# FOLLOW-UP: What is the 'zero-point energy' (or 'vacuum energy') in quantum physics? Is it really possible that we could harness this energy?

The earlier replies to this question established the implausibility of drawing on the zero point energy for practical use. Matt Visser of Washington University in St. Louis adds some technical details:

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.

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1. 1. BillT 09:09 PM 2/2/09

Can you update this article and provide some information on these two gentlemen? They have been doing research in this field for some time and were awarded a patent in May.

http://www.calphysics.org/Patent7379286.pdf

2. 2. Liljencroowna 04:01 PM 5/25/09

Yes, I agree with BillT.

3. 3. allen007 07:16 PM 10/17/09

Here is just a thought. There is inherently "energy" in space, as there is energy in the exhaust of a jet as it travels through the atmosphere. Is it collectible and usable? Not on a safe scale. The problem would be that you may create an energy void at the point of collection, or the path as it may be. Thus changing the dynamics of the local ZPM. Reducing the local ZPM to a true Zero state or it theory worse, creating a true void that may affect space/time itself. Yes this is a stretch, however it is not within out grasp yet to even theorize what may happen to the "space" that we draw any usable energy from, if there is any there to "collect".
If you think of the ZPM as surface tension, as in water, what happens when you disturb the tension? A ripple in a puddle is one thing, a ripple is the spacial dynamics of the solar system, or the galaxy. Where is the science to support the naysayers on this. There is not any. We as a species have not come far enough to meddle in space/time with out KNOWING the consequences BEFORE we "poke the bear with a stick".
If you throw out size and look at things on a equal scale. How much "empty" space, relativity, is there in an atom, compared to a solar system, galaxy, or universe.
It all comes down to humanities definition of scale. There in no truly empty space yet there is also not much of anything in that space either. Like Quarks or string theory, scale is the only thing that is a variable. The rest is a given , that we are trying to find the right math to calculate.

4. 4. Gagh 01:22 PM 3/12/10

"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."

Well, I think this statement is a little bit false. As I understand the quantization of the electromagnetic field, in a certain sense you can see it as an infinite number of harmonic oscillators (each one with a different frequency), but neither are they coupled, nor do they exist in "real" space. Rather, it is just a a formal analogy to such a system of harmonic oscillators, which helps you doing the actual quantization step.

5. 5. zeropoint 11:34 PM 3/16/10

I was initially skeptical that you could every harness <a href="http://www.discoverzeropoint.com">zero point energy</a> products until I went to a demonstration of a new product that did exactly that. Go to http://www.discoverzeropoint.com to find out more.

6. 6. debu 10:52 AM 4/15/10

Vacuum energy is ether and produced at common spherical boundary of our matter and outside antimatter universe on opposite entropy path and injected into our universe to cause expansion and gravity. So vacuum energy total is ever increasing and not zero. Please read the theories of durgadas datta published in ASTRONOMY.NET in year 2002. --durgadas.ddatta@gmail.com

7. 7. Eureka999 02:24 PM 6/27/10

To understand zero point energy it is important to have a handle on qutum gravity at the smallest scale. this also suggest it will be very difficult to ectract energy from inherent space-time energy. See: The formulation of harmonic quintessence and a fundamental energy equivalence equation. Physics Essays 23:311-319

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