Zero-Point Energy: The Lowest and Limitless Energy State

Junho Lee Thomas Jefferson High School for Science and Technology

Unlimited and sustainable energy is a prospect that would solve climate change and support the development of new revolutionary technologies. Unfortunately, nearly all attempts to create it have been thwarted by the laws of thermodynamics: namely, the law of conservation of energy. However, physicists are now exploring new areas in quantum mechanics. The past century of research has led them to believe that the universe is a sea of vast energy called zero-point energy [6], but understanding this energy requires background knowledge in wave-particle duality and Heisenberg’s uncertainty principle.

The dual wave and particle nature of light and matter was advanced by Einstein, de Broglie, and other scientists in the 1900s. This caused a shift in physical models from classical determinism, the idea that particles have a definite position, to probabilistic determinism, the idea that particles do not have exact positions but have probabilities of being found in an area of space. This is because a particle is also a wave and can be found where its wave exists in space, but since a wave does not exist at a single point, the particle also does not have a definite position. However, as Figure 1 depicts, the particle is more likely to be found where the amplitude of the wave is the highest [1].

The position of a particle is not the only aspect that depends on its wave function. The momentum of any particle or object is determined by the wavelength of its wave function, based on the de Broglie equation [4]:

λ = h / p

Where:

λ = wavelength

h = Planck’s constant

p = momentum

In the de Broglie equation, the wavelength is inversely related to the momentum of an object or particle. Therefore, a particle with high momentum has a wave function with a short wavelength, and a particle with a low momentum has a wave function with a long wavelength.

The Heisenberg uncertainty principle states that it is impossible to know both the position and momentum of a particle with great precision; in fact, precise position and momentum have no meaning in quantum physics [3]. Consider Figure 1. Wave A has a single precise wavelength; therefore, its particle has a precise momentum. However, the position of the particle could be anywhere along Area x, making the position imprecise. In contrast, Wave B is more intense in a certain region than in the rest of the wave. Therefore, its particle is most likely to be found within Area y, which is more precise than Area x. So how could we make a wave look more like Wave B in order to precisely determine the position of its particle?

Figure 1. Example of Differing Precisions in Particle Position. In Wave A, the particle may be found anywhere along Area x. In Wave B, the particle is most likely to be found within the more precise Area y due to its higher amplitudes. — *Figure 1*. Example of Differing Precisions in Particle Position. In Wave A, the particle may be found anywhere along Area x. In Wave B, the particle is most likely to be found within the more precise Area y due to its higher amplitudes.

If we allow the wave function of a particle to have multiple possible wavelengths, then we can add these different possible waves together to form a new one. Due to the characteristics of waves, adding multiple waves with different wavelengths causes them to amplify each other in certain areas and cancel out in others. As Figure 2 depicts, the resulting wave now has fluctuating amplitudes and is distinctly more intense in some areas than others. These areas with higher amplitudes are called wave packets, and they become more distinct as we add more waves. Adding waves also increases the amplitudes of these wave packets and decreases amplitude in the rest of the wave, making it possible to determine the position of its particle with greater precision. However, since we are allowing a range of different possible wavelengths, we are making the wavelength imprecise. Furthermore, since momentum is based on wavelength, we are effectively decreasing the precision of the particle’s momentum by increasing the precision of its position. This is Heisenberg’s uncertainty principle [5].

Figure 2. Example of Adding Multiple Waves. Note that this is an example to convey the idea that adding uniform waves creates wave packets, but this figure may not be mathematically accurate. — *Figure 2*. Example of Adding Multiple Waves. Note that this is an example to convey the idea that adding uniform waves creates wave packets, but this figure may not be mathematically accurate.

Zero-point energy is derived from a particular implication about the uncertainty principle: no particle can ever have zero kinetic energy because such a particle would have both a precise position, as well as a precise momentum of zero. Because of this, physicists have concluded that the lowest possible energy state does not have zero kinetic energy, but some amount above zero. As an example, liquid helium does not freeze into a solid under atmospheric pressure no matter how low the temperature is, meaning that it retains energy regardless of temperature [6].

But doesn’t that mean that absolute zero violates the uncertainty principle since no molecule can ever come to a complete stop? While temperature is a measure of vibrational kinetic energy, an object is at absolute zero by definition when it can no longer transfer heat to another object, not necessarily when all molecular motion stops [2]. An object can only transfer heat if it has more thermal energy than the object that receives the heat. Because an object at absolute zero is at zero-point energy, nothing in the universe has less energy, so it cannot transfer heat. Therefore, absolute zero does not violate the uncertainty principle.

Zero-point energy is present throughout the universe, and some calculations estimate that it has an energy density of more than 10110 times that of the radiant energy at the center of the sun. Most modern physicists believe that it is extremely unlikely for humanity to extract usable energy from zero-point energy. While scientists have been able to generate force using zero-point energy, there is yet to be a widely accepted method to generate more energy than is put into a system. Still, it does demonstrate the conversion of zero-point energy. As described above in the context of absolute zero, zero-point energy is not thermal energy because it cannot be transferred as heat. So unlike most promises of “unlimited energy” which have been disproved by the laws of thermodynamics, zero-point energy is not bound by thermodynamics, meaning that its conversion into usable energy cannot be ruled out in theory. As for whether it could be a practical source of energy for humanity, only the future will tell [6].

References

[1] An easy explanation of the basics of quantum mechanics for dummies. (n.d.). ScienceStruck. Retrieved June 6, 2020, from https://sciencestruck.com/basics-of-quantum-mechanics-for-dummies

[2] The Editors of Encyclopaedia Britannica. (2019, January 18). Absolute zero. Encyclopædia Britannica. Retrieved June 6, 2020, from https://www.britannica.com/science/absolute-zero

[3] The Editors of Encyclopaedia Britannica. (2020, May 27). Uncertainty principle. Encyclopædia Britannica. Retrieved June 6, 2020, from https://www.britannica.com/science/uncertainty-principle

[4] Helmenstine, A. M. (2018, July 11). de Broglie equation definition. ThoughtCo. Retrieved June 6, 2020, from https://www.thoughtco.com/definition-of-de-broglie-equation-604418

[5] Norton, J. D. (n.d.). The quantum theory of waves and particles. Einstein for Everyone. Retrieved June 6, 2020, from https://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/quantum_theory_waves/index.html

[6] Zero-point energy. (n.d.). Calphysics. Retrieved June 6, 2020, from http://www.calphysics.org/zpe.html