

Let’s start with the physics. If the vacuum has an energy density of 10-to-the-power-of-ridiculous ergs/cm^3 where is it? Why can’t we pull infinite free energy out of nothing? The answer lies in entropy and the 2nd law of thermodynamics. Entropy can be thought of a measure of the “specialness” of the arrangement of a system of particles; higher entropy means a more disordered arrangement. The universe tends towards disorder, and so a highly unusual arrangement will decay over time; the entropy of a closed system always increases. That’s the 2nd law of thermodynamics right there. We harness that decay of order whenever we draw energy from a system.

For example the piston in a car engine only rises when the interior chamber becomes much hotter than the exterior. The combined volume of the inside and outside of the piston chamber is in a low-entropy configuration – it’s a special, “unusual” configuration of particles. In its return to high-entropy equilibrium, energy is extracted and your car accelerates. But try to drive your car in a dense 1500 Kelvin atmosphere and that piston has no reason to expand – it’s already in equilibrium. Your car doesn’t go anywhere…  and then it explodes.

So even if a system contains a lot of energy that energy may be inaccessible. This would be the case with even an extremely energetic quantum vacuum. On its own, the vacuum is the same everywhere; it’s already in perfect equilibrium. Energy is extracted in the movement towards equilibrium; in the increase of entropy. No such movement is possible for the vacuum, and so the vacuum contains no useful energy. This is why so-called zero-point energy machines are baloney. They claim to access an inexhaustible source of energy, but no such source exists.

In order to access vacuum energy we’d need to introduce a disequilibrium. In fact we’d need to reduce the vacuum energy in one region of space. The universe would then try to fill that energy hole and we could harness that to extract work. In fact there’s one way to do that: with the Casimir effect. If you bring a pair of conducting plates very close together, a proportion of the virtual particles will be excluded from between them. By cutting off certain frequency modes between the plates you lower the vacuum energy in that region. The result is a pressure differential that produces a measurable force, pulling the plates together.  We talk about this in detail here. So what about building a Casimir engine? Unfortunately no. While that initial pull between the plates may seem like a free lunch, to extract continuous energy you need to pull the plates apart again. This takes as much energy as you originally gained.

Another popular notion is that the reduction of energy between Casimir plates can be considered negative energy, and so could be useful for all of those wonderful things that negative energy can do: like opening wormholes or creating an Alcubierre warp field. If we define the average vacuum energy as “zero”, then the Casimir effect produces negative energy. Unfortunately the vacuum energy between Casimir plates is very much positive in an absolute sense. The gravitational effect of energy depends on its absolute value. That means the vacuum energy between Casimir plates still produces positive curvature, not the negative curvature required for warp drives.

Another popular “use” for the quantum vacuum is as a medium to push against for propulsionless engine systems like the EM drive. This notion is especially silly. The fact is, any acceleration of a real particle involves a transfer of momentum between real particles via virtual particles. Virtual particles, and hence the quantum vacuum, mediate all forces. However it’s not possible to transfer momentum from a real particle to the vacuum without getting another real particle out the other end. That momentum must be given up by the vacuum to produce real particles again. Those particles would become the propellant, carrying momentum away. In the case of the EM drive, the proposal is that microwaves within the drive’s resonance chamber push against the quantum vacuum. If particles are somehow extracting momentum from the resonance chamber, then they’re giving it up again to real particles – probably photons – on the outside. This would certainly produce thrust, but no more than the rather anemic photonic thruster.

So don’t believe the hype. Vacuum energy is real, and it is part of the fundamental clockwork of the universe. It’s probably very weak, weighing in at 10^-8 ergs/cm^3. Regardless of its strength it’s NOT accessible to us as an energy source or as a miracle resource for fast space travel. Sorry internet.

All that said, the quantum vacuum does have its uses. Just ask the gecko. Geckos are able to cling to almost any surface by making use of van der Waals forces, which are essentially the same thing as the Casimir force. The pads of gecko feet are covered with millions of tiny hairs call setae. These hairs split into millions of spatula-shaped ends that are around .2 micrometers in diameter. When the gecko presses its cute little feet onto any surface, a fraction of these hairs are close enough to the surface so that Casimir forces come into effect. Geckos literally manipulate vacuum energy to climb walls.

This suggests a good challenge question. Let’s say that adult geckos are able to efficiently apply 200 thousand setae at any one time to a surface, and each seta produces sufficient van der Waals force to withstand 200 microNewtons of shear force. How many geckos do you need to catch and put on leashes in order to drag you up any wall, using only the power of the quantum vacuum?

And I guess we should have an extra credit question: as we saw last week, the theoretical density of the vacuum energy of the electromagnetic field is estimated by integrating the energy in all possible frequency modes up to some cutoff frequency. You get that the vacuum energy density is proportional to the fourth power of that cutoff frequency. Based on the vacuum energy densities we’ve already talked about, answer me this: what cutoff frequency is needed for this theoretical estimate to give the energy density implied by dark energy? And is this a possible maximum virtual photon frequency given the results of Casimir effect experiments? Why or why not?

Email your answers to pbsspacetime@gmail.com within two weeks of release of this video. Use the subject line Zero-Point Challenge because we filter by subject line. And make sure you show all your work! We’ll choose 6 correct answers to win one of our t-shirts, so you can show of your mastery of mysteries of space time.