Nothing Matters: How the Study of Vacuum Energy is Proving Catastrophic

Let’s imagine the simplest possible experiment, how much energy is contained in an empty box? Energy comes in many forms such as heat, light and the movement of objects. So, if we take a box, remove the air particles, cool it, and place it in deep space far away from any gravitational fields, The amount of energy present should be zero, right? Unfortunately, things are never that simple. Two of our most successful physical theories, quantum field theory and general relativity, both predict that this empty box should have some energy contained inside. Even stranger, quantum field theory points to a vacuum energy that is 10^120 (1 with 120 zeroes after it) times larger than what Albert Einstein’s general relativity predicts. A disagreement this colossal, between two of our strongest theories, is what scientists call a catastrophe. A scientific catastrophe is a very exciting thing, quantum field theory or general relativity must fall, or a new theory must take their place.

Fig 1: An illustration of 2D quantum fields, and the creation of particles from their vibration. [Creative Commons]

Quantum field theory states that all fundamental particles are simply strong vibrations of a given field. So, an electron is just a strong vibration in the electron quantum field, as seen in Figure 1. These quantum fields are everywhere, even in our empty box. To try to stop these fields from wiggling around, we cool the box to absolute zero temperature. However, Heisenberg’s uncertainty principle tells us that there is a limit to how much we can know about a particle. We can never know exactly where a particle is and where it is going. Therefore the fields can never be still, even at zero temperature they continue to wiggle. They continue to have energy despite our best efforts, and due to the equivalence of mass and energy, ‘virtual’ particles are briefly created and destroyed. The energy of this constant quantum hum is not small either, when we had add up the energy of all the different quantum fields, we get roughly 10^112 erg/cm3. The strange units are not too important here, but know that this is a huge amount of energy for a small amount of empty space. Physicist Richard Feynman famously noted that, “One teaspoon of empty space contains enough energy to boil all the oceans in the world.”

Fig 2: A Poster illustrating the connection between Einstein’s general relativity Equations and the expansion of the universe. [Creative Commons]

Alternatively, General relativity uses experimental evidence to provide is with a hint at this vacuum energy. Our universe is almost entirely an empty vacuum. We can see that all astronomical objects, planets, stars even galaxies are moving away from each other. The universe is expanding. We have known since the late 1990s that the universe is expanding at an increasing rate. There must be a source causing this expansion. It is denoted in Einsteins equations by the Greek letter lambda, “Λ”, and is known as the cosmological constant. This can be seen in Figure 2. This pushing source has been labelled dark energy and could be our vacuum energy. In fact, the vacuum energy being the cause of the accelerating expansion of the universe would be quite an elegant explanation. The vacuum energy creates more empty space, this new empty space then has its own vacuum energy, so the universe expands faster and faster. The energy required for such an expansion has been calculated to be 10^-8 erg/cm3. This is about 100 million times less energy than what a mosquito would use to flap its wings once. From this tiny value we have our huge disagreement with quantum field theory, which is both a great catastrophe and an exciting opportunity.

So what is being done to solve this problem? The most promising experimental work being done is taking place deep in a Sardinian mine, named the Archimedes Project. This project aims to weigh ‘nothing’ and study the interaction of the vacuum energy with gravity. Archimedes’ principle states that an object surrounded by a fluid will be pushed away by force equal to the weight of fluid the object displaces. This can be seen when a beachball placed underwater is pushed upwards by the fluid around it. In this project’s case, the beachball is replaced by a a chamber of metal plates, surrounded by a vacuum. The weight of the vacuum can then be figured out by studying the force on the metal plates. This experiment is an incredibly difficult task as any external interactions on the metal plates could skew the results. This is the reason that the location of a Sardinian mine was chosen, due to its isolation and low seismic activity. On this challenge, Physicist Vivishek Sudhir of MIT stated, “In experiments like this, the whole world works against you.” Despite the obstacles that face us, I am confident that a solution will be found for the energy of empty space, and it will change our understanding of reality fundamentally.

Max Murphy

References:

[1] L.D. Faddeev and A.A. Slavnov, Gauge Fields: Introduction to Quantum Theory, Cambridge University Press (1995).

[2] Clara Moskowitz, “The Cosmological Constant is Physics Most Embarrassing Problem”, Scientific American Magazine Vol. 324 No. 2 (February 2021), p. 24, https://www.scientificamerican.com/article/the-cosmological-constant-is-physics-most-embarrassing-problem/

(Date Accessed: 7/5/24)

[3] Calloni, E. and Caprara, S. and Laurentis, M. De and Esposito, G. and Grilli, M. and Majorana, E. and Pepe, G.P. and Petrarca, S. and Puppo, P. and Rapagnani, P. and Ricci, F. and Rosa, L. and Rovelli, C. and Ruggi, P. and Saini, N.L. and Stornaiolo, C. and Tafuri, F. “The Archimedes experiment”, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Elsevier BV, 2016, DOI: https://doi.org/10.1016/j.nima.2015.09.071

[4] Manon Bischoff, “How Much Does ‘Nothing’ Weigh?”, Scientific American Magazine Vol. 328 No. 5 (May 2023), p. 62, https://www.scientificamerican.com/article/how-much-does-nothing-weigh/

(Date Accessed: 7/5/24)

[5] Prat, J. and Hogan, C. and Chang, C. and Frieman, J. “Vacuum energy density measured from cosmological data”, Journal of Cosmology and Astroparticle Physics,IOP Publishing (2022), DOI: http://dx.doi.org/10.1088/1475-7516/2022/06/015},

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